Superminaren/cebik
1
0
Fork 0
mirror of https://github.com/antenna2/cebik.git synced 2026-10-15 17:24:11 +02:00
Code Issues Packages Projects Releases Wiki Activity

Initial commit

Browse Source
This commit is contained in:
Lonney
2024-12-20 13:27:36 -09:00
commit b54ed3ab5b
8026 changed files with 146431 additions and 0 deletions
Download Patch File Download Diff File Expand all files Collapse all files
content/mu/mu0.html
+68
View File
@@ -0,0 +1,68 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="keywords" content="Small Beams">
<title>Modeling and Understanding Small Beams Index</title>
<link rel="stylesheet" href="../styles.css">
</head>
<body>
<table width="100%" cellspacing="0" cellpadding="0" border="0">
<tr>
<td width="200" align="center"><img src="../images/yagicad.gif" align="left" width="125" height="62" border="2" vspace="5"></td>
<td align="center">
<h1>Articles from <i>Communications Quarterly</i><br>
Modeling and Understanding Small Beams</h1>
</td>
<td width="200" align="center"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5"></td>
</tr>
</table>
<center>
<h3>L. B. Cebik, W4RNL</h3>
</center>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<p>Because I have received numerous requests for reprints, I am placing at the site revised versions of the most substantial articles (listed below) that have been printed in <b><i>Communications Quarterly</i></b> at least 2 years past (1997 and before). Because of limitations in the reproduction process, the scanned figures may be less than optimal. However, the main text and equations have been converted into HTML and .GIF from my manuscripts. A few characters that do not readily convert from one program to another may turn up missing, and I shall reinsert them as I discover them.</p>
<p>I have taken the occasion to add to the texts references to notes at this site that carry on discussions and investigations begun in these studies. Hence, everything is incomplete. Despite these limitations, I hope some of the articles are useful to you. (* items have not yet been converted and appear in page .GIF form.)</p>
<p><b>"The Effects of Antenna Height on Other Antenna Properties: A Computer Study,"</b> <i>Communications Quarterly</i> (Fall, 1992), 57-79. See <a href="../../magazines/">Magazines Page</a>.</p>
<p><b>"Modeling and Understanding Small Beams:"</b></p>
<ul>
<li>
<a href="mu1a.html"><b>Part 1: "The X-Beam,"</b></a> <i>Communications Quarterly</i> (Winter, 1995), pp. 33-50
</li>
<li>
<a href="mu2a.html"><b>Part 2: "VK2ABQ Squares and The Modified Moxon Rectangle,"</b></a> <i>Communications Quarterly</i> (Spring, 1995), pp. 55-70
</li>
<li>
<a href="mu3a.html"><b>Part 3: "The EDZ Family of Antennas,"</b></a> <i>Communications Quarterly</i> (Fall, 1995), pp. 53-71
</li>
<li>
<a href="mu4a.html"><b>Part 4: "Linear-Loaded Yagis."</b></a> <i>Communications Quarterly</i> (Summer, 1996), pp. 85-106
</li>
<li>
<a href="mu5a.html"><b>Part 5: "The ZL Special,"</b></a> <i>Communications Quarterly</i> (Winter, 1997), pp. 72-90
</li>
<li>
<a href="mu6a.html"><b>Part 6: "Fans, Bowties, Butterflies, and Dragonflies,"</b></a> <i>Communications Quarterly</i> (Spring, 1997), pp. 81-97
</li>
<li>
<a href="mu7a.html"><b>Part 7: "Shrunken Quads,"</b></a> <i>Communications Quarterly</i> (Summer, 1997), pp. 71-92
</li>
<li>
<a href="mu8a.html"><b>Part 8: "Capacity Hats,"</b></a> <i>Communications Quarterly</i> (Fall, 1997), pp. 61-79
</li>
</ul>
<p>A number of the ideas in these articles have been updated with further information that appears in other notes at this site. For example, there are updates on the Moxon Rectangle, EDZ antennas, ZL Specials and other phased 2-element beams, and quad beams. Therefore, the articles above should be read as initial studies, not as finished, final, or authoritative treatises.</p>
<p>You may also note some changes along the way. When I began my modeling efforts, MININEC was the only readily available software. It was followed by NEC-2 and finally NEC-4. Likewise, my initial TurboCAD-for-DOS sketches have slowly evolved into drawings that used a more advanced Windows version of the program. Graphs started in Quattro-Pro-for-DOS have also evolved through version 7 for Windows. However, if you can bear the evolution of computer tools as well as antenna information, there may still be a useful item or two in the collection.</p>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<p><i>Updated 7-25-99. &COPY; L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Amateur Radio Page</a></p>
<p class="topics-footer">Topics: <a href='../topics.html#small-beams'>Small Beams</a></p><br>
</body>
</html>
content/mu/mu1a-1.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 3.7 KiB

content/mu/mu1a-10.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 7.2 KiB

content/mu/mu1a-11.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 3.5 KiB

content/mu/mu1a-2.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.5 KiB

content/mu/mu1a-3.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.4 KiB

content/mu/mu1a-4.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.2 KiB

content/mu/mu1a-5.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 4.8 KiB

content/mu/mu1a-6.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 4.9 KiB

content/mu/mu1a-7.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 4.9 KiB

content/mu/mu1a-8.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 10 KiB

content/mu/mu1a-9.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 11 KiB

content/mu/mu1a.html
+410
View File
@@ -0,0 +1,410 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="keywords" content="X Beam, HF Upper, Small Beams">
<title>Modeling and Understanding Small Beams Part 1: The X-Beam</title>
<link rel="stylesheet" href="../styles.css">
</head>
<body>
<center>
<h1>Modeling and Understanding Small Beams</h1>
<h3>Part 1: The X-Beam</h3>
<p><b>L. B. Cebik, W4RNL</b></p>
</center>
<center>
<img src="../images/colorbar.gif" width="591" height="3">
</center>
<p>Between miniature loop antennas and full size arrays exists a special class of antennas: the small beams. Small beam antennas are intriguing and misunderstood. To some, they represent the search to achieve something for nothing. Like lotteries and sweepstakes, they receive as much moral disapproval as technical discrediting. To others, they are a necessity, since something is at least better than nothing. Space and money are the chief motivations to build a mini-beam of one or another design.</p>
<p>Quite frankly, for me, small beams are fun. Many types of small beams have received only casual empirical development. What their performance limits may be remains a mystery in the literature. Here, computer modeling can offer a service by estimating with buildable accuracy antenna gain, front-to-back ratio, overall azimuth and elevation patterns, and feedpoint conditions. For under $30 per antenna, with hardware store parts, I can test what modeling tells me ought to be the case.</p>
<p>In this series, we shall look at several contemporary small beams, including the folded X-beam, the modified Moxon rectangle, the linear-loaded Yagi, fan-element Yagis, shrunken quads, capacity-hat Yagis, ZL-Specials, and the parasitic EDZ. The last is admittedly not small in element length, but it is short and cheap. Our purpose is not to recommend any of the designs. Rather, the goal is to understand what each design can and cannot do. Only then can one assess what each beam's place may be in the scheme of amateur antennas.</p>
<center>
<strong>Standards of Comparison</strong>
</center>
<p>Small beams appeal to the builder because they are manageable. They are "hands-on" devices, not set and forget store items. On 10 meters, where all the beams in this series were modeled and tested, dimensions are reasonable as one-person projects. Moreover, the results are generally scalable down to at least 20 meters with little adjustment. Moreover, since 10 meters is closed part of the day, even during sun spot maxima, one can test the antennas without causing QRM. A temporary mast about 20-feet long, a method to prop it securely but not permanently, some feedline, a small rig (like the HTX-100 I use), a good noise bridge and SWR meter, and a reliable helper (like N4TZP, my XYL) are all one needs to try out a few 10-meter mini-beams.</p>
<p>However, a good modeling program makes an even better beginning. It permits one not only to reject numerous ideas that simply are not worth the effort of building, but as well it puts dimensions close enough to reality so that adjustments go in the right direction the first time. Most of all, a modeling program allows a relatively rapid investigation of the most significant antenna properties, which produces an understanding of the antenna to be tested. This series will contain extensive notes on the modeling aspect of these investigations to show the evolution of various designs. These notes may also prompt kindred spirits to try some directions not taken here and to uncover some possibilities that have eluded me. Modeling data in this series will often be given for free space (to permit ready general comparisons), at 20 feet (a common height for portable antennas), and for 35 feet (a common permanent installation height).</p>
<p>There are several general propositions about small beams that underlie both our knowledge and our mythology:</p>
<p>1. Small beams generally have narrower bandwidths than full size beams. This proposition is true, but it is not always the limiting factor that we may think it is.</p>
<p>2. Small beams present complex construction problems. The truth of this proposition depends upon the sort of antenna construction with which you are comfortable. If you have only slipped tubing in and out of other tubing in normal Yagi construction fashion, then some closed geometry beams will seem ungainly at first sight. However, if you look at plumbing and electrical supplies and see antenna possibilities, then small beams offer a pleasant challenge. But, admittedly, a few require careful construction.</p>
<p>3. Small beams give reduced performance. In its absolute form, this proposition may be the most mythical of all. At design center, some small beams can outperform their full size brethren in one or another specification, with only a small sacrifice in other areas. For example, some of the beams in this series--all two-element parasitic types--will outperform the standard two-element Yagi in front-to-back ratio with little loss of forward gain over a small bandwidth. And, for certain operators, this property may be just the one desired. This fact does not mean that the small beams are superior, for many have other deficiencies. Rather, every beam must be measured against a particular set of applications.</p>
<center>
<img src="mu1a-1.gif" width="405" height="302" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1. Composite free space azimuth patterns of a wide-band 2-element Yagi from 28 to 29 MHz.
</center>
<p>As a standard of comparison, let's present a well-known 2-element Yagi with a driven element and a reflector. Using 1-inch aluminum tubing, the driven element is 16-feet long, the reflector is 17.5 feet long, and the spacing is 4.25 feet.<a href="mu1a.html#N_1_"><sup>(1)</sup></a> The resonant feedpoint impedance is about 32 ohms at 28.5 MHz. What makes this antenna a good standard of comparison for understanding the mini-beams in this series is that it is well-behaved. As <b>Fig. 1</b> and <b>Table 1</b> demonstrate, the beam maintains its characteristics across a 1 MHz span of 10 meters with excellent consistency. Free space forward gain varies by about 0.76 dBi, while the front-to-back ratio varies by less than 1 dB. Variations over real ground at 20 feet and 35 feet are somewhat greater, but still quite minor.</p>
<pre> Wide-Band 2-Element Yagi Performance
Frequency (MHz) 28.00 28.25 28.50 28.75 29.00
Free Space
Gain (dBi) 6.7 6.5 6.3 6.1 5.9
F-B ratio (dB) 10.3 11.0 11.2 11.0 10.6
Impedance (R jX) 24 - 17 28 - 8 32 + 1 36 + 9 40 + 18
20' high
Gain (dBi) 11.7 11.5 11.3 11.2 11.1
F-B ratio (dB) 13.3 12.2 10.9 9.7 8.8
Impedance (R jX) 27 - 21 30 - 13 34 - 5 37 + 2 39 + 10
35' high
Gain (dBi) 12.0 11.9 11.7 11.5 11.4
F-B ratio (dB) 12.7 13.7 13.5 12.6 11.5
Impedance (R jX) 27 - 17 31 - 8 35 + 0 40 + 8 43 + 15
Note: Performance figures for 20 and 35 foot heights were taken over average ground (also called medium
earth: dialectric constant = 13, conductivity = 5 milliSiemens/meter). See text for antenna dimensions and
material.
Table 1. Performance characteristics in free space, at 20 feet, and at 35 feet of a wide-band 2-element Yagi
using a driven element and a reflector.</pre>
<p>The antenna's performance in terms of raw gain and front-to-back ratio at design center is modest. However, 6.3 dBi forward gain (free space) and 11.2 dB front-to-back ratio are quite serviceable figures compared to the free space gain of a wire dipole (about 2.15 dBi). You can design Yagis for another dB of forward gain and alternatively for a somewhat greater front-to-back ratio, but only at the expense of bandwidth. Thus, the given design seems well suited to its role as a standard of comparison. With it in mind, we can turn to the first of our small beams.</p>
<center>
<strong>The Folded X-Beam</strong>
</center>
<p>In Volume 1 of <em>The Antenna Compendium</em>, Brice Anderson presented dimensions for a folded X-beam for the upper HF bands.<a href="mu1a.html#N_2_"><sup>(2)</sup></a> His empirically derived antennas have received both praise and censure within amateur circles.<a href="mu1a.html#N_3_"><sup>(3)</sup></a> Unfortunately, much of the criticism has stemmed from one remark born of enthusiasm: the X-beam rivals a 3-element beam in performance. I have known some 3-element tribanders of older design which might fit the remark, but newer designs likely reduce the claim to approaching the performance of a full-size 2-element beam.</p>
<p>Anderson built his X-beams using a driven element and a director element to match as closely as possible a 50-Ohm line without additional components. His aim was a design that home builders could replicate and use reliably across a chosen band. In achieving this goal, he produced a 2-element parasitical beam with less than its full potential for gain and front-to-back ratio. Nevertheless, the X-beam as Anderson presented it may well serve hams operating in very limited space. With dimensions approximately a quarter wavelength on a side, the X-beam is a compact way to achieve some gain and some front-to-back ratio in a compact arrangement. Indeed, those who build X-beams generally do not seek to equal the performance of a 3-element Yagi, but only to achieve an improvement both in gain and in signal rejection relative to fixed-position dipoles. The X-beam will certainly do that.</p>
<center>
<strong>Modelling the X-Beam</strong>
</center>
<p>Computer modelling via MININEC offers us a chance to understand better some of the characteristics of the X-beam. Due to its complex geometry, full of acute angles, it is not the simplest beam to model. However, the auto-tapering feature of ELNEC 3.02 permits some reliable looks at X-beam performance under various conditions.<a href="mu1a.html#N_4_"><sup>(4)</sup></a> Similar work can be done using the bent-wire correction feature of AO 6.0, if one uses enough wire segments.<a href="mu1a.html#N_5_"><sup>(5)</sup></a> The X-beam is worth the effort to examine, especially if one wants to get more than minimal results from it.</p>
<center>
<img src="mu1a-2.gif" width="386" height="434" border="2" vspace="5" hspace="9">
</center>
<center>
<p>Fig. 2. TRU-X beam configuration and azimuth pattern at 35' above average earth.</p>
</center>
<p><strong>Where Does the X-Beam Come From?</strong> Any two wires, one of which is fed, will show some degree of parasitic element properties if they are not too dissimilar in length, not too far apart, and not at right angles to each other. Paralleling elements is efficient, but not necessary. One can construct a true X-beam (or TRU-X), as shown in <b>Fig. 2</b>, and alter the dipole pattern to show a bit of gain in a favored direction. With over 3 dB gain above a dipole in the same setting (35' in <b>Fig. 2</b>), the TRU-X might be a useful beam were it not so large and were the pattern something less than a 3-leaf clover. The side lobes are only 4 dB down from the main lobe, inviting confusing QRM.<a href="mu1a.html#N_6_"><sup>(6)</sup></a></p>
<center>
<img src="mu1a-3.gif" width="391" height="430" border="2" vspace="5" hspace="9">
</center>
<center>
<p>Fig. 3. Roman-X beam configuration and azimuth pattern at 35' above average earth.</p>
</center>
<p>Now, let us bend back the ends of the X-elements to form a Roman X, as shown in <b>Fig. 3</b>. This simple act pushes the side lobes toward the back, reduces them, and increases forward gain. A comparison of the patterns in <b>Fig. 2</b> and <b>Fig. 3</b> reveals the differences. Forward gain can improve by up to 1 dB over the TRU-X, while the side lobes are down 7 dB from the main lobe. However, as <b>Table 2</b> shows, the Roman-X is a big antenna relative to these marginal improvements. Both the TRU-X and the Roman-X produce beams are, in general, about the same breadth as, but unequal in performance to, a standard 2-element Yagi. <b>Table 2</b> compares the dimensions for the X configurations and for the Yagis.</p>
<pre> Performance and Dimensions of the Tru-X and Roman-X Antennas
Performance (in free space):
Antenna Gain Front-to-Back Band width Source Impedance
(dBi) (dB) (degrees) R +/- X
Tru-X
Max. Gain 5.5 16.4 58 42.8 + 3.1
Max. F-B 5.2 29.5 62 51.8 + 2.5
Roman-X
Max. Gain 6.3 12.1 58 41.2 + 27.3
Max. F-B 5.7 23.1 62 59.8 + 25.3
Dimensions:
Antenna DE Dir Total Side-side Total Front-back
Length Length Length Length
Tru-X 20.6' 20.4' 14.5' 14.5'
DE = 2 x Arm Dir = 2 x Arm
Roman-X 21.4' 20.4' 17.4' 9.8'
DE = 2 x (Arm + Tail) Dir = 2 x (Arm + Tail)
Typical 2-element Yagis
DE + Dir 17.0' 15.6' 17.0' 4.0'
DE + Ref 16.0' 17.5' 17.5' 4.3'
X-Beam 6.9' + 3.8' 6.9' + 3.3' 9.8' 9.8'
DE = 2 x (Arm + Tail) Dir = 2 x (Arm + Tail)
Table 2. Dimensions of Tru-X, Roman-X, DE + Dir Yagi, DE + Refl Yagi, and X-beam antennas.</pre>
<p>If we bend the ends of the Roman-X wires still further back until the director ends and driven element ends point at each other, we can retain the performance of the Roman-X in a square only slightly greater than a quarter wavelength on a side, as shown in <b>Fig. 4</b>. This is the X-beam Anderson presented in Volume 1 of <em>Antenna Compendium</em>, and <b>Fig. 4</b> shows the dimensions he recommended for 10 meters.<a href="mu1a.html#N_7_"><sup>(7)</sup></a> The question is whether it is worth building such an antenna, on the assumption that a 3-element Yagi is out of the question at one's location.</p>
<center>
<img src="mu1a-4.gif" width="366" height="366" border="2" vspace="5" hspace="9">
</center>
<center>
<p>Fig. 4. Configuration and terminology of the X-beam.</p>
</center>
<p><strong>Basic Anderson Performance</strong>: In order to answer the question, I constructed numerous computer models of Anderson's design and variations upon it. In the process, I discovered some general patterns of theoretic interest, as well as some other patterns and progressions that pointed to performance improvements. The end result was a better understanding of what X-beams could and could not do and a better sense of what I should and should not do in playing with them. Throughout, I shall presume construction methods similar to those used by Anderson and retain his terminology, calling the angular tubing the arms and the bent-back wire ends the tails.</p>
<center>
<img src="mu1a-5.gif" width="392" height="304" border="2" vspace="5" hspace="9">
</center>
<center>
<p>Fig. 5. Representative azimuth pattern of the X-beam, configured for best match to 50-Ohm coaxial cable.</p>
</center>
<p>The initial stage in the work was to see what MININEC might tell about Anderson's beam. I modeled his dimensions for 10 meters (28.5 MHz), using 0.5" diameter aluminum tubing and #18 wire. The result was a beam with modest gain over a real dipole in free space, at 20 feet (a common height for portable beams on 10), and at 35 feet (a common 10-meter fixed installation height). The results appear in <b>Table 3</b>, with <b>Fig. 5</b> showing a representative azimuth pattern for the "best match" configuration at 35 feet above average earth (dielectric constant 13, conductivity 5 mS/m). Three aspects of the figure are especially notable. First, the gain over a dipole in the same position is less than 3.5 dB and not up to average 2-element Yagi figures. The front-to-back ratio is also modest, but odd. The side lobes quartering to the rear are less than 10 dB down from the main lobe, which limits signal rejection in these directions. These rearward lobes will remain, no matter how much front-to-back ratio is achieved in the 180-degree direction. Third, the input impedance is in the mid-30-Ohm range, which permits a direct coax connection with an SWR ratio of under 2:1. One can either live with or cancel the remnant reactance at the feedpoint with not too much trouble.</p>
<pre> Properties of a 10-Meter X-beam
Antenna A: Basic Anderson design: Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.79', Dir = 3.29'.
Environment Gain Take-Off F-B Ratio Beam width Source Impedance
(dBi) Angle (dB) (degrees) R &PlusMinus; X
Free Space 5.5 -- 20.9 66 36.3 - 19.2
20', ave. gnd. 10.7 24 11.8 74 38.6 - 12.1
35', ave. gnd. 10.9 14 17.1 68 34.3 - 16.1
Antenna B: +0.2' to Tails: Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.99', Dir = 3.49'.
Free Space 6.6 -- 13.0 62 20.3 + 0.4
20', ave. gnd. 11.6 23 24.2 66 22.9 + 1.9*
35', ave. gnd. 11.9 14 15.4 62 20.3 + 1.9
Antenna C: +0.3' to Tails: Arms 0.5" dia., 6.92' long, Tails #18, DE = 4.09', Dir = 3.59'.
Free Space 6.9 -- 7.0 58 14.1 + 15.1
20', ave. gnd. 11.9 23 10.6 62 15.3 + 15.1
35', ave. gnd. 12.1 14 7.9 60 14.3 + 15.6
* Dimensions of antenna B were optimized for a 20' height above average earth. Free space models require
adjustment for low heights and require real earth models.
Performance figures for 20 and 35 foot heights were taken over average ground (also called medium earth:
dialectric constant = 13, conductivity = 5 milliSiemens/meter).
Table 3. Properties of a 10-meter X-beam in free space and at 20 and 35 feet over medium earth.</pre>
<p>Attempts to improve performance led to some alteration of the element dimensions, while adhering to Anderson's advice to keep the tail lengths a certain amount different--on 10 meters, 6 inches. This procedure lent consistency to all my models, which allowed the patterns and progressions to appear more easily. My first attempts lengthened all the elements by 0.2 feet per end. As <b>Table 3</b> shows, the resulting antenna increased in gain by a small but useful amount. However, the front-to-back ratio increased by much more. Nonetheless, the rearward side lobes did not materially shrink. <b>Fig. 6</b>, a representative azimuth pattern, displays the side lobes quite well. Finally, the input impedance decreased into the mid-20-ohm range. This antenna promised improved performance at the cost of requiring a 2:1 matching system.</p>
<center>
<img src="mu1a-6.gif" width="393" height="302" border="2" vspace="5" hspace="9">
</center>
<center>
<p>Fig. 6. Representative azimuth pattern of the X-beam, configured for maximum front-to-back ratio.</p>
</center>
<p>Increasing the tail lengths by 0.3 feet over the original Anderson dimensions produced further changes in X-beam characteristics. Gain increased to equal or surpass average 2-element Yagis. However, as <b>Table 3</b> shows, the front-to-back ratio decreases dramatically. Yagis with 2 elements show a similar phenomenon when optimized for maximum gain. <b>Fig. 7</b> shows a representative "max gain" X-beam azimuth pattern. Finally, the source impedance dropped into the mid-teens range.</p>
<center>
<img src="mu1a-7.gif" width="396" height="305" border="2" vspace="5" hspace="9">
</center>
<center>
<p>Fig. 7. Representative azimuth pattern of the X-beam, configured for maximum gain.</p>
</center>
<p>None of these models represents the absolute peak of coax match, front-to-back ratio, or gain that might be obtained with an X-beam. Rather, they are models designed to find out about where various parameters end up with changes of element length. Initial observations of the data in <b>Table 3</b> suggested that with the X-beam, one cannot wholly rely on a free-space model. Modeling over the anticipated real terrain of the antenna is a must. Since MININEC calculates the source impedance over perfect ground, not the modeled ground, slight differences between the models and reality are the order of the day.</p>
<p>Constructing an X-beam without loading requires a tuning process that opposes what we normally do. If we wish to move from best 50-Ohm match to maximum front-to-back ratio, we must lengthen the element tails, a process that requires more forethought than merely snipping dipole wires.</p>
<p><strong>Loading the X-Beam</strong>: If we could achieve some desirable improvements in X-beam performance by changing element lengths, the next question was whether similar results might be obtained by loading the director. This idea came from W2EEY's X-beam that I encountered in <em>Antenna Roundup</em>, Vol. 2.<a href="mu1a.html#N_8_"><sup>(8)</sup></a> <b>Table 4</b> shows some initial results. Using the original Anderson dimensions, we can achieve the performance of the maximum front-to-back ratio model and the maximum gain model by placing a series inductor of the proper reactance at the center point of the director. Although the models use a lossless inductor as the loading element, reasonably high-quality coils should not reduce the performance figures significantly.</p>
<pre> Properties of a 10-Meter X-beam with an Inductively Loaded Director
Antenna: Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.79', Dir = 3.29'.
Environment Dir Xl Gain Take-Off F-B Ratio Beam width Source Impedance
(Ohms) (dBi) Angle (dB) (degrees) R &PlusMinus; X
Antenna A: Anderson best 50-Ohm match design
Free Space 0 5.5 -- 20.9 66 36.3 - 19.2
20', ave. gnd. 0 10.7 24 11.8 74 38.6 - 12.1
35', ave. gnd. 0 10.9 14 17.1 68 34.3 - 16.1
Antenna B: Maximum front-to-back ratio design
Free Space + 6 5.9 -- 27.6 64 29.7 - 19.6
20', ave. gnd. +12 11.4 24 24.0 68 26.1 - 15.7
35', ave. gnd. +10 11.5 14 27.2 64 24.9 - 16.6
Antenna C: Maximum gain design
Free Space +23 6.8 -- 6.9 58 13.1 - 9.9
20', ave. gnd. +23 11.7 24 10.3 62 14.3 - 10.2
35', ave. gnd. +20 12.1 14 10.3 60 15.5 - 11.8
Note: Loading permits each antenna to be optimized for each environment.
Performance figures for 20 and 35 foot heights were taken over average ground (also called medium earth:
dialectric constant = 13, conductivity = 5 milliSiemens/meter).
Table 4. Properties of a 10-meter X-beam with an inductively loaded director in free space and at 20 and 35
feet over medium earth.</pre>
<p>There is no need to display further azimuth patterns from this point onward, since one of the progressions began to show itself at this point. Best match, maximum front-to-back, and maximum gain patterns each look alike, whatever means are used to arrive at them. Moreover, the resistive component of the source impedance remains in the same ball park for each category: the mid-30s for best match, the mid-20s for maximum front-to-back ratio, and the mid-teens for maximum gain.</p>
<p>Inductive loading is usually less preferable than capacitive loading, wherever a choice is available. Therefore, following W2EEY's lead, the next set of models lengthened the director tails to require a capacitive load for each X-beam category. By increasing the capacitive loading, one can move from best match through maximum front-to-back ratio to the maximum gain level. At the same time, one passes smoothly through the three source impedance ranges. The result is an X-beam that permits adjustment with the turn of a knob.</p>
<p>Anderson recommended a constant length difference between driven element and director tails. However, since a variable capacitor is capable of tuning the system to the desired characteristics and since the driven element reactance remains stable across the span of adjustments, we may depart from Anderson's empirically-derived constraint and resonate the capacitively loaded X-beam. <b>Table 5</b> shows in finer detail the result of returning the driven element to an approximately resonant length while leaving the director long for capacitive tuning. The results are precisely comparable to those for all other models.</p>
<pre>Properties of a Resonant 10-Meter X-beam with a Capacitively Loaded Director
Antenna: Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.99', Dir = 3.79'.
Dir Load Gain F-B Ratio Band Width Source Impedance Side Lobe Side Lobe
-Xc (dBi) (dB) (degrees) R &PlusMinus; X Angle (deg) Ratio (dB)
Environment 1: Free Space
-15 6.9 6.9 58 13.7 + 8.1 100 (est) -9.0 (est)n. 1
-20 6.8 10.1 60 17.0 + 4.4 101 -9.1
-25 6.5 14.4 62 21.1 + 1.5 105 -9.4
-30 6.2 21.1 64 26.2 - 0.3 108 -9.4
-35 5.9 51.5 66 31.4 - 0.9 112 -9.4 n. 2
-40 5.6 22.2 68 35.6 - 0.4 115 -9.2
-45 5.3 16.8 68 39.7 + 0.8 118 -9.0
-50 5.0 13.9 70 43.1 + 2.3 121 -8.7 n. 3
Environment 2: 20' above average earth, takeoff angle 23 degrees
-15 11.8 10.4 62 14.9 + 8.2 101 -9.2 n. 1
-20 11.8 16.3 66 19.1 + 5.1 105 -9.4
-25 11.5 33.0 68 23.9 + 3.5 109 -9.4 n. 2
-30 11.3 21.2 70 28.9 + 3.4 114 -9.2
-35 11.0 15.2 72 33.3 + 4.5 118 -8.8
-40 10.8 12.2 74 37.0 + 6.5 123 -8.4
-45 10.5 10.2 74 39.7 + 8.9 127 -8.0 n.3
Environment 3: 35' above average earth, takeoff angle 14 degrees
-15 12.2 7.8 60 13.9 + 8.7 100 -9.0 n. 1
-20 12.1 11.6 62 17.2 + 5.4 102 -9.2
-25 11.8 16.8 64 21.3 + 3.1 106 -9.5
-30 11.5 24.3 66 25.5 + 1.8 110 -9.5 n. 2
-35 11.2 22.1 68 29.7 + 1.6 113 -9.3
-40 10.9 16.9 68 33.4 + 2.2 117 -9.1
-45 10.6 13.8 70 36.6 + 3.5 120 -8.8
-50 10.5 11.8 72 39.2 + 5.0 124 -8.5 n. 3
Note 1: maximum gain Note 2: maximum front-to-back ratio Note 3: best coax match
Performance figures for 20 and 35 foot heights were taken over average ground (also called medium earth:
dialectric constant = 13, conductivity = 5 milliSiemens/meter).
Table 5. Properties of a resonant 10-meter X-beam with a capacitively loaded director in free space and at 20
and 35 feet over medium earth.</pre>
<p>In fact, the representative azimuth patterns shown in earlier figures are taken from the 35' model of this X-beam. Moreover, rearward side-lobe angles shown in <b>Table 5</b> apply to all the models within a few degrees and with close matching of their level below the main lobe. Additionally, the X-beam does not lend itself to close stacking or interlacing. W9PNE confirmed my own modeling failures in correspondence: no one he knew had had any luck trying to create a compact multi-band X-beam assembly.</p>
<p><strong>Changing Materials and Frequencies</strong>: Since not everyone has access to the same materials, I checked the sensitivity of the X-beam in <b>Table 6</b> to variations in arm diameter and tail thickness. Increasing the arm diameter to 1" and the tail wires to #12, while preserving the dimensions of the antenna in <b>Table 5</b>, produced the results shown in <b>Table 6</b>. Those who are only used to working with linear elements, where fat equals electrically long, may be surprised to find that both the driven element and the director play short. Both require lengthening to match the antenna in <b>Table 5</b>. (Those who have modeled quads with wires and tubing of varying diameters will not find the phenomenon strange at all.) The requisite lengthening--on the order of 0.2' to 0.3' per tail--approaches the point of requiring slightly longer arms to keep the tails from nearly touching. In the end, varying the materials of an X-beam by any significant amount requires either a new model for a blueprint or some empirical experimentation.</p>
<pre>Properties of a 10-Meter X-beam with Thicker Arms and Tails and with a Capacitively Loaded Director
Antenna: Arms 1.0" dia., 6.92' long, Tails #12, DE = 4.29', Dir = 3.79'.
Environment Dir Xl Gain Take-Off F-B Ratio Beam width Source Impedance
(Ohms) (dBi) Angle (dB) (degrees) R &PlusMinus; X
Antenna A: Best 50-Ohm match design
Free Space -25 5.3 -- 15.7 70 39.9 - 2.9
20', ave. gnd. -25 10.5 24 9.6 76 39.5 + 5.3
35', ave. gnd. -25 10.7 14 13.0 70 36.7 - 0.4
Antenna B: Maximum front-to-back ratio design
Free Space -15 5.9 -- 33.0 66 31.4 - 4.8
20', ave. gnd. - 5 11.6 24 53.0 68 24.0 - 0.4
35', ave. gnd. -10 11.5 14 24.2 66 26.5 - 2.3
Antenna C: Maximum gain design
Free Space + 5 7.0 -- 6.9 58 13.4 - 4.4
20', ave. gnd. + 5 11.9 24 10.5 64 14.5 + 4.3
35', ave. gnd. + 5 12.3 14 7.7 60 13.6 + 4.8
Performance figures for 20 and 35 foot heights were taken over average ground (also called medium earth:
dialectric constant = 13, conductivity = 5 milliSiemens/meter).
Table 6. Properties of a 10-meter X-beam with thicker arms and tails and with a capacitively loaded director in
free space and at 20 and 35 feet over medium earth.</pre>
<p><strong>SWR Bandwidth</strong>: Developing 2:1 SWR bandwidth curves does help us determine which of the design variations will best serve a specific application. The bandwidth of the X-beam appears to be little better or worse than most antennas. <b>Table 7</b> charts two models of the X-beam at 35', the first of which is the original Anderson specifications. Referenced either to the center frequency resistive component of the source impedance or to a 50-ohm cable, the Anderson design provides a broad curve within the usual 2:1 SWR limits. The curves are graphed in <b>Fig. 8</b>. Note that as the frequency increases, the design transitions from a "best match" condition to a "max gain" condition, with the "max front-to-back" condition occurring about three-fourths of the way through the 1 MHz spread. Although the gain and front-to-back ratio drop off seriously at the lowest end of the band, performance is quite adequate throughout most of the range. Anderson's empirical findings once more vindicate themselves, especially for the individual with limited space who needs a monoband beam for full-band use.</p>
<center>
<img src="mu1a-8.gif" width="400" height="311" border="2" vspace="5" hspace="9">
</center>
<center>
<p>Fig. 8. 2:1 SWR bandwidth graph for the Anderson 10-meter X-beam in <b>Table 2</b>.</p>
</center>
<pre> X-Beam Bandwidth Characteristics
Antenna: Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.79', Dir = 3.29' @ 35'
Design center: 28.5 MHz (original Anderson design)
Frequency
(MHz) 28.00 28.25 28.50 28.75 29.00
Gain (dBi) 9.9 10.3 10.9 11.5 12.0
Front-to-back
ratio (dB) 8.9 11.6 17.1 33.8 13.1
Beam width
degrees 72 70 68 66 62
Source Impedance
R +/- X 42.1 - 26.1 39.4 - 21.5 34.3 - 16.1 27.2 - 8.4 19.5 + 3.1
SWR (50)1 1.797 1.706 1.710 1.913 2.569
SWR (Ctr)2 2.020 1.808 1.594 1.433 1.766
Antenna: Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.99', Dir = 3.79' @ 35'
Director load (Xc) = -30; Load = 1.86&thorn;10-10F (186 pF) @ design center: 28.5 MHz
Frequency
(MHz) 28.00 28.25 28.50 28.75 29.00
Gain (dBi) 10.3 10.9 11.5 12.1 12.1
Front-to-back
ratio (dB) 11.6 16.9 24.3 12.0 5.5
Beam width
degrees 72 68 66 62 58
Source Impedance
R +/- X 37.0 - 12.9 32.3 - 6.7 25.5 + 1.8 18.4 + 14.0 13.3 + 29.5
SWR (50)1 1.524 1.596 1.961 2.959 5.141
SWR (Ctr)2 1.744 1.390 1.074 2.030 4.800
1 SWR (50) gives the calculated SWR relative to a 50-Ohm feedline.
2 SWR (Ctr) gives the calculated SWR relative to the approximate center design frequency impedance (25.5
Ohms).
Table 7. Frequency-related properties of the original Anderson design and of an X-beam optimized at 28.5 MHz
for maximum front-to-back ratio.</pre>
<p>Using the capacitively loaded antenna at 35' of <b>Table 5</b>, I converted the load reactance at 28.5 MHz into a capacitance for insertion into the model as a LaPlace figure. The results of a selective frequency sweep appear in <b>Table 7</b> and are graphed in <b>Fig. 9</b>. Again, the lower line references the SWR to the center frequency, while the upper line references it to 50 ohms. The figures suggest that the 2:1 SWR bandwidth exceeds 750 kHz on 10 meters. However, most of the bandspread lies below the design center. Therefore, when planning an antenna for a specific bandspread, the designer should center the model about two-thirds to three-fourths the way up the spectrum. Like the Anderson design, this X-beam changes its characteristics from a "best match design" through a "max F-B" design to a "max gain" design. If a particular characteristic is especially needed at a specific frequency, one must design for that frequency and live with the results at other frequencies.</p>
<center>
<img src="mu1a-9.gif" width="400" height="309" border="2" vspace="5" hspace="9">
</center>
<center>
<p>Fig. 9. 2:1 SWR bandwidth graph for the director-loaded 10-meter X-beam in <b>Table 5</b>.</p>
</center>
<center>
<strong>Building an X-Beam</strong>
</center>
<p>Because a folded X-beam for 10 meters is under 10 feet on a side, garage construction is easy. A 10-pound package is easy to achieve, which means that a simple mast will hold the antenna, and antenna raising is a simple matter. At the risk of repeating some of what Brice Anderson has said about building an X-beam, let's look at some possibilities.</p>
<p><strong>Basic Structure</strong>: For a number of reasons relating to the bandwidth of the antenna, "permanent" X-beam installations should consider using Anderson's original recommendations for dimensions. Although the rear lobe of the antenna will be wide and gain will not be maximum, matching the antenna to a 50-ohm cable and transmitter is vastly simplified. In fact, a simple sleeve balun (such as the W2DU model or those available through Radio Works) may be the only device between the coaxial feedline and the antenna terminals or connector.</p>
<p>Refer to <b>Fig. 10</b> for some construction details. Although this figure shows elements relevant only to a hilltopper version of the X-beam, it also reveals the basic construction technique for all X-beams. For 10 meters, a plywood plate 18 inches on a side supports the X members. Scrap plywood 3/8 to 1/2 inch thick will easily bear the antenna load. My technique for attaching the antenna to the mast is to cut a circular hole in the plywood at the exact center to admit an 18-inch length of 1-inch nominal diameter Schedule 40 PVC. Two 2-inch L-brackets support the plate. Stainless steel bolts (#10 x 2") run through the pipe to clamp the L-brackets, while 1-inch #10 bolts hold the plate. This method has proven superior to butting the pipe against the plate in terms of getting a true 90-degree angle.</p>
<center>
<img src="mu1a-10.gif" width="391" height="383" border="2" vspace="5" hspace="9">
</center>
<center>
<p>Fig. 10. Construction details of a collapsible hilltopper X-beam with beta match and remote director tuning.</p>
</center>
<p>Drill the plywood for the X-members, using 2-inch #10 bolts for the fasteners closest to the mast stub and 1 1/2-inch #10 bolts about a half inch from the plate corners. (All hardware is stainless steel, now more readily available in hardware stores.) I used a drill press to drill the tubing, keeping the two holes per piece aligned by dropping a long nail through the first hole and matching it to a reference vertical. The only other holes needed are at the X-member far ends, about 1/4-inch in for attaching the perimeter line and the tails.</p>
<p>Disassemble the basic X and weather treat the plywood. Spar varnish has been a standard, but scrap plywood often admits moisture through gaps in the edge. A more weather-proof alternative is to fiberglass epoxy the board, using epoxy-soaked glass cloth strips to cover the edges. A simple boat repair kit will serve several beams. Before coating the board, enlarge all holes slightly. Then heavily coat their edges. When everything is set, use the correct drill bit to reestablish bolt holes and some sandpaper to refit the mast stub. An orbital sander (or heavier) with course paper will make quick work of smoothing and leveling the surface. The result is weather-proof nearly forever.</p>
<p>When the hub and X members are reassembled, run a perimeter line of 1/8-inch nylon rope or cord, using the end bolts as attachment points. Solder ring connectors on the tails and place them on the end bolts with an additional nut. Add very short leads (with ring connectors) to a coax connector and attach the ring connectors to the underside bolt extensions for the driven element, using additional #10 nuts. Add a shorting bar across the bolt extensions of the director.</p>
<p>My model bolts the mast stub inside a 3-foot length of 1 1/4-inch PVC, which then slips over the main mast. A pair of heavy sheet metal screws locks the larger diameter stub to the mast. Alternatively, the larger diameter stub can be cut to match the length of the inner stub and the pair locked in a rotator.</p>
<p>Although the result is light, it is mechanically sound. My test beams have survived winds in excess of 45 miles per hour without damage. The perimeter line dampens vibrations and reduces metal fatigue. Rain cannot reach the coax connections on the underside of the plate. The end result is simple and long-lived.</p>
<p><strong>Adjustment</strong>: Since the lowest obtainable SWR does not coincide with the antenna's best performance, careful adjustment is required. Adjusting the tail lengths of the director will affect the resistive component of the driven element impedance, while changing the tail length of the driven element will alter its reactive component. If the center frequency is to be in the lower portion of the 10-meter phone band, alter the tail lengths so that the lowest SWR (whatever its value) is just about at the 28.0 MHz point. Then alter the driven element tail lengths to reduce the SWR at the center frequency further by bringing the driven element to resonance. Since initial adjustments may require lengthening elements, do not install ring connectors until the tail length is set.</p>
<p><strong>A Hilltopper Version of the X-Beam</strong>: The ability to capacitively load the director for optimum performance suggested that the folded X-Beam would make a compact collapsible antenna for portable hilltop operations. <b>Fig. 11</b> shows the theoretic coincidence of five patterns across the first MHz of 10-meters with the antenna director adjusted in each case for maximum front-to-back ratio at a 20-foot height level over medium ground, the average conditions for my portable operations.</p>
<center>
<img src="mu1a-11.gif" width="355" height="309" border="2" vspace="5" hspace="9">
</center>
<center>
<p>Fig. 11. Azimuth patterns of the hilltopper X-beam at 20' from 28.0 to 29.0 MHz.</p>
</center>
<p>Since local hardware stores carried only 3/4-inch, 0.050-inch wall thickness aluminum tubing, I remodeled the antenna for this material. With 6' 11" arms, the director and driven element tails became functions of the tuning and matching system. Since a beta match requires driven element shortening, its tails worked out to be 3' 11" long to provide a requisite 25 ohms of capacitive reactance. The director element had to be lengthened so that the tuning capacitor could electrically shorten it; 4' 1" tails provided for this factor. (Note: despite that fact that the physical length of the driven element is shorter than the parasitic element, the electrical lengths are reverse and the beam remains a driven element-director arrangement.)</p>
<p>Beta matches are easily calculated from information in the <em>ARRL Antenna Book</em>.<a href="mu1a.html#N_9_"><sup>(9)</sup></a> I set 25 ohms as the desired feedpoint impedance, since this is close to optimum for maximum front-to-back performance from the antenna. A beta match was then calculated for a 2:1 reduction in impedance. Coil construction utilizes data from recent editions of the <em>ARRL Handbook</em><a href="mu1a.html#N_10_"><sup>(10)</sup></a>. The coil required a 50 ohm inductive reactance, which works out to about 0.28 uH, or 6 turns spaced over 3/4 inch with a 1/2 inch diameter, using #12 wire.</p>
<p>Antenna construction is identical to that described for the "permanent" model, with only a few changes to accommodate collapsing the antenna and adding the tuning and matching elements. First, the beta-match coil has ring connectors on its very short leads and connects across the driven element inner bolt extensions. Second, a half wavelength (adjusted for velocity factor, about 16') of 450-ohm ladder line attaches to the director bolt extensions in place of the shorting bar. At the other end of line, which is within easy operator reach, are two pin jacks. The tuning capacitor has pin terminals to mate with the jacks. The line is spaced from the mast by plastic spray can tops with four punched holes. Cable ties hold the tops to the mast every few feet, and smaller cable ties hold the line to the tops.</p>
<p>Every use of the antenna sacrifices a few cable ties during disassembly. However, the process of putting up and taking down the remote tuning system is quick. The capacitor goes into a protective box when not in use, and the line (with caps attached) rolls up semi-neatly.</p>
<p>The bolts marked "P" on <b>Fig. 10</b> are pivot bolts; they are loosened for antenna transport and storage. The others are removed to free the arms to pivot and then replaced in their plate holes for storage. The perimeter line is looped over the arm point marked "L" and removed when the antenna is not in use. The entire assembly is then pivoted so that all arms point the same way. Use care not to distort the beta match inductor. Fold the tail lines neatly along the lengths of the nestled arms. The resulting compact mass fits in my hatchback, with a tape-wrapped bundle of four 5-foot sections of TV mast and a small box for the capacitor and line. Guy rope (and tent pegs for use when no trees are handy) completes the collection of antenna materials.</p>
<p><strong>Adjustment</strong>: Using the antenna is simply a matter of putting it up and tuning the remote director capacitor for minimum SWR. More accurately, SWR minimum is optimum at the design center frequency only. Below center frequency, use slightly less capacitance than for absolute minimum SWR (within the usual 2:1 transmitter limits) and above center frequency, use slightly more. These guidelines are a function of the complex resistance-reactance combinations that occur off center frequency and the desire to hold the antenna at the maximum front-to-back ratio point.</p>
<p>Initial adjustment is similar to the procedure used for the permanent model. Tune the capacitor for the lowest SWR at the center frequency and then trim the driven element tails for a further drop.</p>
<p>Variations in materials can create significant differences from modeling figures. For example, the hilltopper model used plastic covered speaker wire as a convenience in cutting identical tails. However, this material yielded tails that were electrically long for both elements. (Only a very small part of this excess can be attributed to the modeling limitations of MININEC, since the segment lengths at the apex are very short when properly tapered.) I anticipated a need for a capacitor covering a range of 10 to 45 ohms capacitive reactance (about 125 to 570 pF) to tune the range from 28 to 29 MHz. With the wire used, a 100 pF variable capacitor covered the resultant 80 to 220 ohm range (25 to 70 pF).</p>
<p>The tails also required 6 inches of pruning each to place the SWR curve well within the desired band. However, the result was a curve that went below 1.15:1 at 28.300 MHz and rose to 1.5:1 at 28 MHz and to 1.9:1 at 29 MHz. Local point-to-point contacts verify the pattern as generally in accord with the shape shown in <b>Fig. 11</b>. Performance is detectably better than with a reference dipole placed on the same mast, with the reasonably sharp null to the rear being more pronounced than the forward gain.</p>
<center>
<strong>Overall Evaluation</strong>
</center>
<p>This goals of this edxercise have been, first, to model the X-beam in order to understand its performance characteristics, and, second, to build test models to cross check theory and to enjoy some contacts. The effort does not aim either to praise or to bury the X-beam. The X-beam is a parasitic 2-element beam, but not a 2-element Yagi in either appearance or performance. However, for those with restricted budgets and space, it may provide significant improvements in performance over a dipole or other simple antenna. The X-beam lends itself to home construction, since hardware store aluminum tubing and fastenings combine with scrap wire and a few other parts to make a sturdy antenna.</p>
<p>One ingredient in making the decision to build an X-beam should be the pattern of usual QRM that one finds exasperating. If that QRM comes directly off the rear of a dipole, then a "max F-B" X-beam set-up may be quite helpful. However, if the QRM angles in off the rear (for example, QRM in St. Louis from New England and Florida when the beam points due west), then it may be wise to hold out for a small Yagi. Otherwise, the operator can expect similar results from the two designs.</p>
<p>The Yagi has long been the standard against which we compare beams. In that comparison, the X-beam has some deficiencies. First, X-beam gain only approaches the 2-element Yagi as the pattern deteriorates. Moreover, the X-beam has rearward lobes that are not eliminable and that are only about 1.5 S-units down from the main lobe.</p>
<p>However, the Yagi standard rests upon some operating assumptions that may not hold true for all hams. The standard presumes a desire to work one station in a favored direction, with all other signals reduced, if not eliminated. Hence, maximum forward gain and front-to-back ratio are assumed to be desirable in all cases. Of course, 5 to 7 element Yagis approach this standard well. Some amateur radio operations may not benefit from this standard. For example, local and even wide area nets may suffer from an inability to hear stations in "off" directions. Casual band sweeping in search of a rag chew may benefit from a less directive antenna while still profiting from a little gain and front-to-back ratio. In short, an antenna must be judged by reference to an application as well as to certain performance specifications.</p>
<p>The X-beam is flat and compact. As a cheap ($25 to $35 dollars, depending on local hardware store prices), easily built antenna that fits on a mast (instead of a tower) with a TV rotator (or simply an "Armstrong" rotator), the antenna lends itself to some home applications. Its turn radius is a little less than that of a rotatable dipole. But, for me, it comes into its own as a collasible, tunable hilltopper.</p>
<p>In sum, the X-beam is not a magic antenna, but neither should it be automatically discarded from the list of potentially useful ham antennas. Instead, it is an antenna with both possibilities and limitations. If its possibilities fit a particular set of needs and its limitations do not hinder operation more than those of other antennas, then it could be the right choice for some hams.</p>
<p>However, it is only one of several small beams that one might choose to build. Before putting an X-beam in the attic, you may want to compare it with another interesting beam that uses a closed geometry: the modified Moxon rectangle. We shall look at this unjustly neglected mini-beam next time.</p>
<center>
Notes
</center><br wp="BR1">
<br wp="BR2">
<p><a name="N_1_" id="N_1_">1.</a> This beam is quite obviously a minor variation of the Yagi presented by Bill Orr, W6SAI, in <em>CQ</em> (December, 1990, pp. 83-84). For modeling purposes, the driven element has been lengthened to resonance.</p>
<p><a name="N_2_" id="N_2_">2.</a> Brice Anderson, W9PNE, "Designing X-Beams," <em>Antenna Compendium</em>, Vol. 1 (Newington: A.R.R.L., 1985), pp. 64-66.</p>
<p><a name="N_3_" id="N_3_">3.</a> For some words of praise, see Michael Harris, KM4UL, "Ten for 10," <em>73</em> (April, 1991), pp. 52-56. This builder concludes that he is "confident that you'll find this to be a compact, high performance beam which is easy to build and won't lighten your pocket book. Enjoy it!" For a contrasting viewpoint, see the remark by Brian Beezley that he built into the X-Beam antenna description in AO 5.0: "By no means does this antenna live up to the claims made for it, which include performance comparable to that of a 3-element Yagi!" It is not clear whether Beezley based his conclusion on the analysis of this one model.</p>
<p><a name="N_4_" id="N_4_">4.</a> ELNEC, an enhanced version of MININEC, is available from Roy Lewallen, W7EL, P.O. Box 6658, Beaverton, OR 97007.</p>
<p><a name="N_5_" id="N_5_">5.</a> AO 6.0 is also an enhancement of MININEC (with an additional antenna optimizing feature) available (until recently) from Brian Beezley, K6STI.</p>
<p><a name="N_6_" id="N_6_">6.</a> Incidentally, it is this configuration--and not the Anderson configuration--against which Moxon recommends in his study of small antennas. Indeed, Moxon might appreciate the folded model of the X, given the many folds in some of his recommended antennas, such as the VK2ABQ square, an interesting antenna in its own right. See L. A. Moxon, <em>HF Antennas for All Locations</em> (R.S.G.B., 1982), pp. 81-83 and 172-175. However, he might object to the quartering rear lobes of the X-beam.</p>
<p><a name="N_7_" id="N_7_">7.</a> For those wishing to scale the X-beam to other bands, Anderson provides the following formulas. Arm length (ft) = 195/f (MHz); Total driven element length (ft) = 603/f (MHz); Driven element tail (ft) = 106.5/f (MHz); Total director element (ft) 575/f (MHz); and Director tail (ft) = 92.5/f (MHz). (Anderson, p. 64) Although the choice of materials--tubing diameter for the arms and wire size for the tails--will alter the required dimensions, #18 wire and tubing with a length-to-diameter of about 200:1 will make these dimensions a good starting point for modeling.</p>
<p><a name="N_8_" id="N_8_">8.</a> W2EEY, "The X Beam on 20," in <em>Antenna Roundup</em>, Tom Kneitel, K2AES, ed. (Port Washington: Cowan Publishing Corp., 1966), pp. 60-62; originally published in <em>CQ</em> (June, 1965). Incidentally, W2EEY's X-beam has different proportions than Anderson's design. Modeled without the all-metal support spider, from which the arms are insulated by plastic hose, the beam shows a free space gain of 6.0 dBi and a front-to-back ratio of about 26 dB in a "max F-B" model. The input impedance is low and capacitively reactive: not a good direct match to 50-ohm coax. Moreover, the director required considerable inductive loading, not the capacitive loading specified by the author. The differences between the model and the actual antenna are likely due to W2EEY's construction method.</p>
<p><a name="N_9_" id="N_9_">9.</a> Beta matching is described in detail in the 16th edition of <em>The ARRL Antenna Book</em> (Newington, 1992), pp. 26-21 to 26-23.</p>
<p><a name="N_10_" id="N_10_">10.</a> <em>The ARRL Handbook</em> (Newington, 1992), p. 2-18.</p>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<p><a href="mu0.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to Article Index Page</a></p>
<p class="topics-footer">Topics: <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#small-beams'>Small Beams</a>, <a href='../topics.html#x-beam'>X Beam</a></p><br>
</body>
</html>
content/mu/mu2a-1.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.0 KiB

content/mu/mu2a-10.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 9.5 KiB

content/mu/mu2a-11.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 10 KiB

content/mu/mu2a-12.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 10 KiB

content/mu/mu2a-13.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 11 KiB

content/mu/mu2a-14.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 21 KiB

content/mu/mu2a-15.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 8.6 KiB

content/mu/mu2a-16.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 11 KiB

content/mu/mu2a-17.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 9.2 KiB

content/mu/mu2a-2.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 3.8 KiB

content/mu/mu2a-3.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 3.7 KiB

content/mu/mu2a-4.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 2.5 KiB

content/mu/mu2a-5.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 3.6 KiB

content/mu/mu2a-6.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 3.8 KiB

content/mu/mu2a-7.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 3.7 KiB

content/mu/mu2a-8.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 3.7 KiB

content/mu/mu2a-9.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 2.8 KiB

content/mu/mu2a.html
+280
View File
@@ -0,0 +1,280 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="keywords" content="Moxon, HF Upper, Small Beams">
<title>Modeling and Understanding Small Beams Part 2: VK2ABQ Squares and The Modified Moxon Rectangle</title>
<link rel="stylesheet" href="../styles.css">
</head>
<body>
<center>
<h1>Modeling and Understanding Small Beams</h1>
<h3>Part 2: VK2ABQ Squares and The Modified Moxon Rectangle</h3>
<p><b>L. B. Cebik, W4RNL</b></p>
</center>
<center>
<img src="../images/colorbar.gif" width="591" height="3">
</center>
<p>Miniature directive antennas appeal to hams with little space. Commercially, the Butternut HF5B has enjoyed good success. However, its price tag has led numerous hams to look for home brew antennas. The folded X-Beam, examined in Part 1 of this series, was brought to ham attention by W2EEY as a simplified birdcage and empirically perfected by W9PNE. It has some proponents as well as a few critics. In the U.S., little else seems available to the home brewer.</p>
<p>The VKs and Gs, however, have long been familiar with a square antenna about the same size as the folded-X. The basic idea for the antenna is simple: take a single quad loop and tip it 90 degrees to put the wire in the horizontal plane. At the midpoints of the sides (calling the feedpoint wire the front and the parallel wire to it the rear), cut the loop and insulate the cut ends from each other while preserving the loop. It is reported that VK2ABQ, the antenna's sire, used coat buttons for insulators. The antenna now looks like a 2-element parasitic beam with a driven element and a reflector. It provides gain and front-to-back differential. Folding the ends inward, relative to a Yagi in normal linear configuration improves the front-to-back ratio at the loss of some theoretically possible forward gain. Moreover, loops for several bands (typically, 10, 15, and 20) can be laid out concentrically and fed from a single coaxial cable. <b>Fig. 1</b> shows the general layout.</p>
<center>
<img src="mu2a-1.gif" width="400" height="282" border="2" vspace="5" hspace="9">
</center>
<center>
Fig.1. General outline of a VK2ABQ "square" beam.
</center>
<p>There is an older history to the square, which you can read in <a href="../tales/old.html"><b>Everything Old Is New Again</b></a>.</p>
<p>One problem the potential square-builder faces in trying to replicate the VK2ABQ antenna is finding the right dimensions. The problem is not a lack of dimensions, but too many sets. <b>Table 1</b> and its notes list several sets taken from a couple of British sources.<a href="mu2a.html#N_1_"><sup>(1)</sup></a> Apparently, the antenna is somewhat sensitive both to the wires for the bands not in operation and to the method of construction. Different builders have used different amounts of metal in the hub and support spokes, leaving the new builder to play endlessly with wire lengths with not much clue as to what the goal should be. Although I have only scanned the literature, it appears that American builders have largely ignored the design. In fact, no one seems to have modeled the antenna to find out what it can theoretically do for amateur operation.</p>
<pre> A Sampling of Recommended Dimensions for the VK2ABQ "Square" Beam
Source* Moxon, p. 168; Hawker p. 334 Hawker, pp. 315-316
Arm length 6' 2" 6' 0" 5' 9" 5' 11"
Perimeter length 34' 9" 33' 11" 32' 6" 33' 5"
Side length 8' 9" 8' 6" 8' 2" 8' 4"
Formula/side 248/f (MHz) 242/f (MHz) 232/f (MHz) 238/f (MHz)
*See Note 1 at end of text for references cited here. All dimension in feet and nearest inches:
Table 1. A sampling of recommended dimensions for the VK2ABQ "square" beam.</pre>
<p>L. A. Moxon, in his <em>HF Antennas for All Locations</em>, provides the essential clue: "the main benefit [of a beam] accrues from the reduction of interference during reception, though the 4 to 6 dB gain provided by typical amateur beams is an important bonus and probably the reason which carries the most weight with the majority of amateurs."<a href="mu2a.html#N_2_"><sup>(2)</sup></a> Here is a theory of beam operation quite unAmerican is style: instead of gain, Moxon strives for front-to-back ratio as the most crucial aid to ham operation. His statement is an affirmation of the "good ears" theory of operation. Even more, it forms the basis for his rectangular improvement upon the VK2ABQ square.</p>
<p>Moxon's revelation of the operative notions behind his compact beam-building efforts provided the clue that made possible a venture into modeling these beams with MININEC. The goals were to ascertain their general performance capabilities and to find patterns of development toward optimum performance. By judiciously loading the reflector, one can fairly quickly find the maximum front-to-back ratio. Then, by adjusting dimensions, the modeler can create a pure loop, that is, one with little or no reactance at the driven element source and with little or no requirement for reflector loading.</p>
<p>Finally, there was the task of discovering whether the model dimensions play out in practice. For this exercise, I chose a single band antenna, a 10-meter version of an optimized Moxon rectangle to be precise. Construction minimized metal throughout. The results brought together several interrelated questions. First, given the complex geometry of this antenna, would MININEC reliably model reality? Second, was the antenna too sensitive to any metal in its plane to reflect its idealized MININEC model? Third, would the antenna live up to its theoretical promise? Finally, where does the VK2ABQ/Moxon antenna fit in the world of miniature or small or simple antennas?</p>
<p>This report tries to provide some tentative answers to a few of these questions by taking a systematic look at this "fallen-quad" beam. We shall examine a progression of models that begins with the VK2ABQ and ends up with an optimized Moxon rectangle. Then we shall look at the construction and performance of a real model. The report has some limitations, however. First, it does not model multiband versions of the antenna. Second, the use of metallic masts and hub spiders has not been explored. Nonetheless, the results are both promising and useful. They provide an understanding of the VK2ABQ/Moxon beam potential, and they form a basis for constructing some interesting real antennas for both limited space and portable operation.</p>
<center>
<strong>The VK2ABQ Square</strong>
</center>
<p>Moxon's search for a little gain and a lot of front-to-back ratio excludes the folded X-Beam from consideration here. <b>Fig. 2</b> shows why. Although the front-to-back ratio of an X-Beam can be very considerable in the narrow path directly opposing maximum gain, there are quartering rear sidelobes that never decrease far below about 10 dB less than maximum gain. On 10 meters in the U.S., such a pattern, which can yield a forward gain slightly higher than either of the designs we shall explore here, may satisfy the ham with limited space. Elsewhere in the world--on 20 and 15 especially--those rearward lobes would increase QRM levels excessively. One can sacrifice gain if the overall front-to-rear-area ratio can be improved. Precisely here lies the inspiration behind Fred Caton's invention, the VK2ABQ square.</p>
<center>
<img src="mu2a-2.gif" width="361" height="297" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2. Free space azimuth pattern of a folded X-Beam per Anderson.
</center>
<p>Using the original design, optimized for least reflector loading and least reactance at the feedpoint, but retaining the close-spaced element ends, early models achieved respectable performance. <b>Fig. 3</b> shows the performance of an optimized model, while <b>Table 2</b> supplies the dimensions and analysis figures of the models that led up to this performance. For those unused to trying to capture an antenna with a model, the process may prove instructive.</p>
<center>
<img src="mu2a-3.gif" width="339" height="294" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 3. Free space azimuth pattern of VK2ABQ model #6 (Table 1).
</center>
<pre> A Sampling from the Series of VK2ABQ "Square" Antennas Modeled
Antenna Dimensions (feet) Reflector Gain Front-to-Back Source Z
X Y Space El. Length Load (&PlusMinus;X) (dBi) (dB) (R &PlusMinus; X)
1. 8.8 8.8 0.2 17.4 0 4.2 16.3 133 + 23
2. 9.0 8.8 0.8 17.0 +45 4.5 22.4 103 - 14
3. 9.1 8.8 1.0 16.9 +60 4.3 22.2 94 - 28
4. 9.2 8.8 1.2 16.8 +60 4.6 30.6 94 - 19
5. 9.4 8.8 1.4 16.8 +60 4.7 34.2 88 - 24
6. 9.8 8.8 1.6 17.0 +47 4.7 26.6 88 - 8.0
Note: All performance values are calculated free space figures.
Table 2. A sampling from the series of VK2ABQ "square" antennas modeled.</pre>
<p>Beginning with a model only slightly smaller than the largest encountered in British sources, I modeled antenna 1. Since all sources on the VK2ABQ recommended extremely close spacing of the driven element and reflector ends, I held this spacing at 0.2' or less. The resulting inductive reactance at the feedpoint showed that driven element was long. Moreover, the front-to-back ratio, while slightly better than a typical 2-element Yagi, was not up to expectations.</p>
<p>Tackling the second problem first, I began to increase the spacing between element ends. This move shortened the element lengths, since I held the front-to-back (Y) dimension constant. The front-to-back ratio began to improve dramatically, as models 2, 3, and 4 demonstrate. However, to achieve this calculated performance, it was necessary to insert an inductive load into the center of the reflector element, suggesting that the reflector was short for optimum performance. Note that in all models of the VK2ABQ, the elements are the same length, a design that is counterintuitive for someone familiar with Yagi configurations.</p>
<p>Model 5 achieves the best front-to-back performance, but at the cost of considerable inductive reactance at the feedpoint and the need for sizable reflector loading. Model 6 lengthened the element to bring down the feedpoint reactance successfully. However, it widens the gap between element ends beyond optimum and still requires reflector loading.</p>
<p>Modeling ceased at this point because of several factors. First, the forward gain of the beam was not improving significantly. The best VK2ABQ, while providing exceptional front-to-back ratio, produced a forward gain only bit higher than that of a single quad loop mounted in the normal plane. Second, the model was departing from square to a degree that made the Moxon rectangle the next logical step in the work.</p>
<p>However, before departing the VK2ABQ, we should notice the general pattern in <b>Fig. 3</b> once more. Unlike the X-Beam (<b>Fig. 2</b>), the VK2ABQ puts all its power in the forward lobe, with a beam width that settles in around 88 to 90 degrees between -3 dB points. The main lobe extends around to the sides so that direct side rejection is only half the front-to-back ratio. In comparison, the X-Beam has good front-to-side ratio (at the expense of the rearward lobes), and the dipole, single quad loop, and 2-element Yagi antennas have excellent front-to-side ratios. None of these antennas, however, can even approximate the VK2ABQ for the clean and empty wide rear quadrants. This feature may be useful in more than one application.</p>
<center>
<strong>The Moxon Rectangle</strong>
</center>
<p>To achieve better performance, Moxon lengthened the front and rear elements and shortened the side tails. The resulting rectangle requires very little more turning radius than the square, but improves the gain of the antenna considerably. Modeling Moxon's beam required some initial guesses at the actual 10-meter dimensions, since the builder created u-shaped insets at the corners to handle excess wire needed to make up the perimeter.<a href="mu2a.html#N_3_"><sup>(3)</sup></a> Nonetheless, only two steps yielded a pretty good Moxon beam model. <b>Fig. 4</b> shows the general outline of the Moxon rectangle, while <b>Table 3</b> shows the progression of models and their results.</p>
<center>
<img src="mu2a-4.gif" width="393" height="271" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 4. General outline of a Moxon "rectangle" beam.
</center>
<pre> A Sampling from the Series of Moxon "Rectangular" Antennas Modeled
Antenna Dimensions (feet) Reflector Gain Front-to-Back Source Z
X Y Space El. Length Load (&PlusMinus;X) (dBi) (dB) (R &PlusMinus; X)
1. 11.2 6.6 0.2 17.6 -20 5.3 22.5 115 + 86
2. 11.0 6.6 0.2 17.4 - 5 5.2 21.3 114 + 69
3.* 10.4 6.6 0.2 16.6 DE +30 5.3 18.7 103 + 5.1
17.0 Re
4. 11.0 6.6 0.8 16.6 DE +35 5.5 37.0 80 - 3.6
17.0 Re
5. 11.0 6.7 0.8 16.6 DE +20 5.5 35.0 81 - 4.2
17.0 Re
6. 11.2 6.6 0.8 16.6 DE + 5 5.5 33.6 79 - 2.7
17.4 Re
*Models from this point onward use unequal lengths for the driven element and the reflector.
Note: All performance values are calculated free space figures.
Table 3. A sampling from the series of Moxon "rectangular" antennas modeled.</pre>
<p>The initial models preserved the VK2ABQ close end spacing (although Moxon widened the gap). Model 2 is especially interesting, since it shows excessive driven element length in the inductively reactive source impedance. The reflector is about right for this configuration. However, the front-to-back ratio is not up to VK2ABQ standards. The next moves were a simultaneous increase of the gap between ends and an unbalancing of the forward and rear elements. Moxon prefers matched elements, tuning each of them to optimum performance remotely. That way, he can reverse the beam and do away with expensive and maintenance-intensive rotators. However, rotators are a way of life in the U.S. (a TV rotator will likely handle a 3-band Moxon beam), and there are many uses for portable beams that are hand-rotated or fixed in the field. Thus, I decided to continue the exercise in unequal element lengths.</p>
<p>In models 3, 4, and 5, we can see the approach to a model that would have a roughly resonant feedpoint and require no loading of the reflector. The last model, number 6, is considered optimum for these reasons. <b>Fig. 5</b> provides a free space azimuth pattern for comparison to other antennas. The modified Moxon rectangle is a close match to RG-11 or RG-59 coax for direct feed. The differentials of front-to-back ratio in models 4, 5, and 6 make little difference in practice, and the forward gains of the three models are the same.</p>
<center>
<img src="mu2a-5.gif" width="339" height="297" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 5. Free space azimuth pattern of Moxon rectangle #6 (Table 3).
</center>
<pre> A Performance Comparison Among the VK2ABQ, the Moxon, and Some Reference Antennas
Antenna Conditions Refl. Load Gain Front-to-Back Source-Z
(&PlusMinus;X ohms) (dBi) (dB) (R &PlusMinus; X)
VK2ABQ #6 (Table 2) Free Space +47 4.7 26.6 88 - 8
35' Ave Gnd* +47 10.3 30.8 98 - 13
Moxon #6 (Table 3) Free Space + 5 5.5 33.6 80 - 3
0 5.6 24.1 76 + 1
20' Ave Gnd - 5 11.1 20.4 81 - 6
0 11.0 18.9 85 - 10
35' Ave Gnd + 5 11.0 25.5 88 - 3
0 11.1 21.9 83 + 1
2-element Yagi (DE + Refl.) Free Space -- 6.3 11.2 32 + 1
(16.0'/17.5'/4.25' space) 35' Ave Gnd -- 11.7 13.5 35 &PlusMinus; 0
Single loop quad, #18 copper wire Free Space -- 3.2 -- 127 + 4
(L=1040/f(MHz) or 9.12' per side) 35' Ave Gnd -- 8.5 -- 125 - 6
Wire dipole, #18 copper wire Free Space -- 2.1 -- 72 &PlusMinus; 0
(L= 468/f(MHz) or 16.42' 35' Ave Gnd -- 7.7 -- 86 - 8
*Average ground or earth: dielectric constant = 13, conductivity 5 mS/m
Note: Compare free space figures only to other free space figures and over-ground figures only to other over-
ground figures.
Table 4. A performance comparison among the VK2ABQ, the Moxon, and some reference antennas.</pre>
<p>Free space is not a fully adequate indicator of these quasi-loop beams over real ground. The potential for needing reflector loading was too great simply to build the free space model and hope it would work. <b>Table 4</b> presents some comparative figures. Without any reflector load at all, the Moxon 6 model promised adequate performance at both 20 feet (a typical portable height) and 35 feet (a typical home-installation height) above medium earth. The 20' Moxon exhibits a small wide swell in rear coverage (<b>Fig. 6</b>), while the 35' Moxon demonstrates a more stepped appearance (<b>Fig. 7</b>). Both front-to-back ratios are reasonable for the heights, although neither reaches the level of the tiny free space rear lobes.</p>
<center>
<img src="mu2a-6.gif" width="342" height="294" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 6. Azimuth pattern of Moxon rectangle #6 20' above average earth.
</center>
<center>
<img src="mu2a-7.gif" width="345" height="292" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 7. Azimuth pattern of Moxon rectangle #6 35' above average earth.
</center>
<center>
<img src="mu2a-8.gif" width="337" height="292" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 8. Free space azimuth pattern of a reference 2-element Yagi.
</center>
<p>The Moxon beam shows a gain midway between the VK2ABQ and the typical 2-element Yagi. <b>Fig. 8</b> provides a free space azimuth pattern for a typical 2-element Yagi as a reference standard against which to compare the Moxon rectangle. Why the Moxon rectangle's gain is less than that of a linear 2-element Yagi, despite the absence of power in the rear lobe, may raise some questions. However, such questions reveal 2-dimensional thinking. Antennas are three dimensional devices. Besides forward and back, power may radiate up and down and anywhere between. Both the VK2ABQ and the Moxon rectangle radiate considerably more power to the sides and at high radiation angles relative to the horizontal than 2-element Yagis. <b>Fig. 9</b> demonstrates the difference in free space high angle radiation between the VK2ABQ and the Yagi, while a comparison of <b>Fig. 3</b> and <b>Fig. 8</b> reveals the 18-degree beamwidth difference. Although these properties hold down forward gain, they may prove useful in other applications.</p>
<center>
<img src="mu2a-9.gif" width="340" height="290" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 9. Free space elevation patterns of the Yagi in Fig. 8 and the VK2ABQ square in Fig. 3.
</center>
<p>Of concern to every small beam builder are bandwidth considerations for both the pattern and the feedpoint impedance. <b>Fig. 10</b> and <b>11</b> display the pattern bandwidth in sets of azimuth patterns taken at five points between 28 and 29 MHz. At 28 MHz and a 20-foot height, the front-to-back ratio of the rectangle drops to about 11 dB. At 29 MHz, the figure is also about 11 dB. These figures approximate a 2-element Yagi, but the Moxon exceeds the Yagi between 28.25 and 28.75. A similar pattern of reduced front-to-back ratio at band edges appears with the antenna at 35 feet, but the effect is smaller. Except for the lowest edge of the 10-meter band, the front-to-back ratio remains above 15 dB and above 25 dB at design center. At both heights, the forward gain, while less than that of a 2-element Yagi, remains fairly constant across the band.</p>
<center>
<img src="mu2a-10.gif" width="337" height="301" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 10. Pattern bandwidth of the Moxon rectangle at 20' using composite azimuth patterns at a 24-degree take-off angle.
</center>
<center>
<img src="mu2a-11.gif" width="339" height="296" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 11. Pattern bandwidth of the Moxon rectangle at 35' using composite azimuth patterns at a 24-degree take-off angle.
</center>
<p>With respect to feedpoint impedance, the Moxon rectangle is well-behaved across the entire first MHz of 10 meters. Since the design center frequency impedance is about 80 ohms at all heights, 75-ohm coax provides the best match, as shown in <b>Fig. 12</b> and <b>13</b>. However, the SWR relative to a 50-ohm transmitter output and cable never exceeds 2:1 from 28 to 29 MHz, thus simplifying matching requirements. As the test model verified, these anticipated values are close to reality, despite the limitation of MININEC in calculating impedance and SWR for perfect grounds only.</p>
<center>
<img src="mu2a-12.gif" width="400" height="313" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 12. SWR bandwidth of the Moxon rectangle at 20' for 50 and 75 ohm cables.
</center>
<center>
<img src="mu2a-13.gif" width="400" height="317" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 13. SWR bandwidth of the Moxon rectangle at 35' for 50 and 75 ohm cables.
</center>
<p>The Moxon rectangle's 3 dB gain over a dipole at the same elevation is useful, but the most significant Moxon feature is the reduction in all rear directions of potential QRM. At 6 dB per S-unit, the Moxon beam promises (at least, in model form) to reduce QRM by more than a full S-unit and perhaps as much as 2 S-units compared to a 2-element Yagi. Whether the beam could deliver on its model's promise required an exercise in building.</p>
<center>
<strong>Building a Moxon Rectangle</strong>
</center>
<p>Since the diversity of VK2ABQ dimensions in the literature suggests a sensitivity to the conductivity of the antenna structure, the portable Moxon beam requires a minimum of metal to test the model dimensions. Therefore, the beam I built was an exercise in plywood, PVC, and nylon cord. See <b>Fig. 14</b>. A center platform of well-varnished or fiber-glassed 3/8" plywood measured 22.4" by 13.2". These dimensions assured that the rectangular X-frame would have the proper angles. A pair of #10 1 1/2" stainless steel bolts (with washers and nuts) secures each of the four half-inch nominal thin-wall PVC arms. In place of the bolts nearest the corners of the platform, one may use 1/2" nominal PVC conduit clamps with #8 stainless steel hardware. Fifth and sixth arms project from the platform to the center of the driven element to support the feedline and to the center of the reflector element.</p>
<center>
<img src="mu2a-14.gif" width="426" height="294" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 14. Construction sketch of the 10-meter test Moxon rectangle.
</center>
<p>The platform has a center hole to pass a 3-foot length of 1" nominal schedule 40 PVC pipe. Two 2" corner brackets secure the platform to the pipe 18" down from the top. The brackets use bolts that pass through a bracket, the pipe, and the opposing bracket. Short #10 stainless steel hardware secures the brackets to the platform. Note that the brackets are above the platform, since it will rest on the 1 1/4" nominal PVC mast pipe, with a pair of bolts through the nested pipes to lock them together.</p>
<p>At the upper end of the platform pipe, an X-cut--enlarged and smoothed--provides a channel for eighth-inch nylon support cord. The cord ends pass through holes in opposing arms about 2/3rds the way out to the corner. Several wrappings of the cord before knotting reduce stress on this light guy. <b>Fig. 15</b> provides guidance for setting up the support guys.</p>
<center>
<img src="mu2a-15.gif" width="423" height="178" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 15. Sketch of the support guy system used with the test Moxon rectangle.
</center>
<p>Each arm is 6'6" long. Mounted on the plate about 1" from the center point (to allow room for the pipe hole), the arms extend about an inch beyond the precise corner points. Quarter-inch holes through the arm in the plane of the wire permit the insertion of plastic tubing to reduce stress on the element wires that pass through them.</p>
<p>Measure each element with some excess. Thread each element through the plastic corner tubes. To the ends of each element, attach about a foot of nylon cord to tie the element ends together and maintain spacing between them. Add the guys running across the X-cut in the vertical pipe. The result will be a well-braced Moxon rectangle for use in up to moderate winds.</p>
<p>Use part of the driven element's excess wire to provide whatever is needed to attach a simple dipole center insulator and coax fitting. When you are satisfied that the dimensions are correct enough for initial testing, snug up all the tie-off points. Do not solder the element ends wires yet, since some length adjustment may be needed to put the beam on target. (In fact, after completing all length adjustments, remove the cord from the element end. Solder the wrapped wire to secure it and make a loop. After cooling, reinsert the cords and resnug the assembly. This caution is needed, since nylon cord melts well before solder does.) Attach 75-ohm coax to the dipole center insulator, taping it to the extra PVC arm. One can also insert a choke or sleeve balun here to reduce chances of RF traveling down the outside of the coax braid. Alternatively, one can insert a 75-to-50 ohm balun or unun and use 50-ohm coax to the rig.</p>
<p>It is not necessary to make any of the initial adjustments and tests with the beam in the air. Lay the beam over a wooden prop so that the reflector is a few feet off the ground and the driven element points to the sky. With a low power signal, adjust the driven element lengths for the lowest SWR at the frequency of choice. Now erect the antenna in the normal plane at least 15 feet high. With a small signal source and a receiver, adjust the reflector for minimum signal off the rear. Try to keep the element ends about 9 to 10 inches apart. The SWR of the driven element should not be adversely affected. However, you may wish to lower the antenna and redo the driven element length one more time to finish the adjustment task. Only the most finicky operator should need to make further adjustments at height.</p>
<p>With minimal metallic mass in the mounting, the Moxon rectangle adjusts quite closely to the model dimensions. Although my test set-up does not permit test range figures, the antenna performs to expectations at a height of 20 feet. For signal strength, it does not quite match my 2-element beam at 35 feet, but the front-to-back ratio is much better, despite the height disadvantage. If you feed the antenna with 50-ohm coax cable, expect an SWR that varies from 1.5:1 to 1.9:1 in a rippling fashion across the first MHz of 10-meters. The normal dip in the resonance curve only appears with 75-ohm cable.</p>
<p>Point-to-point tests with local operators located 10 to 15 miles from the station confirmed the modeling exercises quite well. Using both received signals and reports of transmitted signals, the front-to-back ratio of the antenna averaged better than 4 S-units on a variety of transceivers, compared to a little over 2 S-units for my HF5B at 35 feet. The front-to-side ratio averaged a between 1 and 2 S-units, but signals fell off rapidly as the beam was rotated past the side point to the rear. These results cannot be translated into the 20-foot azimuth pattern figures (<b>Fig. 6</b>), since that pattern is taken at an elevation angle of greater than 20 degrees and assumes no ground clutter. Moreover, the relationship of S-units on a transceiver meter to dB of front-to-back ratio is too uncertain for quantitative comparison. However, for practical operation, the basic characteristics of the Moxon rectangle appear satisfactorily confirmed. Nonetheless, other construction methods using a greater metal mass in the support structure may require more extensive adjustment.</p>
<p>The wood-wire-PVC model of the modified Moxon rectangle has withstood stormy wind gusts of about 45 m.p.h., far above the design goal for the portable antenna. However, in continuous use, the wood platform is bound to age, and the thin nylon rope will fray. For permanent installations, a more robust construction method may be in order. Models of the rectangle using 3/4" aluminum tubing suggest that only the driven element needs adjustment to compensate for the fatter element diameter. Shortening the driven element tails by about 0.2' each, while maintaining the spacing from the ends of the reflector tails, brings the beam's operating characteristics into line with the wire model.</p>
<center>
<strong>Some Applications of the Moxon Rectangle</strong>
</center>
<p>The Moxon rectangle offers the ham with limited space the chance for a compact directional beam. Adding elements concentrically for other bands is possible. Moxon reported interaction between elements 15 and 10 meters and offers some hints on curing the problem. Of course, the multiband builder will have to experiment with element lengths for peak performance, as will the builder who uses more metal to support the arms.</p>
<p>If the builder does not make Gordian knots in the nylon guys and stays, the beam should disassemble in 15 minutes for transportation. The broad main lobe of the Moxon rectangle may serve Field Day and other operations well. It rivals W7EL's Field Day Special, but may be erected where there are no trees for end supports.<a href="mu2a.html#N_4_"><sup>(4)</sup></a> On either coast, a single fixed position would cover most of the U.S., while inland, a TV rotator or an Armstrong assistant will rotate the beam with ease. For many contests and other applications, front-to-back ratio may serve the operation better than raw gain.</p>
<p>The antenna offers a further potential. Given the wide beam angle both horizontally and vertically, plus the exceptional front-to-back ratio, the Moxon rectangle provides a very smooth curve in both X and Y planes when pointed straight up. See <b>Fig. 16</b> and <b>Fig. 17</b>. Off the flat of the reoriented beam, models show almost horizon to horizon coverage with minimal dips in the pattern at a wavelength height. Side-to-side, the coverage is very smooth, although it may require a pair of rectangles, each tipped 30 degrees or more to extend coverage to near the horizon. The patterns exhibit none of the vertical holes of vertical dipoles nor any of the pattern irregularities of simple horizontal antennas. Since satellite operations have reached the point for many birds of not requiring steerable arrays, the Moxon rectangle may be serviceable as a simple fixed antenna. Hybrid construction using aluminum tubes or rods for what are now the horizontal elements, with wire and cord for the ends, may simplify the building process, but preconstruction modeling is recommended to check the effects of larger element diameters.</p>
<center>
<img src="mu2a-16.gif" width="344" height="291" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 16. Elevation pattern of a vertically-oriented Moxon rectangle beam (#6) off the flat plane of the antenna.
</center>
<center>
<img src="mu2a-17.gif" width="336" height="294" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 17. Elevation pattern of a vertically-oriented Moxon rectangle beam (#6) off the edge plane of the antenna.
</center>
<p>Modeling the modified Moxon rectangle at 144.5 MHz with #14 copper wire for the elements produced the following dimensions: a rectangle 2.36' long by 1.32' wide, with a driven element 3.40' total length and a reflector 3.62' total length. These lengths translate into 0.52' end pieces for the driven element and 0.63' end pieces for the reflector, with a 0.17' space separating the end pieces. The 2-meter model showed all the properties of the 10-meter version at 1 wavelength above ground or ground plane. Elevated to several wavelengths above ground and pointed straight up, the patterns develop deep nulls between adjacent nulls lobes that multiply with height. Therefore, VHF and UHF scalings of the rectangle might use an artificial ground plane (a wire screen) below the reflector to tailor the pattern even further.<a href="mu2a.html#N_5_"><sup>(5)</sup></a> The driven element impedance drops to about 65 ohms due to the larger element diameter relative to the wavelength of the signal. This suggests that tubing models might approach a good match to 50-ohm coax. (A 10-meter model using 0.75 aluminum tubing produced a calculated 72-ohm source impedance, a 9 percent reduction relative to the #14 wire version.)</p>
<center>
<strong>Overall Evaluation</strong>
</center>
<p>In our quest for gain, we may have overlooked the important "good ears" principle of effective amateur operations. The modified Moxon rectangle presented here, as an improvement of the VK2ABQ square, offers exceptional front-to-back ratio with only two elements. Moreover, its pattern offers other potentials usable by field operators and possibly even by satellite operators. The beam lends itself to home construction with components easily accessed from hardware and home improvement outlets. As the "loose ends" in this report suggest, the modified Moxon rectangle offers a fertile field for experimentation with other materials. All in all, it is an antenna worth further study; even more, it is an antenna worth further use.</p>
<p>Some of the further experimentation is reported on in the notes at this site. See the <a href="../moxon/moxpage.html"><b>Moxon Rectangles and Online Calculator</b></a> page, where you will find a growing number of items on wire and tubing Moxons for HF and VHF.</p>
<p>However, if tubing and wire are more to your building taste than PVC and plywood, there are small beams for you. For example, linear-loaded Yagis can be 25% shorter than full-size Yagis with little loss in performance. But that is for next time.</p>
<center>
<strong>Notes</strong>
</center>
<p><a name="N_1_" id="N_1_">1.</a> See L. A. Moxon, <em>HF Antennas for All Locations</em> (R.S.G.B., 1982), p. 168; see also Pat Hawker, <em>Amateur Radio Techniques</em> (R.S.G.B., 1980), pp.315-316, p. 320, and p. 334. For a summary of work on the VK2ABQ square and the Moxon rectangle, see Erwin David, G4LQI, Ed., <em>HF Antenna Collection</em> (RSGB, 1991), pp. 23-28.</p>
<p><a name="N_2_" id="N_2_">2.</a> Moxon, p. 67.</p>
<p><a name="N_3_" id="N_3_">3.</a> Moxon, pp. 172-175.</p>
<p><a name="N_4_" id="N_4_">4.</a> See Roy Lewallen, W7EL, "<a href="https://www.eznec.com/Amateur/Articles/Field_Day_Special.pdf" target="_blank">Try the 'FD Special' Antenna</a>," <em>QST</em> (June, 1984), pp. 21-24.</p>
<p><a name="N_5_" id="N_5_">5.</a> See <em>A.R.R.L. Antenna Book</em>, 16th Ed. (Newington: A.R.R.L., 1991), pp. 19-7-19-9 for ideas in this vein.</p>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<p><a href="mu0.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to Article Index Page</a></p>
<p class="topics-footer">Topics: <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#moxon'>Moxon</a>, <a href='../topics.html#small-beams'>Small Beams</a></p><br>
</body>
</html>
content/mu/mu3a-1.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 2.2 KiB

content/mu/mu3a-10.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.4 KiB

content/mu/mu3a-11.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.3 KiB

content/mu/mu3a-12.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.0 KiB

content/mu/mu3a-13.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 3.7 KiB

content/mu/mu3a-2.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 7.4 KiB

content/mu/mu3a-3.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 7.5 KiB

content/mu/mu3a-4.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 8.3 KiB

content/mu/mu3a-5.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 7.9 KiB

content/mu/mu3a-6.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 4.9 KiB

content/mu/mu3a-7.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 14 KiB

content/mu/mu3a-8.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 6.1 KiB

content/mu/mu3a-9.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.7 KiB

content/mu/mu3a.html
+520
View File
@@ -0,0 +1,520 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="keywords" content="EDZ / Zepp, HF Upper, Small Beams, W8JK">
<title>Modeling and Understanding Small Beams Part 3: The EDZ Family of Antennas</title>
<link rel="stylesheet" href="../styles.css">
</head>
<body>
<center>
<h1>Modeling and Understanding Small Beams</h1>
<h3>Part 3: The EDZ Family of Antennas</h3>
<p><b>L. B. Cebik, W4RNL</b></p>
</center>
<center>
<img src="../images/colorbar.gif" width="591" height="3">
</center>
<p>The Extended Double Zepp (EDZ) has been a lonely antenna for most of its life, since Hugo Romander, W2NB, introduced its potential to the amateur community in 1938. Even its vertical cousin, the Extended Single Zepp, seems to have changed its name to the 5/8 wavelength ground plane to avoid identification with the EDZ.<sup>1</sup> By contrast, everyone knows about the family of antennas related to the half wavelength dipole: the quarter wavelength ground plane, the 2-, 3-, and more-element Yagis, the ZL-Special. The EDZ also spawns a family of antennas that include parasitic and phase-fed beams. This report tries to fill in some of the family tree without necessarily recommending everything that the computer modeling says is theoretically possible with the EDZ. What looks good on the computer may not work out in backyard practice. However, the ideas we shall consider may spur someone else to realize some of the potential shown by EDZ beams.</p>
<p>Here is a sample: A good 2-element dipole-based Yagi shows about 3 1/2 dB gain over a similarly placed wire dipole. To achieve 6 dB gain over that same piece of wire requires 4 to 5 elements. Suppose one could make an 2-element antenna with the same 6 dB gain over the original wire. That fact would qualify the EDZ beam as a small beam in boom length, although not in element length. Both parasitic and "135-degree" phase-fed versions of the EDZ promise the computer to give the indicated performance. However, achieving that performance will impose severe restrictions that mark the antennas for special purposes under narrowly defined circumstances.</p>
<p>For this study, all antennas are referenced to 10-meters, with any exceptions clearly noted. Within limits, the results can be scaled, at least within the upper HF region of the spectrum.</p>
<center>
<strong>The Basic EDZ</strong>
</center>
<p>Before turning to the more distant cousins of the EDZ, let's begin at home with the basic horizontal EDZ. It is a wire antenna, about 1 1/4 wavelengths long, fed in the center. It presents a high, complex impedance at the feedpoint, ordinarily necessitating the use of parallel feeders and an antenna tuner. <b>Fig. 1</b> suggests the basic set-up.</p>
<center>
<img src="mu3a-1.gif" width="434" height="281" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1. The basic structure of a horizontal single-wire EDZ antenna.
</center>
<p>The chief advantage of the EDZ over a resonant half wavelength dipole is bidirectional gain. See <b>Fig. 2</b>, which provides patterns for free space half wavelength and EDZ dipoles. Relative to a wire dipole, whether in free space or over real ground, the EDZ provides about 2.9 dB gain over the resonant dipole, with a bandwidth in the main lobe some 45 degrees narrower. For the cost of wire, the EDZ provides some significant advantages.</p>
<center>
<img src="mu3a-2.gif" width="299" height="273" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2. Free space azimuth patterns of a 1/2 wl dipole and a single-wire EDZ antenna.
</center>
<p>Some authors have provided formulas for cutting the EDZ. The most common is based on the long wire length formula:</p>
<p>L (in feet) = 984 (N - 0.025)/ f (in MHz), where N = number of wavelengths, or</p>
<p>L (in feet) = 1205/f (MHz).</p>
<p>Beers prefers a constant of 1218, while recent editions of <em>The ARRL Antenna Book</em> call for 0.64 per side, which yields a numerator of 1258.<sup>2</sup></p>
<p>Most wire models using #12 to #18 show their maximum gain in 10-meter models with a length closer to 1225/f (MHz). However, such number-crunching devices are misleading. They obscure the fact that selecting the length of an EDZ is always a compromise between gain and another factor that dipole builders do not have to confront: side lobes. <b>Fig. 3</b> overlays three EDZ patterns for wires of different lengths. The pattern with the greatest gain also has large side lobes and a narrow beam width. The other patterns show slightly less gain (less than -0.1 dB), but the shortest model (L= 1180/f (MHz)) also has the least off-axis gain. The cost of smaller sidelobes is a higher capacitive reactance at the feedpoint. In the end, selecting a length for an EDZ may be determined less by absolute gain potential than by the amount of off-axis QRM to be tolerated. <b>Table 1</b> summarizes the modeled variations of gain and front-to-sidelobe ratio for 10 meter antenna lengths from 41.4' to 44.6' in free space.</p>
<center>
<img src="mu3a-3.gif" width="299" height="267" border="2" vspace="5" hspace="9">
</center>
<center>
3. Three free space azimuth patterns for short (41.4'), medium (43.0') and long (44.6') EDZ antennas.
</center>
<pre> EDZ Antenna Length vs. Gain and Sidelobes
Length #12 Copper Wire #18 Copper Wire
(Feet) Gain (dBi) Front-to-Side Gain (dBi) Front-to-Side
Lobe Ratio (dB) Lobe Ratio (dB)
41.4 4.94 -15 4.90 -16
41.8 4.98 -13 4.94 -14
42.2 5.01 -11 4.96 -11
42.6 5.02 -10 4.98 -10
43.0 5.03 - 9 4.98 - 9
43.4 5.02 - 8.5 4.97 - 8.5
43.8 5.00 - 8 4.95 - 8
44.2 4.96 - 7 4.91 - 7
44.6 4.90 - 6.5 4.85 - 6.5
delta G=0.13 dB delta F-S=8.5 dB delta G=0.13 dB delta F-S=9.5 dB
Notes:
1. Antenna model is for 28.5 MHz in free space.
2. Gain figures are recorded to 2 decimal places for comparison purposes only. Single digit
differences in the first decimal column are unlikely to be significant to performance.
3. Front-to-side lobe ratios are estimated from antenna plots. Higher accuracy is not required
to show the trend in sidelobe growth with antenna length.
Table 1. EDZ antenna length vs. gain and front-to-side lobe ratio.</pre>
<p>Had <b>Fig. 3</b> showed further shortening of the antenna wire, eventually the side lobes would have disappeared--just as the antenna length approached a single full wavelength. Moving in the other (longer) direction, the main lobe gain quickly falls off to yield the traditional 6-petal pattern of a 1 1/2 wavelength antenna. <b>Fig. 4</b> illustrates these extremes.</p>
<center>
<img src="mu3a-4.gif" width="297" height="269" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 4. Comparative free space azimuth patterns for 1 wl, 1.25 wl, and 1.5 wl wire antennas.
</center>
<p>With the EDZ, there are also subtleties occasioned by antenna height. Within the usual amateur backyard building limits (20 to 70 feet antenna height), antenna gain will vary, with peaks at the 5/8, 1 1/8, and 1 5/8 wavelength heights and minima at the 7/8, 1 3/8, and 1 7/8 wavelength heights. Unfortunately, the 7/8 wavelength height, about 30 feet on 10 meters and 35 feet on 12 meters, is often a tempting and convenient amateur construction height. However, moving up a quarter wavelength in height (to about 39 feet on 10 meters) can increase gain by 1.6 dB over the 7/8 wavelength point and decrease the main lobe take-off angle by 4 degrees, with a consequent increase in radiation at the lower angles most favorable to DX. Above a height of 1 1/2 to 2 wavelengths, the gain fluctuations with height become insignificant, but the radiation at low radiation angles continues to increase. Half wavelength dipoles also show such fluctuations at about the same heights, but to a much lesser degree. Gain variations with height result from reflected antenna currents being reinduced into the wire at phase angles that vary according to antenna height. The same phenomenon also creates a varying feed point impedance.<sup>3</sup></p>
<p>The EDZ is a nonresonant antenna, displaying great capacitive reactance. Within the range of reasonable lengths (about 41.5' to 44.5' on 10 meters), the antenna shows a feedpoint impedance ranging from 175-j930 at the short end to 110-j640 at the long end. The impedance--both the resistive and reactive components--falls off more rapidly as the length passes the midpoint (43'), where the impedance is about 150-j840 .</p>
<p>Most commonly, hams feed the EDZ with open-wire or similar parallel transmission lines and an antenna tuner. This style of operation permits the operator to use the antenna on other bands in a way similar to the use of center-fed (double) Zepps in the 1930s. (I suspect that this fact contributed much to the name "extended double Zepp.") More recently, Yardley Beers reminded us that impedance matching need not be done at a distance from a highly reactive antenna. He developed a system of transformer matching between the antenna and a coaxial feedline. The secondary of the transformer not only provided the step-up ratio for the resistive component of the impedance, but as well provided the inductive reactance to compensate for the antennas natural capacitive reactance.<sup>4</sup></p>
<p>Stub matching to a 50- coaxial feedline is also possible by selecting a line (for example, 450-Ohm parallel line) and, by calculation or experiment, choosing a length that results in a 50-Ohm resistive impedance when a suitable stub is connected in parallel across the junction of the matching section and the main feedline. A 44-foot long #14 wire 10-meter EDZ at about 35 feet above average ground would require a 450- (.95 VF) matching section just over 5-feet long and a parallel shorted stub of the same material just over 1.2 feet to provide a perfect match to 50- coax. Setting more precise dimensions than these would require information on the antenna's feedpoint impedance over the actual terrain of the site. Stub matching should result in a very reasonable 2:1 SWR bandwidth of over 800 kHz on 10 meters. See the Appendix to review the characteristics of stub matching and a method of calculating the elements of such a system.<sup>5</sup></p>
<center>
<strong>The 180-Degree Phased 2-Element EDZ</strong>
</center>
<p>John Reh, K7KGP, was perhaps the first in recent times to experiment with 2-element arrangements of the EDZ, developing a 180-degree phased array of identical elements spaced 1/8 wavelength apart. The antenna is an extension of one version of the "two-section W8JK," which used 1 wavelength elements. <b>Fig. 5</b> provides free space patterns of the 8JK and the phased EDZ antennas, both bidirectional arrays, along with a single element EDZ. The phased EDZ provides about 1.1 dB gain over the 8JK and about 2.9 dB gain over a single EDZ. This is equivalent to about 5.8 dB gain over a 1/2 wavelength wire dipole equally situated.</p>
<center>
<img src="mu3a-5.gif" width="296" height="264" border="2" vspace="5" hspace="9">
</center>
<center>
Fig.5. Comparative free space azimuth patterns for the 8JK, the single-wire EDZ, and the 2-element 180&deg; phase-fed EDZ array.
</center>
<p>One advantage of the 180-degree phased EDZ array, like all other 180-degree phased arrays of any length, is the immunity of the antenna to variations in gain and impedance with changes in height. From 0.5 to about 2 , the gain of the array climbs quickly and then more slowly to essentially flat-top above 1.2 . The impedance remains quite constant, with the reactance varying by less than &PlusMinus; 1 . The difference in these characteristics from their counterparts in a single-wire antenna is due to the cancellation of radiation vertically (both incident and reflected), thus reducing the complexity of radiation interactions with the elements with changes in height. <b>Fig. 6</b> compares the elevation patterns of a single wire EDZ with its 180-degree phased counterpart over medium earth at a height of 35 feet, about 1 at 10 meters.</p>
<center>
<img src="mu3a-6.gif" width="303" height="166" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 6. Elevation patterns over real ground for the single-wire and the 2-element 180&deg; phase-fed EDZ antennas.
</center>
<p><b>Fig. 7</b> shows the general outline of the phased array, along with two feed systems. Dimensions of the elements are not critical. Neither is the exact spacing. Construction can consist of two #18 copperweld or #12-14 copper wires with spreaders every 5 to 8 feet. For 10 meters, 4.5' lengths of thin wall PVC thin-wall conduit serve well. Hack saw slots into the ends to point 4.3' to 4.4' apart. Drill the ends of the cuts to pass the wire with friction. Leaving the burrs on the holes increases friction and holds the wires in place. Press the wires into the slots until they reach the holes. A 2-year test of this system showed no tendencies for the spreaders to slip from their initial positions, even without any adhesives or additional wire ties. Single end supports (towers, trees, guyed masts, etc.) are adequate for the antenna if the element ends, extended by 3/16 to 1/4 inch diameter sun-resistant synthetic rope, are attached to a longer and studier PVC length. Schedule 40 material is strong enough to permit the installation of eye-bolts. The end ropes pass through the eye-bolts and down to a tie off point for raising and lowering the antenna.</p>
<center>
<img src="mu3a-7.gif" width="552" height="399" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 7. General construction outline of a 2-element 180&deg; phase-fed EDZ array with two different methods of feed.
</center>
<p>Feed systems are numerous, but only two are shown here. Section A. in <b>Fig. 7</b> shows individual feedlines brought together with a reactance-cancelling stub, while Section B. shows a taut section of feedline between the elements, with a section dropped vertically to the coaxial cable junction. Either system will work over a narrow frequency range. It is possible to model feedline sections and correlate the results with feedline calculations using standard formulas.<sup>6</sup> Calculations used standard 450-ohm line with a velocity factor of 0.95, while MININEC models used #18 wire spaced 0.083' (1") apart and NEC models specified transmission line lengths, impedances, and velocity factors. Of course, MININEC models do not treat feedline as feedline, but as part of the radiating structure where the fields tend to cancel each other. Nevertheless, the resulting figures came within construction variations of each other.</p>
<p>For an array consisting of two 44' #14 elements spaced between 4.3' and 4.4' at 28.5 MHz, the feedpoint impedances of the elements are each approximately 20-j650 . For reasonable variations in these dimensions (up to a half foot shorter and wire as thin as #18 copperweld), the resistive component will vary by an Ohm or 2, while the reactive component may range between -600 and -800 .</p>
<p>To achieve a Vee-shaped junction of two feedlines that in parallel produce a resistive impedance of 50 when a compensating parallel stub is added, requires a pair of lines, each nearly 5 feet long. Remember, one of the two lines has a half-twist to place the elements 180 out-of-phase. Where they join at the point of the Vee, a shorted stub only about an inch to an inch and a half long provides the proper compensation. Is the stub essential? Without the stub, the antennas feed impedance at the junction of the Vee is about 3 resistive and 12 reactive.</p>
<p>Only general figures are given here, because exact numbers depend upon knowledge of all the antenna and feedline variables for a given installation. In the area of line length required for a 50-Ohm match, the impedance shows a rapid change per unit length. Hence, a very fractions of an inch of line length may separate the impedance values generated by slight variations on a given version of the antenna. Trimming must be done in small increments. Series or parallel capacitors of a capacitive stub will compensate for the remnant reactance.</p>
<p>Using a taut 4.4' line between elements, with a further feedline centered at the 2.2' mark yields a different situation. Each line--a bit under 25 in length--shows an impedance of about 8.5-j300 at the junction point of the two, for a parallel combination of 4.25-j150 . Various models of this structure gave values of 3.9 to 4.3 resistive, with a reactive component of 140 to 175 . Connecting a single length of 450 feedline vertically from this junction a usable stub-main feed junction about 1.5 feet down the line. A very short shorted stub (about 2 inches long) in parallel across the junction will provide the 50- match to a coaxial feeder. Due to the very low resistive component of the junction, special care should be taken to ensure as lossless and weatherproof a set of connections as possible. Moreover, the very high reactance-to-resistance ratio indicates that the match will have a quite narrow bandwidth.</p>
<p>Models also suggest an untried scheme as a variant on <b>Fig. 7B</b>. Without a twist in the line, divide the antenna structure down the middle of the taut feedline, with each half fed in the center of its side of the line. Cross-connect the two resulting feedpoints in a parallel connection (essentially putting the twist at the connection), and the feedpoint impedance will be about 4.5-j150 , ready for the same connecting line as above.</p>
<p>Of course, the use of coax may be set aside and the parallel feeders run all the way to the station antenna tuner. Several factors recommend this method in preference to a stub match. First is the criticalness of the system tuning. Matching sections require lengths over which both resistance and reactance are changing by great amounts per unit of line length. With either the Vee or the flat-top stub-feed systems shown, the 2:1 SWR bandwidth is just over 100 kHz wide at 10 meters.</p>
<p>Second, the dimensions just given apply to a single height for the experimental antenna; alterations of antenna height from the 35' model height will require total recalculation. Indeed, the more critical the dimensions of a matching line and stub, the more ease of adjustment a good antenna tuner will provide.</p>
<p>The resulting array produces a pair of opposing narrow main lobes (28 to 32) with sidelobes about 50 off-axis and down about 12 to 14 dB, depending upon the exact choice of element lengths, spacing, and wire size. At a wavelength in height (35' at 10 meters), the take-off angle is about 13 with a -3 dB point at 7 above ground. Models also suggest that interaction between the antenna elements and the feeding-phasing structure may reduce gain by up to a dB from the theoretical optimum. The missing power reappears in the 90 off-axis directions, reducing the front-to-side ratio by a small but determinant amount. Nonetheless, for a fixed array where both forward and reverse directions may be useful but do not usually result in QRM, this antenna may be worth the work it takes to pruning it to a particular frequency and to a match with the transceiver.</p>
<center>
<strong>Parasitic EDZ Beams</strong>
</center>
<p>If one could make the 2-element EDZ unidirectional, one might achieve a little more gain, plus have the advantage of reduced QRM from the rear. Theoretically, there are two ways of achieving this goal: a. create a parasitical beam, and b. phase-feed the rear element in a manner similar to the ZL Special. Table 2 shows a comparison of the free space gains of models of the full EDZ family, along with a standard half wavelength wire dipole and the 2-element Yagi that has been used as a reference in earlier installments of these reports.</p>
<pre> Relative Free-Space Gains of Various Antennas in the EDZ Family
Antenna Gain (dBi)
1/2 wl Dipole 2.07
1-el. EDZ 4.85
2-el. reference Yagi 6.30
2-el. EDZ, 180-degree phase fed 7.85-8.10
2-el. EDZ, parasitic 8.70-9.25
2-el. EDZ, 135-degree phase fed 8.95-9.30
Notes:
1. The "2-el. reference Yagi" refers to the modified W6SAI 10-meter beam used as a standard of
broadband 2-element design throughout this series.
2. All values are derived from computer models and, except for the reference Yagi, average
several designs using, as relevant, different element lengths, spacings, and wire sizes.
Table 2. The relative free-space gains of various antennas in the EDZ family, along with a
reference dipole and Yagi.</pre>
<p>The idea for a two-element beam based on the double extended Zepp was first presented to me in 1991 by Brian Egan, ZL1LE, who proposed for his computer studies of a 15-meter model element spacing of 100 inches, with one element fed and the other a loaded reflector. My concern for keeping the wires properly spaced led me to consider closer spacing, something in the neighborhood of 1/8 wavelength spacing, as used in the ZL Special. The result was the development of two different, but related antenna concepts. One is a double extended Zepp version of the ZL Special, with phased feed. The other, following ZL1LE's lead, uses two elements of the same length, with one fed and the other loaded as a reflector. The computer says both should work quite similarly. The ZL Special version (referred to as the 5/4ZLS hereafter) offers the potential for eliminating loading coils. The symmetrical antenna (referred to as the ZL1LE hereafter) offers the potential for reversibility, allowing me to orient it toward Europe and toward down-under just by moving an accessible feedline.</p>
<center>
<img src="mu3a-8.gif" width="581" height="220" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 8. General construction outline of a ZL1LE 2-element EDZ parasitic beam.
</center>
<p>The original ZL1LE antenna used wide spaced elements. The modified version shown in <b>Fig. 8</b>, uses 1/8 wavelength spacing (4.39 feet) between two equal length elements. The forward element is fed, while the rear element is parasitic. However, to achieve any forward gain and significant front-to-back ratios, the rear element must be loaded inductively. With a carefully selected load, and minimizing losses in the load inductor, the antenna is capable of potentially superior performance. The gain at most heights averages across the design bandpass better than 14.5 dBi, or about 6.5 dB better than a dipole of equal height and orientation. The front-to-back ratio for various models runs from just under 20 dB to more than 30 dB.</p>
<center>
<img src="mu3a-9.gif" width="298" height="263" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 9. Azimuth patterns for two versions of the ZL1LE parasitic EDZ beam at 35' above real ground.
</center>
<p><b>Fig. 9</b> shows the azimuth patterns for two model beams at a 35' height. The patterns with smaller sidelobes and a smaller front-to-back ratio (about 23 dB) uses #12 copper elements 41.67' long, spaced 4.39' apart and requires a reflector load of 1035 . The version with larger sidelobes and a higher front-to-back ratio uses 44' elements at the same spacing, with the same wire and a 685 reflector load reactance. As with any member of the EDZ family, balancing various characteristics determines the final choice of design. In any event, one must model the parasitic EDZ beam over real ground, as in <b>Fig. 9</b>, to gain a perspective on the actual characteristics. The free space pattern yields a pattern whose rear lobes look like miniatures of the forward lobes, a picture that does not hold over real ground.</p>
<p>Table 3 compares the modeled performance of the ZL1LE antenna in two versions to the performance of a single element EDZ and of a 2-element 180-degree phase-fed array. Also noted are the necessary changes in loading inductor for the parasitic element to achieve maximum front-to-back ratio at each height. Below a height of about 2 , the parasitic EDZ beam in almost any form is height sensitive with respect to gain, front-to-back ratio, and the required loading inductance to achieve maximum front-to-back ratio. A height of about 1 provides the best combination of gain and front-to-back ratio. In fact, experimental models of the antenna appear to lose much of their dx potential if not at least 1 above ground.<sup>7</sup></p>
<pre> Comparisons of Antenna Models Based on the Extended Double Zepp
HeightGain Front-to- Front-to S/L Beam Source Source Load
(Feet)(dBi) Back Ratio Side Ratio Gain Width Resistance Reactance Z=10+jXL
(dB) (dB) (dBi) (&deg;) R (Ohms) -XC (Ohms) XL (Ohms)
Single Wire EDZ (42.8' Elements, #18 Copper)
F.S. 4.9 10 -5 32 162 840
20 11.3 10 1 36 128 860
25 10.0 10 -1 34 150 810
30 9.6 10 -1 34 193 830
35 11.0 10 1 34 159 870
40 11.0 10 1 32 137 830
45 10.0 10 0 32 173 820
2-Element EDZ, 180&deg; Phase-Fed Array (42.8' Elements, #18 Copper)
F.S. 7.8 15 -7 30 26.4 (x2) 820
20 12.2 17 -5 32 26.3 822
25 12.8 16 -3 32 25.2 820
30 12.7 15 -2 32 26.8 819
35 12.9 15 -3 32 27.0 820
40 13.2 15 -3 32 25.9 820
45 13.2 15 -3 32 26.1 819
2-Element Parasitic EDZ Beam (42.8' Elements, #18 Copper)
F.S. 8.7 16.4 11.8 -3.1 32 89.8 775 950
20 14.3 18.0 13.5 0.8 34 80.7 792 905
25 13.6 11.9 13.0 0.5 34 76.6 777 945
30 13.1 18.1 12.3 0.7 32 97.1 760 980
35 14.4 25.3 12.8 1.6 32 96.0 775 935
40 14.4 13.2 12.0 2.4 32 79.1 785 930
45 13.8 14.3 11.9 1.9 32 88.3 768 970
2-Element Parasitic EDZ Beam (41.67' Elements, #12 Copper)
F.S. 8.8 15.4 14.0 -5.0 34 102.0 830 1055
20 14.5 16.9 15.8 -1.3 36 94.8 852 1000
25 13.7 11.1 14.0 -0.3 36 86.2 832 1050
30 13.5 16.9 14.7 -1.2 34 109.3 813 1095
35 14.5 23.4 15.1 -0.6 34 110.0 830 1035
40 14.6 12.5 14.0 0.6 34 89.2 843 1025
45 13.9 13.4 14.0 -0.1 34 99.1 822 1080
Notes:
1. F.S. = free space 2. Sidelobe figures estimated from graph for bidirectional antennas.
3. Loading coil assumed to have an approximate Q of 100
Table 3. Comparisons of antennas based on the Extended Double Zepp as modeled at typical
amateur construction heights and optimized (where necessary) for maximum front-to-back ratio.</pre>
<p>The source impedance for the antenna shows a large capacitive reactance which requires compensation. Assuming the use of a suitable inductance to eliminate the reactance, the feedline impedance, now only resistive, is roughly twice that of the normally used 50-ohm coaxial cable. A 2:1 quarter-wave matching section of 75 ohm cable cut to design center frequency would likely yield an acceptable match. A linear choke, such as the W2DU ferrite choke balun, would be apt between the feedline and the matching section.</p>
<p>Since this antenna requires inductors in both elements, one to cancel the series capacitive component of the source impedance and the other to load the reflector, the system holds potential for being used as a fixed beam whose direction is reversible. However, if the components are mounted at the antenna, it is unlikely that anyone would climb a structure to readjust the inductor values. However, the inductors need not be mounted at the antenna.</p>
<p>Low loss parallel feedline--450-ohm is recommended for its ability to withstand power and weather--permits both matching inductors to be mounted closer to the ground. A wavelength (assuming .95 velocity factor) at 28.5 MHz is about 32.8 feet, and a half wavelength is 16.4 feet. For 10-meter antennas at 20 or 35 feet, feedline runs to a platform near the ground are feasible with a length of line that permits the impedance conditions at the element centers to replicate. Using rotary or tapped inductors, one can adjust the loading and the compensating inductors with comfort and ease. A chart of settings would ensure quick adjustment. Installing a coaxial connector near each coil would permit shifting the feedline from one element to the other, thus permitting the direction of the beam to be reversed.</p>
<p>The reason for employing this scheme is to achieve a reversible fixed beam. A 44'-element beam was constructed for reversible parasitic operation. I mounted a rotatable 5' plank on the end of a 4-by-4 sunk in the ground. One end of the plank held the reflector inductor, the other held the driven element matching system. Rotating the plank and reconnecting the feedlines reversed the antenna. A modified version of the Beers matching system converted the driven element impedance to 50-ohm coax values. <b>Fig. 10</b> shows two systems tried with equal success. One uses a rotary coil with a fixed 3-turn link of #18 solid hook-up wire. The other uses a fixed 2-turn link over a fixed coil of 8 turns of 1.5" diameter, 10 turns per inch stock, with a 50 pF variable capacitor in series with the link to control the degree of coupling. Either system amounts to installing an antenna tuner at the antenna, a multiple of a half wavelength below it.</p>
<center>
<img src="mu3a-10.gif" width="508" height="212" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 10. Two feed systems for the ZL1LE parasitic EDZ beam.
</center>
<p>Tuning the inductor to maximum front-to-back ratio requires a variable inductor and a signal source several wavelengths behind the antenna. Coil variability should range of 4.0 to 6.5 uH to cover a 10-meter reactance range of 770 to 1100 . A 10 uH variable inductor picked up at a hamfest provided sufficiently sharp tuning for tests. Of course, weather-proofing the tuning components is essential for this scheme.</p>
<p>Test results showed that the parasitic EDZ beam has excellent gain and reasonably good front-to-back ratio for the frequency to which everything is tuned. However, without retuning--especially the reflector inductor--everything goes to pot very quickly as one tunes off frequency, especially downward. SWR curves do not necessarily provide significant information in this connection. After adjustment of all the variables for 28.5 MHz, an SWR meter in the coaxial feedline showed under 2:1 between 28.1 and 28.9 MHz. However, below the design frequency, the beam had lost its unidirectional characteristic.</p>
<p>Table 4 models the effects of off-frequency use of the parasitic EDZ. If the value of X<sub>L</sub> is low by 10%, the reflector becomes a director, and the beam reverses its direction. Using values of X<sub>L</sub> optimal for a frequency 0.5 MHz higher in the 10-meter band results in performance similar to that of the bidirectional array. A higher X<sub>L</sub> value, optimal for a lower frequency, results in a gradual drop in gain and a more rapid drop in front-to-back ratio. If one must choose a single inductor value for the reflector coil, the best choice is the optimum value for the lowest operating frequency in the band. However, the large variation in optimum inductance required across a wide band like 10 meters suggested that the parasitic EDZ beam is best used as a fixed-direction, fixed-frequency or narrow band antenna. For that use, however, it is inexpensive compared to a Yagi with similar gain and front-to-back ratio.</p>
<pre> Performance of a 2-Element Parasitic EDZ with Nonoptimum Reflector Loading
Measurement Optimum Frequency Optimum Load Reactance Gain Front-to
Frequency for XL Used Reactance (XL) Used (XL) (dBi) Ratio (dB)
28.0 MHz 28.0 MHz 1030 Ohms 1030 Ohms 14.6 22.3
28.5 905 1030 13.7 8.0
29.0 795 1030 13.0 5.2
28.0 MHz 28.5 MHz 1030 Ohms 905 Ohms -12.4 -0.9
28.5 905 905 14.6 22.3
29.0 795 905 13.6 8.0
28.0 MHz 29.0 MHz 1030 Ohms 795 Ohms -12.9 -3.4
28.5 905 795 -12.5 -0.9
29.0 795 795 14.6 22.0
Note: Modeled antenna used 2 42.8' elements, #18 copper wire space 4.39' apart at a height of 20'
over medium earth. Similar results were obtained with other "equal-element" parasitic models at
various heights above ground.
Table 4. Performance of a representative 2-element parasitic EDZ with nonoptimum reflector loading.</pre>
<p>One untested potential for the ZL1LE antenna is at 2 meters, where materials and dimensions make the antenna self-supporting. Using 0.75" diameter aluminum tubing, one can construct a beam with a driven element 8.2' long and a reflector 8.6' long, spaced just over 10" apart. Models indicate a reflector load between 250 and 305 ohms at 144.5 MHz. The source impedance is about 50-j290 , which simplifies the process of matching the antenna to coaxial cable to the elimination of the reactance alone. Due to the increase in element diameter to element length ratio, bandwidth increases over HF wire models and may cover a full megahertz of the band without undue loss of gain or front-to-back ratio if the antenna is optimized near the low end of the desired frequency range.</p>
<p>Such antennas almost exist. One commercial advertisement includes a double 5/8 wavelength vertical, that is, two such antennas end to end. The same ads indicate that some directionality will result if the antenna is mounted on the side of a tower, which apparently forms an untuned reflector. Perhaps some day a manufacturer who can control the reflector loading reactance within tight specifications may produce a true 2-meter ZL1LE.</p>
<center>
<img src="mu3a-11.gif" width="296" height="262" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 11. Azimuth pattern for a 2-meter version of the parasitic EDZ beam mounted vertically with the center 35' above real ground.
</center>
<p>The horizontal advantages of the 2-meter antenna for low-end CW and SSB operations, despite bandwidth restrictions, are the same as for HF models. However, <b>Fig. 11</b> shows an azimuth pattern of the antenna mounted vertically, with the center 35' above ground. The bandwidth to half-power points is about 135 and the gain is over 13 dBi. The utility of such an antenna at a ham station for both repeater and Packet work seems obvious, and three of these antennas arrayed around a tower might well increase the range of any repeater. The lack of suitable VHF test equipment must leave the development of a working model of the 2-meter ZL1LE to others.</p>
<center>
<strong>Phase-Fed EDZ Beams</strong>
</center>
<p>The phase-fed version of the two element EDZ beam consists of two unequal length elements spaced 4.31' apart for 28.5 MHz. The directly-fed forward element is 42.3 feet long, while the phase-fed rear element is 44.7 feet long. Configured as a wire beam, this assembly is unidirectional. Computer models show a peak gain of 14.7 dBi across the 1 MHz design bandwidth, with an average front-to-back ratio of about 20 to 23 dB, peaking at about 30 dB. The beamwidth is a narrow 34 degrees. All of these figures apply to a 35-foot height for the antenna. <b>Fig. 12</b> shows the pattern of the antenna as optimized for 28.5 MHz.</p>
<center>
<img src="mu3a-12.gif" width="298" height="257" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 12. Azimuth pattern of a phase-fed EDZ beam (54ZLS) 35' above real ground.
</center>
<p>Experience with ZL-Special would suggest that with 1/8th wavelength spacing, the rear element should be fed 135 out-of-phase with the forward element. Modeling suggests otherwise. The model whose pattern appears in <b>Fig. 12</b> is current phase fed at 143 to achieve maximum front-to-back ratio. Since the proposed method of feed is a twisted parallel feedline section, the modeling technique was altered. The rear element is modeled in the opposite direction from the forward element, and the phasing directly applied as -37 to the rear element source point. This technique yields identical pattern figures, but provides correct information on current and voltage amplitudes and phases for use in calculating phasing lines.</p>
<p>The chief difficulty in implementing the 5/4ZLS version of the 2-element EDZ is feeding two elements with highly reactive components in such a way as to ensure that equal power flows to both elements and that the rear element is about 143 out of phase with respect to the forward element. The source impedances for the model under discussion are 100-j830 and 5-j660 for the forward and rear elements respectively. I have been unable to discover any cable of any length that will provide the proper phasing in the manner of the traditional ZL Special. Moreover, the demands of this antenna may exceed even the flexibility of a phasing network. The high reactances at the feedpoint place any network in a region which is experiencing very rapid changes in current phase and in impedance per unit length. Regretfully, the 54ZLS has had to be consigned to the realm of antennas with theoretical potential but no present feasibility.</p>
<p>Nevertheless, models do suggest that the dimensions of this antenna, when fed as a Yagi, will produce excellent unidirectional gain and a good front-to-back ratio with a reflector load of 675 . In essence, the ability to adjust the reflector loading substitutes for a phasing line in bringing the reflector current to the correct magnitude and phase to achieve a deep rear null. However, no unidirectional EDZ array will do much better than about 20 dB front-to-rear ratio when including all parts of the rear lobes.</p>
<p>It is worth noting, however, that what we call "phasing" lines in antennas like the ZL Special are actually impedance transformers, with or without the half twist. Explorations of models using approximately 1/8th half-twist parallel transmission lines between two identical elements produced an alternative means of matching an EDZ to 50- coaxial cable. A two-element version of the 10-meter EDZ with such a connecting section made up from 600- (.95 VF) parallel line shows an almost perfect impedance for coaxial-cable feed. The gain of the antenna is about the same as a single element EDZ (about 11 dBi at 35 feet over medium earth), with a slight (less than 0.9 dB) difference between the two main lobes. The SWR is less than 2.5:1 over the first MHz of 10-meters. For the cost of an additional element and some separators, the builder can produce a coax-fed adjustment-free EDZ.</p>
<center>
<strong>Summary</strong>
</center>
<p>Understanding the possibilities for EDZ arrays and beams depends, as we have seen, on understanding the basic properties of the single element EDZ antenna. Two-element arrays, either bidirectional or unidirectional are possible and feasible--if they fit the operating needs and circumstances of a particular station. As wire beams, they are fixed and thus fit for point-to-point communications. Their narrow bandwidths and beamwidths reinforce this type of use. Moreover, they are not forgiving of casual building and tune-up practices.</p>
<p>There remains much to be learned about the behavior and the possibilities of EDZ beams. A bit of that data appears in other notes at this site, for example, <a href="../edz/edz.html"><b>EDZ Beam Update</b></a>; <a href="../edz/edzfeed.html"><b>Feeding the EDZ</b></a>; and <a href="../vhf/eb.html"><b>Phased Yagis, EDZ Beams, and Landstorfer-Sacher Yagis</b></a>.</p>
<p>If thelimiting factors factors are not deterrents to building one of the EDZ family of beams, but part of the needs of a station, then the operator can expect considerable gain over many other types of wire antennas. Moreover, the cost of these antennas, including wire elements and feedlines, is well below the cost of Yagis with equal gain (and equal front-to-back ratio for the ZL1LE). EDZ beams may have a small but not insignificant niche in the spectrum of amateur antennas. I do not recommend them, since recommendation would require a detailed knowledge of too many variables directly related to the communications situation in which the antenna might play a part. However, I do recommend further experimentation, modeling, calculation, and ingenuity in pursuit of getting the most out of this interesting family of antennas. EDZs and other nonresonant arrays may have gone unjustly neglected in our dipole-and-coax age.<sup>8</sup></p>
<center>
<strong>Notes</strong>
</center>
<p>1. This tongue-in-cheek introduction does have a serious point. The Jones handbook mentions the 5/8 wavelength vertical, especially as a broadcast antenna, as early as 1936, if not before. See Frank C. Jones, <em>Jones Radio Handbook</em>, 3rd Ed. (San Francisco: Pacific Radio Publishing Co., 1936), pp. 73-74. However, see Hugo Romander, W2NB, "The Extended Double-Zepp Antenna," <i>QST</i>, June, 1938. The antenna remained much neglected after this initial introduction to the ham community.</p>
<p>2. Yardley Beers, "The 5/4-Wavelength Dipole: A Revival," <em>Communications Quarterly</em> (November, 1990), pp. 40-41. Jerry Hall, Ed., <em>The ARRL Antenna Book</em> (Newington, ARRL, 1991), p. 8-34.</p>
<p>3. See L. B. Cebik, "The Effects of Height on Other Antenna Properties," <em>Communications Quarterly</em> (Fall, 1992), pp. 57-79.</p>
<p>4. Beers, "The 5/4-Wavelength Dipole: A Revival," pp. 41-44.</p>
<p>5. K7KGP's 12-meter EDZ, shown in recent <em>ARRL Handbooks</em>, can mislead builders, since his stubless match applies only to the antenna feedpoint impedance figures he lists. See <em>The ARRL Handbook</em> (Newington: ARRL, 1992), p. 33-11. The matchline he specifies leaves an Ohm or 2 of remnant reactance, much too little to be of concern. Except in very rare cases, other feedpoint impedance figures will require a stub to compensate for reactance at the junction of the matchline and the main feedline. The Appendix to this article provides a method of directly calculating both the matchline and stub elements of a stub-matching system.</p>
<p>6. See Terman, <em>Radio Engineer's Handbook</em> (New York: McGraw-Hill, 1943), pp. 185-186, among other sources (for example, Johnson's <em>Antenna Engineering Handbook</em>, 3rd Ed.), for the basic formulas for calculating the impedance, current, and voltage along a lossless transmission line for any length from the load. Fortunately, these formulas are amenable to simple basic programming that, in addition to figures for specific line lengths, will produce charts of results for any desired interval. Such charts permit estimation of desirable line lengths within trimming range. As previously noted, it is also possible to use these formulas to calculate required stub-matching systems; see the Appendix.</p>
<p>7. A 2-element Yagi at 35' provided stronger signals on 10 meters on the eastern U.S. to VK/ZL path than an initial experimental model of the EDZ beam at 25', despite the fact that models estimated roughly equal radiation in the 5 to 10 elevation region. Raising the wire antenna resolved the problem. However, the experience impressed upon me the importance of choosing antenna heights such that the lowest required path angle clears fields of obstructions, such as nearby woods with 70' trees and the like. The effect can be dramatic.</p>
<p>8. All patterns shown in this discussion were plotted on ELNEC 3.02, but figures cited have been cross-checked on various programs and by various means of calculation (including versions of NEC-2 and NEC-4).</p>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<center>
<strong>Appendix</strong>
</center>
<center>
<strong>Stub Matching: A Review</strong>
</center>
<p>As long as hams wish to use or experiment with antennas like the Extended Double Zepp and others that present complex feedpoint impedances, stub matching will remain one alternative method of matching the antenna to a 50- feedline. Most discussions of stub matching, however, appear almost wholly in qualitative terms. The purpose of this discussion it to convert that discussion into quantitative terms. We shall proceed by reviewing the basic concept of stub matching, presenting the basic equations for calculating the elements of a stub-matching network, and finally using a simple BASIC implementation of those equations to solve a couple of exemplary problems.</p>
<center>
<strong>The Stub-Matching System</strong>
</center>
<p>Most antenna manuals give the simple equations for calculating the reactance of both shorted and open transmission line stubs. However, these treatments regularly omit similar equations for calculating the length of the line between the antenna and the stub-feedline junction. So let's begin again.</p>
<p><b>Fig. 13</b> shows the basic structure of a typical stub-matching system. It consists of the antenna with its complex feedpoint impedance, a length of matching-feedline (the Line) leading to the critical junction, a reactive Stub, and the main feedline (the Feed) leading to the power source, ordinarily a transmitter or transceiver. The functions of the antenna and the main feedline are well-known, but the functions of the other two elements require brief comment.</p>
<center>
<img src="mu3a-13.gif" width="413" height="237" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 13. Basic elements of a stub-matching network
</center>
<p>The matching-feedline operates as an impedance transformer. When there is a complex antenna feedpoint impedance or a mismatch between the antenna impedance and the matching-feedline impedance, the overall impedance, as well as the resistive and reactive components of that impedance, will vary along the line. These values are normally given as series values. If the line type (that is, its characteristic impedance) is properly chosen, at some point along the line, the resistive component of the impedance will be of such a value that its corresponding parallel value will equal the characteristic impedance of the main feedline. This point defines the correct length of matching feedline to use.</p>
<p>Ordinarily, at the junction of the matching-feedline and the main feedline, there will also be a reactive component to the overall impedance. Although usually given as a series value, it too has a corresponding parallel value. A reactance of the opposite type but of the same magnitude will compensate for the junction reactance. In this exercise, the compensating reactance will be composed of a feedline stub, even though lumped components (capacitors or inductors) are also usable with somewhat greater losses in some instances. Compensating for the parallel reactance will leave a parallel resistance equal to the main feedline. With the reactance compensated, the resulting series resistance value will be the same value, thus effecting a match to the main feedline.</p>
<center>
<strong>Calculating the Matching-Feedline and Stub Lengths</strong>
</center>
<p>Often left to graphical analysis along with some miscellaneous calculations, the calculation of match-line and stub systems can be direct. With the advent of home computers and BASIC, the reputed tediousness of the calculations is no longer a hindrance. Indeed, a simple computer program is faster than most graphical methods (some of which have been computerized).</p>
<p>The process begins by understanding that along a match-line, we are seeking the point at which the parallel-equivalent value of the series resistance is equal to the characteristic impedance of the main feedline. Associated with these values is a value of series reactance and its parallel equivalent. If we call the series resistance and reactance the target values, then we define R<sub>T</sub> and X<sub>T</sub>. Let Z<sub>F</sub> be the characteristic impedance of the main feedline. Then, using the series-to-parallel resistance conversion equation,</p>
<center>
<img src="mu3ae1.gif" width="400" height="80">
</center>
<p>Solving for X<sub>T</sub><sup>2</sup>, we get</p>
<center>
<img src="mu3ae2.gif" width="400" height="71">
</center>
<p>Before using equation (2), we must calculate the reflection coefficient, rho, (actually its square) of the antenna-to-match-line system. Let the match-line characteristic impedance by Z<sub>M</sub>. Then, using the antenna feedpoint impedance, R<sub>L</sub> &PlusMinus; jX<sub>L</sub>, we can calculate.</p>
<center>
<img src="mu3ae3.gif" width="400" height="85">
</center>
<p>Using this figure for rho, we can then calculate the value of series resistance at the point in the line defined by equation 2, using that equation to remove reactance values from the calculation of R<sub>T</sub>:</p>
<center>
<img src="mu3ae4.gif" width="400" height="86">
</center>
<p>The target value of reactance is, of course, the square root of equation 2.</p>
<p>The equation, in various forms, for calculating the impedance, Z<sub>in</sub>, anywhere along a transmission line back from a load, Z<sub>L</sub>, is well known.<sup>1</sup> That equation can be rewritten as separate equations for R<sub>in</sub> and X<sub>in</sub>, which will be more useful for present purposes. We shall use equations for lossless lines for three reasons. First, the lengths of line involve--all well under a wavelength, have losses far less significant than other potential error factors that enter the use of matching stubs. Second, for most types of transmission line, the most imprecise figure is the velocity factor of the line to be used, and most ham do not have access to laboratory grade measuring equipment to bring experimental determination of that figure under 5%. Third, physically replicating a calculated antenna, especially one with a significant reactive component at the feedpoint, usually results in departures from calculated values. Nevertheless, a calculation of the anticipated matching line and stub lengths will do much better than put one in the ball park: it will allow one to make a close play at the plate.</p>
<p>Since we wish the matching line to yield a resistive impedance component that correlates with the characteristic impedance of the main feedline, we may begin with the formula that has appeared in the <em>ARRL Handbook</em> in the 80s and early 90s.<sup>2</sup></p>
<center>
<img src="mu3ae5.gif" width="550" height="115">
</center>
<p>where R<sub>L</sub> is the resistive component of the antenna impedance, X<sub>L</sub> is the reactive component of the antenna impedance, Z<sub>O</sub> is the characteristic impedance of the matching section transmission line, and R<sub>in</sub> is the resistive component of the impedance at a distance l<sub>r</sub> from the antenna along the line. In this exercise, R<sub>in</sub> is precisely our target value of resistance, R<sub>T</sub>. For our purposes, we shall assume that l<sub>r</sub> is in radians, although in general, it might also be in degrees relative to a wavelength at the frequency of interest for the antenna.</p>
<p>The matching line length calculation simply requires us to solve equation (1) for l<sub>r</sub> and to convert that length in radians into degrees and feet. A rewrite of equation (1) yields a quadratic:</p>
<center>
<img src="mu3ae6.gif" width="600" height="92">
</center>
<p>Solving for l<sub>r</sub>, we obtain</p>
<center>
<img src="mu3ae7.gif" width="600" height="167">
</center>
<p>Note that there are two solutions, since for every 180 of line length (under mismatch conditions), there will be two points at which the resistive component of the impedance has the same value.</p>
<p>The limiting case is where the value under the radical in equation (7) goes to less than zero. This condition indicates that, with the combination of line values chosen for the antenna impedance values measured or derived from a modeling program, the resistive component never reaches the chosen main feed line characteristic impedance. The solution to this problem is usually to select a different transmission line for the matching line section.</p>
<p>Equation (7) returns two lengths in terms of radians along a wavelength. We can convert these lengths to a more familiar measurement in degrees by the equation</p>
<center>
<img src="mu3ae8.gif" width="400" height="78">
</center>
<p>where l<sub>r</sub> is the length in radians and l<sub>d</sub> is the length in degrees. Transformation of these lengths into feet involves the equation</p>
<center>
<img src="mu3ae9.gif" width="400" height="100">
</center>
<p>where L<sub>f</sub> is the required length in feet, f<sub>MHz</sub> is the frequency of interest in MHz for the antenna, and VF is the velocity factor of the matching section transmission line.</p>
<p>Using the value of l<sub>r</sub>, we may calculate the remnant reactance by using the <em>Handbook</em> formula for X<sub>in</sub>:</p>
<center>
<img src="mu3ae10.gif" width="500" height="150">
</center>
<p>where all of the variables have the same meaning as in equation (7). Applying equation (10) to the two lengths resulting from equation (7) will yield opposing values of reactance. We may choose to match either with a stub. Alternatively, we may calculate the reactance values directly from the square root of equation (2), assigning the signs this way: the reactance associated with the shorter line length will have the sign of the reactance at the antenna feedpoint.</p>
<p>For the stub calculations, we shall first convert the reactance into a parallel value to facilitate mechanical connections for the stub.</p>
<center>
<img src="mu3ae11.gif" width="400" height="87">
</center>
<p>where R<sub>s</sub> is the main feedline characteristic impedance, X<sub>s</sub> is the calculated input remnant reactance, and X<sub>p</sub> is the equivalent parallel reactance which the stub is to compensate.</p>
<p>Reversing the signs of the reactances gives the values that must be returned by appropriate compensating stubs. The length of a shorted stub, when the desired reactance is known, is given by</p>
<center>
<img src="mu3ae12.gif" width="400" height="79">
</center>
<p>and the length of a corresponding open stub is given by</p>
<center>
<img src="mu3ae13.gif" width="400" height="69">
</center>
<p>where X<sub>in</sub> is the desired reactance, Z<sub>O</sub> is the characteristic impedance of the transmission line used for the stub, and l<sub>S</sub> and l<sub>O</sub> are the lengths of shorted and open stubs, respectively. Since the values of l<sub>S</sub> and l<sub>O</sub> are in radians, they can be converted into feet by the same means used to convert the length of the matching line.</p>
<p>The final step is to select the best combination of matching line and stub for the proposed antenna. Ordinarily--for least loss and mechanical simplicity--the combination with the shortest matching line and stub is most desirable.</p>
<center>
<strong>A Simple Utility BASIC Program for Stub Matching</strong>
</center>
<p>The calculations for a stub-matching system lend themselves to a simple utility program in BASIC or almost any other language. <b>Fig. 14</b> gives the listing for my own program, replete with my personal programming quirks. Lines 10-130 set up the input values for the calculation. Lines 140 through 170 calculate the target resistance value along the match-line. Lines 180-440 calculate the length of the matching-line section and the series resistance and reactance values at that point. The equations is broken down into components to precalculate repetitive parts. Line 200 catches the case where the value under the radical is less than zero. Lines 360-410 calculate the reactance for each of the solutions to equation (7), once more with the relevant equation broken down into segments or normalized. (These lines also recalculate the input resistance of the matching line; I put this in while setting up the program as a check and never took it out, since it involves only a few extra lines. The technique is useful for error catching during the program writing process. However, using R<sub>T</sub> and X<sub>T</sub> and bypassing these steps would shorten the program somewhat.)</p>
<pre>
10 'file STUB.BAS
20 CLS:COLOR 11,1,3:CLS
30 PRINT" General Solutions for Stub Matching,": PRINT" given Antenna R & X plus
Line, Stub, & Feed Zo":PRINT" L. B. Cebik, W4RNL":PRINT
40 PRINT"For any antenna load R and X, this program finds the Line and Stub length neededto match any
feedline Zo, if a match is possible with the proposed Line, Stub, and Feed Zo values.":PRINT
50 INPUT "Enter Antenna Load Resistance in Ohms ",RL
60 INPUT "Enter Antenna Load Reactance in Ohms ",XL
70 INPUT "Enter Frequency (in MHz) ",FQ
80 INPUT "Enter Zo of Line (from antenna to stub) ",ZL
90 INPUT "Enter Velocity Factor of Line (as decimal) ",VFL
100 INPUT "Enter Zo of Feed (from stub junction to rig) ",ZF
110 INPUT "Enter Velocity Factor of Feed ",VFF
120 INPUT "Enter Zo of Stub (from line-feed junction) ",ZS
130 INPUT "Enter Velocity Factor of Stub ",VFS
140 RLS=(RL*RL):XLS=(XL*XL):ZLS=(ZL*ZL):RIS=(RI*RI)
150 RHOS=(((RL-ZL)*(RL-ZL))+XLS)/(((RL+ZL)*(RL+ZL))+XLS)
160 RT=((ZL*ZL)*(1-RHOS))/((ZF*(RHOS-1))+((2*ZL)*(RHOS+1))):RI=RT
170 'IF (ZF*RT)-(RT*RT)&lt;0 THEN 350 ELSE XT=SQR((ZF*RT)-(RT*RT))
180 A=(XLS/ZLS)+(RLS/ZLS)-(RL/RI):B=2*(XL/ZL):C=1-(RL/RI)
190 IF A=0 THEN A=1E-08
200 NUM=((B*B)-(4*(A*C))):IF NUM&lt;0 THEN 350
210 TLP=(B+SQR((B*B)-(4*(A*C))))/(2*A)
220 TLM=(B-SQR((B*B)-(4*(A*C))))/(2*A)
230 LP=ATN(TLP):LM=ATN(TLM)
240 PI=3.141592654#
250 LPD=(LP*180)/PI:LMD=LM*180/PI
260 IF LPD&lt;0 THEN LPD=180+LPD
270 IF LMD&lt;0 THEN LMD=180+LMD
280 LPF=(LPD*VFL)/(.3660131*FQ):LMF=(LMD*VFL)/(.3660131*FQ)
290 PRINT"Possible line lengths are A. ";LPF;"feet and B. ";LMF;"feet."
300 LR=LP:GOTO 360
310 RIA=RI:XIA=XI:PRINT"For Line length A., Rs= ";RI;"Ohms and Xs= ";XI;"Ohms."
320 LR=LM:GOTO 360
330 RIB=RI:XIB=XI:PRINT"For Line length B., Rs= ";RI;"Ohms and Xs= ";XI;"Ohms."
340 GOTO 440
350 IF NUM&lt;0 THEN PRINT"There are no possible solutions with this combination of of antenna
impedance and line impedance.":GOTO 710
360 IF RL=0 THEN RL=1E-08
370 RA=RL/ZL:XA=XL/ZL:T=TAN(LR):TS=T*T
380 DA=(1-(XA*T))*(1-(XA*T)):DB=(RA*T)*(RA*T):DN=DA+DB
390 RS=RA*RA:XS=XA*XA
400 RN=RA*(1+TS):XK=XA*(1-TS)
410 XM=((1-RS)-XS)*T:XN=XK+XM:RZ=RN/DN:XZ=XN/DN:RI=ZL*RZ:XI=ZL*XZ
420 IF LR=LP THEN GOTO 310
430 IF LR=LM THEN GOTO 330
440 PRINT"For a record of these calculations, press &lt;Print Screen&gt;."
450 PRINT:PRINT"Press &lt;C&gt; to continue."
460 I$=INKEY$:IF I$="c" OR I$="C" THEN GOTO 470 ELSE 460
470 CLS:PRINT:PRINT"Stub Calculations:":PRINT
480 PRINT"Option A: Rs= ";RIA;" and Xs= ";XIA;" Ohms
490 XPA=((RIA*RIA)+(XIA*XIA))/XIA:XCOMPA=(-1*XPA)
500 PRINT"The required parallel stub reactance to compensate is ";XCOMPA;"Ohms."
510 LRL=ATN(XCOMPA/ZS):LDL=(ABS(LRL)*180)/PI
520 IF XCOMPA&lt;0 THEN LDL=180-LDL
530 LFL=(LDL*VFS)/(.3660131*FQ)
540 LRC=ATN(ZS/XCOMPA):LDC=(ABS(LRC)*180)/PI
550 IF XCOMPA&gt;0 THEN LDC=180-LDC
560 LFC=(LDC*VFS)/(.3660131*FQ)
570 PRINT:PRINT"The required SHORTED STUB length is ";LDL;"degrees or ";LFL;"feet.
580 PRINT"The required OPEN STUB length is ";LDC;"degrees or ";LFC;"feet.
590 PRINT:PRINT:PRINT"Option B: Rs= ";RIB;" and Xs= ";XIB;" Ohms
600 XPB=((RIB*RIB)+(XIB*XIB))/XIB:XCOMPB=(-1*XPB)
610 PRINT"The required parallel stub reactance to compensate is ";XCOMPB;"Ohms."
620 LRL=ATN(XCOMPB/ZS):LDL=(ABS(LRL)*180)/PI
630 IF XCOMPB&lt;0 THEN LDL=180-LDL
640 LFL=(LDL*VFS)/(.3660131*FQ)
650 LRC=ATN(ZS/XCOMPB):LDC=(ABS(LRC)*180)/PI
660 IF XCOMPB&gt;0 THEN LDC=180-LDC
670 LFC=(LDC*VFS)/(.3660131*FQ)
680 PRINT:PRINT"The required SHORTED STUB length is ";LDL;"degrees or ";LFL;"feet.
690 PRINT"The required OPEN STUB length is ";LDC;"degrees or ";LFC;"feet.
700 PRINT:PRINT"Press &lt;Print Screen&gt; to complete the record of calculations."
710 PRINT:PRINT"For another run, press &lt;A&gt;; to quit, press &lt;Q&gt;."
720 I$=INKEY$:IF I$="a" OR I$="A" THEN 10 ELSE IF I$="Q" OR I$="q" THEN 730 ELSE 720
730 END
Fig. 14. Program listing for STUB.BAS
</pre>
<p>The results of the calculations so far can be recorded on paper by a program pause and a &lt;Print Screen&gt; command. Since two screens of material will fit on one piece of paper, do not &lt;Form Feed&gt; at this time. Lines 450-710 calculate the required parallel reactive components and the stub values that will compensate for them, two values for each line length. A second &lt;Print Screen&gt; will combine this information with the input values for a complete record. A sample double screen printout appears in <b>Fig. 15</b>. The antenna is a 10-meter (28.5 MHz) Extended Double Zepp with a 450- stub match system for a 50- feedline where the EDZ models a feedpoint impedance of 141-j694 . Option A is 5.0' with a shorted stub of 1.2' or an open stub of 9.4', and option B is 5.5' with a shorted stub of 15.2' or an open stub of 7.0'. Option A and a shorted stub provide the mechanically simplest system to implement. You can truncate the decimals in the results almost anywhere, since in most cases, results to the nearest ohm and tenth of a foot will be close enough to permit antenna system adjustment.</p>
<center>
General Solutions for Stub Matching,
</center>
<center>
given Antenna R & X plus Line, Stub, and Feed Zo
</center>
<center>
L. B. Cebik, W4RNL
</center>
<p>For any antenna load R and X, this program finds the Line and Stub length needed to match any feedline Zo, if a match is possible with the proposed Line, Stub, and Feed Zo values.</p>
<p>Enter Antenna Load Resistance in Ohms 141.36</p>
<p>Enter Antenna Load Reactance in Ohms -693.56</p>
<p>Enter Frequency (in Mhz) 28.5</p>
<p>Enter Zo of Line (from antenna to stub) 450</p>
<p>Enter Velocity Factor of Line (as decimal) .95</p>
<p>Enter Zo of Feed (from stub junction to rig) 50</p>
<p>Enter Velocity Factor of Feed .66</p>
<p>Enter Zo of Stub (from line-feed junction) 450</p>
<p>Enter Velocity Factor of Stub .95</p>
<p>Possible lines lengths are A. 5.038553 feet and B. 5.485493 feet.</p>
<p>For line length A., Rs= 41.10245 Ohms and Xs= -19.12316 Ohms.</p>
<p>For line length B., Rs= 41.10246 Ohms and Xs= 19.12327 Ohms.</p>
<p>For a record of these calculations, press &lt;Print Screen&gt;.</p>
<p>Press &lt;c&gt; to continue.</p>
<p>Stub Calculations</p>
<p>Option A: Rs= 41.10245 Ohms and Xs= -19.12316 Ohms.</p>
<p>The required parallel stub reactance to compensate is 107.4669 Ohms.</p>
<p>The required SHORTED STUB length is 13.43154 degrees or 1.223229 feet.</p>
<p>The required OPEN STUB length is 103.4315 degrees or 9.419658 feet.</p>
<p>Option B: Rs= 41.10246 Ohms and Xs= 19.12327 Ohms.</p>
<p>The required SHORTED STUB length is 166.5685 degrees or 15.16963 feet.</p>
<p>The required OPEN STUB length is 76.56851 degrees or 6.973203 feet.</p>
<p>Press &lt;Print Screen&gt; to complete the record of calculations.</p>
<p>For another run, press &lt;A&gt;; to quit, press &lt;Q&gt;.</p>
<center>
Fig. 15. Typical output sheet from STUB.BAS
</center>
<p>One caution is necessary with the use of calculating programs. Unlike graphical solutions, calculating programs give no feel for the sharpness or broadness of the results, that is, how small physical variations from the calculations will affect the adjustments. In general, the higher the ratio of reactance to resistance at the antenna feedpoint, the sharper the curve. In these cases, small physical variations may require extensive adjustment of the calculated lengths.</p>
<p>Recent <em>ARRL Handbooks</em> have presented an interesting 12-meter EDZ cut to a length that provides a feedpoint impedance of 142-j555 .<sup>3</sup> With 450- transmission line (VF=.95), both options yield 5'5" of matching line with negligible reactance, obviating the need for a stub. The impedance presented by the matching line to the coax is 55 . In fact, using the program with a feedline impedance of 50 produces a "no possible solution message." The lesson is that before giving up on a combination, try raising or lowering the feedline impedance by 10% to see if a solution emerges. The resulting SWR on the coax will be well within limits. However, K7KGP's antenna is quite unusual, and exact reproduction or scaling for other bands may require extensive on-site adjustment.</p>
<p>These examples only sample the use of a utility BASIC program in making matching-section calculations. The limits of stub matching are far wider than these examples. Of course, modeling the results on NEC with transmission-line capabilities permits all calculations to be verified.</p>
<center>
<strong>Notes</strong>
</center>
<p>1 See, for example, Terman, <em>Radio Engineer's Handbook</em>, p. 186, or Kuecken, <em>Exploring Antennas and Transmission Lines by Personal Computer</em>, pp. 180-181.</p>
<p>2 See, for example, p. 16-2 of the 1987 <em>Handbook</em> for a normalized version of the equation or p. 16-3 of the 1992 <em>Handbook</em> for a non-normalized version.</p>
<p>3 See, for example, the 1992 <em>Handbook</em>, p. 33-11.</p>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<p><a href="mu0.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to Article Index Page</a></p>
<p class="topics-footer">Topics: <a href='../topics.html#edz-zepp'>EDZ / Zepp</a>, <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#small-beams'>Small Beams</a>, <a href='../topics.html#w8jk'>W8JK</a></p><br>
</body>
</html>
content/mu/mu3ae1.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 612 B

content/mu/mu3ae10.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 1.8 KiB

content/mu/mu3ae11.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 661 B

content/mu/mu3ae12.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 650 B

content/mu/mu3ae13.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 601 B

content/mu/mu3ae2.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 569 B

content/mu/mu3ae3.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 913 B

content/mu/mu3ae4.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 983 B

content/mu/mu3ae5.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 1.3 KiB

content/mu/mu3ae6.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 1.4 KiB

content/mu/mu3ae7.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 2.2 KiB

content/mu/mu3ae8.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 548 B

content/mu/mu3ae9.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 745 B

content/mu/mu4a-1.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 4.6 KiB

content/mu/mu4a-10.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 16 KiB

content/mu/mu4a-11.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 6.9 KiB

content/mu/mu4a-12.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.0 KiB

content/mu/mu4a-13.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 4.8 KiB

content/mu/mu4a-14.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.8 KiB

content/mu/mu4a-15.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 30 KiB

content/mu/mu4a-16.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 20 KiB

content/mu/mu4a-17.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.0 KiB

content/mu/mu4a-18.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.9 KiB

content/mu/mu4a-19.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 6.6 KiB

content/mu/mu4a-2.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 4.9 KiB

content/mu/mu4a-20.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 16 KiB

content/mu/mu4a-3.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 23 KiB

content/mu/mu4a-4.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 22 KiB

content/mu/mu4a-5.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 21 KiB

content/mu/mu4a-6.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 7.1 KiB

content/mu/mu4a-7.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 6.8 KiB

content/mu/mu4a-8.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 7.0 KiB

content/mu/mu4a-9.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 4.8 KiB

content/mu/mu4a.html
+452
View File
@@ -0,0 +1,452 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="keywords" content="Yagi, Loading, HF Upper, Small Beams">
<title>Modeling and Understanding Small Beams Part 4: Linear-Loaded Yagis</title>
<link rel="stylesheet" href="../styles.css">
</head>
<body>
<center>
<h1>Modeling and Understanding Small Beams</h1>
<h3>Part 4: Linear-Loaded Yagis</h3>
<p><b>L. B. Cebik, W4RNL</b></p>
</center>
<center>
<img src="../images/colorbar.gif" width="591" height="3">
</center><br wp="BR1">
<br wp="BR2">
<p>The most common reason for designing and building a small, 2-element beam or array is the size. Whether for home or portable field use, small antennas have a niche in the ham world.</p>
<p>There is a second, often overlooked reason for building antennas with reduced dimensions relative to a standard 2-element Yagi: increased front-to-back ratio. Standard, closed spaced (approximately 1/8) Yagis are not capable of large front-to-back ratios because the parasitic reflector will not be positioned or sized to have the correct current level and phase angle for maximum rejection off the rear. Most notably, the Moxon rectangle achieves close to optimal reflector conditions. Its altered geometry attains a very high front-to-back ratio for a 2-element array. The cost is about a half dB of forward gain.</p>
<p>A second strategy that will also improve the front-to-back ratio is to shorten the Yagi elements while maintaining the close spacing. With center- or linear-loading of both the driven element and the reflector of a 2-element Yagi with about 1/8 spacing, the front-to-back ratio increases from about 12 dB to about 18 dB, a full S-unit of improvement. Models of the beam show that the current amplitude and phase more closely approach values necessary for a complete rearward null than those for a full size 2-element Yagi. As with the Moxon rectangle, the short beam's forward gain drops about a half dB in the process. Additionally, the bandwidth of the beam decreases.</p>
<p>The result of modeling and testing these ideas was a 2-element 10-meter Yagi with 12' elements, which is a 25% savings in size, turning radius, and weight. In addition, the antenna uses 6' lengths of hardware store aluminum tubing for the elements, making parts acquisition easier. (Note, however, that the aluminum tubing usually available at hardware centers does not have the strength and durability of tubing used by commercial antenna manufacturers. This factor has little affect on small, weight-balanced 2-element beams for 10 meters, but may be very significant in tapered-element 20-meter models.<sup>1</sup>)</p>
<center>
<strong>Linear-loading Vs. Inductive Loading</strong>
</center>
<p>The principle of center loading is very old and well-understood. A coil at the center of a shortened inductor compensates for the capacitive reactance that results from shortening the element from its naturally resonant length (approximately 1/2), thus restoring resonance. A parasitic element, such as a reflector may be similarly shortened and use an inductor to compensate for the resultant capacitive reactance until its relationship to the driven element is as optimal as possible. Center-loaded dipoles and Yagis have appeared in numerous antenna books over the decades.</p>
<p>The performance of a center-load dipole or Yagi depends largely upon the Q of the inductor. A shortened antenna, solely by virtue of its shortening, will show a reduction in gain relative to an unshortened antenna used as the reference. We might let a center-loaded dipole or Yagi use theoretic inductors with infinite Q (that is, with no resistance) to form a base line for comparisons. Then, by selectively establishing values of Q for the inductors and modeling the result (via a program such as MININEC), some rough comparisons become possible.</p>
<pre> A Comparison of Gain and Other Properties of Center-Loaded
and Linear-Loaded Dipoles and Yagis
1/2 wl Dipole: 12' 0.75" diameter aluminum
Type QLoad Gain Impedance
dBi R&PlusMinus;jX
C-L Inf. 1.93 28 + 0.4
C-L 50 1.24 33 + 0.5
C-L 100 1.57 31 + 0.5
C-L 200 1.75 30 + 0.5
C-L 300 1.81 29 + 0.5
L-L --- 1.82 29 + 0.3
2-Element Yagi: DE = 11.6' 0.75" diameter aluminum; RE = 12' 0.75" diameter aluminum
Type QLoad Gain Front-to-Back Impedance
dBi Ratio dB R&PlusMinus;jX
C-L Inf. 6.20 20.0 17 - 0.7
C-L 50 4.21 13.2 22 - 3.9
C-L 100 5.14 15.8 19 - 2.4
C-L 200 5.65 17.6 18 - 1.6
C-L 300 5.83 18.3 18 - 1.3
L-L --- 5.82 18.4 17 - 2.8
C-L DE=200 5.02 13.2 19 - 3.9
RE= 50
C-L DE= 50 4.84 17.6 22 - 1.6
RE=200
Notes: C-L = center-loaded; L-L = linear-loaded. All values taken from models in free space and
include materials losses (aluminum). As an indicator of loading coil losses, QLoad=XL/RL. XL for
DE=250 Ohms; for RE=257 Ohms. Antennas L-L are linear-load with a 4' loading element of #12 wire in a
vertical plane, with the upper wire 1.2" below the main element and the lower wire 1.2" below the upper
wire.
Table 1. A comparison of gain and other properties of center-load and liner-loaded dipoles and Yagis.</pre>
<p><b>Table 1</b> summarizes two such exercises, one for 12' aluminum dipoles at 28.5 MHz, the other for a 2-element Yagi of similar element length at the same frequency. The table shows Qs of 300, 200, 100, and 50 as typically realizable values, although sustaining an inductor at a Q of 200 or more in outdoor conditions is unlikely. A Q of 100 is more likely. Note the decrease in performance with the decrease in Q for both the dipole and the Yagi.</p>
<center>
<img src="mu4a-1.gif" width="527" height="172" border="2" vspace="5" hspace="9">
</center>
<center>
Fig.1 A schematic diagram of a dipole element with linear loading.
</center>
<p>A linear load is simply a folded continuation of the main element, usually (but not necessarily) of a lighter (hence, thinner) material, as shown in the dipole sketch in <b>Fig. 1</b>. Linear loading can be introduced anywhere along an antenna element, including current and voltage maxima points, but we shall restrict our focus here to current nodes, that is, to the center point of 1/2 elements. Although there are numerous reports of empirically generated antennas using linear loading, little has been quantified in amateur literature.<sup>2</sup> As a start toward this goal one may juxtapose linear-loaded dipoles and Yagis with their center-loaded counterparts. For comparison with the center-load models of both dipoles and Yagis in <b>Table 1</b>, I added a linear-load model with #12 wire extending 2' either side of the element center in a vertical plane below the main element. The upper wire is 1.2" below the main element, and the lower wire is 1.2" below the upper wire.</p>
<p>A model of the linear-loading element is only approximately comparable to the model of the center-loaded element because of differences in modeling conventions. A loading inductor (or capacitor) is treated in both NEC and MININEC as a nonradiating item inserted into the structure. By contrast, the linear-loading structure is part of the overall radiating structure of the antenna. Moreover, since most versions of MININEC permit but one material, the models are all-aluminum, even though in practice the linear-load element will usually be copper. Nevertheless, figures for the linear-loaded model given in <b>Table 1</b> are roughly comparable with the center-loaded results and indicative of relative performance. In both cases, the material losses of the main aluminum element are included in the model.</p>
<p>Whether a dipole or a Yagi, the gain of linear-loaded elements tends to surpass that of the corresponding center-loaded elements by a significant amount. So, too, does the front-to-back ratio of the Yagi model. If we assume that a Q of 100 is a reasonable and sustainable figure for a center-loading inductor, then linear loading becomes a very attractive alternative in shortened horizontal antennas. It generally requires a center-loading coil Q of 300 or better to reach the performance of a linear-loaded Yagi.</p>
<p>The last two entries under the Yagis in <b>Table 1</b> are included to demonstrate the effects of losses should only one of the Yagi's two elements exhibit more than design losses, perhaps due to weathering. Reduction of reflector Q results in a lower front-to-back ratio and a higher reactive component to the feedpoint impedance. In contrast, reduction of the driven element Q results in a lower antenna gain and a higher resistive component of the antenna feedpoint impedance. Understanding these differences can be an aid to trouble shooting antenna problems.</p>
<center>
<strong>A Preliminary Method of Calculating Linear Loads</strong>
</center>
<p>The resemblance of a centered linear-loading element to a transmission line is no accident. In fact, each half of the linear-loading element can be viewed as a shorted, inductive transmission line stub, and this view provides a basis for approximate calculations of the element length. Each half of the element represent a reactance, and the two halves are in series.</p>
<p>The designer can derive the required total reactance of a shortened dipole by simply using MININEC or NEC to model the short element at the desired frequency. Alternatively, one can measure the feedpoint impedance of an actual main element without loading. The capacitive reactance at the feedpoint requires exact compensation by an equal inductive reactance provided by either a center loading coil or, as here, a shorted length of transmission line.</p>
<p>Materials for a linear-loading element are a matter of designer preference within the limits of good structure. Given the selection of wire, rod, or tubing for the linear load, the process of calculating the linear load begins by determining the characteristic impedance, Zo, of the proposed load line, using the standard approximation,</p>
<center>
<img src="mu4ae1.gif" width="400" height="73">
</center>
<p>where S is the spacing between the wire centers and d is the wire diameter, both in the same units.<sup>3</sup></p>
<p>From the value of Zo and the desired reactance, determine the line length in electrical degrees, L<sub>E</sub>, from the equation,</p>
<center>
<img src="mu4ae2.gif" width="400" height="82">
</center>
<p>where X<sub>L</sub> is the total desired reactance. The doubling of Zo in the denominator provides for the length of each half of the linear loading element. Converting the length into feet requires the design frequency, F<sub>R</sub>, the assumption of a velocity factor of 1, and the equation</p>
<center>
<img src="mu4ae3.gif" width="400" height="70">
</center>
<p>Remember to double the length for the full element.</p>
<p>The utility of this calculation procedure is limited. There are two generally popular geometries for constructing linear-loaded center elements. <b>Fig. 2</b> compares the "end-on" appearance of vertical-plane geometry with triangular geometry. Because the load lines of the triangular arrangement are usually equi-spaced from the main element, the transmission-line calculation produces useable results as a first approximation for building. However, the vertical-plane geometry places one "side" of the transmission line closer to the main element, thus disrupting the presumed equal currents and voltages essential to the calculation's accuracy.</p>
<center>
<img src="mu4a-2.gif" width="432" height="302" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2. Vertical-plane and triangular geometries for linear-loading sections.
</center>
<p>Calculations of triangular linear load elements correspond in the main with models of fully structured antennas within about 2 to 3 percent. Because of limitations in modeling linear-loaded antenna structures, the calculations are as good as the model as a guide to building.<sup>4</sup> However, transmission-line calculations vary from modeling results for vertical-plane antennas by 15 to 30 percent, depending upon the particular line size and spacing. The calculations tend to call for radically shorter linear load elements than actually needed. To get a handle on vertical-plane linear loading arrangements requires a different technique.</p>
<center>
<strong>Calibrating Vertical-Plane Linear Loads</strong>
</center>
<p>A standard Yagi element or a dipole antenna shows a set of currents that decrease continuously but not linearly from the feedpoint, since the elements are roughly resonant. An element with a linear-loading element has an overall wire length (counting both the element tube and the load wire) that is longer than a half wavelength. Hence, the current rises as one moves away from the feedpoint, reaching a secondary maximum over halfway out the loading element and reaching a primary maximum on the way back in toward the junction with the tube. The inequality of currents in the outgoing and incoming wires of a vertical-plane linear-loading element verifies that the loading element is not acting as a pure transmission-line element. The current along the element does not rise much and the tube-to-load element junction shows over 99% of the current. Essentially, the radiation produced by the currents in the loading element cancel, leaving the tube element radiation to dominate the far field pattern. Cancellation is not perfect, thus leaving a high current level over a greater length of the antenna element than with lower-Q center loading schemes.</p>
<p>Correlating models of linear-loaded dipoles with center-loaded counterparts permits a rudimentary calibration of linear-loaded dipole of both vertical-plane and triangular geometries. Free space models of fixed-length main elements with variable linear loads were checked for resonant frequency as indicated by a near-zero reactance. Then, using the same frequency, an equivalently long dipole of the same material was center loaded to resonance by the same test. The requisite reactance became the center-load lossless-inductor reactance for the linear load. Flipping between copper and aluminum elements (both tubing and linear-load wire) produced no change in the resonant point. As noted above, the modeling process is subject to certain limitations of both MININEC and NEC.</p>
<pre> Sample table of linear-loaded dipoles listing gain, feedpoint impedance, resonant
frequency, equivalent center-load reactance, and approximate Q
Antenna element = 12' 0.75" diameter aluminum
Linear load = #12 wires spaced 2" (0.167') from antenna element; 2" (0.167') from each other
Antenna-to-linear load geometry: vertical plane
Linear load Gain Z (R&PlusMinus;jX) Resonant Equivalent Approximate
length - ft dBi Ohms Frequency Center-load equivalent
MHz Reactance Q
Ohms
0 (self- 2.13 72.2 + 0.01 38.94 ----- -----
resonance)
1 2.01 49.4 + 0.00 35.04 85.4 225
2 1.94 37.4 - 0.02 31.84 157.7 303
3 1.85 29.6 - 0.00 29.34 217.4 294
4 1.78 24.4 - 0.01 27.12 273.9 326
5 1.69 20.7 - 0.00 25.20 327.2 327
6 1.60 18.0 - 0.02 23.58 375.8 334
Notes:
1. Antennas were considered resonant if the remnant reactance was less than 0.05 Ohm. Figures are
rounded from 3- and 4-place decimal results.
2. Equivalent Q is determined by finding a value of resistance for the center load inductance at the
given reactance that produces an antenna gain equal to that of the corresponding linear-loaded model.
Q results are subject to variables of the modeling process and are likely no more reliable than 10 to
15 percent.
Table 2. Sample table of linear-loaded dipoles listing gain, feedpoint impedance, resonant
frequency, equivalent center-load reactance, and approximate Q.</pre>
<p><b>Table 2</b> provides a sample of the data developed for just one linear-load configuration: a vertical-plane arrangement with a #12 wire spaced about 2" from the main element and 2" apart for a 12' element. The table clearly shows the decrease of gain as the linear element is lengthened, along with the increase in equivalent reactance and the decrease in resonant frequency. Since the goal was to develop dimension figures adequate to the start of home construction, resonance was defined as a remnant feedpoint reactance of less than 0.05.</p>
<center>
<img src="mu4a-3.gif" width="475" height="660" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 3. Linear load line equivalent reactances (to a lossless center loading inductor) between ratios of 1:12 to 1:2 for (a.) a 12' 0.75" diameter aluminum main antenna element and for (b.) a 24' 0.75" diameter aluminum main antenna element for 6 linear-load configurations.
</center>
<p><b>Fig. 3a</b> and <b>3b</b> show the results of six dual runs on linear elements (1/2 dipoles) of different lengths, materials, and spacing. Each type of element shows a reasonably linear increase in equivalent reactance with increases in length. (Note that the element length is for the folded element; the actual wire length is twice that amount plus connecting leads.) Extrapolation to intermediate lengths and similar but deviant linear-load configurations is possible for other required values of reactance.</p>
<center>
<img src="mu4a-4.gif" width="459" height="660" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 4. Equivalent Qs of linear load lines (relative to a center loading inductor) between ratios of 1:12 to 1:2 for (a.) a 12' 0.75" diameter aluminum main antenna element and for (b.) a 24' 0.75" diameter aluminum main antenna element for 6 linear-load configurations.
</center>
<p>Although the equivalent reactance was derived using zero-loss center-loading inductors, an indication of equivalent Q was derived by adding resistance to the inductor until the antenna gain was the same as the linear-loaded model. <b>Table 3</b> provides the data on equivalent Q-ranges for the linear-load geometries shown in the graphs in <b>Fig. 4a</b> and <b>4b</b>, with specific data on gain and Q for one typical linear section length. <b>Fig. 5a</b> and <b>5b</b> provide gain profiles for 6 variations each using 12' and 24' 0.75" diameter aluminum main elements.</p>
<center>
<img src="mu4a-5.gif" width="459" height="660" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 5. The gain of dipoles with varying lengths of linear loading between ratios of 1:12 to 1:2 for (a.) a 12' 0.75" diameter aluminum main antenna element and for (b.) a 24' 0.75" diameter aluminum main antenna element for 6 linear-load configurations.
</center>
<pre> A comparison of linear-loaded dipoles listing geometry, materials,
Q range (for all load lengths), and gain and Q (with a 4' or 8' load length)
Antenna Geometry & Range of Q Gain with Q with
# Materials (1-6' length) 4' linear section 4' linear section
Antenna element = 12' 0.75" diameter aluminum; load length = 4'
1 VP, 0.25" rod 1075-355 1.90 812
sp: 0.25'/0.25'
2 VP, 0.125" rod 532-328 1.82 487
sp: 0.25'/0.25'
3 VP, #12 wire 355-267 1.74 343
sp: 0.25'/0.25'
4 VP, #12 wire 334-224 1.78 326
sp: 0.167'/0.167'
5 VP, #12 wire 293-183 1.82 293
sp: 0.1'/0.1'
6 Tri, #12 wire 411-233 1.80 411
sp: 0.1'/0.1'
Antenna Geometry & Range of Q Gain with Q with
# Materials (1-12' length) 8' linear section 8' linear section
Antenna element = 24' 0.75" diameter aluminum; load length = 8'
1 VP, 0.25" rod 739-600 1.91 632
sp: 0.25'/0.25'
2 VP, 0.125" rod 375-229 1.81 352
sp: 0.25'/0.25'
3 VP, #12 wire 256-225 1.72 256
sp: 0.25'/0.25'
4 VP, #12 wire 238-168 1.75 232
sp: 0.167'/0.167'
5 VP, #12 wire 213-138 1.77 196
sp: 0.1'/0.1'
6 Tri, #12 wire 313-185 1.76 266
sp: 0.1'/0.1'
Note: VP = linear load elements in vertical plane with antenna element; Tri = linear elements in triangular
configuration with antenna element.
Table 3. A comparison of linear-loaded dipoles listing geometry, materials, Q range (for all load lengths), and
gain and Q (with a 4' or 8' load length).</pre>
<p>Triangular geometry loads do not fully overlap their vertical-plane counterparts. As shown in <b>Fig. 3a</b> and <b>3b</b>, the close-spaced triangular arrangement of #12 wire turns out to parallel closely the reactance progression of vertically planed #12 wire spaced more widely (0.167' vs. 0.1') or 1/8" rod spaced at 0.125'. However, the equivalent Q of the triangular configuration shows a clear peak at midlength load element sizes, as shown in <b>Fig. 4a</b> and <b>4b</b>. In common with the vertical plane #12 linear-load configuration, the #12 triangular configuration shows a more rapid fall-off in gain after the 4' point with 12' main elements and after the 6' point with 24' main elements. See <b>Fig. 5a</b> and <b>5b</b>. The rapid reduction in gain for close-spaced #12 linear-load elements suggests that the break points on the graph represent the limit of their effective use compared to other configurations.</p>
<p>Besides the linear relationship between element length and equivalent center-loaded lossless-inductor reactance, certain other trends in <b>Fig. 3, 4, and 5</b> are noteworthy:</p>
<p>1. Spacing: For a given geometry, load-length, and wire size, antenna element gain decreases and Q increases as spacing increases.</p>
<p>2. Wire size: For a given geometry, load-length, and spacing, antenna element gain and Q increase as the wire size increases.</p>
<p>3. Geometry: For a given load-length, spacing, and wire size, a triangular geometry yields a higher Q than the vertical-plane geometry, but provides less antenna element gain.</p>
<p>4. Diameter: As main element and linear section wire diameters decrease relative to a wavelength at the signal frequency, reactance increases slowly and Q decreases.</p>
<p>5. Long linear elements: As the ratio of linear-load length to main element length exceeds 5:12, both the equivalent center-load reactance and Q tend to depart from a relatively linear curve. Note that, although the Q curves for 0.125" and 0.25" diameter linear-load elements seem to depart radically from the #12 vertical-plane models, a closer examination of the curves show that they are topographically similar, with a fairly complex magnitude adjustment factor.</p>
<p>6. Short linear elements: As the ratio of linear-load length to main element length falls below 1:6, both the equivalent center-load reactance and Q tend to depart from a linear curve, with the Q falling off rapidly.</p>
<p>7. Recommended linear element lengths: Between ratios of 1:6 and 5:12 of the linear-load element to the main element, equivalent reactance and Q curves are nearly linear, as is the rate of decrease in antenna element gain with increased linear-load length. As noted, close-spaced #12 linear-load elements depart from this near-linearity of gain and Q beyond certain "break" points, which limit their applicability.</p>
<p>One further trend also deserves notice: the longer the loading element (or the higher the reactance of any center-loading means), the lower the resistive feedpoint impedance. Linear-loading elements in the vicinity of one-third the total length of the main element show a resistive component between 20 and 30 , depending upon design. A direct match to 50- coaxial cable is accordingly not feasible, although simple beta, gamma, balun, and transformer matching systems are available. For anyone concerned about the small mismatch that exists between a full size dipole (72 nominal) and 50- coax, a short linear load of 1/12 the main element length is a solution. The result is, in almost any construction mode, a feedpoint impedance within &PlusMinus;5 of the coaxial cable's Zo. Of course, the main element will have to be shortened from full size, but the decreased size produces negligible gain loss (less than 0.1 dB).</p>
<p>For shortened Yagi designs or portable field dipoles, a close-spaced linear element approximately 1/3rd the length of the main element represents a good compromise among a number of factors to consider when designing a shortened antenna. It maintains element gain at a high level, while effecting a significant shortening of the overall element length. Specific design objectives, of course, may require a departure from these very general recommendations.</p>
<p>The linear-loading section curves developed for 12' and 24' main elements can be used directly for 10- and 20-meter beams by extrapolation. Extrapolations for other bands will be less precise, but sufficient for reasonable construction estimates. A recommended alternative is to create a set of curves for the specific materials to be used in a given project. With almost any antenna modeling program, the task is an evening's work. In the end, no matter how extensive the modeling, home construction techniques will rarely be exact enough with respect to replicating the modeled spacing among the parts of a linear-loaded element to permit building without adjustment. However, the tables and graphs do provide some initial quantitative guidance. For those who prefer to use the transmission-line stub calculations as a foundation for building, <b>Table 4</b> provides a set of generalized deviance factors for correcting the calculations to correspond with each of the types of linear loads described here. The averaged factor holds for linear-load lengths between about 15 and 40 percent of the main element length. The progressions of correction factors may also serve as a guide to builders using load dimensions outside the range of those analyzed here.</p>
<pre> Correction Factors for Using Transmission Line Calculations
With Some Lengths of Vertical-Plane Linear-Loading Elements.
12' Aluminum Main Element Models
Linear-Load Characteristics: Multiply Transmission-Line
Diameter Spacing from Spacing Between Calculations by This Value
Main Element L-L Elements to Agree with Modeling Results
#12 (.0808") 0.1' (1.2") 0.1' (1.2") 1.30
#12 0.167' (2") 0.167' (2") 1.23
#12 0.25' (3") 0.25' (3") 1.15
0.125 0.25' 0.25' 1.18
0.25 0.25' 0.25' 1.24
#12 0.1' 0.1' (triangular) 1.05
24' Aluminum Main Element Models
Linear-Load Characteristics: Multiply Transmission-Line
Diameter Spacing from Spacing Between Calculations by This Value
Main Element L-L Elements to Agree with Modeling Results
#12 (.0808") 0.1' (1.2") 0.1' (1.2") 1.27
#12 0.167' (2") 0.167' (2") 1.23
#12 0.25' (3") 0.25' (3") 1.18
0.125 0.25' 0.25' 1.21
0.25 0.25' 0.25' 1.27
#12 0.1' 0.1' (triangular) 1.03
Note: Because MININEC models return slightly long dimensions, coreection factors may be reduced by up to 3%.
Table 4. Correction factors for using transmission line calculations with some lengths of vertical-plane linear-
loading elements.</pre>
<center>
<strong>Designing a 2-Element Linear-Loaded Yagi</strong>
</center>
<p>The technique of using center-load reactance as a substitute for a linear-loaded element for dipole modeling carries over into the design of 2-element Yagis. Choosing a set of main element lengths, center-loading them for the desired antenna performance (within the limits imposed by shortening the elements), and replacing the center loads with their equivalent linear-loading elements can produce buildable models. Since changing the magnitude of a center-load inductive reactance is far quicker in all antenna modeling programs than changing the complex dimensions of a linear loading element, the design process is significantly shortened.</p>
<p>As a design example, let us select 12' main elements of 3/4" diameter aluminum as the main elements for a 2-element shortened Yagi for a center frequency of 28.5 MHz. A little element juggling, along with the addition of center loads for the elements of about 250 each produced a reasonable design with the following properties: Driven element: 11.6'; reflector: 12.16'; spacing: 4.25'. The extension of the reflector did not violate my intention to use 6' lengths of hardware store aluminum tubing, since construction would place the two lengths about 2" (0.167') apart. The anticipated gain of the array (using a Q of 300 for both loading coils) was 5.8 dBi, with a front-to-back ratio of about 18 dB. The feedpoint impedance of the center-loaded beam calculated by the modeling program was about 17.</p>
<center>
<img src="mu4a-6.gif" width="295" height="275" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 6. Free space azimuth pattern for a linear-loaded 2-element beam with close-spaced elements.
</center>
<p>The chart for 12' aluminum elements shows a linear-loading element of #12 wire, spaced 0.1' (about 1.2") and 4' long corresponds closely to the 250- center-loading inductors. Substituting the required linear sections into the model yielded a 2-element beam with the same gain, front-to-back ratio, and feedpoint impedance as the center loaded model. <b>Fig. 6</b> shows the free space azimuth pattern of the beam design. Since modeling an antenna with linear-loading sections requires extensive and careful element segment tapering techniques with MININEC programs, the resultant antenna description is quite large. Those with slower computers or restricted RAM may wish to skip this step and go directly from the graphs to the shop. However, it pays to check an extrapolated design to ensure against errors.</p>
<center>
<img src="mu4a-7.gif" width="299" height="275" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 7. Azimuth pattern at 23&deg; elevation for the 2-element linear-loaded beam at a height of 20' above medium real ground.
</center>
<p>A 2-element beam, like every other array, will tend to vary in gain and front-to-back ratio at heights above real ground below about 2. As a check on the design, patterns were run at the angle of maximum radiation for heights of 20' and 35', with the results shown in <b>Fig. 7</b> and <b>Fig. 8</b>. However, as usable as these performance expectations are, this step did not end the design process.</p>
<center>
<img src="mu4a-8.gif" width="293" height="274" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 8. Azimuth pattern at 14&deg; elevation for the 2-element linear-loaded beam at a height of 35' above medium real ground.
</center>
<p>Because one of the main uses for shortened antennas is for portable field operations, I anticipated building the linear-loaded Yagi so as to make it transportable. Under these conditions, it is possible to add to the reflector a tuning capacitor remotely placed some multiple of a half wavelength from the antenna and connected by a suitable length of parallel feeder (450-, in this case). This required lengthening the linear element of the reflector purposely to make it inductive. Lengthening the linear section of the reflector to 5' (2.5' either side of center) permitted the use of loading capacitance between about 50 and 95 pF to retune the reflector back to maximum front-to-back ratio.</p>
<p>A second design modification was required by the use of a beta-match to convert the 17- feedpoint impedance to the 50- coax value. Shortening the driven element linear section to 3.7' (1.85' either side of center) yielded the requisite 23 ohms of capacitive reactance in the driven element to go with the 32.7- inductive reactance across the feedpoint terminals (0.18 uH or about 4 turns of #12 copper wire, 1/2" in diameter and 1/2" long at 8 turns per inch).<sup>5</sup> <b>Fig. 9</b> shows the general scheme of the beta match applied to the linear-loaded antenna.</p>
<center>
<img src="mu4a-9.gif" width="514" height="191" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 9. General scheme of the beta match used with the 2-element linear-loaded beam.
</center>
<p>These modifications for portable use actually improve one aspect of the antenna's performance: the SWR bandwidth. <b>Fig. 10</b> is a graph of the SWR bandwidth of several antennas, all of which use the same main element dimensions: center-loaded Yagis with Qs of 300 and 100, the unmodified linear-loaded antenna, and the modified version for portable use. That the linear-loaded antenna is equivalent to a center-loaded beam with a Q well over 300 is obvious from the steepness of the SWR curve below the design frequency. The curve for the remotely tuned portable version shows a greater symmetry, with about 700 kHz of usable (&lt;2:1) SWR bandwidth at optimum front-to-back ratio.</p>
<center>
<img src="mu4a-10.gif" width="491" height="361" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 10. Calculated SWR bandwidth for center- and linear-loaded Yagis.
</center>
<p>Actually, the antenna will tune within a 2:1 SWR across the entire first MHz of 10 meters. However, the front-to-back ratio will degrade at the band edges. <b>Fig. 11</b> is a composite pattern of a fixed-reflector model between 28 and 29 MHz. <b>Fig. 12</b> shows the composite free space azimuth pattern of the remotely tuned version over the same spectrum. The minor retuning required for bringing the SWR into the 2:1 range at the band edges does not reduce the front-to-back ratio very much.</p>
<center>
<img src="mu4a-11.gif" width="297" height="264" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 11. Composite free space azimuth pattern for a fixed-reflector linear-loaded 2-element Yagi from 28.0 to 29.0 MHz.
</center>
<center>
<img src="mu4a-12.gif" width="299" height="274" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 12. Composite free space azimuth pattern for a remotely-tuned-reflector linear-loaded 2- element Yagi from 28.0 to 29.0 MHz.
</center>
<p>Tuning the reflector actually improves the front-to-back ratio over real ground relative to a fixed-reflector free-space-derived model. <b>Fig. 13</b> and <b>14</b> show composite patterns for the first MHz of 10 for 20' and 35' elevations respectively, with the reflector in each case tuned for maximum front-to-back ratio. These patterns and numbers, of course, are anticipations bred from models. The final question is whether they can be realized.</p>
<center>
<img src="mu4a-13.gif" width="299" height="269" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 13. Composite 20'-height azimuth pattern for a remotely-tuned-reflector linear-loaded 2-element Yagi from 28.0 to 29.0 MHz.
</center>
<center>
<img src="mu4a-14.gif" width="296" height="264" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 14. Composite 35'-height azimuth pattern for a remotely-tuned-reflector linear-loaded 2-element Yagi from 28.0 to 29.0 MHz.
</center>
<center>
<strong>Constructing and Testing a Test Model</strong>
</center>
<p>Building a linear-loaded beam for portable field use (10-meter hilltopping) is not difficult, because the elements are light. The basic dimensions are these: Driven element: 11.6'; reflector: 12.16'; spacing: 4.25'. Four 6' lengths of 0.75" diameter tubing from the local hardware outlet provided the main elements. With a 2" center spacing, the reflector lengths are correct as purchased, but the driven elements were cut to 5'8" each.</p>
<center>
<img src="mu4a-15.gif" width="459" height="361" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 15. The basic element-to-boom assembly of the test 2-element linear-loaded Yagi with details of the linear load support plate at the main element center point.
</center>
<p>The element-to-boom plates are 1/2" plywood, about 6" to 7" wide and 2' long. As shown in <b>Fig. 15</b>, excess wood was removed from the corners for minimum weight. Each plate was coated with car-repair epoxy for fiberglass patching. This material is more weather-resistant than any other I have found. #10 stainless steel nuts, bolts, and lock washers fasten the element to the plate. (Small U-bolts are recommended for larger antennas.) Since the boom is a 5' section of 1 1/4" nominal diameter Schedule 40 PVC, 1 1/2" U-bolts make the plate-to-boom connection.</p>
<p>The plate-to-boom U-bolts also hold another fixture: the center supports for the linear-loading wire. The test antenna uses #12 solid copper wire linear sections in two pairs: two 2'6" sections for the reflector and two 1'5" sections for the driven element. Each section attaches to a thick plastic plate angled from the outer U-bolt inward, as shown in <b>Fig. 15</b>. A heavy plastic freezer box a little over 4" square and 1" high provided two plates that had the correct angle to place the linear-load wires directly under the main element when mounted to the outer U-bolts. The composition of the plastic ensures good weathering characteristics, and no RF problems have surfaced.</p>
<p>Wires a little over twice each section length were straightened and then bent over a piece of 1 1/4" mast to establish the spacing. Before mounting, I slipped mid-length and end supports over each wire loop. I cut eight 4" by 4" squares from the corners of a squared-off half-gallon plastic jug. On each side of each corner I used a hole-saw to cut 3/4" circles for the main elements and then drilled 1/8" holes for the linear-load wires. Squeezing the corners allows the wire and the main element to pass through each pair of holes. Releasing the corners places the assembly under tension, which keeps the main element and the linear-loading wires aligned. Local storm winds have not moved this assembly, but something stronger is recommended for larger or more permanently mounted antennas.</p>
<p>Solder rings on the ends of the linear-load wires attach the section to bolts (#10 stainless steel) on the center plastic plate. Short #12 wires, also with solder rings provide a junction between the wire assembly and the main aluminum element. Before attaching solder rings to wires, I usually let solder flow all over the ring, since many types will rust in the weather.</p>
<p>The driven element linear section terminates its lower center in a coaxial chassis connector mounted on the plastic plate with the threads facing the mast. A ferrite bead or shield 1:1 balun taped to the boom allows the coax to be run inside or outside the mast, in my case, sections of TV mast. The beta match coil mounts across the plate-to-linear-wire bolts with solder rings. The reflector section center terminates in two pin jacks. For initial testing, a capacitor with mating pins connects at the element. For field use, a half wavelength of 450 parallel feeder terminated at one end with pins and at the other with pin jacks places the capacitor within easy reach for remote adjustment with 20' of mast. A series of plastic spray can tops, each punched with 4 holes for cable ties that clamp the mast and the feeder, space the feeder from the mast.</p>
<p>For testing, solder rings can be omitted from the linear section wires until the correct length is determined. Clamping the wires under washers at the plate will suffice for initial tests. The object is to obtain the lowest possible SWR at the center design frequency by first tuning the reflector capacitor for a minimum reading and then spreading or compressing the beta match turns for a final null. Adjust the length of the wire section to bring the null frequency to the design center. If initial test are close, then minor adjustments can be made by squeezing or spreading the linear wire sections (using the bottom wire only): squeezing lowers reactance and raises the frequency, while spreading increases reactance and lowers the frequency. If significant wire deforming is required, adjust the length instead.</p>
<p>Off center frequency, do not adjust the reflector capacitor for absolutely the lowest SWR. Instead, find the lowest SWR point and then slight off-tune the capacitor (within a 2:1 SWR ratio) in the direction of the setting for the antenna's design center frequency. That will establish a point closer to maximum front-to-back ratio in the absence of a reference signal. Refer to the SWR bandwidth graph for guidance.</p>
<p>The test antenna built to the specifications provided by the graphs and models performed to expectations. As indicated, the linear-loading element on the driven element was somewhat long, partly because the models yield slightly long dimensions and partly because the spacing used was slightly wider than the model for horizontal plane #12 wire elements at 0.1' spacing. Removing 3' of load wire on each side of center brought the antenna to resonance. The reflector element was also somewhat long, requiring a less capacitance than specified. At the design center frequency of 28.5 MHz, 27 pF brought the antenna to maximum front-to-back ratio. Matching required only a small adjustment of the beta-match coil, a matter of squeezing the turns slightly.</p>
<p>With a fixed reflector loading capacitor, the 2:1 SWR bandwidth of the antenna was slightly over 300 kHz, confirming its high Q. A variable capacitor in the reflector increased the bandwidth to nearly 1 MHz, with over 750 kHz of that bandwidth at maximum front-to-back ratio. Performance tests at a 20' height with local line-of-sight signals confirmed about 3 S-units of front-to-back ratio, although these rough tests cannot be equated with the elevated patterns shown in various figures. Nonetheless, they strongly suggest that the antenna performs close to its modeled specifications.</p>
<p>The 2-element linear-loaded Yagi has proven to be a most satisfactory field antenna. Although the linear load assembly on the elements requires some care, once assembled, it is almost as carefree as a full size 2-element Yagi. The added front-to-back ratio shows up in practice, while the half-dB reduction in gain does not. In a fixed-tuned model, the chief drawback is the narrower usable bandwidth: that configuration is most useful where the operator tends to use a small portion of the band. The field version with a tunable reflector overcomes this limitation in large measure, making this antenna a good competitor with a full-size 2-element Yagi.</p>
<p>In addition to yielding a buildable antenna, the modeling that has gone into the development of the linear-loaded Yagi demonstrates something else. Antenna modeling programs are not restricted to providing pattern-pictures of existing antennas. With proper care, they can be used to generate a considerable body of adjunct data of use to antennas builders. The calibration of linear-loading elements is but one example of techniques that can expand the utility of such programs. The more we can interconnect the direct data produced by such programs with other collections of data that are important to antenna design, the better we can understand the antennas we use. Whether this result or the development of linear-loaded Yagis is the more important result of the investigation is a question for fireside, coffee-cup debate on cold evenings when the bands are closed.</p>
<center>
<strong>Notes</strong>
</center>
<p>1 For more expert information on the construction of full size Yagis, see Leeson, <em>Physical Design of Yagi Antennas</em> (Newington: ARRL, 1992).</p>
<p>2 For example, see pages 6-7 and 6-8 of either the 16th or 17th Edition of the <em>ARRL Antenna Book</em>. See also pp. 11-22 and 11-23 of the 16th Edition for W0YNF's linear-loaded 14-MHz driven-element-director Yagi, which uses triangular geometry. A linear-loaded 40-meter dipole also appears in Orr and Cowan, <em>Beam Antenna Handbook</em> (Radio Publications, 1990), pp. 58-59. It uses vertical-plane geometry.</p>
<p>3 For somewhat greater accuracy, especially with large wires and close spacing, substitute for the given equation, the following:</p>
<center>
<img src="mu4ae4.gif" width="400" height="61">
</center>
<p>4 Both MININEC 3.13 and NEC 2 are subject to systematic errors when combining elements of differential radii in complex geometries. The models used in this study are fully-tapered MININEC models. By extensive comparisons with various modeling techniques, including the use of single-wire-size substitutes for various parameters, the utility and general validity of the MININEC models was established. However, the linear-loads called for by those models may be up to 2 to 4 percent long, which closes the apparent gap between transmission-line calculations and the models. Nevertheless, extensive modeling, including modeling the antennas listed in note 2 above, establishes that triangular and vertical-plane geometries are not interchangeable without lengthening the linear-load element. Elements modeled in free space on W0YNF's dimensions and triangular geometry show a feedpoint reactance at 14.2 MHz of less than -10 , although a similar close-space vertical geometry model with the same dimensions show nearly -60 reactance (indicating a need to be longer to achieve resonance). Similarly, the vertical-plane geometry of the Orr dipole for 40 meters required a #12 wire linear load almost 8 feet longer than a #12 wire triangular linear load to achieve resonance with a 44.2-foot 1-inch diameter aluminum main element. The calculated triangular linear load modeled within 3- reactance of resonance.</p>
<p>5 A beta match is a form of L-section match in which the series capacitor is created by shortening the antenna element. A shunt coil completes the section that matches an antenna impedance of less than 50 to the higher impedance of the coaxial cable. Formulas for L-sections appear in almost any handbook. Designing an antenna for resonance on a modeling program and then shortening the driven element by an amount that yields the required value of capacitive reactance provides guidance for building the driven element, usually within limits that permit final adjustment by spreading or compressing turns in the shunt coil. A "hairpin" section of shorted transmission line can also make up the shunt inductor, usually with smaller losses, although the coil's lower Q permits a wider bandwidth. See the ARRL Antenna Book, 16th or 17th Edition, pp. 26-21 to 26-23, for further details, and be sure to read Thomas Cefalo, Jr., WA1SPI, "The Hairpin Match: A Review," <em>Communications Quarterly</em> (Summer, 1994), 49-54, and Gooch, Gardiner, and Roberts, "The Hairpin Match," <em>QST</em> (April, 1962), 11-14, 146, 156.</p>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<center>
<strong>Appendix: How Short Can We Go?</strong>
</center>
<p>After developing the data and model antenna for linear loading, I ran across an article on a 10-meter 2-element Yagi that used 8' elements on a 4' boom with center-loading and a beta hairpin match.<sup>1</sup> That led me to wonder how short we might make a Yagi, given that shortening elements permits an increase in front-to-back ratio at the expense of some gain. The results are interesting and worth passing on.</p>
<pre>Modeled Performance of Shortened 10-Meter Dipoles
Antenna Load Feed Gain in dBi
Length (ft) X<sub>L</sub> Z ------------------------ Q= -----------------
(Ohms) (Ohms) --- 500 400 300 200 100
16.54
(full size) 0 70.9 2.12
14' 131 43.0 2.02 1.98 1.97 1.96 1.94 1.83
12' 247 28.4 1.93 1.86 1.84 1.81 1.75 1.57
10' 366 18.1 1.87 1.70 1.66 1.59 1.46 1.07
8' 510 10.7 1.83 1.43 1.34 1.19 0.90 0.14
6' 697 5.7 1.79 0.83 0.62 0.29 -0.29 -1.70
Table 1. A comparison of the modeled performance characteristics of shortened center-loaded dipoles on 10-meters.</pre>
<p>Beginning with center-loaded dipole performance, I modeled 0.75" aluminum elements ranging from full size (16.54') down to the point where gain in dBi fell below zero (6'). <b>Table 1</b> summarizes the data, while <b>Fig. 1</b> displays it in graphical form. The dipoles were initially modeled using infinite Q (0.0 Ohms resistance) and then rechecked at Qs of 500 down to 100. The infinite-Q reading provides a measure of the natural drop in basic gain as the antenna element becomes shorter. The finite Qs provide a measure of the losses incurred by center-loading the element to resonance with an inductor (or even a linear-loading element). Note the shape of the curve as the Q decreases linearly.</p>
<center>
<img src="mu4a-16.gif" width="412" height="340" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1 A comparison of the gain and the Q of a center-loading inductor for shortened 0.75" aluminum dipoles at 10 meters.
</center>
<p>Although conventional, registering comparisons in terms of one gain figure as a percentage of another may not be greatly informative in making comparisons. Negative gains relative to an isotropic source are possible and do represent radiation by the antenna. The real question is whether the gain of any configuration is adequate to the job to which the antenna is assigned or whether something better may be available. The graph may give a better sense of the manner in which an antenna with decreasing length and centerload-Q may likely disappoint the builder if a full-size dipole is the standard of comparison.</p>
<p>Applying the dipole data selectively to full-size and shortened center-loaded 2-element Yagis produced the data in <b>Table 2</b>. The full-size Yagi used the 4' boom specified for the 8' model and is only a slight variation on the standard used throughout these tests. Models with 8' elements and with 12' elements were run at Qs from infinity to 100 to gauge the performance possibilities of half- and three-quarter-size antennas. With both shortened antennas, the front-to-back ratio is superior to a full-size 2-element Yagi at a cost in gain and SWR bandwidth. However, the 12' model shows a decrease in front-to-back ratio as the Q decreases, while the 8' model increases the front-to-back ratio with Q decreases down to 200.</p>
<pre>Modeled Performance of Shortened 2-Element Yagis
Antenna Gain Front-to-Back Feedpoint
and (dBi) Ratio (dB) Impedance
Load Q (Ohms)
Full-size Yagi<sup>1</sup> 6.63 11.27 29.9
12' Elements
--- 6.24 21.22 16.7
500 6.01 19.98 17.2
400 5.95 19.70 17.3
300 5.86 19.25 17.6
200 5.68 18.43 18.0
100 5.17 16.38 19.3
8' Elements
--- 5.76 13.69 11.0
500 4.88 16.93 12.1
400 4.68 17.92 12.4
300 4.36 19.80 12.8
200 3.78 24.96 13.7
100 2.34 21.83 16.2
Note 1: All antennas modeled with 0.75" aluminum elements and a 4' boom. Full size antenna:
DE = 16.08'; Refl = 17.49'. All driven elements resonated, although in practice, the matching
system may require a different length or load.
Table 2. A comparison of modeled performance characteristics of center-loaded shortened 2-element Yagis.</pre>
<p><b>Fig. 2, 3, and 4</b> provide frequency-swept azimuth patterns in free space for the full-size, the 12' and the 8' models respectively. The full-size model, as expected, shows a consistent rear pattern throughout the 28 to 29 MHz range. In contrast, the rear pattern of the 12' model shows the narrow bandwidth of the maximum front-to-back ratio point, with usable front-to-rear ratios from 28.25 to 29 MHz, as compared to the full-size model. The rear pattern of the 8' model deteriorates much more quickly as the frequency departs from the 28.5 MHz design center. At 28.0 MHz, the antenna is essentially a lossy dipole.</p>
<center>
<img src="mu4a-17.gif" width="314" height="272" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2 Free-space azimuth patterns for a full-size 2-element Yagi from 28 to 29 MHz.
</center>
<center>
<img src="mu4a-18.gif" width="294" height="286" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 3 Free-space azimuth patterns for a shortened 2-element Yagi with 12' elements and inductive center loading having a Q of 300. The largest rearward lobe occurs at 28 MHz, with the smallest rearward lobe occurring at 28.5 MHz.
</center>
<center>
<img src="mu4a-19.gif" width="294" height="276" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 4 Free-space azimuth patterns for a shortened 2-element Yagi with 8' elements and inductive center loading having a Q of 300. The largest rearward lobe, along with the diminished forward lobe, occurs at 28 MHz, with the smallest rearward lobe occurring at 28.5 MHz.
</center>
<p>That the patterns of the shortened Yagis degrade more quickly below design center is also reflected in the SWR bandwidth curves shown in <b>Fig. 5</b>. Even the full size Yagi shows a steeper SWR curve below design center than above. The 12' model is well off match at 28 MHz, while the 8' model reaches a similar departure from match only 250 kHz below design center. The curves suggest that the antennas are best designed for a lower center-frequency, since the SWR increases slowly above that frequency. However sound that conclusion may be with respect to the full-size Yagi, it tells only part of the story with respect to the shortened models: one must also account for the degrading front-to-back ratio as the frequency departs upward from center.</p>
<center>
<img src="mu4a-20.gif" width="413" height="318" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 5 A comparison of the SWR bandwidths of full-size and shortened Yagis with 12' and 8' elements. The shortened Yagi loading coils are assigned a Q of 300.
</center>
<p>Do the numbers condemn the shortest model? Not necessarily. Whether a particular antenna is right to build depends upon a collection of factors that perhaps only the user can balance. A full-size 2-element Yagi exhibits good gain within its class, about 2 S-units of front-to-back ratio, and a broad bandwidth, all at the expense of a larger physical structure. The 12' model shows a decreased bandwidth with respect to front-to-back ratio and SWR, but it maintains reasonably good gain and up to 3 S-units of front-to-back ratio with a size only three-fourths that of the full-size Yagi. The 8' model holds the appeal of a truly portable Yagi with some gain and 3 S-units of front-to-back ratio at its design center frequency. However, its gain is significantly reduced and its bandwidth is quite narrow. Moreover, with a feedpoint resistance in the neighborhood of 12 Ohms, the ratio of loss resistance to radiation resistance is much increased. Nevertheless, a small antenna with some gain over a dipole and a good front-to-back ratio over a narrow bandwidth can have many uses.</p>
<p>Both shortened antennas were modeled for patterns and SWR bandwidth curves at a centerload Q of 300, that obtainable on the 12' model with a linear-loading element. It is dubious whether such a Q could be sustained for either the 12' or the 8' model with inductive loading. Connection losses, weathering losses, and other factors are likely to reduce the Q of even the most elegant loading coil assemblies to levels below 100 unless the antenna is often cleaned or is operated within a protected environment. Unfortunately, as <b>Table 2</b>'s data would suggest, these further reductions in gain might make the antenna less attractive as it weathers. However, for portable use--where assembly and disassembly provide reminders to clean all connections--the antenna may have its niche in the array of antennas in amateur use.</p>
<p>Like almost every other final evaluation question we have encountered, the inquiry, "How short can we go?" has no single reply. User needs, competing designs, parts availability, and building skills all contribute to the final answer for each ham.</p>
<center>
<strong>Notes</strong>
</center>
<p>1. Glenn Blackwell, K4HJJ, "A Half-size Two Element Beam with a Full Size Punch," <em>10-10 International News</em>, 33 (Spring, 1995), 6.</p>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<p><a href="mu0.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to Article Index Page</a></p>
<p class="topics-footer">Topics: <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#loading'>Loading</a>, <a href='../topics.html#small-beams'>Small Beams</a>, <a href='../topics.html#yagi'>Yagi</a></p><br>
</body>
</html>
content/mu/mu4ae1.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 679 B

content/mu/mu4ae2.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 696 B

content/mu/mu4ae3.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 559 B

content/mu/mu4ae4.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 694 B

content/mu/mu5a-1.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 6.6 KiB

content/mu/mu5a-10.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 11 KiB

content/mu/mu5a-11.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 11 KiB

content/mu/mu5a-12.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.0 KiB

content/mu/mu5a-13.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 6.8 KiB

content/mu/mu5a-2.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 6.3 KiB

content/mu/mu5a-3.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 9.4 KiB

content/mu/mu5a-4.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 10 KiB

content/mu/mu5a-5.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 9.6 KiB

content/mu/mu5a-6.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 5.8 KiB

content/mu/mu5a-7.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 9.6 KiB

content/mu/mu5a-8.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 8.8 KiB

content/mu/mu5a-9.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 17 KiB

content/mu/mu5a.html
+436
View File
@@ -0,0 +1,436 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="keywords" content="Phased Array, HB9CV / ZL Special, HF Upper, Small Beams">
<title>Modeling and Understanding Small Beams Part 5: The ZL Special</title>
<link rel="stylesheet" href="../styles.css">
</head>
<body>
<center>
<h1>Modeling and Understanding Small Beams</h1>
<h3>Part 5: The ZL Special</h3>
<p><b>L. B. Cebik, W4RNL</b></p>
</center>
<center>
<img src="../images/colorbar.gif" width="591" height="3">
</center><br wp="BR1">
<br wp="BR2">
<p>When George Prichard (ZL3MH, later ZL2OQ and unfortunately recently deceased) introduced the amateur population in 1949 to 2-element horizontal phased arrays, they promised to overcome all the shortcomings of early home brew Yagis.<sup>1</sup> Early experimental results by F. C. Judd, G2BCX, who dubbed the antenna the "ZL Special" in honor of Prichard's work, seemed to indicate gains as high as 7 dBd and front-to-back ratios as high as 40 dB.<sup>2</sup> Moreover, the antenna was relatively simple to construct: 2 half-wave elements separated by about 45 degrees relative to the frequency of choice and connected by a phasing transmission line with a half twist would produce an array phased 135 degrees with maximum gain and a deep null to the rear. <b>Fig. 1</b> shows the general outline of the antenna, which may use either straight dipoles or folded dipoles.</p>
<center>
<img src="mu5a-1.gif" width="474" height="228" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 1. The basic construction of a ZL Special horizontal 2-element phased array.
</center>
<p>The variability of success in replicating the claimed results has been exceeded only by the variability of explanations of what happens to make a ZL Special work. Moxon and Lewallen have pointed out that the success of any phased array depends not upon shifting the impedance of an element, but upon establishing correct current magnitude and phase angle relationships between the two elements. Indeed, Moxon found that successful ZL Specials were more likely the result of accident than engineering, although Lewallen succeeded in designing replicable and reliable equal-length element models using "twinlead" for use as "Field Day Specials."<sup>3</sup></p>
<p>It would be easy to lose ourselves in the fascinating history of misconceptions of the ZL Special within the amateur community. However, let's look instead at a (not THE) conception of the ZL Special that in fact permits one to design an antenna that will work as predicted. The design technique will combine data supplied by antenna modeling programs, such as NEC and MININEC, with some further algebraic analysis to produce an accurate model of both the geometric and phasing dimensions of the ZL Special problem.</p>
<center>
<strong>The Background for ZL Special Analysis</strong>
</center>
<p>We can reduce the ZL Special problem to an orderly series of propositions and explanations. The following notes are an outline of that process.</p>
<pre>
Wide-Band 2-Element Yagi Performance
Antenna Driven Element Reflector Element Material
Dimensions Length Length Spacing Aluminum
DE + Ref 16.0' 17.5' 4.3' 1" dia.
Free Space:
Frequency (MHz) 28.00 28.25 28.50 28.75 29.00
Gain (dBi) 6.7 6.5 6.3 6.1 5.9
F-B ratio (dB) 10.3 11.0 11.2 11.0 10.6
Impedance (R&PlusMinus;jX) 24 - 17 28 - 8 32 + 1 36 + 9 40 + 18
35' over real medium earth:
Frequency (MHz) 28.00 28.25 28.50 28.75 29.00
Gain (dBi) 12.1 11.9 11.7 11.5 11.4
F-B ratio (dB) 11.7 12.5 12.5 11.9 11.1
Impedance (R&PlusMinus;jX) 26 - 18 30 - 9 34 + 0 38 + 8 42 + 16
Table 1. Performance characteristics in free space and at 35' over real medium earth of a
wide-band 2-element Yagi using a driven element and a reflector.
</pre>
<p>1. <strong><em>The significant reason for phasing 2 horizontal half wavelength elements is front-to-back ratio, not gain</em></strong>. Two phased half wavelength horizontal elements will not significantly exceed the gain of a 2-element Yagi. For reference, the performance figures of the modified W6SAI beam, used as our stand throughout this series, appear in <b>Table 1</b>. Although 2-element Yagis with higher gain are possible, they sacrifice even the modest front-to-back ratio of the Orr beam.</p>
<p>The rational for designing a phased array is to improve the front-to-back ratio of the antenna for QRM reduction. Phasing promises, in the abstract, to produce a deep rear null, while preserving the gain obtainable with a 2-element Yagi. <b>Fig. 2</b> compares the plots (35' above real ground) of the reference Yagi and a modestly well-designed ZL Special.</p>
<center>
<img src="mu5a-2.gif" width="410" height="303" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 2. Comparison of azimuth plots for the reference Yagi and a ZL Special at 28.5 MHz, 35' above real medium earth.
</center>
<p>2. <strong><em>We may think of the ZL Special as a "-45 degree" antenna</em></strong>. Traditionally, we have conceived of the ZL Special as two parallel horizontal elements connected by a short (about 45 degrees) phaseline with a half twist. Thinking in impedance terms, where all values reappear every half wavelength, we subtracted the half-twist line from 180 degrees to obtain 135 degrees phasing. However, we can make two modifications to this traditional view.</p>
<p>First, we may think of the antenna in terms of current phase shifts rather than impedance phase shifts. Current magnitude-phase combinations occur only once per wavelength along a transmission line. Although full length 135&deg; lines will achieve the desired phasing for well-designed models, a 45&deg; length of phaseline with a half twist is not the equivalent of a 135&deg; line with respect to current.</p>
<p>Second we may for modeling purposes move the half twist of the phase line anywhere along the line, including at the point of junction with the rear element. In modeling terms, this move means twisting the element. In practical terms, if the front element is modeled in increasing length values (for example, from -8' to +8'), then the rear element is modeled in decreasing values (for example, from +8' to -8'). The two elements are 180&deg; out of phase, and connected by an untwisted 45 length of phaseline.</p>
<p>With respect to the front element, the rear element is ideally current phased -45&deg; (or 315&deg;). The model will now return correct values for calculating voltage and current along the phaseline, with no change in the impedance transformation. However, as we shall see, impedance transformation is largely incidental to understanding the ZL Special.</p>
<p>3. <strong><em>For any two close-spaced near-resonant elements, there is a value of current magnitude and phase for each element that will yield a deep null to the rear</em></strong>. The values of current phase relative to the front element are roughly proportional to the spacing between elements. <b>Fig. 3</b> shows in graphic form the results of modeling half wavelength elements for maximum front-to-back ratio. The precise angles required by the front and rear current will depend to some degree on the antenna geometry and thus may vary slightly from those graphed.</p>
<center>
<img src="mu5a-3.gif" width="472" height="357" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 3. Graphic representation of the relationship between ZL Special element spacing and the phase angle required for maximum front-to-back ratio.
</center>
<p>The first consequence of the graph is to dispel the idea that the 2-element horizontal phased array is in any sense either a 135&deg; or a -45&deg; antenna. Within reason, there is a continuum of usable spacings and phasings. Consequently, the rationale for using wide-spaced planar folded dipoles for elements is lacking, and computer models can detect no advantage for that geometry.</p>
<center>
<img src="mu5a-4.gif" width="475" height="361" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 4. Front-to-back ratio vs. phase angle for two-element arrays.
</center>
<center>
<img src="mu5a-5.gif" width="475" height="361" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 5. Front-to-back ratio vs. current ratio at element feedpoints for two-element arrays.
</center>
<p>The second consequence of the graph is to indicate why many hams obtain usable results from casually designed ZL Specials, even if somewhat off the critical marks. <b>Fig. 4</b> and <b>Fig. 5</b> graph the results of modeling phased arrays at increasing departures from the optimal current phasing and the optimal current magnitude (relative to a front element current value of 1 at 0). If we arbitrarily set 20 dB front-to-back ratio as the minimum mark of an improved 2-element array relative to the standard Yagi, then ZL Specials may depart considerably from optimal values and still meet the criterion.</p>
<p>4. <strong><em>NEC and MININEC models using separate front and rear element sources are "forced" and may not be amenable to phaseline construction</em></strong>. By judiciously arranging the antenna geometry (element length, diameter, and spacing) and the relative current magnitudes and phase angles, we may obtain a deep rear null in many antenna models. In general, such antennas rarely translate into arrays that work with phasing lines of the ZL Special sort.</p>
<p>Virtually any forced or 2-source model can be built successfully under that condition that each element can be supplied with the correct magnitude and phase angle of current. Perhaps the only practical way to achieve this goal is through a lumped-constant network. ZL1LE has provided the analysis that underlies the design of such networks.</p>
<p>5. <strong><em>Horizontal 2-element phased arrays with phaselines are heavily interactive at all points of measurement</em></strong>. The basic antenna geometry consists of the element diameters and their lengths (both absolute and relative to each other) and the spacing between elements. Slight variations in any parameter will yield different values (magnitude and phase angle) of voltage, current, and impedance at the element feedpoints. The rear element values undergo transformation along the phaseline, depending upon the characteristic impedance and the velocity factor of the transmission line used. The phaseline front terminal values combine with the front-element values to produce a feedline matching situation.</p>
<p>NEC and MININEC 2-source models calculate the feedpoint values of magnitude and phase angle for voltage, current, and impedance for each element. Moreover, for available transmission lines--and for those one might build--we know the characteristic impedance and the velocity factor. Therefore, it is possible to analyze proposed ZL Special designs, to evaluate their feasibility and likely performance, and to adjust the design to a level of satisfactory performance. The following procedure will permit some precision in the process of design.</p>
<center>
<strong>Analyzing ZL Special Designs</strong>
</center>
<p>The analysis of 2-element phased arrays with phaselines is a stepped procedure that uses the values of voltage and current magnitude and phase provided by a 2-source model derived from NEC or MININEC analysis.<sup>4</sup> <b>Table 2</b> lists the meanings of the terms of the following equations as a handy reference. Most 2-source models used to obtain values for the following analysis will normally designate the element 1 current as 1 at a phase angle of 0&deg; and the element 2 current as a set of values optimized by trial. The magnitude of the rear element current will be close to 1 and the phase angle will be close to the value corresponding to the element spacing, as found in <b>Fig. 1</b>. Alternatively, one may use a front element current value of 0.5 and a correspondingly adjusted rear element current close to 0.5. The utility of the alternative will be explained later in the discussion.</p>
<pre>
Equation Terms
E<sub>fr</sub> Voltage at the front element; appears as Element 1 voltage in modeling program outputs;
corresponds to Ein in general equations for transmission lines
I<sub>fr</sub> Current at the front element; appears as Element 1 current in modeling program outputs
E<sub>rr</sub> Voltage at the rear element; appears as Element 2 voltage in modeling program outputs;
corresponds to EL in general equations for transmission lines
I<sub>rr</sub> Current at the rear element; appears as Element 2 current in modeling program outputs;
corresponds to IL in general equations for transmission lines
Z<sub>rr</sub> Impedance at the rear element feedpoint
I<sub>in</sub> Current at the input end of the phasing transmission line; corresponds to Iin in general
equations for transmission lines
E<sub>fp</sub> Feedpoint voltage, equals Efr in "perfect" models of ZL Specials
I<sub>fp</sub> Total current at the antenna system feedpoint
Z<sub>fp</sub> Impedance at the antenna system feedpoint
R<sub>fp</sub> Resistive component of the feedpoint impedance, Zfp
X<sub>fp</sub> Reactive component of the feedpoint impedance, Zfp
I<sub>r2</sub> Recalculated rear element current
l<sub>f</sub> Length in feet
l<sub>m</sub> Length in meters
l<sub>d</sub> Length in electrical degrees
l<sub>r</sub> Length in radians
Z<sub>O</sub> Characteristic impedance of the phaseline
VF Velocity factor of the phaseline
Note: Each term for E, I, and Z will have an associated phase angle, theta.
Table 2. Terms of equations used in the analysis of horizontal 2-element phased arrays
using phaselines.
</pre>
<p>1. For any antenna geometry that yields a "perfect" ZL Special, the voltage at the front element feedpoint will be identical to the voltage at the input end of the phaseline connected to the rear element. We may use this fact as a starting point in our analysis of the antenna design, since it provides the necessary third term (in addition to the values of voltage and current at the rear element feedpoint) for calculating either the characteristic impedance of the phaseline or its length, where the other is given. The basic formula for calculating the voltage along a lossless transmission line is given by the equation,</p>
<center>
<img src="mu5ae1.gif" width="400" height="64">
</center>
<p>where E<sub>L</sub> and I<sub>L</sub> are the rear element feedpoint values, E<sub>in</sub> is the front element feedpoint voltage value, and the parenthetical expressions represent the phaseline length. We may simplify calculations by precalculating the line length into radians to obtain l<sub>r</sub>.<sup>5</sup></p>
<p>Since we cannot calculate the line length and Z<sub>O</sub> simultaneously, we must assume one or the other. Letting the line length equal the element spacing is most convenient. We can always set up a small utility program in BASIC to step the calculation through several plausible values of line length, each of which will require a different Z<sub>O</sub>. We must also make a judicious guess as to the likely velocity factor of the line. In general, if the proposed ZL Special design uses straight dipoles, use a figure in the 0.67 to 0.7 range, since the phaseline will likely have a low Z<sub>O</sub>. If the design uses folded dipoles, then an initial velocity factor of 0.8 will serve, since the range of the phaseline Z<sub>O</sub> will be from about 150 to 350 .</p>
<p>If we select l<sub>r</sub> and VF, rewrite the terms for front and rear element values, and solve for Z<sub>O</sub>, we obtain the following equation:</p>
<center>
<img src="mu5ae2.gif" width="400" height="81">
</center>
<p>If the array design is "perfect," it will require a phaseline with line length l<sub>r</sub> and the characteristic impedance, Z<sub>O</sub> to provide the correct phase and magnitude shift of current to the rear element.</p>
<p>2. To understand the conditions at the antenna feedpoint, we must also know the current at the input end of the phaseline. We may obtain this value from the standard equation for calculating the current along a transmission line (written here in terms of front and rear elements):</p>
<center>
<img src="mu5ae3.gif" width="400" height="77">
</center>
<p>The value of current obtained, along with its phase angle, will also be crucial in evaluating the proposed array design.</p>
<p>3. For the array, if perfect, the total current at the feedpoint is the sum of currents in the two branches, namely, the front element and the phasing line input end, or</p>
<center>
<img src="mu5ae4.gif" width="400" height="48">
</center>
<p>This equation, of course, is for a vector sum.</p>
<p>The phase angle of the total feedpoint current represents in "perfect" models the appropriate source current phase angle to obtain a forward element current phase angle of 0&deg; and a rear element current phase angle of the value obtained from the original model. If fed with a current at 0 phase angle, the antenna forward element will show a phase angle shifted in the positive direction by the amount of the phase angle of I<sub>fp</sub>, with the rear element current shifted positive by the same amount. The net difference between forward and rear element current phases will remain the same.</p>
<p>4. From the front element voltage and the feedpoint current, we may obtain the feedpoint impedance, along with values for the resistive and reactive components:</p>
<center>
<img src="mu5ae5.gif" width="550" height="77">
</center>
<p>The calculation of Z<sub>fp</sub>, of course, is again a matter of vector division involving the subtraction of I<sub>fp</sub>'s phase angle from the phase angle of E<sub>fr</sub>. R<sub>fp</sub> and X<sub>fp</sub> provide the values of resistance and reactance to be matched to the feedline for the system.</p>
<p>5. The preceding steps provide the crucial data for a "perfect" phased array. To test the feasibility of the design, simply recalculate the rear element current, I<sub>r2</sub>, using the calculated value of I<sub>in</sub> and Z<sub>O</sub>, along with E<sub>fr</sub>. Use the standard equation (with terms rewritten for the present problem).</p>
<center>
<img src="mu5ae6.gif" width="400" height="73">
</center>
<p>If the model's chosen geometry is perfect, then this calculation will simply return the current magnitude and phase angle of I<sub>rr</sub>. Anything less than perfect will show a divergence between I<sub>r2</sub> and I<sub>rr</sub>, especially with respect to the phase angle.</p>
<center>
<strong>Evaluating ZL Special Designs</strong>
</center>
<pre>
Test Models of ZL Specials
Name El. Type Front El. Lft Rear El. Lft El. Spacing Lft
Folded Dipole Models
Short 1" Cu 15.36' 15.68' 3.86'
Off Z 1" Cu 16.06' 16.80' 4.31'
1" 1" Cu 16.16' 16.16' 4.27'
3/8" 3/8" Cu 16.26' 16.26' 4.27'
Straight Dipole Models
#12 #12 Cu 16.42' 16.42' 3.46'
5/8" 0.625" Al 16.04' 16.04' 3.46'
3/4" 0.75" Al 16.00' 16.00' 3.46'
Notes: Cu = copper; Al = aluminum. Folded dipole element type dimension = width of the
folded dipole; straight dipole element type dimension = element diameter. The 1" folded dipole
approximates the use of 450-Ohm ladder line as the element, while the 3/8" folded dipole
approximates the use of 300-Ohm twinlead as the element.
Table 3. Test models of ZL Specials discussed in text.
</pre>
<p>Performing the calculations just noted provides a significant body of data by which to evaluate the feasibility of a proposed ZL Special design. <b>Table 3</b> describes 7 models (from among the dozens in my files) for which <b>Table 4</b> provides selected results. The results appear in three groups. The first data group comes from 2-source models and provides the current magnitude and phase relationship between the elements, along with the models projected front-to-back ratio. The second data group comes from calculations in accord with the equation just described, listing the output Z<sub>O</sub>, the return current phase (and its difference from the design value), and the calculated feedpoint impedance. The last data group comes from applying the basic antenna model to a version of NEC capable of handling transmission lines within the model.<sup>6</sup> Using one or more values for the phaseline Z<sub>O</sub>, the data group provides the projected front-to-back ratio and the feedpoint impedance. All the antennas were modeled over real medium earth using NEC's more accurate ground modeling capabilities.</p>
<pre>
Modeling and Calculation Results with Test Models
Model &lt; two-source data &gt; &lt; calculations &gt; &lt; test model results &gt;
Name I @ El. 1 I @ El. 2 F-B (dB) Zo Ohms Rtn I El. 2 Ph. Dif. R jX Zo F-B (dB) R jX
Folded Dipole Models
Short 0.5/0&deg; 0.49/-38.7&deg; 41.89 268.9 -63.61&deg; 24.91&deg; 55.8 -48.9 268.9 12.80 29.5 -18.1
300 12.46 35.3 -12.8
Off Z 0.5/0&deg; 0.49/-42.7 44.95 194.4 -42.63&deg; 0.07&deg; 52.3 36.3 194.4 45.38 52.4 36.3
300 17.95 74.9 56.2
1" 0.5/0&deg; 0.5/-42.9&deg; 39.52 330.2 -41.16&deg; 1.74&deg; 40.8 53.4 330 30.12 43.3 51.3
300 25.64 37.8 44.9
3/8" 0.5/0&deg; 0.49/-42.7&deg; 44.16 330.1 -42.69&deg; 0.01&deg; 42.0 42.7 330 44.19 42.0 42.6
300 27.60 36.6 36.4
Straight Dipole Models
#12 0.5/0&deg; 0.5/-34.75&deg; 29.61 66.9 -35.44&deg; 0.69&deg; 6.7 6.6 71 27.17 7.1 5.8
5/8" 0.5/0&deg; 0.5/-34.75 26.06 67.0 -36.19&deg; 1.44&deg; 7.1 7.7 71 26.63 7.2 8.8
3/4" 0.5/0&deg; 0.5/-34.75 25.66 66.7 -36.57&deg; 1.82&deg; 7.2 7.5 71 25.46 7.2 8.8
See Notes, Table 3.
Table 4. Some modeling and calculation results using test models described in Table 3.
</pre>
<p>The model called "Short" represents a casual design I found in the literature. Although the model calculates a promising phaseline Z<sub>O</sub> of about 269 Ohms, thus suggesting the use of 300- twinlead for both the elements and the phaseline, notice the phase differential between the design figure and the return calculation. In general, any difference greater than &PlusMinus;4 degrees or so is likely to bring disappointment. Moreover, as the phase differential between the design value and the return calculation increases, the feedpoint impedance values grow more inaccurate. Compare the calculated value with either of the test models to the right, noticing the subpar front-to-back figures along the way.</p>
<p>Perhaps what made this model attractive was the wide-band low SWR of the antenna. Frequency sweeping the 300-Ohm phaseline model showed that the antenna would show an SWR below 2:1 for over a MHz of 10 meters. Unfortunately, horizontal 2-element phased arrays cannot be adequately designed by reference to SWR. Feeding the assembly must be the last design step, not the first.</p>
<p>The model named "Off Z" demonstrates another problematic situation. The 2-source model and the calculations show that the design is in principle quite feasible and capable of good performance, as indicated by the tiny 0.07 phase differential. However, the 194-Ohm characteristic impedance of the recommended phaseline is uncommon, to say the least. Attempting to execute this model using the nearest common transmission line as the phaseline, 300-Ohm twinlead, results in a serious degradation of performance. See the test model figures to the right. Phaseline Z<sub>O</sub> should be within about 10% of the calculated value for reasonably successful performance of the array. Unless you can build a short length of your own transmission line, which is quite feasible in many instances, many good models of ZL Specials must be set aside as impractical.</p>
<p>The two models we have so far evaluated used elements based upon Yagi theory: the rear element should--in a driven element-reflector design--be somewhat longer than the forward element. This mode of thinking is detrimental to ZL Special design. The remaining models in the group all use equal element lengths as a starting point. There are good reasons on occasion to alter the length of either (or both) the forward or the rear element, but those reasons have virtually nothing to do with the considerations crucial to Yagi design. We shall look at some design alterations after examining the better models on the list.</p>
<p>The 1" and 3/8" folded dipole models used good care in selecting the current magnitude and phase angle for the rear element, while the straight dipole models were more quickly settled by letting the current ratio between elements be 1:1. The use of 0.5 A as the current value permits a more rapid correlation of values with those of the NEC transmission line models using a source current value of 1 A. In actuality, the total antenna current for the antenna system is slightly higher than 1 A, since the phaseline transforms not only the current phase angle, but its value as well.</p>
<p>Both folded dipole models show similar results, despite their different lengths. Although the figures varies slightly as the length-to-diameter ratio changes, the folded dipole elements for a ZL Special should be about 2.44% shorter than a single self-resonant folded dipole at the frequency of interest. The #12 straight dipole model used elements only about 2% shorter than a self-resonant single dipole, while the tubular elements required a little under 2.9% shortening.</p>
<p>The 1" folded dipole model is interesting because it demonstrates the fall-off in performance (front-to-back ratio) as the phase differential between the design value and return calculation value increases. Although 30 dB is a respectable ratio, it is down nearly 10 dB from the 2-source model with only a 1.74&deg; phase differential. Attending more closely to the rear element current phase angle would likely have resolved the difference, but also resulted in a different value of phaseline Z<sub>O</sub>. Compare this model to the 3/8" model for a closer correlation of all relevant values.</p>
<p>In practical terms, the differential is moot, since 330-Ohm twinlead is not common. Both antennas promise very good performance with a 300-Ohm phaseline, if a figure of 25 to 27 dB for the front-to-back ratio can be considered very good. Compared to the reference Yagi, the figure certainly represent an improvement that may be both detectable and desirable. Note that the phaseline meets the &PlusMinus;10% criterion noted earlier.</p>
<p>Feeding a ZL Special that uses folded dipoles and equal-length elements is little problem. The resistive component of the feedpoint impedance presents a reasonable match to 50-Ohm coax, while the remnant inductive reactance can be canceled by the use of either a capacitive stub or a pair of capacitors, each with half the reactance value, in series with the two sides of the feedline at the feedpoint junction.<sup>7</sup> Indeed, it is characteristic of well-designed ZL Specials using equal length elements to have similar numerical values for the resistive and reactive components of the feedpoint impedance, in other words, for the feedpoint impedance to have a phase angle approaching 45&deg; inductive.</p>
<p>Similar results can be obtained from straight dipoles and 72- nominal twinlead. The three models differ only in the wire size used, with consequential differences in element length. The calculated phaseline Z<sub>O</sub> of 66.7 to 67 Ohms departs from the twinlead impedance by only about 6%, and the transmission-line models of the antennas verify antenna performance. Unfortunately, the very low feedpoint impedances, require careful attention to both design and construction to minimizes losses. A 71-Ohm twinlead or a 75-Ohm coax stub, something over 4' long will provide the required match to 50-Ohm coax, with either a capacitive stub or a parallel capacitor used to cancel the remaining reactance, which will be in the range of 150-200 Ohms.</p>
<center>
<strong>Improving ZL Special Performance</strong>
</center>
<p>One straightforward means of improving ZL Special performance is to construct a phaseline with a characteristic impedance and velocity factor that accords with calculations, after fully optimizing a 2-source model of the desired antenna. However, most builders will be limited to altering the antenna geometry to accord with the available transmission lines. In general, there are only two methods of achieving this goal.</p>
<p>First, you may change the spacing between elements. Unfortunately, element spacing is insensitive to change. Raising the required characteristic impedance of the phaseline for the straight dipole models demanded shortening the spacing to something around 2.5 feet. Lowering the required line impedance of the folded dipole models demanded an increase in spacing to around 7 feet. Neither move seems attractive mechanically.</p>
<p>Second, you may change the ratio of element lengths. Each model with equal-length elements was initially optimized with respect to element length for maximum front-to-back ratio. Only the ratio of element lengths remains to be changed in pursuit of a geometry that requires a phasing line of the desired characteristic impedance. The rule of thumb is this: to decrease the required Z<sub>O</sub>, make the front element shorter than the rear element. To increase the required phasing line Z<sub>O</sub>, make the front element longer than the rear element. The adjustments will be small if the original antenna requires a phaseline Z<sub>O</sub> within 10% of the desired value. In addition, either or both elements may require adjustment.</p>
<pre>
Some Improved Test Models
Name Type Front El. Rear El. El. Spacing &lt; calculations &gt; &lt; test model results &gt;
Wire Lft Lft (feet) Zo Ohms Rtn I El. 2 Ph. Dif. R jX Zo F-B (dB) R jX
Folded Dipole Models
1" Cu 16.06' 16.16' 4.27' 300.2 -42.79&deg; 0.01&deg; 41.3 39.8 300 47.54 41.2 39.8
3/8" Cu 16.23' 16.34' 4.27' 299.8 -42.53&deg; 0.07&deg; 41.4 38.0 300 43.20 41.5 38.0
Straight Dipole Models
5/8" Al 16.10' 15.98' 3.46' 71.0 -34.69&deg; 0.31&deg; 6.4 9.0 71 38.39 6.5 8.9
3/4" Al 15.98' 15.78' 3.46' 71.2 -33.95&deg; 0.80&deg; 5.7 7.3 71 34.17 5.9 7.1
See Notes, Table 3.
Table 5. Modeling and calculation results using improved test models.
</pre>
<p><b>Table 5</b> catalogs four improved models. The folded dipole models have front elements slightly more than 1" shorter than the rear. Not shown on the table are the new design values of rear element current magnitude and phase, which will change as the element-to-element ratio changes.</p>
<p>The straight dipole models show the reverse effect: to raise the required Z<sub>O</sub> from 67 to 71 Ohms, the rear element must be slightly shorter than the front element, with a consequential change in rear current magnitude and phase relative to the front element current. Because the curves approaching the maximum possible front-to-back ratio are steepest above 30 dB or so, very small changes in element dimensions produce large changes in front-to-back ratio.</p>
<p>Having shown that and how it is possible to refine ZL Special performance by adjustment of the antenna geometry, we must note the very proper question of whether such measure a worth while for the average home builder. <b>Fig. 6</b> superimposes two of the straight dipole antenna patterns, one for equal-length elements. the other improved. Although there is some improvement in the overall front-to-rear pattern (taking into account the entire region from 180&deg; to 360&deg;), the improvement is not large compared to the initial improvement over the reference 2-element Yagi.</p>
<center>
<img src="mu5a-6.gif" width="411" height="302" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 6. Comparative azimuth patterns for equal-length element and "improved" versions of the 5/8" straight dipole ZL Special (35' above real medium earth).
</center>
<p>Moreover, achieving the absolute maximum rear null in fixed construction may be beyond the building and measurement capabilities of most hams. Indeed, phased arrays with equal-length elements may have advantages that offset their slightly reduced front-to-back performance. Such an array is reversible if we attach to both elements ladder line feeders that are a multiple of a half wavelength (adjusted for the velocity factor). One feeder is attached to the line to the transceiver, the other left open as an indefinitely large impedance that does not significantly affect antenna operation.</p>
<p>However, carefully pruning a ZL Special for maximum null at the design frequency does center the front-to-rear pattern within a desired frequency span. For a front-to-back null of over 40 dB, the front-to-back ratio degrades uniformly above and below the center frequency. On 10 meters, the front-to-back ratio is better than 25 dB 25 kHz each side of the design center and about 20 dB 50 kHz each side of the design center. Less careful pruning will likely improve the front-to-back ratio in one direction from the center frequency, but degrade it in the other down to about 15 dB.</p>
<center>
<strong>Construction and Placement Notes</strong>
</center>
<p>All of the antennas noted in this analysis have been modeled at 35' above medium or average ground for consistency. More than many antennas, ZL Specials require modeling over real ground, rather than the construction of free space models, because they are somewhat sensitive to ground effects. This applies most especially to the array's front-to-back ratio.</p>
<center>
<img src="mu5a-7.gif" width="464" height="374" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 7. Yagi and ZL Special gain vs. height above ground from 20' to 40' over real medium earth.
</center>
<p><b>Fig. 7</b> and <b>Fig. 8</b> graph the gain and front-to-back ratio, respectively, of the ZL Special (the 5/8" diameter straight dipole model), with the comparable values for the reference Yagi provided as a standard. The gain curves are quite parallel. Their spacing is a graphing convenience; the difference in values makes little, if any, operational difference. However, the excursions in front-to-back ratio for the ZL Special are many times those for the Yagi. The curves are based on a single configuration for each antenna. While the Yagi shows a relative constancy of performance, the variability of the ZL Special's front-to-back ratio suggests that optimizing it for the anticipated height of use is certainly in order.</p>
<center>
<img src="mu5a-8.gif" width="478" height="367" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 8. Yagi and ZL Special front-to-back ratio vs. height above ground from 20' to 40' over real medium earth.
</center>
<p>As a further indication of the fact that Yagis and ZL Special operate according to quite different principles once we move beyond the mutual coupling of elements, the correlation of feedpoint impedance and other parameters differs for the two antennas. ZL Special front-to-back peaks and nulls tend to correspond with peaks and nulls in the reactive component of the feedpoint impedance. For driven-element-reflector Yagis, the front-to-back peaks and nulls correspond with their counterparts in the resistive component of the feedpoint impedance. By way of contrast, to the degree they are detectable, gain peaks and nulls show a reverse correspondence.</p>
<p>There is little that anyone can add to the construction of ZL Special, whether using straight dipoles or folded dipoles. Straight dipoles lend themselves to the use of rotary beam techniques. One caution is required: do not permit metal antenna structural elements (such as a boom or mast) to disturb the balance of the currents in the phaseline. Moreover, the sum of 45 years of ZL Special construction wisdom dictates the following rule: use parallel feedline, not coax, for the phaseline. A mixture of wood, PVC, and similar construction materials for the structural assembly can leave your twinlead phaseline unaffected. Unfortunately, the demise of 70-ohm twinlead as an easily obtained commodity has made the straight-dipole version of the ZL Special an endangered--if not an extinct--species of the antenna. What remains to build are twinlead folded dipole versions.</p>
<p>However, use caution when buying materials for a folded dipole ZL Special. Belden 8230, the standard 300-Ohm twinlead for many amateur applications has #20 stranded conductors and a nominal velocity factor of 0.80. It is the basis for the models and the test antenna studied in this article. Many common local sources of supply for twinlead no longer carry equivalents of this transmission line. The foam lines they do carry often have no listed velocity factory, and it is unlikely that the figure will be 0.80. Velocity factor is important chiefly in the physical length of the phasing line, which is perhaps the most critical factor in building a ZL Special.</p>
<p>Decades ago, when bamboo was cheap, taping 300- twinlead to support elements permitted folded dipole versions of the ZL Special to approximate rotary beam configurations. More recently, the idea of fixed beam installations, whether in an attic or in the field, has regained popularity, if for no other reason than necessity in today's tighter ham quarters. A twinlead ZL Special, following W7EL's lead, makes a good Field Day Special, since it rolls up into a small ball for transportation. Elevated at the ends and pointed roughly toward the main body of hams to be worked, the antenna outperforms dipoles by a good measure. Coastal hams can use a single feedline version, while midwestern operators may wish to opt for a reversible version.</p>
<center>
<img src="mu5a-9.gif" width="520" height="315" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 9. General sketch of a single-mast support structure for testing wire ZL Specials.
</center>
<p>As a test bed for validating modeling figures, I built the single-mast support system shown in <b>Fig. 9, 10, and 11</b>. With inner arms of Schedule 40 PVC and outer triangular sections of lighter PR 315 PVC, the assembly permitted me to place practically no metal in the vicinity of the antenna elements or the phase line. Support arms for the center connections to each folded dipole are optional. If you use them, light-weight half-inch nominal CPVC is recommended. All junctions are glued.</p>
<center>
<img src="mu5a-10.gif" width="496" height="338" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 10. Detail A of the support structure, showing the combination of PVC materials used in its construction.
</center>
<p>Although the assembly is a good bit more rigid than it appears at first sight, I do not recommend it for a permanent installation. The guys do not stabilize the structure in all axes and certain twisting motions are possible in high winds. In lighter winds, the structure is quite stable. Thus, it is adaptable to short-term portable operations if some of the junctions are only press-fitted into the couplings.</p>
<center>
<img src="mu5a-11.gif" width="472" height="361" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 11. Detail B of the support structure, showing the center plate and mast connection.
</center>
<p>Those who wish to hang the elements from their ends might use the 17' length, since a 10-meter 2-element phased array is just over 16' long. My own final version of the support system was about 15'9" long. The ends of each front-to-back arm were slit, with the twinlead pressed in place. A pair of holes punched in the insulation of the twinlead permitted the use of a cable tie to hold the element in place. The short ends sticking out beyond the limits of the structure were self-supporting and easily accessed for pruning.</p>
<p>The antenna tested was the improved 3/8" model in <b>Table 5</b>. The insulation on twinlead elements requires about 1-2% shortening (relative to the models) of the elements for resonance at 10 meters. (Note: the velocity factor of a transmission line used as a radiating antenna element is not the same as the velocity factor of the material used as a transmission line. As a radiator, twinlead is just another type of insulated wire.) The final lengths for the test frequency of 28.5 MHz and a height of slightly more than 20' were 16' and 16'1" using Belden 8230. Feedpoint series capacitors are 300 pF in each leg of the feedline on the antenna side of a choke balun. Since the impedance at resonance is in the neighborhood of 40 Ohms resistive, the lowest SWR does not necessarily indicate the frequency of the null, which will be at a slightly lower frequency. If heights other than 20' to 35' are used, these test numbers may be somewhat different.</p>
<p>Once pruned, the antenna worked as predicted, within the coarse methods available for tests. Point-to-point contacts established a front-to-back ratio at the design frequency that rivaled the Moxon rectangle, described earlier in this series. Performance held up across the first MHz of 10-meters, both in terms of anticipated front-to-back ratio and in terms of an SWR bandwidth within 2:1 limits. Unless one has a very special operating need, the extra work of obtaining a "perfect" null would not likely show up, since it is frequency specific and rapidly flattens with excursions away from the design frequency.</p>
<center>
<img src="mu5a-12.gif" width="516" height="275" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 12. General configuration of the 'BRD Zapper ZL Special.
</center>
<p>One variant of the ZL Special is especially apt for attic use (assuming that the broad surface faces the best QSOs). W9BRD bent the ends of straight dipoles toward each other and phase fed the resultant assembly.<sup>8</sup> <b>Fig. 12</b> shows the general outline of the antenna. The original antenna used equal length elements and a system of voltage feeding a transmission line segment between the element ends on one side. The dimensions shown are for a modified version using #18 wire unequal length elements and a 71- phasing line. The resulting feedpoint impedance is 33 + j45 Ohms, a tolerable match for coax once the inductive reactance is cancelled.</p>
<center>
<img src="mu5a-13.gif" width="402" height="346" border="2" vspace="5" hspace="9">
</center>
<center>
Fig. 13. Azimuth patterns of the 'BRD Zapper at 28.5 MHz, 20' and 35' over real medium earth.
</center>
<p><b>Fig. 13</b> shows the pattern at both 20' and 35' above real medium earth for the 'BRD Zapper. Relative to a model with linear elements, the closed geometry of the 'BRD Zapper costs a little under 0.5 dB of gain. At the higher elevation, the worst rear lobe is down over 25 dB. At 20' (perhaps an average attic height), the front-to-back ratio drops to about 20 dB, although further refinement of the geometry may restore much of the dimple in the most rearward direction. Perhaps the only competitive small parasitical antenna in this respect is the Moxon rectangle, reported on earlier in this series. In fact, either antenna would make a good fixed beam for attic use, and the Moxon would be easier to build, since it requires no phase line. The best reason for noting the 'BRD Zapper here is to demonstrate that the geometry of horizontal 2-element phased arrays is not exhausted by straight and folded dipoles.</p>
<p>In fact, this analysis of ZL Specials has not even come close to exhausting the possibilities for horizontal 2-element phased arrays. The lure of indefinitely deep rear nulls is likely to keep the creative juices flowing in many a ham builder. Hopefully, this exploration into modeling and analyzing ZL Specials has added a modicum of better understanding to the process. The operation of ZL Specials can be understood in terms of the voltages and currents at the terminals of each element and along the transmission line used to establish correct phasing. A combination of modeling and calculation makes the performance of a proposed version of the ZL Special far more predictable than we have thought in the past. My hat is off to all those past experimenters who made workable ZL Specials while laboring under a limiting set of assumptions. That is a testimony to persistence of trial and error efforts.</p>
<p>This study has limited itself to those versions of the 2-element horizontal phased array in which the common feedpoint is identical with the forward element feedpoint. This focus stems from my basic interest in resolving the nature of transmission-line phasing in these antennas. The common feedpoint can be placed anywhere between the elements, with transmission line current magnitude and phase conversion along two lengths of transmission line. This is the operative nature of the HB9CV antenna, some notes on which appear at this site: <a href="../phase/hb.html"><b>The HB9CV Phased Array and Gain Comparisons</b></a>. The use of gamma match line to the elements has often obscurred the nature of this antenna's feed and phase system. For an example of a phased horizontal array feed neither at the phase line center nor at the junction with an element, see my article in <i>Antenna Compendium</i>, Vol. 6 (ARRL), on "Two Hilltoppers for 10-Meters."</p>
<center>
<strong>Notes</strong>
</center>
<p>1. Prichard, "A New Driven Array," <em>Break-In</em> (May, 1949), 13-14; "Two Beams for the Price of One," <em>Break-In</em> (Jul., 1949), 15-17; "Some Notes on the Driven Arrays," <em>Break-In</em> (Sep., 1949), 5-7; and "Further Experimentation with the '3MH' Beam," <em>Break-In</em> (Dec., 1949), 13. ZL3MH credits two U.S. hams, W5LHI and W0GZR, for supplying him with the basic idea for the array, which was apparently developed commercially just prior to World War II. I have been unable to uncover the identities of the two hams who inspired Prichard. However, see the appended bibliography for some fascinating reading on the history of the ZL Special and its workings.</p>
<p>2. Judd, "The ZL Special," <em>Short Wave Magazine</em> (Jul., 1950), 337-339.</p>
<p>3. Moxon, <em>HF Antennas for All Locations</em> (RSGB, 1982), pp. 77, 222.</p>
<p>4. Similar results might be obtained by using any two of the three value sets, since E, I, and Z are interrelated. However, the use of E and I provides a very straightforward set of calculations. Too, concern for graphical outputs from NEC and MININEC often obscures the fact that these programs are precise calculational programs. The limits on the accuracy of the models produced relative to "real" antennas is a separate issue (or set of issues).</p>
<p>5. Supplementary equations for calculating line lengths, along with expansions of the equations in the text for use with complex E and I values are given in an appendix to this discussion.</p>
<p>6. The modeling programs used for this analysis were ELNEC 3 and EZNEC 1.</p>
<p>7. I owe this idea to Roy Lewallen, W7EL, who has implemented it with success. See Lewallen, "<a href="https://www.eznec.com/Amateur/Articles/Field_Day_Special.pdf" target="_blank">Try the 'FD Special' Antenna</a>," <em>QST</em> (Jun., 1984), 21-24.</p>
<p>8. Newkirk, "The 'BRD Zapper: A Quick, Cheap, and Easy 'ZL Special' Antenna," <em>QST</em> (Jun., 1990), 28-29.</p>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<center>
<strong>Appendix 1: Using the ZL Special Equations</strong>
</center>
<p>Using the equations given in the main text for the ZL Special requires that we expand them to account for the fact that each voltage, current, and impedance may be a complex number, that is, a magnitude with a phase angle. As a convenience to anyone who might wish to put these calculations into a utility computer program, the following expansions are provided, along with some convenient additional calculations of casual interest in the analysis of horizontal 2-element phased arrays.</p>
<p>First, the rear element values of E<sub>rr</sub> and I<sub>rr</sub>, along with their associated phase angles, yield the impedance at the rear element, Z<sub>rr</sub>:</p>
<center>
<img src="mu5ae7.gif" width="400" height="74">
</center>
<p>where Z<sub>rr</sub> is the rear element feedpoint impedance and theta<sub>Zrr</sub> is its associated phase angle. Obtaining this figure allows one to determine the impedance phase change along the phaseline as a matter of interest.</p>
<p>The use of <b>Equation 2</b> in the text requires that we first convert the physical length of the phaseline, initially identical to the spacing between elements, into radians. This is a standard two-step process that begins by converting the physical length into an electrical length in degrees:</p>
<center>
<img src="mu5ae8.gif" width="450" height="80">
</center>
<p>where l<sub>d</sub> is the length of the line in degrees, f is the frequency in MHz, VF is the velocity factor of the line, and l<sub>m</sub> and l<sub>f</sub> are the initial lengths in meters and feet, respectively.</p>
<p>Converting degrees into and out of radians requires the familiar equations,</p>
<center>
<img src="mu5ae9.gif" width="400" height="73">
</center>
<p>where l<sub>r</sub> is the electrical length in radians.</p>
<p><b>Equation 2</b> in the text yields a value of Z<sub>O</sub> that produces the desired change of current phase with an incidental change of magnitude:</p>
<center>
<img src="mu5ae10.gif" width="400" height="75">
</center>
<p>Expanded to account for the complex numbers involved, it becomes</p>
<center>
<img src="mu5ae11.gif" width="650" height="85">
</center>
<p>Gathering real and imaginary terms in the numerator allows one to split the equation into its parts. However, since the denominator is also complex, inverting the parts allows further subdivision. Each real and imaginary subdivision pair may be recombined by vector addition. Reinverting and using vector addition once more produces the final result, the Z<sub>O</sub> of the phaseline.</p>
<p>Calculating the current at the input end of the phaseline, given the phaseline Z<sub>O</sub>, is straightforward:</p>
<center>
<img src="mu5ae12.gif" width="400" height="66">
</center>
<p>This equation expands into the following form:</p>
<center>
<img src="mu5ae13.gif" width="750" height="71">
</center>
<p>where the real and imaginary parts of the equation are recombined by vector addition.</p>
<p>Z<sub>in</sub>, the impedance at the input end of the phaseline, can be obtained from E<sub>fr</sub> and I<sub>in</sub> by the same calculation method used to obtain Z<sub>rr</sub>. The difference in the phase angle for the two impedances is the total impedance phase angle change for the phaseline.</p>
<p>Since the total feedpoint current is a vector sum, that is,</p>
<center>
<img src="mu5ae14.gif" width="400" height="48">
</center>
<p>the magnitude and phase angle of I<sub>fp</sub> are determined from</p>
<center>
<img src="mu5ae15.gif" width="905" height="77">
</center>
<p>Precalculation of various recurrent terms, of course, can simplify programming of such equations.</p>
<p>Determination of the feedpoint impedance, resistance, and reactance are self-explanatory from the equations in the main text, with the addition of one item:</p>
<center>
<img src="mu5ae16.gif" width="600" height="75">
</center>
<p>The recalculation of I<sub>r2</sub>, the rear element current magnitude and phase angle, via the standard formula,</p>
<center>
<img src="mu5ae17.gif" width="400" height="72">
</center>
<p>requires an expansion similar to that for calculating input current from load current, with some appropriate sign changes along the way. Expanded, the equation is</p>
<center>
<img src="mu5ae18.gif" width="650" height="53">
</center>
<p>The equation requires completion in the same manner as the calculation of I<sub>in</sub>.</p>
<p>Undoubtedly, this appendix provides superfluous detail for many readers and insufficient detail for others. If it assists a few readers, it will have served its purpose. Those who wish precision beyond the capabilities of average home construction may replace the lossless transmission line formulas with those for lossy lines. Terman's <em>Radio Engineer's Handbook</em> and Johnson's <em>Antenna Engineering Handbook</em> provide ready references.</p>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<center>
<strong>ZL Special Bibliography</strong>
</center>
<p>Bluhm, "The Penny-Pincher's Dream," <em>QST</em> (Dec., 1965), 63-64.</p>
<p>Bradley, "The 'Half ZL Special'--a Beam for the City Dweller," <em>Break-In</em> (Jul., 1989), 9-10.</p>
<p>Bradley, "The 'Half ZL Special' Revisited," <em>Break-In</em> (Sep, 1991), 4-5.</p>
<p>Glover, "ZL Special for 2m," <em>Break-In</em> (Apr, 1985), 12.</p>
<p>Judd, "ZL Special 2m Beam," <em>Out of Thin Air</em>, pp. 56-59.</p>
<p>Judd, "The ZL Special," <em>Short Wave Magazine</em> (Jul., 1950), 337-339.</p>
<p>Kear, "'Five for Five:' (Five Decibels for Five Bucks)," <em>QST</em> (Jan., 1971), 40-42.</p>
<p>Lewallen, "Try the 'FD Special' Antenna," <em>QST</em> (Jun., 1984), 21-24.</p>
<p>McCoy, "The Scotsman's Delight," <em>QST</em> (Jun., 1963),24-26.</p>
<p>Moxon, "Two-Element Driven Arrays," <em>QST</em> (Jul., 1952), 28.</p>
<p>Moxon, <em>HF Antennas for All Locations</em> (RSGB, 1982), pp. 77, 222.</p>
<p>Newkirk, "The 'BRD Zapper: A Quick, Cheap, and Easy 'ZL Special' Antenna," <em>QST</em> (Jun., 1990), 28-29.</p>
<p>Prichard, "A New Driven Array," <em>Break-In</em> (May, 1949), 13-14.</p>
<p>Prichard, "Two Beams for the Price of One," <em>Break-In</em> (Jul., 1949), 15-17.</p>
<p>Prichard, "Some Notes on the Driven Arrays," <em>Break-In</em> (Sep., 1949), 5-7.</p>
<p>Prichard, "Further Experimentation with the '3MH' Beam," <em>Break-In</em> (Dec., 1949), 13.</p>
<p>Prichard, "Two Element Rotary: The '3MH Special,'" <em>Short Wave Magazine</em> (Dec., 1950), 666-667.</p>
<p>Prichard, "The 'ZL Special' Beams, <em>Break-In</em> (May, 1961), 129-130.</p>
<p>Prichard, "ZL Specials in 1985," <em>Break-In</em> (Oct., 1985), 11.</p>
<p>Schick, "A Shortened ZL-Special Beam," <em>CQ</em> (Jul., 1959).</p>
<p>---, "Modified 'ZL' Special, <em>Antenna Roundup</em>, Vol. 2 (Cowan Publishing, 1966), pp. 65-66.</p>
<p>Note: Special thanks go to Elaine Richards, News and Features Editor for PW Publishing Ltd., publishers of <em>Shortwave Magazine</em> and <em>Practical Wireless</em> for her kindness in supplying me with copies of articles on the ZL Special appearing in those journals. My thanks also go to Brian Egan, ZL1LE, for providing copies of ZL Special articles appearing in <em>Break-In</em>, and to Bridget DiCosimo of A.R.R.L. for finding similar materials that have appeared in <em>QST</em>.</p>
<center>
<img src="../images/colorbar.gif" align="middle" width="540" height="4">
</center>
<p><a href="mu0.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Return to Article Index Page</a></p>
<p class="topics-footer">Topics: <a href='../topics.html#hb9cv-zl-special'>HB9CV / ZL Special</a>, <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#phased-array'>Phased Array</a>, <a href='../topics.html#small-beams'>Small Beams</a></p><br>
</body>
</html>
content/mu/mu5ae1.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 911 B

content/mu/mu5ae10.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 766 B

content/mu/mu5ae11.gif
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 1.7 KiB

Some files were not shown because too many files have changed in this diff Show More