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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="MF, Vertical">
+  <title>Pursuing the (Nearly) Perfect Parasitic Vertical Array for 160 Meters Part 1</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>Pursuing the (Nearly) Perfect Parasitic Vertical Array for 160 Meters<br>
+    Part 1: A Review of Design and Modeling Techniques</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>Suppose that you had a vertical array for 160 meters that produced a pattern like the azimuth pattern in <b>Fig. 1</b>. Notice that the elevation angle is 15 degrees, and that the peak front-to-back ratio is nearly 40 dB. What might it take to achieve such a pattern? In most instances, folks would speculate on phased monopoles. Now let's add the ability to remotely switch the direction of the array in 60 degree intervals throughout the entire circle. What might that ability require?</p>
+  <center>
+    <img src="160s-1.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Before our speculation carries us too far into BC-band fields of towers, let me give away the secret. The array is a single driven element about 1/2 wl tall with sloping parasitic guys (or pseudo-guys). It will be the subject of this design study (since my yard and budget are too small for implementation). However, even though based on modeling studies in NEC-4, the array avoids almost all of the modeling flaws that have made parasitic vertical arrays so contentious. In fact, as a prelude to looking at the new array, let's look first at some facts about modeling some well established arrays.</p>
+  <p><b>Buried Radial Systems</b></p>
+  <p>In most 160-meter literature, we find 2 sorts of radial system models, neither of which are accurate models of buried radial systems. By a buried radial system, I mean a set of radials anywhere from near the surface down to about 2' into the soil. In general, this covers most of the radial systems in use at 160-meter installations.</p>
+  <p>The two most common systems used in models of buried radials are the near-ground elevated radial system and the no-radial system using a MININEC ground. Of the two, the latter is the most common, since it is the simplest to model. Of the two, the MININEC ground system creates the worse models, but both are completely inadequate as substitutes for modeling a buried radial system.</p>
+  <p>Modeling a buried radial system requires a version of NEC higher than NEC-2. Obtaining NEC-4, for which there are commercial implementations, is an expensive proposition, and most individuals may find the investment beyond their means relative to the benefits. However, the differences in the models and their results yielded by NEC-4, relative to the weak substitutes currently used, dictates that any individual or institution that wishes to claim any degree of good correlation between models and reality for vertical arrays on 160 meters should have this software.</p>
+  <center>
+    <img src="160s-2.gif" width="701" height="413" border="2" vspace="5" hspace="9">
+  </center>
+  <p>I can illustrate the point with a short series of models. First consider simple 1/4 wl monopole over a field of buried radials whose numbers might vary from 4 to 128. We can model this situation fairly easily in NEC-4. Using <b>Fig. 2</b> as a guide, we can see some of the requirements for such models. The vertical wire must have a junction at the surface (Z = 0) level. The source segment should be the same length as the immediately adjacent segments for maximum accuracy. These requirements set the minimum segment length in the model. One consequence of the minimum segment length is a limit on the diameter of the main element if we retain a safe 4-to-1 length-to-diameter ratio for the complex geometry of radial system models. For our example, let's use 0.001 wl or 0.164 m as the minimum length, which corresponds to a radial field buried about 6.5" deep. I shall use a 25-mm diameter main element and 2-mm diameter radials for the examples.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                    Table 1.  Soil types used in the study
+
+      Soil Type               Conductivity            Permittivity
+                              Siemens/meter           dielectric constant
+      Very Poor               0.001                    5
+      Poor                    0.002                   13
+      Good (Average)          0.005                   13
+      Very Good               0.0303                  20
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>I shall note in passing that my modeling studies show only interesting but faint numerical difference as we move the radial field from about 3" deep to about 25" deep--differences that would not add up to a tenth of a dB difference in performance for any given soil quality. As <b>Table 1</b> indicates, we shall use in these notes the standard sample soil qualities of Very Poor through Very Good to check on differentials based on ground differences. That these labels indicate samples that are indeed fair and that the other aspects of these preliminary notes on modeling are accurate has been demonstrated in a series of articles for <i>The National Contest Journal</i> that appeared in 2001.</p>
+  <p>In order to control the size of models, one may use length-tapering of the elements, including both the main and radial wires. <b>Fig. 2</b> shows the technique in sufficient detail for these notes. The main element is a constant 40-m throughout the monopole exercise, while the radial will be an exact 1/4 wl at 1.83 MHz, the test frequency throughout these notes. However, the key question concerns results.</p>
+  <center>
+    <img src="160s-3.gif" width="649" height="530" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 3</b> provides part of the answer. It summarizes the gain of a 40-m tall monopole over radial fields from 4 to 128 radials over the sample soils. Note that for most of the samples, the far-field gain peaks at about 64 radials. However, for Very Poor Soil, gain continues to rise, even at the 128-radial level, with well over a 3 dB differential when moving from 4 to 128 radials in the system. I should add here that most of standard categories of soil conductivity and permittivity are based on measurements made for AM BC service. Amateurs should not be surprised to find conductivity levels well under 1 mS/m, the lowest value in both the standard charts and the sample types used here. For example, a set of tests on some Maine soil at 7 MHz yielded a conductivity of about 0.2 mS/m, with an indirectly derived permittivity of 7, which happens to be the textbook value for shale. In short, one should not over-estimate the quality of one's soil, even if maps suggest pretty good stuff under foot. The gain line for Very Poor soil comes closest to reflecting experiential reports of signal improvements occasioned by adding radials to one's system.</p>
+  <center>
+    <img src="160s-4.gif" width="654" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The gain curves are reflected in NEC-4 reports of anticipated feedpoint values for monopoles, as shown in <b>Fig. 4</b>. The curves do not begin to converge until we have at least 32 radials under the monopole. At that point, construction variables would mask any ground-occasioned differences in measured values.</p>
+  <p>One of the reasons that so many modelers use the MININEC ground system in vertical modeling is that the NEC-2 alternative of placing a ground plane at about 0.001 wl above ground shows strong correlations to the results of using the no-radial MININEC ground. Unfortunately, the near-ground radial system has only very limited correlations to the buried-radial system we have glanced at so far. Hence, both systems are faulty as adequate models of a buried-radial system.</p>
+  <center>
+    <img src="160s-5.gif" width="652" height="531" border="2" vspace="5" hspace="9">
+  </center>
+  <p>So that we do not encounter graphic grid lock in a morass of lines, let's simply compare sample buried radial systems results to those that would be yielded for the same antenna connected directly to a MININEC ground. This latter facility is available in EZNEC as an adjunct to the normal NEC-2 array of ground options. <b>Fig. 5</b> shows the MININEC-ground curve in relationship to curves for 8, 32, and 128 buried radials, all in NEC-4, for various soil qualities. Although the MININEC curve traces adequately the curves for larger radial systems, it does not come close to reflecting the situation with a smaller radial field.</p>
+  <center>
+    <img src="160s-6.gif" width="649" height="525" border="2" vspace="5" hspace="9">
+  </center>
+  <p>More telling is <b>Fig. 6</b>, a graph of the modeled source resistance values for the same set of models. A MININEC ground provides a single source impedance figure, taken over none of the same ground types, but over perfect ground. It comes close to tracking only the field of 128 radials, with serious deficiencies for any small radial field.</p>
+  <p><b>MININEC vs. Buried Radials for Parasitic-Guy Arrays</b></p>
+  <p>We might live with the differentials between large buried-radial systems and the MININEC no-radial system of modeling were it not for a weakness in the MININEC ground system that almost all modelers of 160-meter arrays routinely overlook. A guy-wire used as a parasitic element slopes and therefore has a horizontal as well as a vertical component to its far field. Virtually all versions of MININEC warn modelers that placing a horizontal antenna closer than about 0.2 wl to the ground results in increasing inaccuracies to the output reports. In general, the gain reports will be increasingly too high and the source impedance reports too low as we bring the wire closer to the ground. The restriction on the MININEC ground accuracy applies not only to driven elements, but as well to parasitic elements and not only to truly horizontal elements, but as well to sloping elements.</p>
+  <center>
+    <img src="160s-7.gif" width="450" height="359" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Let's illustrate the problem with a simple classic array, illustrated in <b>Fig. 7</b>. We shall test this array at 1.83 MHz over the MININEC ground and over a buried radial system. Since both elements are grounded, we shall use a set of intersecting radial systems, outlined in simplified form in <b>Fig. 8</b>. However, the actual modeled system uses 32 radials per intersecting system, with junctions where shortened radials meet. (Techniques for constructing buried models of intersecting radial systems are fully described in the <i>NCJ</i> series noted earlier.) Otherwise, the buried radial system is constructed just as for the single monopole.</p>
+  <center>
+    <img src="160s-8.gif" width="605" height="427" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    <img src="160s-9.gif" width="648" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <p>If we compare MININEC-ground models over various soils to models over buried 32-radial systems (a region where the monopole models converge reasonably well), we find that the MININEC-ground model over-estimates gain by an average of a full dB, as shown in <b>Fig. 9</b>. <b>Fig. 10</b> is even more dramatic, as it reveals the degree of over-estimation of the front-to-back ratio that occurs in the MININEC-ground model compared to the buried-radial model. Given that full-size unloaded horizontally oriented drive-reflector Yagis achieve only about 10 to 12 dB front-to-back ratio maximums, there should be little question as to which model type is the more believable. To see the overall differences between the two types of models, we may compare elevation patterns over good soil of the two models, as shown in <b>Fig. 11</b>.</p>
+  <center>
+    <img src="160s-10.gif" width="645" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    <img src="160s-11.gif" width="640" height="270" border="2" vspace="5" hspace="9">
+  </center>
+  <p>To confirm that the results of the first example are not a simple aberration, let's try another standard guy-wire array using 3 elements, as shown in <b>Fig. 12</b>. The sloping guys function as a director and an inductively loaded reflector. For the buried-radial version of this model, we shall require a system of three 32-radial fields that intersect along two lines, as sketched in simplified form in <b>Fig. 13</b>.</p>
+  <center>
+    <img src="160s-12.gif" width="555" height="315" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    <img src="160s-13.gif" width="624" height="390" border="2" vspace="5" hspace="9">
+  </center>
+  <p>With 2 sloping elements, the differences between the MININEC-ground model and the buried-radial model become further accentuated. <b>Fig. 14</b> compares the gain values over different soil types for the two models. Even over Very Good soil, the MININEC-ground model over-estimates the array gain by a full dB, with that differential growing to nearly 5 dB over Very Poor ground. The front-to-back ratio comparison in <b>Fig. 15</b> is equally impressive, with the MININEC-ground model over-reporting the ratio by an average of 10 dB.</p>
+  <center>
+    <img src="160s-14.gif" width="649" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    <img src="160s-15.gif" width="648" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In addition to these differences, the buried-radial ground model requires a different inductive loading value than needed by the MININEC-ground model: 22 vs. 33 Ohms inductive reactance. Interestingly, the use of a near-ground elevated radial system requires a load in the reflector that is quite close to the MININEC value, further illustrating that neither system adequately substitutes for a buried-radial model--if buried radials happen to be what we are modeling. <b>Fig. 16</b> summarizes the differences in comparative elevation plots for the MININEC-ground and buried-radial models over Good soil.</p>
+  <center>
+    <img src="160s-16.gif" width="640" height="270" border="2" vspace="5" hspace="9">
+  </center>
+  <p>It has been necessary to review the inadequacies of the MININEC-ground system of modeling vertical arrays, especially when the array uses sloping elements, for two major reasons. One reason is the prevalence of the use of such models and their general acceptance as substitutes for models of buried radial systems. The second reason, related to the first, is that the MININEC-ground models present an illusion that guyed monopole arrays come sufficiently close to outstanding performance, especially with respect to the front-to-back ratio, that we need not seriously consider further techniques of improvement.</p>
+  <p>Little could be further from the truth for sloping parasitic monopole arrays. In general, buried-radial system models suggest that both the gain and front-to-back ratio performance of most sloping parasitic element arrays leaves a vast region for improvement. The increments of gain and front-to-back ratio offered by such arrays are worthy, compared to a single monopole, and this level of improvement may be satisfactory for a large number of antenna installations. However, when we compare the performance to the azimuth pattern in <b>Fig. 1</b>, we can easily see that further improvement is possible.</p>
+  <p><b>1/2 Wavelength Phased 1-Tower Arrays</b></p>
+  <p>Before we look at a possible improvement upon a parasitic array, let's briefly review some of the potential for phased arrays using 1/2 wl radiators. Among the classics is the K8UR array (first presented in <i>CQ</i> for December, 1989) that consists of a central grounded tower that functions as a passive element in the system. Surrounding the tower are 4 dipoles, the upper halves of which are attached to non-conductive guy wires. Each wire is angled at 30 degrees relative to the vertical tower, conforming to standard guying practice. At the roughly centered feedpoints, the dipoles are folded back toward the tower, forming another 30 degree angle to it. The entire ensemble resembles the outline sketch in <b>Fig. 17</b>.</p>
+  <center>
+    <img src="160s-17.gif" width="417" height="438" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The reason for the double circles in each dipole is the use of a split feed for each element to ensure centering of the feedpoint. Single feeds on each wire in the segment nearest the center result in only about 1-Ohm differences of resistance and reactance, so simpler modeling is possible. However, when scaled for study in the context of 160 meters, the initial models were disappointing using any method of feed.</p>
+  <p>The K8UR system requires a phased feed system that some literature casually specified as -90 degrees on the forward element, +90 degrees on the rear element, and 0 degrees on the side elements, all at the same current amplitude. Unfortunately, models of this system produce mediocre performance, with front-to-back ratios that do not reach 10 dB over any soil quality.</p>
+  <center>
+    <img src="160s-18.gif" width="640" height="270" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The problem does not lie with the arrangement of the tower and the wires. In fact, excess concern with the spacing of the wires from the tower and the positioning of the fold-back points to yield a square that is 1/4 wl on a side has produced less than optimal performance from the array. <b>Fig. 18</b> compares the elevation patterns of two models of the array. One uses the recommend fold-back point to form the square that is 1/4 wl per side and spaces the wires a minimum of 2.6 m from the central tower. The other model uses a fold-back point that is exactly halfway along the driven wires, while allowing the wires to be within 0.5 m of the central tower. The improvement in the reduction of very high angle radiation by using the mid-point fold-back is clearly evident in this comparison over good quality soil. It holds for every other soil type, with the mid-point version also showing about a degree lower take-off angle over each soil type.</p>
+  <p>In the mid-point model, a 72-m tower simulated by a 250-mm wire forms the central element. 80-m long 2-mm diameter wires form the phased dipoles. Obtaining at least an excellent front-to-back ratio--whatever the gain turns out to be--is simply a matter (for the modeler) of introducing the correct current magnitude and phase for the 4 fed dipoles. In the case of the K8UR array, as modeled here, the process is simplified because the side wires can be left at a magnitude of 1 and a phase angle of zero.</p>
+  <p>For the arrangement noted, over good soil, the forward wire required a current magnitude of 1.05 at a -130 degree angle, while to rear element required a magnitude of 1.06 at 136 degrees to achieve a balance between maximum gain and maximum front-to-back ratio. For good soil, the optimized version of the mid-point model shows a gain of 6.45 dBi at an elevation angle of 17 degrees with a front-to-back ratio of 45 dB and a horizontal beamwidth of 90 degrees. <b>Table 2</b> provides additional performance potentials over various soils.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+     Table 2.  K8UR Array with Mid-Point Dipole Feed
+72-m high 250-mm diameter tower, 80-m long 2-mm diameter center-fed dipoles, no
+radials.
+
+Soil        Gain  TO    Fr-Bk B/W   Feed Current Relative Magnitude and Phase
+Quality     dBi   angle Ratio -3 dB       Dir               Ref         Sides
+Very Poor   3.9   21&deg;   42.6  94&deg;   1.05 @ -130&deg;      1.07 @ 136&deg;       1.0 @ 0&deg;
+Poor        5.4   19&deg;   44.9  92&deg;   1.05 @ -130&deg;      1.06 @ 136&deg;       1.0 @ 0&deg;
+Good        6.5   17&deg;   45.0  90&deg;   1.05 @ -130&deg;      1.06 @ 136&deg;       1.0 @ 0&deg;
+Very Good   8.8   13&deg;   44.0  88&deg;   1.05 @ -130&deg;      1.06 @ 136&deg;       1.0 @ 0&deg;
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The table lists the required relative current magnitudes and phase angles for each active element for each soil type. This information is likely more useful than the resultant feedpoint impedances.</p>
+  <center>
+    <img src="160s-19.gif" width="640" height="400" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The K8UR system is capable of truly outstanding performance using a well-designed phasing system--one capable of handling the inevitable variations that occur from one installation to the next. <b>Fig. 19</b> shows the potential performance over various soils in overlaid azimuth patterns, each taken at the TO angle for the soil type. The array is a bit sensitive. Changes in the side wire phase angle as little as 5 degrees reduced the front-to-back ratio to under 20 dB. Its only other limitation is in direction switching. When fully optimized, the -3 dB bandwidth of under 95 degrees leaves a slight weakness (up to -3 dB) along the bearings that mark the dividing points between available headings.</p>
+  <p>The K8UR array is an example of a phased array that avoids the use of separate towers for the individual active elements. For our purposes, the array forms a touchstone for simpler systems that require only a single driven element. We shall look at a couple of possibilities for parasitic arrays in Part 2.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 1-1-2002. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for December, 2001. 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="160sb.html"><img src="../images/fwdrd.gif" align="bottom" width="36" height="33"> Go to Part 2</a></p>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#mf'>MF</a>, <a href='../topics.html#vertical'>Vertical</a></p><br>
+</body>
+</html>

content/160/160sb.html

@@ -0,0 +1,197 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="MF, Vertical">
+  <title>Pursuing the (Nearly) Perfect Parasitic Vertical Array for 160 Meters Part 2</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>Pursuing the (Nearly) Perfect Parasitic Vertical Array for 160 Meters<br>
+    Part 2: Some Parasitic Possibilities</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>In Part 1 of this short series, we examined the modeling practices by which analysis of 160-meter vertical arrays are made and designs created. In addition, we took a brief look at phased arrays using a single central support, of which the K8UR system is one of the most outstanding.</p>
+  <p>In this part, we shall examine the possibilities of using a single driven element and using parasitic wires--guys--in order to create a vertical array. Whether or not practical, the possibilities are most interesting from a design perspective. Throughout, we shall observe the modeling cautions established in Part 1, with all modeling done over radial systems in NEC-4 unless clearly specified otherwise.</p>
+  <p><b>A 4-Guy Parasitic Array</b></p>
+  <p>It is possible to transform a version of the K8UR array into a parasitic array. However, the guys would extend in the normal fashion. Immediately lost would be the suppression of very high angle radiation from the antenna. In return, the builder would gain the simplicity of feeding a single element without concern for relative current magnitude and phase on the guys. The resulting array would have the appearance of the outline in <b>Fig. 20</b>.</p>
+  <center>
+    <img src="160s-20.gif" width="402" height="438" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The achieve maximum performance from the array, it is necessary to use a guy angle a bit less than the standard 30 degrees: about 27 degrees appears optimum. As well, as <b>Table 3</b> shows, the director, the reflector, and the two side guys have different lengths. The table shows these values along with modeled performance data. The feedpoint impedance assumes base feeding of the 1/2 wl central tower, although shunt feeding and other systems are equally applicable to the array.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+    Table 3.  A 4-Guy Parasitic Array
+Tower:  80-m high, 250-mm diameter, base 1 m above ground; guys: 25-mm diameter,
+spaced 0.6 m from tower with virtual anchor point at 78.7 m; no radials.
+
+Soil        Element Length-m        Gain  TO    Fr-Bk  B/W        Feed Z
+Quality     Dir   Ref   Sides       dBi   angle ratio  -3 dB      R +/- jX
+Very Poor   72.75 79.0  83.5        2.4   26&deg;   29.3   154&deg;       1590-4950
+Poor        71.25 79.0  84.0        3.9   22&deg;   32.1   130&deg;       1330-4750
+Good        70.5  79.0  84.0        5.0   20&deg;   40.1   121&deg;       1200-4700
+Very Good   68.25 79.0  83.5        7.2   15&deg;   40.4   112&deg;        910-4690
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <center>
+    <img src="160s-21.gif" width="640" height="750" border="2" vspace="5" hspace="9">
+  </center>
+  <p>To illustrate the pattern types produced by the array, <b>Fig. 21</b> provides the azimuth and elevation patterns over Good soil. Because it is common practice to place this type of array over a radial system, I modeled the system in 3 configurations for each soil type. The table shows the values for the model using no radials under the driven tower. <b>Fig. 22</b> graphs the gain of this configuration, along with two radial systems, one at ground level (Z=0) and the other with the radials buried 0.001 wl (about 0.164 m or 6.5") below ground. The radial systems consisted of 32 wires, each 2 mm in diameter and 1/2 wl long (81.91 m).</p>
+  <center>
+    <img src="160s-22.gif" width="647" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The graph shows that maximum improvement occurs with buried radials over Very Poor soil, an improvement of about 1.2 dB relative to the radial-less system. However, the use of radials does increase the elevation angle of maximum radiation by 2 degrees for Very Poor soil--and by lesser amounts for better soils. The use of radials in models shows virtually no improvement over Very Good soil.</p>
+  <p>In principle, the 4-guy parasitic array gives the builder the advantage of a system that is relatively easy to feed--something like a set-and-forget array. However, constructing the array is somewhat finicky. Changing the reflector length by as little as 0.5 m drops the front-to-back ratio to the 20 dB region, and slight length variations in the side guys have similarly large effects upon performance. Only the director shows slow changes in performance with changes in length. Hence, for any given installation where the ground conditions are not fully known, the potential for mis-building the 4-guy array is great.</p>
+  <p>A second disadvantage associated with the 4-guy array lies in the area of switching directions. Changing directions with the array requires altering the parasitic guys so that for each one, three lengths are possible. The complexities of such switching are likely no less than trying to optimally phase a K8UR array. Consequently, it is a strong question mark as to whether this system could live up to the promise of a parasitic system to provide greater simplicity than a fully phased guy-dipole array.</p>
+  <p><b>The Basic 7-Element 1/2 Wavelength Parasitic-Guy Array</b></p>
+  <p>The following section of this report outlines a potential improvement on the 1/2 wl parasitic guy arrays that is based on an antenna developed for AM BC use. It achieves--at only a slight reduction of array gain--the desired simplicity of switching with full horizon coverage for a steerable array. As well, the array is forgiving of small construction errors--that is, changes in element length yield only small changes of performance for all elements.</p>
+  <p>The array employs a driven element that is roughly 1/2 wl long. Automatically, a 79.2-m main element places this array outside the structural capabilities of most 160-meter operators, but that is no hindrance to a study of the antenna. In the course of the discussion, a number of modeling issues will arise, such as modeling with and without a radial system. These questions will be addressed along the way.</p>
+  <center>
+    <img src="160s-23.gif" width="540" height="375" border="2" vspace="5" hspace="9">
+  </center>
+  <p>First, however, we should look at the antenna under study, sketched in <b>Fig. 23</b>. It consists of a central driven element, fed at the base. There is virtually no difference in performance when the antenna base is raised and lowered between 1 m from the ground to about 3.5 m from the ground, so long as everything else in the design remains the same.</p>
+  <p>The guys are 6 in number, 3 acting as directors and 3 as reflectors. Experiments began with the standard 3-element guyed system and proceeded to a 4-element system, as 2 of three equally spaced guys became reflectors. The double reflector systems showed some improvement. Adding the third reflector guy in line with the director (for a 5-element array) again showed improvement. However, not until I added the two remaining directors to fill out the sloping parasitic system at 60 degree intervals did improvements reach their limit.</p>
+  <p>The headings of <b>Table 4</b> and <b>Table 5</b> provide dimensions for the radials for two radically different models. The first uses a large 250-mm diameter main element (roughly 10"), with 25-mm diameter (about 1") guys. The second employs a more modest 25-mm (1") main element, with 2-mm (between AWG #14 and AWG #12) guys. The differences between the performance levels of the two versions range from less than 0.1 dB over Very Good soil to about 0.2 dB over Very Poor soil for all cases modeled.</p>
+  <p>The change in main element and guy diameters does require a small shift in parasitic element lengths for optimal performance. The reflector length changes are minimal: 81.5 m for the fat main element, 82.0 m for the thin driver. The changes needed in the director lengths are more extensive: 67.9 m for the fat driver, 71.0 m for the thin main element. All three directors and all three reflectors may each have identical lengths.</p>
+  <p>The guys may turn out to be, for some installations, pseudo-guy wires. They begin in fairly close proximity to the main elements, spaced only far enough away for safety relative to the high voltages at the ends of both elements. Each parasitic guy begins about 0.6 m away from the main element, about 1.1 m down from the peak height of the main element. The dimensions are partial functions of performance optimization and partial functions of the angle of the guys relative to the main element. The designation "pseudo-guy" arises from the fact that an angle of 27 degrees relative to the driver turns out to be best for the parasitic guys. (The angles away from 27 degrees toward 24 degrees and toward 30 degrees result in a slow rate of performance degradation. Thus, concern over precision--for example, in a worry over catenary angle changes--would be misplaced.) Since the optimal angle is less than normally used for top guys in commercial installations, the parasitic guys may best be implemented as non-structural wires. Of course, to prevent unwanted interactions, the structural guys are presumed to be composed of non-conductive materials. Incidentally, given the element diameters involved, all elements are modeled as copper. Changes in materials make differences only in the 0.0X column of gain figures and less than 1 dB in the front-to-back figures.</p>
+  <p><b>Performance and Radials</b></p>
+  <p><b>Table 4</b> and <b>Table 5</b> present the modeled performance figures for the two versions of the array. Note that there are three sets of figures for each antenna model. The first group models the antenna over various soils using no ground radial system. The second places a radial system exactly at ground level. Had the driven element been connected to this junction, NEC-4 would have yielded some unusable figures. However, with no source segment attached to the Z=0 junction, the calculations produce normal results. The third set of figures places a radial system 0.001 wl below ground, the same depth as used with earlier models. In the present array, each radial is 81.91 m long, that is, a half wavelength. Both the at-ground and buried radial systems consist of 32 radials each.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Table 4.  7-element parasitic array: Version A
+
+Driver = 79.2-m vertical, 250 mm diameter; 3 reflectors = sloping 25-mm guys,
+81.5 m; 3 directors = sloping 25-mm guys, 67.9 m; single 81.91-m (0.5 wavelength)
+radial system, 2 mm diameter, uniform segmentation: 21 segments per 1/2
+wavelength (where used); NEC-4.
+
+Soil Type         Gain  TO Angle    Front-to Back     Source Impedance
+                  dBi   degrees     Ratio dB          R +/- J X Ohms
+
+No Radials
+Very Poor         2.15  25          19.92             3256 + j 3760
+Poor              3.70  23          23.84             3329 + j 3806
+Good              4.78  20          28.12             3350 + j 3854
+Very Good         6.86  15          36.07             3410 + j 3893
+
+32 Radials, 1/2 wavelength long, at ground level
+Very Poor         2.64  26          22.38             3234 + j 3818
+Poor              4.03  23          26.41             3331 + j 3843
+Good              4.99  20          30.16             3362 + j 3878
+Very Good         6.90  15          36.41             3415 + j 3897
+
+32 Radials, 1/2 wavelength long, 0.001 wavelength below ground
+Very Poor         3.27  27          25.54             3316 + j 4000
+Poor              4.28  24          27.67             3364 + j 3937
+Good              5.08  20          31.29             3390 + j 3917
+Very Good         6.91  15          36.10             3420 + j 3905
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Table 5.  7-element parasitic array:  Version B
+
+Driver = 79.2-m vertical, 25 mm diameter; 3 reflectors = sloping 2-mm guys, 82
+m; 3 directors = sloping 2-mm guys, 71 m; single 81.91-m (0.5 wavelength) radial
+system, 2 mm diameter, uniform segmentation: 21 segments per 1/2 wavelength
+(where used); NEC-4.
+
+Soil Type         Gain  TO Angle    Front-to Back     Source Impedance
+                  dBi   degrees     Ratio dB          R +/- J X Ohms
+
+No Radials
+Very Poor         1.94  25          22.02             2701 + j 2431
+Poor              3.55  23          26.85             2698 + j 2325
+Good              4.66  20          31.97             2724 + j 2266
+Very Good         6.77  15          33.13             2706 + j 2185
+
+32 Radials, 1/2 wavelength long, at ground level
+Very Poor         2.48  26          25.44             2779 + j 2398
+Poor              3.90  23          30.75             2732 + j 2294
+Good              4.89  21          33.94             2735 + j 2238
+Very Good         6.81  15          33.31             2706 + j 2178
+
+32 Radials, 1/2 wavelength long, 0.001 wavelength below ground
+Very Poor         3.18  27          30.37             2844 + j 2214
+Poor              4.19  24          33.09             2770 + j 2203
+Good              5.00  21          35.41             2741 + j 2188
+Very Good         6.83  15          32.73             2707 + j 2168
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>All the of models used the same set of element lengths. There is little change if one extends the towers close to the ground (&lt;1 m). As well, it is possible to develop specific reflector and director lengths, not only for each central driven element diameter, but as well for each soil type. However, the reflector will vary only about 1 m across the range of soils used in this study, while the director may vary as much as 4 m.</p>
+  <p>The 6-guy parasitic array does not reach the gain levels of the K8UR optimally phased system for any given soil type. The K8UR advantage in gain is a consistent 0.6 dB, largely because the beamwidth of the parasitic array is about 35 degrees wider between -3 dB points than the fully phased array. The beamwidth of the parasitic guy array varies between 128 and 129 degrees for all versions. As well, the 6-guy system does not cancel out the very high angle radiation as well as an optimally phased K8UR array.</p>
+  <p>Compared to the 4-guy system, the 6-guy array has slightly less gain (0.3 to 0.4 dB), but equal front-to-back potential. Unlike the 4-guy system, the parasitic element lengths are less critical, especially the directors. For instance, over very good ground, one model varied the length of the director by a total of 5 m with a net change of gain of 0.05 dB and a net change of front-to-back ratio of under 2 dB. The reflector lengths are somewhat more critical. However, the key is to keep all directors and all reflectors as close to the same length as feasible. Once this is achieved during construction, one gains the advantage of operational simplicity in the 6-guy array: once set, it requires no operational adjustments and few mechanical adjustments over the lifetime of the system.</p>
+  <center>
+    <img src="160s-24.gif" width="650" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In <b>Fig. 24</b>, we can see the modeled gain differences among the different modeled radial systems. As soil quality improves, the differentials in gain disappear. Even with Very Poor soil. there is a maximum differential of about 1.1 dB between the no-radial and the buried radial models for the fat-element version shown in the graph. The thin-element version shows a differential of 1.25 dB.</p>
+  <center>
+    <img src="160s-25.gif" width="647" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 25</b> shows differentials in front-to-back ratio, using the fat main element. Once again, the greatest differential occurs over Very Poor Soil and amounts to about 5 dB. As the soil quality improves, the differentials decrease. The thin element numbers can be easily garnered from <b>Table 5</b>.</p>
+  <center>
+    <img src="160s-26.gif" width="640" height="270" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In <b>Fig. 26</b>, we can compare the performance of the radial-less version of the antenna over various soils, using overlaid elevation patterns. Since the far-field performance is not just a function of what is occurring within the near-field region of the antenna, but depends also on the soil quality at a distance in the so-called Fresnel zone, we expect rising performance with improved soil quality. Anyone interested in a study of the antenna in more complex soil conditions can create an inner and outer soil quality differentiation using standard NEC capabilities.</p>
+  <p>A secondary factor involved with soil quality is the elevation angle of maximum radiation (Take-Off or TO angle). Here, the tables make a good guide to modeling report numbers. Although all three versions of each of the two models show a 15 degree TO angle over Very Good soil, we should also note the increasing TO angle as we move the radials from ground to below-ground level for Very Poor soil. The differences are not large, but they are consistent for both the fat and thin main element models.</p>
+  <p>As main elements go, both the fat and thin elements are short, relative to a resonant length. However, they are both approaching the region in which resistance and reactance approach their peaks. The thinner element is electrically shorter and thus shows lower resistance and reactance numbers at the source. Interestingly, bringing either main element within 1 m of ground suffices to carry the element beyond resonance so that it shows a capacitive reactance.</p>
+  <center>
+    <img src="160s-27.gif" width="529" height="299" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The small changes in antenna performance occasioned by the presence or absence of a radial system under that antenna are bound to arouse questions relative to experiential reports of much greater changes for real 1/2 wl vertical systems. The differential of experience and modeling does not represent a fault of the modeling software, but owes to a quite different factor. Because the model places the source directly on the element, it represents a simplified model of the actual antenna system. An actual antenna might look something like the system on the right of <b>Fig. 27</b>, where a network does more than simply transform impedance for the convenience of the feedline to the remote source. The network also completes the antenna system at ground. For maximum system efficiency (or minimal loss), the source ground point and the antenna base ground point must show zero potential differential. At best, we can only approximate this condition in real systems, and a large radial system is one way to achieve this goal.</p>
+  <p>The simplified model that uses a source placed on the element represents, then, the maximum that such a system can achieve. Any losses in portions of the system not modeled must be separately accounted for, or one must create an adequate model that will accurately show such losses. In the end, one must view even the model using an extensive buried-radial system as a simplified model of the full antenna system. Since each parasitic element--as well as the main element--is coupled to the ground (with or without radials), the results that might emerge from a fully adequate model would be affected in rather complex ways. Even over Very Good soil, where the presence of a radial system appears to have minimal consequences for radiation patterns, overall system effectiveness considerations for physical antennas still make the use of a considerable radial system advisable with 1/2 wl radiators and parasitic elements.</p>
+  <p><b>Some Further Possibilities and Concerns</b></p>
+  <p>On the assumption that implementing the array is feasible enough to entertain further development thoughts, there are a few cautions to observe. Foremost is lightning protection. The matching network should provide a full and heavy path from deep ground to the main element. For many purposes, such a path will yield relatively good protection for the unterminated parasitic elements in the array. However, if the location of the antenna is in any way sensitive, then added protections should be provided to the lower ends of the parasitic guys in the form of very high impedance RF but very low impedance charge paths to ground. At the very least, each parasitic element should be provided with a static discharge path. An array of this order is not a toy and should be treated with the same care as commercial BC installations.</p>
+  <center>
+    <img src="160s-28.gif" width="558" height="398" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Having registered due caution, we can turn to happier potentials of the array. One of the more interesting is the fact that with a switch and a half dozen remote relays, we can steer the direction of the array in 60 degree increments. <b>Fig. 28</b> shows the simplicity of the switching arrangement: a 3-pole, 6-position rotary switch. The object is to convert a director into a reflector with the remote relay adding a length of guy to a director. (Of course, relays with wide terminal separation and high voltage contacts are necessary, and should not be operated with power applied to the antenna.)</p>
+  <p>Since opposing guys will always be of opposite types (reflector or director), the simple switch suffices to provide relay activation, so long as the contacts are properly staggered to direct the antenna according to operator wishes. The indicated clockwise change in direction can be altered to suit the user's needs. Missing from the figure is the return line from each relay coil.</p>
+  <p>For most purposes, the broadness of the array pattern will not yield great increases in signal strength for a single 60 degree change in heading. However, one may also think of the switching arrangement as a rear null direction switch. The switch position might easily become a method of increasing the signal-to-noise ratio by deep-nulling a bit of QRM. The directional capabilities of the system give the array a bit of an advantage over shorter phased systems which would require several towers to achieve the same directional capabilities.</p>
+  <center>
+    <img src="160s-29.gif" width="637" height="319" border="2" vspace="5" hspace="9">
+  </center>
+  <p>As a second potential for the array, consider erecting two of them spaced about 1/2 wl apart. The array might well look like the outline sketch in <b>Fig. 29</b>. For both sub-arrays, the directors are all on one side of the line between the two elements, with all of the reflectors on the other side. If we feed the system in phase, we obtain some interesting improvements in both gain and directivity.</p>
+  <center>
+    <img src="160s-30.gif" width="640" height="400" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 30</b> shows the azimuth pattern of the 250-mm diameter version of the array over good soil at a TO angle of 21 degrees. In exchange for a decrease in the absolute 180 degrees front-to-back ratio, we obtain an entire rear area that is never worse than 18 dB down from the forward lobe. As well, the forward lobe now has a beamwidth of under 64 degrees.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+               Table 6.  Two 7-element parasitic arrays in phase
+
+For each array:  Driver = 79.2-m vertical, 250 mm diameter; 3 reflectors =
+sloping 25-mm guys, 81.5 m; 3 directors = sloping 25-mm guys, 67.9 m;  array
+spacing 81.95 m (1/2 wl); NEC-4.
+
+Soil Type   Gain  TO Angle    Front-to Back     Beamwidth   Source Impedance
+            dBi   degrees     Ratio dB          degrees     R +/- J X Ohms
+
+No Radials
+Very Poor   4.88  26          15.99             63          3837 + j 3726
+Poor        6.46  23          19.06             60          3914 + j 3726
+Good        7.58  21          21.54             58          3793 + j 3750
+Very Good   9.63  15          26.54             56          4062 + j 3733
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p><b>Table 6</b> shows the entire set of numbers reported for the large-diameter version of the array. The smaller diameter figures are similar. For every level of soil quality, the gain increases between 2.75 and 2.8 dB, with a worst-case beamwidth (Very Poor soil) of 63 degrees. As well, the front-to-back ratio reflects the performance around the entire rear section of the pattern.</p>
+  <p>The increase in performance has its price. The dual array is now a single direction affair--or at most, a reversible direction array, if there are two desired directions close to 180 degrees apart. Lost is the ability to swing the array in 60 degree increments at the twist of a switch.</p>
+  <p><b>Conclusion</b></p>
+  <p>The 7-element parasitic-guy array described here is just a design exercise, not intended for implementation in the amateur radio environment. However, it does demonstrate what may be possible in terms of achieving phased performance from a single parasitic array through the judicious placement and dimensioning of guys. In the process of developing the array, the exercise has also let us set into some perspective the fairly poor state of modeling of previous sloping-guy parasitic arrays and to show some directions that promise better modeling results.</p>
+  <p>One final note: the array design (for any frequency and variation of materials) is proprietary and described by permission for information purposes only. Commercial applications may not be undertaken without express permission or license, and a patent application may presently be pending. However unlikely such applications may be, this note is a necessary final word on our foray into developing a nearly perfect parasitic vertical array.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 2-1-2002. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for January, 2002. 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><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a><br>
+  <p class="topics-footer">Topics: <a href='../topics.html#mf'>MF</a>, <a href='../topics.html#vertical'>Vertical</a></p><br>
+</body>
+</html>

content/160/160v.html

@@ -0,0 +1,40 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="MF, Vertical">
+  <title>Modeling 160-Meter Vertical Arrays Index</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Modeling 160-Meter Vertical Arrays</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p>Nowhere else on the amateur allocations are vertical antennas and arrays more widely used than on 160 meters. The advent of antenna modeling software has made the design and analysis of such arrays far easier than earlier pencil-and-paper and cut-and-try methods. In fact, the ease with which one can use modern software tools may also be the root of some problems that beset such array work. One difficulty is a lack of appreciation of what these tools have to offer and where they meet their limits. In some cases, the software offers us more than we know how to use wisely, because we are not fully aware of what the different options really mean. The ground quality options offered to us by modeling software is a case in point.</p>
+  <p>A second group of problems surrounds the availability of shortcuts, again, mostly in the area of ground concerns. NEC-2 offers us a highly accurate Sommerfeld-Norton ground calculating system, but this most commonly used form of NEC does not permit the modeling of buried radial systems. A work-around is the use of radials placed very close to the ground--within about 0.001 wavelength. A more tempting shortcut offered on some implementations of NEC-2 is the MININEC ground. With this system, we simply omit the radials and let the vertical monopole elements touch the ground. Very often we use these alternatives to a buried-radial system without knowing much about their accuracy relative to a more complete model. That lack of knowledge has led to numerous inadequate and possibly misleading models.</p>
+  <p>NEC-4 has the ability to handle buried wires and hence permits the complete modeling of a radial system. The models correlate quite well to reality and to standard calculations used by such engineering efforts in fields such as the AM broadcast industry. The question at hand is how well the short cut and substitute models measure up to full models of arrays using vertical antenna elements.</p>
+  <p>Let's be a bit more specific in what each part of the series will cover. In this first part, we shall examine some baseline data on 1/4 wavelength verticals using various types of modeled ground systems available to us within versions of NEC. In the second part, we shall seek a more comprehensive view and appreciation of the relative effects of soil conductivity and permittivity (relative dielectric constant) on the performance of our baseline antenna model. Since the project will simultaneously involve some problems associated with using the MININEC (no-radial) ground system and with the construction of models of radial systems, we shall tackle both problems in Part 3. The 4th episode will be devoted to a potpourri of models of some common vertically polarized antennas we typically use on 160 meters, as we seek some guidelines for the most adequate modeling possible. In the final installment, we shall look at the suggested use of inner and outer ground qualities to simulate a radial system.</p>
+  <p>This series of items, each which has appeared in <i>The National Contest Journal</i> in 2000-2001, will address these and related questions of significance to modeling 160-meter vertical arrays. Each episode in the 5-part collection will appear at this site after it has appeared in print. I hope the notes are useful to you.</p>
+  <p><a href="160v1.html"><b>1. Some Baseline Data</b></a> (Nov/Dec, 2000, pp. 19-24)</p>
+  <p><a href="160v2.html"><b>2. Appreciating Conductivity and Permittivity</b></a> (Mar/Apr, 2001, pp. 4-9)</p>
+  <p><a href="160v3.html"><b>3. Complex Radial Systems and Limitations of the MININEC (No-Radial) Ground</b></a> (May/Jun, 2001, pp. 3-8)</p>
+  <p><a href="160v4.html"><b>4. A Potpourri of 160-Meter Vertical Antennas and Modeling Issues</b></a> (Jul/Aug, 2001, pp. 4-9)</p>
+  <p><a href="160v5.html"><b>5. The Use of Multiple Ground Qualities in Lieu of Radials</b></a> (Sep/Oct, 2001, pp. 4-9)</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 08-01-01. &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><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#mf'>MF</a>, <a href='../topics.html#vertical'>Vertical</a></p><br>
+</body>
+</html>

content/160/160v1.html

@@ -0,0 +1,447 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="MF, Vertical">
+  <title>Modeling 160-Meter Vertical Arrays Part 1: Some Baseline Data</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Modeling 160-Meter Vertical Arrays<br>
+    Part 1: Some Baseline Data</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p>For rather obvious reasons, 160 meters shows a higher percentage of vertical antennas and arrays relative to the total number of antennas in use than any other band. With the advent of NEC and MININEC, the tools that we use for designing and analyzing antennas for 160 have shifted from hand calculations to computer-aided design programs. However, the more I read, the less content I am that we have a full appreciation for what those modeling programs tell us. No where is the absence of understanding more evident than in the treatment of radial systems, whether they are attached to the antenna as part of its structure or simply lie beneath an independent antenna element.</p>
+  <p>There are two major ways that we might proceed in at least partially correcting this relative vacuum. One is mathematical and has recently been started by Rudy Severns, N6LF, in "Verticals, Ground Systems, and Some History, " QST (July, 2000), 38-44. An alternative route is to do some systematic modeling related to 160-meter vertical antennas and arrays. By capturing in a reasonably comprehensive way the span of results that antenna modeling systems present to us, we can gain some perspective and reasonable expectations of well-wrought antenna models.</p>
+  <p>This series will take the latter approach. In this first part, we shall examine some baseline data on 1/4 wavelength verticals using various types of modeled ground systems available to us within versions of NEC. In the second part, we shall seek a more comprehensive view and appreciation of the relative effects of soil conductivity and permittivity (relative dielectric constant) on the performance of our baseline antenna model. Since the project will simultaneously involve some problems associated with using the MININEC (no-radial) ground system and with the construction of models of radial systems, we shall tackle both problems in Part 3. The 4th episode will be devoted to a potpourri of models of some common vertically polarized antennas we typically use on 160 meters, as we seek some guidelines for the most adequate modeling possible. In the final installment, we shall look at the suggested use of inner and outer ground qualities to simulate a radial system.</p>
+  <p>There is some disputation afoot regarding the adequacy of models of just the sort that we shall examine relative to the performance of the physical antennas modeled. This series will not address that cluster of questions, since that larger topic necessarily involves the use of adequate testing methodology upon actual antennas as one side of the coin. Here, we shall be looking at what sorts of things different kinds of models tell us, and the number of variations on radial system modeling alone will more than fill our plate. However, a thorough understanding of what such models tell us is the other side of the coin under discussion, so I shall not be wholly blind to implications of the work done here.</p>
+  <p>Throughout these episodes, I shall be using both NEC-2 and NEC-4 in commercial implementations--EZNEC, GNEC, and NEC-Win Plus. These programs have input and output facilities that greatly ease the construction and interpretation of models, such as radial-makers, and the like. I shall indicate which level of NEC is used for every model explored. As well, the major output of this study is an array of data presented in tables and graphs. I shall limit text to an amount necessary to take a guided walk through the data, but it would require a book to extract every nuance from the information gathered. You may wish to study the data at length and draw further inferences from them.</p>
+  <h3>The 1/4-Wavelength Vertical Monopole and Its Radial System</h3>
+  <center>
+    <img src="1601-1.gif" width="561" height="465" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    1. The basic 1/4 wavelength monopole and variations among models used in this study.
+  </center>
+  <p>Any model of a 1/4 wavelength vertical monopole must necessarily include several elements, shown in <b>Fig. 1</b>. Of course, there is the vertical element itself. In all cases, I shall use a 40-m tall element that is 25 mm in diameter. (Because metrics are so common in 160-meter antenna work, all dimensions will be in metric form. 25 mm is just under 1" in diameter.) Wherever a radial system is used, it will consist of 2 mm diameter wire (about 0.0787" or between AWG #14 and AWG #12). Everything will be copper for simplicity and because changes of material in these models yield changes in results that have no affect on the trends in which we shall be most interested. The test frequency will be 1.83 MHz, and therefore 1/4 wavelength radials will be 40.96 m long.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 1.  Soil types used in the study.
+
+Soil Type         Conductivity            Permittivity
+                  Siemans/meter           dielectric constant
+Very Poor         0.001                    5
+Poor              0.002                   13
+Good (Average)    0.005                   13
+Very Good         0.0303                  20
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Beneath the antenna will be the ground, as defined by a combination of conductivity and dielectric constant (permittivity). <b>Table 1</b> lists the de facto standard range of values typically used as a fair sampling of the effects of soil quality on antenna performance. In the next part of our exploration, we shall look at the question of whether this short table represents a fair sampling or not. For the moment, we may content ourselves with these categories. Their origin lies in the table of found in <i>The ARRL Antenna Book</i> (p. 3-6), which is itself an adaptation of the table presented by Terman in <i>Radio Engineer's Handbook</i> (p. 709), taken from "Standards of Good Engineering Practice Concerning Standard Broadcast Stations," <i>Federal Register</i> (July 8, 1939), p. 2862.</p>
+  <p>The four levels of soil quality--Very Poor, Poor, Good, and Very Good--have been a standard set of ground quality models since they were placed into early versions of ELNEC by Roy Lewallen, W7EL. Unfortunately, the "Good" category has obtained the alternate label "Average," which may be dubious, even if it is the general default used in most commercial implementations of NEC. Hence, we see more antennas modeled over "Average" ground than any other sort. The practice presents no hindrance to the understanding of models of horizontally polarized antennas, but it may create some limitations in our thinking about verticals for the MF and lower HF region.</p>
+  <p>We shall bypass some inherent limitations of all NEC models at MF and lower HF. NEC presumes a flat uncluttered terrain and a uniform soil constitution beneath the antenna. Neither condition may obtain in any given situation. Although we can model important ground clutter with wire grid assemblies, we cannot capture in a NEC model the stratified soil that may underlie a given antenna site. Since our work will be limited to comparisons among models, these limitations will not affect the results.</p>
+  <p>Now to the crux of the problem with modeling vertical arrays on 160 meters: we can use a considerable number of modeling techniques related to the radial system to make comparisons among antennas. Here is the short list of common radial system modeling techniques:</p>
+  <ul>
+    <li>1. Buried radials: available only in versions of NEC above 2, which in practical terms of commercial implementations, requires NEC-4. Exigencies of modeling wires near the surface usually result in the use of length-tapered elements to yield finite model sizes.</li>
+    <li>2. Elevated radials, within 0.001 wavelengths of ground to simulate buried radials. This is the standard NEC-2 method of handling of radial systems, although there are two major versions:</li>
+    <li>2a. Uniform segmentation of all wires, which results in very large models for adequately segmented antennas with 30 or more radials.</li>
+    <li>2b. Length-tapered elements, which yield smaller models, often able to be run on segment- limited implementations of NEC.</li>
+    <li>3. Use of the MININEC ground (available with the NEC core in versions of EZNEC) without modeling the radial system itself.</li>
+  </ul>
+  <p>To look at the ways in which these modeling systems converge and diverge, we can take a simple 1/4 wavelength monopole for 1.83 MHz and model it in each system using (where relevant) from 4 to 128 1/4 wavelength radials over each type of soil quality shown in Table 1. The number of radials will double in each step. This will give us a baseline of data for making some comparisons among the systems. Throughout, I shall list results in more numeric detail than might be significant for practical operation. Since we are interested in the numerical trends internal to modeling, the added precision of recorded results is wholly appropriate.</p>
+  <h3>Elevated and Buried Radial System Results</h3>
+  <p>The notion of elevated and buried radial systems, as used here, are limited to radial systems near the soil surface. (Placing a radial system on or under the soil is not possible in NEC-2 and placing the radial system at Z=0 in NEC-4 yields unusable results. Hence, our choices are limited.) For NEC-2 or NEC-4, we may follow a standard practice of placing the radial system at the minimum recommended height above ground. For the frequency in use, the 0.001 wavelength recommendation translates into a height of 0.164 m or about 6.5". By simple raising the entire system by this height from its initially modeled ground level, we may use standard uniform segmentation of the elements. However, because a radial system is a complex structure, use of the minimum segmentation levels (about 10 per half wavelength) will often not yield convergence of the model. The models used here employed 20 segments per quarter wavelength. Remember that this type of model is said to simulate buried radials.</p>
+  <center>
+    <img src="1601-2.gif" width="646" height="530" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    2. Gain reports of the 1/4 wavelength monopole over various soil qualities for 4 to 128 radials for an above-ground uniformly segmented model.
+  </center>
+  <p>Although NEC-2 recommends a limit of about 30 wires to a single junction, the limitation does not apply to NEC-4. Therefore, the uniform segmentation models over the various soil types proceeded to 128 radials. Whether NEC-4 can handle this number of wires at a junction for the models involved is indicated by the results. (Even in NEC-2, all of the models easily pass the average gain test, with the highest deviation from a perfect 1.000 appearing with only 4 radials: 1.0397. The 128-radial model produce an average gain test result of 1.0096. However, the average gain test is a necessary but not sufficient test of model adequacy and does not reveal every possible flaw in models.) Table 2 and Fig. 2 provide the data in different forms. For uniform segmentation, the smooth curves in Fig. 2 indicate that nothing erratic happens at the uppermost numbers of radials.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 2.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, uniform segmentation: 20 segments per wire; radials 0.001 wavelength above ground;
+NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  5 wires; 100 segments
+Very Poor         -2.15       27                44.51 + j 22.49
+Poor              -0.51       25                42.07 + j 27.30
+Good               0.51       22                42.84 + j 29.04
+Very Good          2.30       17                43.82 + j 25.37
+
+8-radials:  9 wires; 180 segments
+Very Poor         -1.61       27                38.90 + j  6.11
+Poor              -0.05       24                37.59 + j  9.71
+Good               0.96       22                38.52 + j 11.79
+Very Good          2.74       17                39.64 + j 12.17
+
+16-radials:  17 wires; 340 segments
+Very Poor         -1.42       27                36.80 + j  0.02
+Poor               0.08       25                36.29 + j  2.88
+Good               1.09       22                37.27 + j  4.45
+Very Good          2.90       16                38.14 + j  5.74
+
+32-radials:  33 wires; 660 segments
+Very Poor         -1.38       27                35.93 - j  2.20
+Poor               0.07       24                35.92 + j  0.55
+Good               1.09       22                36.96 + j  1.89
+Very Good          2.93       17                37.87 + j  3.15
+
+64-radials:  65 wires; 1300 segments
+Very Poor         -1.31       27                35.19 - j  2.92
+Poor               0.05       25                35.81 - j  0.21
+Good               1.02       22                37.09 + j  1.22
+Very Good          2.91       16                38.02 + j  2.57
+
+128-radials:  129 wires; 2580 segments
+Very Poor         -1.18       27                34.43 - j  2.57
+Poor               0.11       25                35.43 - j  0.26
+Good               0.98       22                37.07 + j  0.99
+Very Good          2.86       17                38.25 + j  2.52
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>However, the data reported by NEC-4 are interesting in their own right. The region of 16 to 32 radials is where the curves level off and modeling additional radials produces no further significant increases in the modeled far field gain, with the possible exception of the worst soil qualities. Moreover, the curves are nearly congruent, indicating that for each soil type, increasing the number of radials has a similar effect on gain. The impedance data in <b>Table 2</b> indicates a similar set of trends for the source resistance. Indeed, from 32 radials upward, the source impedance changes virtually negligibly.</p>
+  <p>The model sizes listed in <b>Table 2</b> provide ample incentive to use length tapering on the elements to reduce model size. 32 radials of uniform segmentation at the specified density of 20 per 1/4 wavelength overrun the 500-segment limitation of some programs. However, by using length tapering of each wire toward the junction, a 32-radial model requires only 397 segment. The standards of length tapering used in the model are based on two factors. First, the buried radial model will require wires as short as 0.001 wavelength (0.164 m). Hence, this figure became the lower length limit for tapering, with 0.04 wavelength selected as the upper limit. Standard length- segmenting features on programs like EZNEC begin with a wire of the shortest specified length and add wires of progressively doubled lengths until the maximum segment length is reached. The remaining element length is then segmented at a segment length that does not exceed the limit. Second, as shown in a detail of <b>Fig. 1</b>, the segments on either side of the source segment should be the same length as the source segment. For the above-ground radial system, this stricture required a separate source wire from 0.164 m to 0.328 m above ground, with the tapering of the element beginning above that point.</p>
+  <center>
+    <img src="1601-3.gif" width="647" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    3. Gain reports of the 1/4 wavelength monopole over various soil qualities for 4 to 128 radials for an above-ground tapered-length element model.
+  </center>
+  <p>The results from this set of models appear in <b>Table 3</b> and <b>Fig. 3</b>. Impedance values in the table are slightly lower than for the uniformly segmented model simply because the source (which may be pictured as centered in its segment) is located closer to the radial junction. However, the range of values is quite similar, as we would expect from comparable models. The gain curves in <b>Fig. 3</b> are almost clones of those in <b>Fig. 2</b>. Once more the region between 16 and 32 radials marks a practical peak beyond which values do not change significantly by any standard.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001 wavelength
+above ground; NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  31 wires; 61 segments
+Very Poor         -1.90       27                41.91 + j 18.38
+Poor              -0.33       25                40.27 + j 22.38
+Good               0.66       22                41.28 + j 23.89
+Very Good          2.45       17                42.26 + j 21.04
+
+8-radials:  55 wires; 109 segments
+Very Poor         -1.47       27                37.49 + j  3.69
+Poor               0.03       25                36.84 + j  6.82
+Good               1.01       22                37.99 + j  8.78
+Very Good          2.81       17                38.89 + j  9.56
+
+16-radials:  103 wires; 205 segments
+Very Poor         -1.34       27                35.91 - j  1.80
+Poor               0.09       25                36.08 + j  0.89
+Good               1.06       22                37.37 + j  2.61
+Very Good          2.92       16                37.91 + j  4.36
+
+32-radials:  199 wires; 397 segments
+Very Poor         -1.29       27                35.09 - j  3.55
+Poor               0.09       25                35.69 - j  1.05
+Good               1.04       22                37.24 + j  0.48
+Very Good          2.92       16                37.83 + j  2.46
+
+64-radials:  391 wires; 781 segments
+Very Poor         -1.23       27                34.36 - j  3.63
+Poor               0.10       25                35.24 - j  1.36
+Good               1.02       22                36.97 - j  0.10
+Very Good          2.91       16                37.91 + j  1.99
+
+128-radials:  775 wires; 1549 segments
+Very Poor         -1.12       27                33.81 - j  3.04
+Poor               0.17       25                34.80 - j  0.95
+Good               1.03       22                36.51 + j  0.04
+Very Good          2.87       16                37.97 + j  1.89
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>When we bury radials in a NEC-4 model, we should adhere to a number of required and advisable modeling practices. The radial junction is 0.164 m below ground. There must be a segment junction at the Z=0 point. As well the source should be above ground, and its adjacent segment lengths should be equal. These needs dictate that we once more use 0.001 wavelength as the shortest wire length in the tapered length elements, as shown in another detail of <b>Fig. 1</b>. We can place a wire of this length from the radial junction to the ground level and one more above it as the source junction. The length-tapering process then ensures that all of these conditions are met. The choice of the 25 mm diameter main element in all of these models easily meets recommended length-to-diameter ratio recommendations in all versions of NEC. The choice of burying the radials 0.001 wavelength deep was occasioned by the desire to make the models in this episode as structurally comparable as possible. In a future episode, we shall examine techniques for burying radial closer to the ground surface.</p>
+  <center>
+    <img src="1601-4.gif" width="648" height="530" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    4. Gain reports of the 1/4 wavelength monopole over various soil qualities for 4 to 128 radials for an below-ground tapered-length element model.
+  </center>
+  <center>
+    <img src="1601-5.gif" width="646" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    5. Source resistance reports from two models over Very Poor and Very Good soil: above-ground and below-ground radial systems.
+  </center>
+  <p>The results of this model appear in <b>Table 4</b> and <b>Fig. 4</b>. Immediately apparent from the table is the much higher range and higher initial values of source impedance. Only over Very Good soil does the impedance of the 4-radial model approach that shown for the comparable above-ground radial system models. For lesser quality soils, impedances remain higher until we reach the 32- radial models. <b>Fig. 5</b> compares tapered-length above- and below-ground radials systems in terms of the source resistance--limited to Very Poor and Very Good soils to avoid a graphic grid lock of lines. Although the Very Good soil below- and above-ground curves parallel each other, the Very Poor soil resistance lines dramatically show much wider differences. If we use the premise that the below-ground radial system better reflects the situation of most real installations, then the notion that the above-ground system is adequate for modeling radial systems is thrown into jeopardy.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 4.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001 wavelength
+below ground; NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  32 wires; 62 segments
+Very Poor         -4.37       27                87.04 + j 25.31
+Poor              -2.49       25                72.45 + j 19.47
+Good              -0.71       23                60.96 + j 20.42
+Very Good          2.10       17                47.34 + j 14.52
+
+8-radials:  56 wires; 110 segments
+Very Poor         -3.11       28                65.90 + j 18.09
+Poor              -1.51       25                58.63 + j 15.18
+Good              -0.04       23                52.43 + j 15.94
+Very Good          2.60       17                44.34 + j 12.60
+
+16-radials:  104 wires; 206 segments
+Very Poor         -1.61       28                52.71 + j 12.43
+Poor              -0.16       25                49.71 + j 12.18
+Good               0.86       23                46.79 + j 12.83
+Very Good          2.79       16                42.20 + j 11.18
+
+32-radials:  200 wires; 398 segments
+Very Poor         -1.32       27                44.89 + j  7.54
+Poor               0.17       25                43.44 + j  9.55
+Good               1.12       22                42.67 + j 10.46
+Very Good          2.94       17                40.48 + j 10.03
+
+64-radials:  392 wires; 782 segments
+Very Poor         -1.19       27                40.68 + j  4.11
+Poor               0.32       25                39.43 + j  7.08
+Good               1.26       22                39.73 + j  8.50
+Very Good          3.05       17                39.06 + j  9.07
+
+128-radials:  776 wires; 1550 segments
+Very Poor         -1.12       28                38.60 + j  2.18
+Poor               0.17       25                37.32 + j  5.29
+Good               1.03       23                37.91 + j  6.99
+Very Good          2.87       17                37.94 + j  8.27
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The gain curves, read either from the table or the graph, also show a much wider span of values as we add radials. In general, not unexpectedly, the worse the soil quality, the greater the influence of adding more radials to the radial system. Indeed, the span of gain values and their progression, especially in the Very Poor soil category, tends to reflect better some operational reports than do the above-ground radial system models.</p>
+  <h3>Some Miscellaneous Modeling Issues</h3>In setting up the models for developing some baseline data, I restricted the main element diameter to 25 mm in order to easily meet the length-to-diameter requirements within the tapered length models. <b>Table 5</b> tends to show why this move is needed and may serve as a caution about hasty modeling. The first portion of the table shows the results (from 4 to 32 radials) of increasing the element diameter to 0.164 m (a reasonable but approximate substitute for a standard Rohn tower section). With a length-to-diameter ratio of 1:1, the values--although usable for some purposes--show considerable wandering relative to the progressions in <b>Fig. 3</b>, the above-ground tapered length system with a 25 mm element.
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 5.  Increasing the diameter of the vertical monopole to 0.164 m and to 0.25 m.
+
+A. 40-m vertical monopole, 164 mm (0.001 wavelength) diameter; 40.96-m (0.25 wavelength)
+radials, 2 mm diameter; tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001
+wavelength below ground; NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  32 wires; 62 segments
+Very Poor         -1.65       27                40.65 + j 17.92
+Poor              -0.14       25                39.82 + j 21.57
+Good               0.83       22                41.16 + j 23.06
+Very Good          2.64       17                42.11 + j 21.49
+
+8-radials:  56 wires; 110 segments
+Very Poor         -1.65       27                40.11 + j  7.46
+Poor              -0.18       24                39.81 + j 10.76
+Good               0.80       22                41.25 + j 12.80
+Very Good          2.62       17                42.24 + j 14.04
+
+16-radials:  104 wires; 206 segments
+Very Poor         -1.51       27                38.41 + j  2.69
+Poor              -0.10       24                38.77 + j  5.54
+Good               0.88       22                40.30 + j  7.32
+Very Good          2.74       17                41.00 + j  9.36
+
+32-radials:  200 wires; 398 segments
+Very Poor         -1.56       27                38.33 + j  1.12
+Poor              -0.18       25                39.15 + j  3.76
+Good               0.77       22                40.95 + j  5.31
+Very Good          2.66       17                41.76 + j  7.61
+
+B. 40-m vertical monopole, 250 mm (0.001 wavelength) diameter; 40.96-m (0.25 wavelength)
+radials, 2 mm diameter; tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001
+wavelength below ground; NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  32 wires; 62 segments
+Very Poor         -1.19       27                36.97 + j 17.53
+Poor               0.32       25                36.26 + j 20.92
+Good               1.29       23                37.53 + j 22.29
+Very Good          3.10       17                38.47 + j 20.82
+
+8-radials:  56 wires; 110 segments
+Very Poor         -1.26       28                37.07 + j  8.09
+Poor               0.21       24                36.84 + j 11.19
+Good               1.19       22                38.22 + j 13.05
+Very Good          3.01       17                39.21 + j 14.20
+
+16-radials:  104 wires; 206 segments
+Very Poor         -1.42       27                37.94 + j  3.78
+Poor               0.00       25                38.36 + j  6.58
+Good               0.98       22                39.91 + j  8.29
+Very Good          2.84       17                40.67 + j 10.35
+
+32-radials:  200 wires; 398 segments
+Very Poor         -1.52       27                38.33 + j  2.31
+Poor              -0.14       25                39.21 + j  4.93
+Good               0.82       22                41.05 + j  6.46
+Very Good          2.70       16                41.94 + j  8.77
+
+C.  40-m vertical monopole, 250 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, uniform segmentation: 20 segments per wire; radials 0.001 wavelength above ground;
+NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  5 wires; 100 segments
+Very Poor         -1.97       27                44.41 + j 24.37
+Poor              -0.39       24                42.67 + j 28.77
+Good               0.62       22                43.72 + j 30.49
+Very Good          2.43       17                44.73 + j 28.03
+
+8-radials:  9 wires; 180 segments
+Very Poor         -1.57       27                40.01 + j 10.70
+Poor              -0.04       25                39.17 + j 14.23
+Good               0.96       22                40.34 + j 16.30
+Very Good          2.76       16                41.41 + j 17.24
+
+16-radials:  17 wires; 340 segments
+Very Poor         -1.42       27                38.24 + j  5.37
+Poor               0.04       25                38.18 + j  8.34
+Good               1.04       22                39.46 + j 10.06
+Very Good          2.89       17                40.27 + j 11.87
+
+32-radials:  33 wires; 660 segments
+Very Poor         -1.36       27                37.20 + j  3.45
+Poor               0.04       24                37.72 + j  6.23
+Good               1.03       22                39.23 + j  7.75
+Very Good          2.90       17                40.09 + j  9.72
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Increasing the diameter further to .25 m (a bit less than 10") yields values that continuously decrease as we add radials, suggesting their unreliability. However, for above-ground radial system models, returning to the standard or uniform segmentation corrects the difficulty, since at 20 segments per 1/4 wavelength, the length-to-diameter relationships are well within limits.</p>
+  <p>The upshot of this exercise is that it may be very difficult to adequately model some monopole and radial systems where the monopole is very fat and the radials are buried very close to the ground surface. However, in Part 3, we shall show at least one way around this problem.</p>
+  <center>
+    <img src="1601-6.gif" width="648" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    6. NEC-2 and NEC-4 gain reports over Very Good soil for uniformly segmented and tapered- length element models.
+  </center>
+  <center>
+    <img src="1601-7.gif" width="648" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    7. NEC-2 and NEC-4 source resistance reports over Very Good soil for uniformly segmented and tapered-length element models.
+  </center>
+  <p>For those restricted to modeling in NEC-2, the natural question to ask is how well NEC-2 values correspond to those we have so far viewed from NEC-4. Only the figures from <b>Tables 2</b> and <b>3</b> are relevant, since NEC-2 does not permit buried radials. <b>Table 6</b> shows the results of running the <b>Table 2</b> and <b>Table 3</b> models in NEC-2, up to 32 radials to remain within the recommended junction limitations. The figures are well within usable agreement, although the NEC-2 gain numbers tend to run a bit higher and the resistance figures a bit lower than those yielded by NEC-4. <b>Fig. 6</b> compares NEC-2 and NEC-4 standard and tapered-length values for gain, while <b>Fig. 7</b> does the same for the source resistance--both over Very Good Soil. The high degree of parallelism among the curves suggests that NEC-2 is as usable as NEC-4 with respect to these types of modeled radial systems.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 6.  NEC-2 Values for Table 2 and Table 3 models (to 32 radials only).
+
+A.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm diameter,
+uniform segmentation: 20 segments per wire; radials 0.001 wavelength above ground; NEC-2.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  5 wires; 100 segments
+Very Poor         -2.09       27                43.91 + j 20.92
+Poor              -0.50       25                42.00 + j 25.72
+Good               0.53       23                42.60 + j 27.69
+Very Good          2.50       17                41.87 + j 26.15
+
+8-radials:  9 wires; 180 segments
+Very Poor         -1.56       27                38.48 + j  4.94
+Poor              -0.06       25                37.74 + j  8.53
+Good               0.95       23                38.58 + j 10.80
+Very Good          2.86       17                38.53 + j 12.81
+
+16-radials:  17 wires; 340 segments
+Very Poor         -1.37       27                36.36 - j  1.40
+Poor               0.05       25                36.56 + j  1.78
+Good               1.05       23                37.59 + j  3.69
+Very Good          2.98       17                37.49 + j  6.51
+
+32-radials:  33 wires; 660 segments
+Very Poor         -1.29       27                35.19 - j  3.20
+Poor               0.06       25                36.04 - j  0.51
+Good               1.04       23                37.38 + j  1.24
+Very Good          2.99       17                37.39 + j  4.25
+
+B.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm diameter,
+tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001 wavelength above
+ground; NEC-2.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  31 wires; 61 segments
+Very Poor         -1.74       27                40.38 + j 16.41
+Poor              -0.22       25                39.26 + j 20.34
+Good               0.79       23                40.12 + j 22.01
+Very Good          2.73       17                39.71 + j 21.23
+
+8-radials:  55 wires; 109 segments
+Very Poor         -1.36       27                36.57 + j  3.14
+Poor               0.09       25                36.31 + j  6.29
+Good               1.08       23                37.34 + j  8.39
+Very Good          2.99       17                37.39 + j 10.58
+
+16-radials:  103 wires; 205 segments
+Very Poor         -1.23       27                35.06 - j  2.01
+Poor               0.15       25                35.56 + j  0.73
+Good               1.14       23                36.75 + j  2.60
+Very Good          3.07       17                36.69 + j  5.49
+
+32-radials:  199 wires; 397 segments
+Very Poor         -1.18       27                34.17 - j  3.63
+Poor               0.15       25                35.15 - j  1.13
+Good               1.12       23                36.57 + j  0.55
+Very Good          3.07       17                36.64 + j  3.52
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>We have not so far looked at the use of the MININEC ground as a means of simplifying models of vertical antennas. In this system, we simply connect the base of the vertical to ground and omit the ground radials. <b>Table 7</b> corrects this absence in quick order. Note that the source impedance of a model using the MININEC ground calculation system is invariant for the 25-mm and the 250-mm diameter models, since it is calculated by reference to perfect ground and not to the particular soil type specified for the other output figures.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 7.  MININEC Values:  40-m vertical monopole, direct connection to ground (no radials),
+fed at the lowest segment; NEC-4.
+
+A.  25 mm diameter
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+Perfect                                         37.08 + j  6.12
+Very Poor         -1.00       27
+Poor               0.31       25
+Good               1.41       23
+Very Good          3.16       17
+
+A.  250 mm diameter
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+Perfect                                         39.01 + j 12.67
+Very Poor         -0.99       27
+Poor               0.32       25
+Good               1.42       23
+Very Good          3.17       17
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>How we should characterize the gain reports of the MININEC ground simplification might be initially puzzling. However, there is one condition under which the three NEC-based ground systems converge--at 32 radials. For the examples used in this baseline exploration, the gain values for each soil types are very close indeed for the two above-ground systems and the buried system. Fig. 8 shows the convergence, with the MININEC no-radial values shown in the separate higher line. In general, MININEC ground system gain values tend to be overly optimistic relative to those yielded by ground systems using radials.</p>
+  <center>
+    <img src="1601-8.gif" width="650" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    8. 32-radial system gain reports over various soil types for all models, with MININEC-ground (no-radials) added.
+  </center>
+  <p>Although the MININEC no-radial modeling system might be a usable substitute for the above- ground radial systems, it is certainly no substitute for the NEC-4 buried radial system. Simplified MININEC-ground models are wholly insensitive to the variations in source resistance exhibited by the buried-radial system. Moreover, the buried-radial system itself varies from other NEC radial systems by showing performance increases beyond the 32-radial level. As we shall see in Part 3, there are some possible illicit uses of the MININEC no-radial system that can result in significant antenna analysis errors.</p>
+  <p>In general, then, the most sensitive method of modeling 1/4 wavelength monopoles is to use a buried radial system (assuming the actual or proposed antenna will place the radials either on or below ground). However, this technique is available only in NEC-4 among currently available commercial implementations of NEC. Second choice among those restricted to NEC-2 is to use 32-radial models, and to use length-tapering if there is a 500-segment limitation in the program. However, above-ground radial system models will not approach the sensitivity of more adequate methods, especially over Poor to Very Poor soils, if these models are substitutes for a buried radial system.</p>
+  <p>There are contexts in which one should not replace the most sensitive modeling methods with substitutes that are not fully consistent in output with the best techniques. Casual modeling for personal satisfaction is one matter, but serious work is quite another. For modeling which others might treat as authoritative for antenna design, analysis, or selection, only the most sensitive techniques will do, even if reaching this level involves upgrading software or being patient while very large (2500-segment) models run.</p>
+  <p>Although we have established a kind of baseline for 160-meter vertical antenna systems, we have only spot-checked the possible values of conductivity and permittivity that characterize the soils over which we model antennas. To appreciate the ways in which these two parameters affect the outcome of modeling efforts, we shall do a more thorough survey next time.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 03-10-01. &COPY; L. B. Cebik, W4RNL. This item originally appeared in</i> The National Contest Journal <i>(Nov./Dec., 2000), pp. 19-25. 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="160v2.html"><img src="../images/fwdrd.gif" align="bottom" width="36" height="33"> Go to Part 2</a></p>
+  <p><a href="160v.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Series Index</a></p>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#mf'>MF</a>, <a href='../topics.html#vertical'>Vertical</a></p><br>
+</body>
+</html>

content/160/160v2.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="MF, Vertical">
+  <title>Modeling 160-Meter Vertical Arrays Part 2: Appreciating Conductivity and Permittivity</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Modeling 160-Meter Vertical Arrays<br>
+    Part 2: Appreciating Conductivity and Permittivity</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p>In the first installment of this series, we established a data baseline relative to 160-meter 1/4 wavelength vertical antennas, exploring the types of modeled radial systems and the number of radials used in each system. We concluded that, as a model of the typical buried radial system, only a model of a buried system appears to be sufficiently sensitive to changes occasioned by differences in soil quality. Other alternatives have, at best, only limited correlations to the physically buried system.</p>
+  <p>Our exploration was limited by the use of four "standard" soil types, and we raised the question of whether these standards represented a fair sampling of conditions underlying a vertical antenna. This question is part of a larger one: how do the combined effects of soil conductivity and permittivity (relative dielectric constant) influence the performance of vertical antennas within the context of NEC modeling systems?</p>
+  <p>We might take a strictly mathematical approach to this question, since the ground effects are calculated (in the Sommerfeld-Norton ground system that is part of NEC) by standard engineering formulations. However, for many modelers, this approach fails to generate a set of reasonable expectations of antenna performance. Therefore, a second approach may be preferable: to take a standard antenna and ground radial system of varying numbers of radials and to model it using a wide span of combinations of conductivity and permittivity. We shall use this second approach in this episode, with the hope of eliciting some useful patterns of thought about ground effects on a vertical antenna system. Once more, the data tables will outweigh the text by a considerable margin.</p>
+  <h3>Conductivity and Permittivity</h3>Soil conductivity is measurable in units of Siemens (or "mhos") per meter (S/m), the inverse of resistivity in Ohms per meter. Of the two relevant ground quality properties, it is the more intuitive. Measurements are relatively frequency specific so that a general DC or low frequency RF measurement may not be exact for a proposed antenna system in the MF or lower HF region. The calculation systems in which conductivity plays a roles normally do not account for variations in the value by virtue of soil stratification, but instead presume an average value that characterizes a homogenous soil beneath the antenna.
+  <p>Permittivity or the relative dielectric constant is less well understood by many amateurs. The main use of the dielectric constant with which most of us are familiar pertains to capacitors: a capacitor can become more compact by using a dielectric with a high value. Soils exhibit the same property. Some values of the relative dielectric constant for materials relevant to antennas installation appear in <b>Table 1</b>, which is derives from John D. Kraus, <i>Antennas</i>, 2nd Ed. (1988), pp. 665 and 851.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 1.  Some permittivity (relative dielectric constant) values (from Kraus, Antennas, 2nd
+Ed.).
+
+Material                      Dielectric Constant
+Vacuum                        1.0
+Dry air                       1.0006
+Fresh snow                    1.5
+Clay Soil                     14
+Sandy Soil                    10
+Slate stone                   7
+Urban ground                  4
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Soil qualities are categorized by combinations of values for both conductivity and permittivity. In <b>Table 2</b> is a listing of the soil types found in the table of found in <i>The ARRL Antenna Book</i> (p. 3-6), with the type descriptions truncated. The ARRL table is taken from Terman's <i>Radio Engineer's Handbook</i> (p. 709), which derives from "Standards of Good Engineering Practice Concerning Standard Broadcast Stations," <i>Federal Register</i> (July 8, 1939), p. 2862. Immediately apparent in the <b>Table 2</b> listing is the fact that there are many more soil quality types than the standard four that we used in Part 1.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 2.  Some soil types (from ARRL Antenna Book).
+
+Type                   Conductivity          Permittivity          Category
+Pastoral 1             0.0303                20                    Very Good
+Pastoral 2             0.01                  14
+Flat marshy            0.0075                12
+Pastoral 3             0.006                 13
+Pastoral 4             0.005                 13                    Average (Good)
+Rocky                  0.002                 12-14                 Poor
+Sandy                  0.002                 10
+City                   0.001                  5                    Very Poor
+Heavy Industrial       0.001                  3                    Extremely Poor
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>However, there is a pattern of mutual increases in both conductivity and permittivity, and the range of each is finite. (I have omitted both fresh and salt water as too special to warrant inclusion here.) Conductivity ranges from 0.001 S/m to a bit over 0.03 S/m, with a greater degree of differentiation among lower values. Permittivity values tend to be more linearly arranged, with a maximum value of 20. The minimum "vacuum" or free space value would be 1. With these patterns in mind, we stand a chance of acquiring an appreciation for the relative effects of each of the two variables on vertical antenna performance over the full span of possibilities within a finite project.</p>
+  <p>The span of conductivity values lends itself to a Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, and 34 mS/m. A linear progression of dielectric constants (1, 5, 9, 13, 17, 21) covers this range well. Within the matrix of these values are combinations either exactly or very close to values in the standard soil quality chart. However, if we look at all of the values in the matrix, we might acquire a perspective on the relative effects of each component. Finding where the standard values fit within the overall matrix of possible values is the goal of our exercise.</p>
+  <center>
+    <img src="1602-1.gif" width="703" height="421" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    1. Basic techniques to construct the buried radial system vertical monopole used in developing the data in <b>Tables 3-1</b> through <b>3-8</b>.
+  </center>
+  <p>All we need now is an antenna model to which we can apply these values. Let's use the 1/4- wavelength 40-m tall vertical, 25 mm in diameter, that we employed in Part 1. We shall use a radial system buried 0.001 wavelength deep in the various soils. The model dictates the use of NEC-4, and the details of the fine structure of the tapered-length elements appear in <b>Fig. 1</b>. The radials are 2 mm in diameter, and everything is copper.</p>
+  <h3>The Results</h3>The detailed results of the exercise in systematic modeling appear in <b>Tables 3-1</b> through <b>3-8</b>. Each table represents a different level of conductivity, with sub-tables for each level of dielectric constant in the progression. Each combination of conductivity and permittivity is carried through systems of 4, 8, 16, 32, and 64 radials to check the modeled effects of the radials system size. In the Gain and Source Resistance columns, I have identified the maximum and minimum values. The Source Reactance column identifies the minimum values of reactances for each radial system size as a measure of the nearest approach to resonance.
+  <p>Before walking through the tables themselves to observe some interesting detailed phenomena, we might well show some summary results. For every combination of conductivity and permittivity value, there is a range of gain values and a range of source resistance values as we increase the number of radials from 4 to 64. These figures are indicative of certain important trends in the tables.</p>
+  <center>
+    <img src="1602-2.gif" width="649" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    2. Maximum and average gain differentials for 4 to 64 radial systems and dielectric constant between 1 and 21 plotted against conductivities of 0.001 to 0.34 S/m.
+  </center>
+  <p><b>Fig. 2</b> is a graph of the maximum and the average differential of gain values for changes in the radials system for all values of permittivity for each of the conductivity levels. The importance of showing both sets of numbers together is this: the higher the difference between maximum and average gain values, the greater difference that the value of dielectric constant makes to antenna performance. In contrast, the lower the differential between maximum and average values, the less the importance of the dielectric constant to antenna performance.</p>
+  <p>Two aspects of the graph are of special note. First, as the conductivity value rises above about 0.005 S/m, the difference between the maximum and the average values becomes insignificant. For soils with a conductivity of about 0.008 S/m, the value of permittivity makes no significant difference to antenna performance. Below a conductivity value of about 0.005 S/m, permittivity can make a considerable difference in performance. Second, at the highest values of conductivity explored, the overall change in gain between 4 and 64 radials falls well under 1 dB, regardless of the permittivity value.</p>
+  <center>
+    <img src="1602-3.gif" width="709" height="530" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    3. Maximum and average gain differentials for 4 to 64 radial systems and conductivities of 0.001 to 0.34 S/m plotted against dielectric constants between 1 and 21.
+  </center>
+  <p><b>Fig. 3</b> illustrates the same point from the opposing perspective of permittivity. The graph plots gain differentials for the span of 4 to 64 radials for each level of conductivity against dielectric constant. This graph replicates the conclusion that wide changes in the dielectric constant make little difference to soils with conductivities above the 0.005 S/m level. However, the chart adds another conclusion to our list. Changes in the dielectric constant value in the region from 1 to 9 makes a far greater difference in performance than values above that level.</p>
+  <center>
+    <img src="1602-4.gif" width="649" height="525" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    4. Maximum and average source resistance differentials for 4 to 64 radial systems and dielectric constants between 1 and 21 plotted against conductivities of 0.001 to 0.34 S/m.
+  </center>
+  <p>Similar conclusions derive from examining the source resistance data in the same manner. <b>Fig. 4</b> plots of maximum and average differentials of source resistance, with the lines beginning to merge at the 0.005 S/m level. Above that level of conductivity, differences in permittivity have little effect on the source resistance. To take the obverse perspective, <b>Fig. 5</b> plots the source resistance as a function of the relative dielectric constant for each sampled level of conductivity. Except to repeat the initial conclusion, one might well ignore the lines for conductivity values above 0.005 S/m. The curves for lower values of conductivity show an interesting pattern of effects from changing values of permittivity. Differentials do not peak at the lowest combination of conductivity and permittivity. Instead, peaks occur at different levels of permittivity for each of the lower values of conductivity.</p>
+  <center>
+    <img src="1602-5.gif" width="705" height="526" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    5. Maximum and average source resistance differentials for 4 to 64 radial systems and conductivities of 0.001 to 0.34 S/m plotted against dielectric constants between 1 and 21.
+  </center>
+  <p>The upshot is that higher levels of conductivity show great regularity in gain and source resistance values as they vary while we increase the number of radials in the system. However, at lower levels of conductivity, permittivity plays a more variable role in setting maximum and minimum values of gain and gain differential, as well as source resistance and resistance differentials. To explore this a bit further, let's take a short walk through some of the tables.</p>
+  <h3>A Short Look at the Tables</h3>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-1 through 3-8.  160-meter vertical monopole: 40 m tall, 25 mm diameter; 40.96-m
+(0.25 wavelength) radials, 2 mm diameter, tapered segmentation: 0.001 to 0.04 wavelength
+per wire; radials 0.001 wavelength below ground; NEC-4.  "TO Angle" = elevation angle of
+maximum radiation.  For each sub-table, a trailing "+" means the highest value in that
+category and a trailing "-" means the lowest value in that category, where category is the
+column parameter except for the values of source reactance, in which case the minimum
+values are shown for each level of radials.
+
+Table 3-1.  Conductivity = 0.001
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                     -4.76-        28                     86.13                 34.14
+ 8                     -3.62         28                     65.93                 21.77
+16                     -2.84         27                     53.89                 13.57
+32                     -2.37         28                     46.89                  7.88
+64                     -2.13         28                     42.93                  4.28
+Dielectric constant = 5
+ 4                     -4.37         27                     87.04+                25.31
+ 8                     -3.11         28                     65.90                 18.09
+16                     -2.18         28                     52.71                 12.43
+32                     -1.61         27                     44.89                  7.54-
+64                     -1.32         27                     40.68                  4.11-
+Dielectric constant = 9
+ 4                     -3.80         27                     83.72                 17.87
+ 8                     -3.56         27                     64.66                 14.62
+16                     -1.56         27                     51.87                 11.75
+32                     -0.88         27                     43.49                  8.12
+64                     -0.54         27                     38.93                  4.91
+Dielectric constant = 13
+ 4                     -3.28         27                     79.27                 14.23
+ 8                     -2.11         26                     62.60                 12.19
+16                     -1.13         26                     51.36                 10.94
+32                     -0.39         26                     43.13                  8.66
+64                      0.01         26                     38.30                  5.87
+Dielectric constant = 17
+ 4                     -2.91         25                     76.43                 12.50
+ 8                     -1.74         26                     60.59                 10.98
+16                     -0.79         26                     50.59                 10.24
+32                     -0.03         26                     42.92                  8.94
+64                      0.41         26                     38.00                  6.63
+Dielectric constant = 21
+ 4                     -2.59         25                     74.33                 10.32-
+ 8                     -1.45         26                     59.13                 10.24-
+16                     -0.52         25                     49.82                  9.83-
+32                      0.24         25                     42.80                  9.10
+64                      0.70+        25                     37.93-                 7.21
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-2.  Conductivity = 0.002
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                     -2.80-        25                     72.68                 29.22
+ 8                     -1.90         26                     59.18                 20.31
+16                     -1.26         25                     50.59                 14.44
+32                     -0.83         25                     44.92                 10.17
+64                     -0.58         26                     41.35                  7.11
+Dielectric constant = 5
+ 4                     -2.79         26                     73.51+                25.71
+ 8                     -1.85         25                     59.44                 18.46
+16                     -1.14         25                     50.44                 13.57
+32                     -0.65         26                     44.43                  9.77
+64                     -0.38         25                     40.68                  6.89
+Dielectric constant = 9
+ 4                     -2.68         25                     73.39                 22.33
+ 8                     -1.70         25                     59.27                 16.69
+16                     -0.95         25                     50.16                 12.80
+32                     -0.42         25                     43.95                  9.58
+64                     -0.11         25                     40.04                  6.88-
+Dielectric constant = 13
+ 4                     -2.49         25                     72.45                 19.47
+ 8                     -1.51         25                     58.63                 15.18
+16                     -0.74         25                     49.71                 12.18
+32                     -0.16         25                     43.44                  9.55
+64                      0.17         25                     39.43                  7.08
+Dielectric constant = 17
+ 4                     -2.29         25                     71.39                 17.11
+ 8                     -1.31         25                     58.05                 13.93
+16                     -0.54         25                     49.43                 11.63
+32                      0.06         25                     43.25                  9.50-
+64                      0.42         25                     39.15                  7.28
+Dielectric constant = 21
+ 4                     -2.06         25                     70.02                 15.30-
+ 8                     -1.11         25                     57.27                 12.98-
+16                     -0.34         25                     49.03                 11.21-
+32                      0.27         25                     43.03                  9.52
+64                      0.65+        25                     38.91-                 7.55
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-3.  Conductivity = 0.003
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                     -1.77         24                     66.44                 26.48
+ 8                     -1.01         23                     55.74                 19.15
+16                     -0.44         24                     48.79                 14.29
+32                     -0.04         24                     43.94                 10.72
+64                      0.19         23                     40.72                  8.04
+Dielectric constant = 5
+ 4                     -1.82-        24                     67.10                 24.55
+ 8                     -1.02         24                     56.00                 18.07
+16                     -0.42         24                     48.79                 13.73
+32                      0.01         24                     44.76                 10.46
+64                      0.27         24                     40.42                  7.91
+Dielectric constant = 9
+ 4                     -1.81         24                     67.37+                22.58
+ 8                     -0.98         24                     56.07                 16.98
+16                     -0.36         24                     48.73                 13.18
+32                      0.10         24                     43.56                 10.24
+64                      0.38         24                     40.11                  7.83-
+Dielectric constant = 13
+ 4                     -1.75         24                     67.30                 20.73
+ 8                     -0.91         24                     55.96                 15.98
+16                     -0.27         24                     48.59                 12.70
+32                      0.22         24                     43.36                 10.09
+64                      0.52         24                     39.82                  7.83-
+Dielectric constant = 17
+ 4                     -1.66         24                     66.96                 19.05
+ 8                     -0.82         24                     55.72                 15.07
+16                     -0.16         24                     48.41                 12.27
+32                      0.34         24                     43.17                  9.98
+64                      0.66         24                     39.57                  7.89
+Dielectric constant = 21
+ 4                     -1.55         23                     66.43                 17.58-
+ 8                     -0.71         24                     55.39                 14.28-
+16                     -0.05         24                     48.20                 11.90-
+32                      0.47         24                     43.00                  9.90
+64                      0.80+        23                     39.37-                 7.97
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-4.  Conductivity = 0.005
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                     -0.64         22                     60.19                 23.25
+ 8                     -0.01         22                     52.16                 17.60
+16                      0.45         22                     46.82                 13.77
+32                      0.80         22                     42.93                 10.93
+64                      1.03         23                     40.17                  8.73
+Dielectric constant = 5
+ 4                     -0.68         23                     60.59                 22.36
+ 8                     -0.04         22                     52.34                 17.09
+16                      0.44         22                     46.88                 13.49
+32                      0.80         22                     42.89                 10.80
+64                      1.04         22                     40.06                  8.67
+Dielectric constant = 9
+ 4                     -0.71-        22                     60.88                 21.43
+ 8                     -0.05         23                     52.47                 16.55
+16                      0.44         22                     46.90                 13.20
+32                      0.82         22                     42.84                 10.66
+64                      1.07         22                     39.94                  8.62
+Dielectric constant = 13
+ 4                     -0.71-        23                     60.96                 20.42
+ 8                     -0.04         23                     52.43                 15.94
+16                      0.47         23                     46.79                 12.83
+32                      0.86         22                     42.67                 10.46
+64                      1.12         22                     39.73                  8.50-
+Dielectric constant = 17
+ 4                     -0.71-        23                     61.15+                19.58
+ 8                     -0.04         22                     52.55                 15.50
+16                      0.48         22                     46.87                 12.64
+32                      0.89         23                     42.71                 10.42
+64                      1.16         22                     39.72                  8.56
+Dielectric constant = 21
+ 4                     -0.69         22                     61.14                 18.70-
+ 8                     -0.01         22                     52.52                 15.01-
+16                      0.52         23                     46.83                 12.38-
+32                      0.93         22                     42.65                 10.33-
+64                      1.22+        23                     39.62-                 8.56
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-5.  Conductivity = 0.008
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                      0.26         21                     55.68                 20.58
+ 8                      0.77         21                     49.51                 16.19
+16                      1.15         20                     45.32                 13.14
+32                      1.45         21                     42.17                 10.84
+64                      1.66         21                     39.81                  9.01
+Dielectric constant = 5
+ 4                      0.22         21                     55.92                 20.14
+ 8                      0.74         20                     49.63                 15.93
+16                      1.14         21                     45.36                 12.99
+32                      1.44         20                     42.17                 10.76
+64                      1.66         21                     39.77                  8.98
+Dielectric constant = 9
+ 4                      0.19         20                     56.12                 19.67
+ 8                      0.73         21                     49.73                 15.65
+16                      1.13         21                     45.40                 12.83
+32                      1.44         21                     42.16                 10.68
+64                      1.66         20                     39.73                  8.95
+Dielectric constant = 13
+ 4                      0.17         21                     56.42                 19.20
+ 8                      0.71         21                     49.81                 15.37
+16                      1.12         21                     45.43                 12.67
+32                      1.44         21                     42.15                 10.60
+64                      1.67         21                     39.68                  8.92
+Dielectric constant = 17
+ 4                      0.16         21                     56.42                 18.73
+ 8                      0.70         20                     49.87                 15.10
+16                      1.12         21                     45.45                 12.52
+32                      1.45         21                     42.13                 10.53
+64                      1.68         20                     39.64                  8.90
+Dielectric constant = 21
+ 4                      0.15-        21                     56.52+                18.26-
+ 8                      0.70         21                     49.92                 14.82-
+16                      1.12         21                     45.46                 12.36-
+32                      1.46         21                     42.12                 10.45-
+64                      1.70+        21                     39.60-                 8.88-
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-6.  Conductivity = 0.013
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                      1.04         19                     51.99                 18.19
+ 8                      1.45         19                     47.28                 14.85
+16                      1.77         20                     44.02                 12.47
+32                      2.01         19                     41.51                 10.63
+64                      2.20+        19                     39.54                  9.15
+Dielectric constant = 5
+ 4                      1.02         19                     52.12                 17.96
+ 8                      1.44         19                     47.35                 14.71
+16                      1.75         19                     44.05                 12.38
+32                      2.01         19                     41.51                 10.58
+64                      2.20+        19                     39.52                  9.12
+Dielectric constant = 9
+ 4                      1.00         19                     52.24                 17.74
+ 8                      1.42         19                     47.42                 14.57
+16                      1.74         19                     44.08                 12.30
+32                      2.00         19                     41.52                 10.53
+64                      2.20+        20                     39.51                  9.11
+Dielectric constant = 13
+ 4                      0.98         19                     52.34                 17.51
+ 8                      1.41         19                     47.48                 14.43
+16                      1.73         19                     44.10                 12.21
+32                      2.00         20                     41.52                 10.49
+64                      2.19         19                     39.50                  9.08
+Dielectric constant = 17
+ 4                      0.97         20                     52.44                 17.27
+ 8                      1.40         19                     47.53                 14.29
+16                      1.73         20                     44.13                 12.13
+32                      1.99         19                     41.52                 10.44
+64                      2.19         19                     39.48                  9.06
+Dielectric constant = 21
+ 4                      0.95-        19                     52.53+                17.03-
+ 8                      1.39         19                     47.57                 14.14-
+16                      1.72         19                     44.15                 12.04-
+32                      1.99         19                     42.52                 10.39-
+64                      2.20+        20                     39.37-                 9.05-
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-7.  Conductivity = 0.021
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                      1.70         18                     49.04                 16.17
+ 8                      2.03         18                     45.45                 13.65
+16                      2.28         17                     42.91                 11.81
+32                      2.49         18                     40.90                 10.36
+64                      2.65+        17                     39.28                  9.16
+Dielectric constant = 5
+ 4                      1.69         18                     49.11                 16.05
+ 8                      2.02         18                     45.49                 13.58
+16                      2.28         18                     42.93                 11.76
+32                      2.48         17                     40.91                 10.33
+64                      2.65+        18                     39.27                  9.15
+Dielectric constant = 9
+ 4                      1.67         17                     49.18                 15.94
+ 8                      2.01         18                     45.53                 13.50
+16                      2.27         18                     42.95                 11.71
+32                      2.48         18                     40.92                 10.30
+64                      2.65+        18                     39.27                  9.13
+Dielectric constant = 13
+ 4                      1.66         18                     49.24                 15.82
+ 8                      2.00         18                     45.57                 13.42
+16                      2.26         18                     42.97                 11.67
+32                      2.47         18                     40.92                 10.27
+64                      2.64         18                     39.27                  9.12
+Dielectric constant = 17
+ 4                      1.65         18                     49.30                 15.71
+ 8                      1.99         18                     45.60                 13.36
+16                      2.25         18                     42.98                 11.63
+32                      2.47         18                     40.93                 10.25
+64                      2.64         18                     39.26-                 9.11
+Dielectric constant = 21
+ 4                      1.64-        18                     49.35+                15.60-
+ 8                      1.99         18                     45.63                 13.28-
+16                      2.25         18                     43.00                 11.58-
+32                      2.46         18                     40.93                 10.22-
+64                      2.64         18                     39.26-                 9.10-
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-8.  Conductivity = 0.034
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                      2.26         16                     46.62                 14.44
+ 8                      2.53         16                     43.87                 12.56
+16                      2.73         16                     41.91                 11.15
+32                      2.90         17                     40.32                 10.01
+64                      3.04+        17                     39.00                  9.07
+Dielectric constant = 5
+ 4                      2.26         17                     46.66                 14.39
+ 8                      2.52         16                     43.90                 12.52
+16                      2.73         17                     41.92                 11.13
+32                      2.89         16                     40.33                 10.00
+64                      3.04+        17                     39.00                  9.06
+Dielectric constant = 9
+ 4                      2.25         16                     46.69                 14.34
+ 8                      2.52         17                     43.92                 12.49
+16                      2.72         16                     41.93                 11.11
+32                      2.89         16                     40.33                  9.99
+64                      3.03         16                     39.00                  9.06
+Dielectric constant = 13
+ 4                      2.24         16                     46.72                 14.28
+ 8                      2.51         16                     43.94                 12.45
+16                      2.72         17                     41.94                 11.08
+32                      2.89         17                     40.34                  9.97
+64                      3.03         16                     39.00                  9.04
+Dielectric constant = 17
+ 4                      2.24         17                     46.76                 14.23
+ 8                      2.51         17                     43.96                 12.41
+16                      2.71         16                     41.95                 11.06
+32                      2.88         16                     40.34                  9.96
+64                      3.03         17                     39.00                  9.04
+Dielectric constant = 21
+ 4                      2.23-        17                     46.79+                14.16-
+ 8                      2.50         16                     43.98                 12.37-
+16                      2.71         17                     41.97                 11.03-
+32                      2.88         17                     40.35                  9.94-
+64                      3.02         16                     39.00-                 9.03-
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>In <b>Table 3-1</b>, we have the lowest value of conductivity examined: 0.001 S/m. Lower values of conductivity have been measured for some antenna sites. However, this table includes the lowest value on the ARRL chart. In fact, the value 0.001 S/m with a dielectric constant of 5 is the Very Poor category. Interestingly, this combination yields the highest source resistance, even though the lowest gain occurs with a 0.001 S/m--1 combination. Although soils with very low conductivity and very high dielectric constant are improbable, the lowest values of reactance occur with the highest values of permittivity for radial systems between 4 and 16 radials. However, for larger radial systems, the lowest reactance values occur with a dielectric constant of 5. (Contrast this variability with <b>Tables 3-5</b> through <b>3-8</b>, where the lowest reactance values for all sizes of radial systems occurs with the highest values of permittivity.)</p>
+  <p>A change in conductivity from 0.001 S/m to 0.002 S/m makes a large difference on the modeled gain performance of the test antenna at lower levels of permittivity, as shown in <b>Table 3-2</b>. However, when we reach a permittivity of 9 (close to the standard of Poor soil), the differences from a conductivity of 0.001 S/m have shrunk considerably. Nevertheless, at this dielectric constant level, differentials between 4 and 64 radial systems level off in the 2.6 dB region--which is still sufficient reason to increase a radial system to the maximum feasible size.</p>
+  <p>In both <b>Tables 3-2</b> and <b>3-3</b> (for conductivities of 0.002 and 0.003 S/m, respectively), we continue to find that the minimum gain values and that maximum source resistance values do not occur at the extremes of the chart. Indeed, minimum gain shows a progression toward a higher values of dielectric constant with increases in conductivity. Maximum source resistance shows the same trend, but does not wind up in the same dielectric constant box as minimum gain.</p>
+  <p><b>Table 3-4</b>, for a conductivity of 0.005 S/m represents a broad middle set of grounds with charted dielectric constants in the 12-14 range. In the table, minimum gain covers a broad range of permittivity--9 to 17, with the peak source resistance appearing at a permittivity of 17. However, for any size radial system, the curves are beginning to broaden. With 64 radials, the modeled gain varies only by 0.19 dB over the entire range of dielectric constants. Nonetheless, considerable variation remains in both the gain and source resistance columns for small to large radial systems.</p>
+  <p>With <b>Table 3-5</b>, we enter the region of greatest regularity in phenomena, indicating the reduced influence of dielectric constant--or, what amounts to the same thing, the domination of conductivity as the major ground factor affecting antenna performance. Both gain and source resistance maximums and minimums occur with a dielectric constant of 21. <b>Tables 3- 6</b> through <b>3-8</b> reflect similar trends. With Very Good soil, or its nearest tabular counterpart (0.034 S/m and 21), the difference between 4 and 64 radials models out at under a 0.8 dB difference in gain--at least for the particular model of a monopole and radial system used in this exercise.</p>
+  <p>Our quick stroll through the tables should be somewhat of a revelation, especially when set against the standard soil quality values displayed in <b>Table 2</b>. In most instances, for a given value of conductivity, the associated value of dielectric constant in the standard listing reflects one of the minimums or maximums, as relevant from the broader modeled <b>Tables 3-1</b> through <b>3-8</b>. At the lower values of conductivity, the dielectric constant not only plays a larger role in determining modeled antenna performance, but as well, that influence varies from one value to the next of conductivity. The standard listing in <b>Table 2</b> tends to capture the maximum combined influence of both factors.</p>
+  <p>As a consequence, the use of the "short" list of four values (Very Poor, Poor, Good, and Very Good) tends to be a fair sampling of the soil quality properties as they influence modeled vertical antenna performance. The large stretch between the values associated with Good soil (0.005 S/m and 13) and those associated with Very Good soil (0.0303 S/m and 20) becomes quite reasonable in view of two factors. First, as conductivity increases greatly, the amount of change in antenna performance for any given size radial system between conductivity steps decreases significantly. Second, variations in the dielectric constant become relatively insignificant. Hence, the seemingly odd values associated with Very Good soil become as good as any other figures for conductivities above 0.02 S/m.</p>
+  <p>There are, of course, very good mathematical reasons for the patterns that we have observed. However, by presenting the calculations in combination with a standardized vertical antenna model, the consequences of those calculation become perhaps a bit more vivid--and perhaps even a bit more useful in establishing patterns of reasonable expectation for antenna models. Of course, the results given here apply to 160 meters and to a 1/4 wavelength monopole with a buried radial system. Rather than extrapolate the results too far from the situation modeled, one should develop a comparable systematic modeling study for such other antenna system structures and frequencies as may be of greatest interest.</p>
+  <p>We have so far limited ourselves to single radial systems and single element vertical arrays. In the next episode, we shall look at ways to develop models of more complex situations, along with some limitations of using the MININEC ground as a substitute for actually modeling radials.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 03-10-01. &COPY; L. B. Cebik, W4RNL. This item originally appeared in</i> The National Contest Journal <i>(Mar./Apr., 2001), pp. 4-9. 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="160v3.html"><img src="../images/fwdrd.gif" align="bottom" width="36" height="33"> Go to Part 3</a></p>
+  <p><a href="160v.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Series Index</a></p>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#mf'>MF</a>, <a href='../topics.html#vertical'>Vertical</a></p><br>
+</body>
+</html>

content/160/160v3.html

@@ -0,0 +1,257 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="MF, Vertical">
+  <title>Modeling 160-Meter Vertical Arrays Part 3: Complex Radial Systems</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Modeling 160-Meter Vertical Arrays<br>
+    Part 3: Complex Radial Systems and<br>
+    Limitations of the MININEC (No-Radial) Ground</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p>In our examination of 160-meter vertical antenna modeling, we have noted that it is advisable to model full ground radial systems in lieu of using short-cut methods. As well, models of</p>
+  <p>buried radial systems appear to replicate best actual buried radial systems. We also examined the effects of soil conductivity and permittivity on model predictions, and established that--within limits--the now-traditional soil types that range from Very Poor to Very Good provide a reasonable sampling of modeled vertical antenna behavior.</p>
+  <p>These results strongly suggest that anyone who wishes seriously to model 160-meter vertical antennas or arrays should develop some modeling techniques that allow the efficient development of radial systems. In this episode, we shall look at a few of these techniques. In addition, we shall also examine some further reasons for using them.</p>
+  <h3>Complex Radial System Construction</h3>With simple radial systems consisting of a single set of radials--however many may be required--the "radial-maker" facilities within commercial implementations of NEC provide the most rapid construction. We simply specify the radial parameters and how many we need, and the automated software does the rest. The actual mathematics of radials is fairly simple, but becomes tedious when done with a calculator. With a specimen radial of a certain length, we can obtain the angle for each succeeding radial by dividing the total number need into 360 degrees. If we set the first radial along the X-axis, then the angle and a little sine and cosine work will net us the X and Y coordinates of each radial. We need only calculate for the first 90 degrees of the circle, since the remaining radials will have the same absolute numerical values, with only sign changes to place the new radial in the proper quadrant.
+  <p>Length-tapering the radial elements (and the vertical element as well) proves useful, especially for buried radial systems. In such cases, we need at least a 1-segment wire from the surface (Z=0) to the buried radials. Since the source will be placed as low as possible on the main element above ground and since it is most accurate to have the segments on either side of the source the same length as the source segment, the segments near the junction of the element and radials often require very short lengths. With uniform segmentation, the models become exceptionally large if the radial system is larger than about 16 radials. By tapering the segment lengths toward the junction area to the shortest necessary length, we can reduce the size of the model and speed run times.</p>
+  <p>The technique in its simplest form--with a single set of 1-segment wires handling the source and radial junction region, as shown in Part 1 of this series--limits the main element diameter that we may model accurately. Using a 0.001 wavelength minimum segment length, which is about 0.164 m or 6.5" at 1.83 MHz, element diameters may be limited to something below this figure. Although linear elements may use segment length-to-diameter ratios as low as 1:1, more complex geometries may dictate a larger ratio, sometimes as high as 4:1. For any given case, convergence testing and the average gain test are both applicable to evaluating the adequacy of a model.</p>
+  <p>For fatter main elements or for radials buried at a shallow depth, we may wish to resort to a different technique of modeling radials. See <b>Fig. 1</b>. In this sketch, we have shallow radials and a "fat" main element. Let's suppose that the diameter is about 0.125 m and that we wish to maintain a 4:1 length-to-diameter ratio for each segment. The shortest segment length we can use is 0.5 m. Suppose also that the radials are at some shallow depth under the surface, perhaps 0.05 m. This figure is only 0.0003 wavelength. Using the simple technique of buried radial construction would involve us in modeling conflicts.</p>
+  <center>
+    <img src="1603-1.gif" width="688" height="435" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 1. Modeling tapered-length elements and radials for shallow radial systems or for large-diameter elements.
+  </center>
+  <p>However, we may slope our radials from the main element to the surface and then to the buried level portion of the radial. If the base of the main element is 0.05 m above ground, then two 1-segment wires per radial will satisfy NEC-4 requirements for the radial start. We may then length-taper the remaining portion of each radial. As well, we can set the length of the source region of the main element as a 1-segment wire that is 0.5 m long. Then the main element may be length-tapered above that point. In both cases, a minimum segment length of 0.5 m will satisfy the need for equal segment lengths on each side of the source segment.</p>
+  <center>
+    <img src="1603-2.gif" width="647" height="453" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 2. Simplified sketch of the junction between two intersecting radial systems.
+  </center>
+  <p>If we become serious about modeling 160-meter verticals, then we shall be placing each 1/4 wavelength monopole element on a radial system. For many designs, we may end up with overlapping radial systems. <b>Fig. 2</b> shows a 2-system example, simplified to 16 radials for clarity. Note that three of the radials overlap in this case. To prevent the calculating core from rejecting the model because wires intersect at "mid-segment" points, we can resort to several strategies. Displacing one radial system vertically is one possibility, although it leads to potential models that do not reflect the actual system design. Most overlapping radial systems end up with junctions of the radials that would otherwise overlap. The modeler should thus shorten the radials so that they form a junction along the line labels "radial junction line" in the sketch. The junction points may be connected with an actual modeled wire or left open, according the actual physical radial system being modeled.</p>
+  <center>
+    <img src="1603-3.gif" width="623" height="423" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 3. Simplified sketch of the junction between three intersecting radial systems.
+  </center>
+  <p>In some cases, we may have more than 2 intersecting radial systems. <b>Fig. 3</b> shows three systems, more closely spaced than the pair in <b>Fig. 2</b>. The more closely spaced the main elements in an array, the more intersecting radials we shall encounter. Perhaps the most complex system of which I am aware is a 5 element array, with 4 radial systems forming a square around the central system.</p>
+  <center>
+    <img src="1603-4.gif" width="553" height="418" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 4. Calculating the revised coordinates for intersecting radials.
+  </center>
+  <p>Recalculating the coordinates of radial ends so that the radial intersections are correctly placed and segmented is a straight forward process. <b>Fig. 4</b> can provide some guidance. Let the "main" radial system be centered at X=0 and Y=0. If we know the radial junction line coordinate for at least one axis, we can take the ratio of that coordinate relative to the coordinate of the full length radial. Since we are working with congruent triangles for each radial, the new coordinate in the other axis will be reduced by the same ratio. As well, in a uniformly segmented radial, the ratio will also determine the new level of segmentation for the shortened radial. The new coordinate and segmentation data will equally apply to the radial that intersects the one just calculated.</p>
+  <p>Although the work is a bit tedious, it is necessary to construct reasonably correct models of intersecting radial systems. For large systems, one might transfer the work to a utility program or a spreadsheet.</p>
+  <h3>Why Not Simplify?</h3>The detail work required to set up complex radial systems often leads modelers to accept short-cut methods that yield smaller, simpler models. The standard technique is to use a MININEC ground with no radials, with the attendant assumption that the results approximate those which one might obtain with a full radial system. I suspect that we had better test the assumption.
+  <center>
+    <img src="1603-5.gif" width="458" height="391" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 5. Using tilting 1/4 wavelength monopoles to test the limits of the MININEC no-radial ground system.
+  </center>
+  <p><b>Fig. 5</b> represents our initial test case. Let's set up a vertical over ground. We shall run the vertical over the standard 4 ground qualities (Very Poor, Poor, Good, and Very Good) using 3 systems. First is the MININEC ground with the vertical connected at its lower end directly to the surface--with no radials. The second system is a 32-radial array that is 0.001 wavelength above the ground. The third is a 32-radial array buried 0.001 wavelength below the surface. The choice of 32 radials stems from our observation in Part 1 that with this size radial system, we obtain the closest correlation among modeled results in NEC-4. Radials and the main element will be length- tapered for model economy. As always, the radial systems are set within the Sommerfeld-Norton ground calculation system.</p>
+  <p>Subsequently, we shall perform the same set of modeling runs with the main element tilted from vertical by 30 degrees, 45 degrees, and 60 degrees, as indicated in <b>Fig. 5</b>. If the simplified MININEC no-radial ground system is an adequate approximation of a 32-radial system, then the level of correlation that occurs with the main element exactly vertical should hold up for the tilt-tests.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 1.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25
+wavelength) radials, 2 mm diameter, tapered segmentation: 0.001
+to 0.04 wavelength per wire (where used); NEC-4.
+
+Soil Type      Gain           TO Angle       Source Impedance
+               dBi            degrees        R +/- J X Ohms
+
+A.  Antenna Vertical
+
+MININEC (no-radial) ground
+Very Poor      -1.00          27             37.08 + j  6.12*
+Poor            0.31          25             *MININEC Impedance
+Good            1.41          23             is over perfect
+Very Good       3.16          17             ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor      -1.29          27             35.09 - j  3.55
+Poor            0.09          25             35.69 - j  1.05
+Good            1.04          22             37.24 + j  0.48
+Very Good       2.92          16             37.83 + j  2.46
+
+32 Radials, 0.001 wavelength below ground
+Very Poor      -1.61          27             44.89 + j  7.54
+Poor           -0.16          25             43.44 + j  9.55
+Good            0.86          22             42.67 + j 10.46
+Very Good       2.79          17             40.48 + j 10.03
+
+B.  Antenna Tilted 30 Degrees
+
+MININEC (no-radial) ground
+Very Poor       0.74          32             29.19 - j  0.42*
+Poor            1.37          29             *MININEC Impedance
+Good            1.97          25             is over perfect
+Very Good       3.13          18             ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor      -0.23          31             26.46 - j  7.68
+Poor            0.79          27             26.64 - j  5.59
+Good            1.51          24             27.62 - j  4.19
+Very Good       3.10          18             27.95 - j  2.30
+
+32 Radials, 0.001 wavelength below ground
+Very Poor      -1.74          31             46.21 - j  1.30
+Poor           -0.26          28             40.20 + j  2.82
+Good            0.67          24             37.53 + j  5.67
+Very Good       2.48          18             33.65 + j  5.50
+
+C.  Antenna Tilted 45 Degrees
+
+MININEC (no-radial) ground
+Very Poor       1.77          36             20.36 - j 10.10*
+Poor            2.01          32             *MININEC Impedance
+Good            2.30          27             is over perfect
+Very Good       3.06          19             ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor      -0.07          35             19.55 - j 14.31
+Poor            0.81          31             19.35 - j 12.65
+Good            1.45          26             19.77 - j 11.44
+Very Good       2.94          19             19.63 - j 10.39
+
+32 Radials, 0.001 wavelength below ground
+Very Poor      -2.05          35             39.46 - j  7.78
+Poor           -0.60          31             32.61 - j  3.80
+Good            0.32          26             29.35 - j  0.97
+Very Good       2.12          19             25.01 - j  1.96
+
+D.  Antenna Tilted 60 Degrees
+
+MININEC (no-radial) ground
+Very Poor       3.32          44             10.58 - j 25.59*
+Poor            3.05          37             *MININEC Impedance
+Good            2.93          31             is over perfect
+Very Good       3.07          21             ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor      -0.08          38             11.33 - j 24.68
+Poor            0.74          34             10.77 - j 23.70
+Good            1.34          28             10.78 - j 22.95
+Very Good       2.70          21             10.48 - j 22.34
+
+32 Radials, 0.001 wavelength below ground
+Very Poor      -2.99          42             31.17 - j 16.75
+Poor           -1.51          35             23.80 - j 13.34
+Good           -0.55          30             20.15 - j 10.89
+Very Good       1.26          21             15.69 - j 13.14
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The results of the runs appear in <b>Table 1</b>. In portion A, the results are the same as those presented in Part 1 of this series. Perhaps the only serious departure from a reasonably close correlation of results lies in the source impedance values for the buried radial system.</p>
+  <center>
+    <img src="1603-6.gif" width="648" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 6. Gain reports over various ground qualities for a monopole tilted 30 degrees from vertical.
+  </center>
+  <p><b>Fig. 6</b> summarizes the gain data from portion B of the table. The gain data divergence for Very Poor soil has grown from 0.61 dB for the vertical main element to 2.48 dB for the element with a 30&deg; tilt, with lesser divergence as the soil quality improves. The MININEC ground shows a single impedance value, since it is calculated over perfect ground, while the above-ground radial system shows a tight set of values in the same region. However, the source impedance values for the buried-radial system show a wider spread and coincides with the spread of gain values.</p>
+  <center>
+    <img src="1603-7.gif" width="647" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 7. Gain reports over various ground qualities for a monopole tilted 45 degrees from vertical.
+  </center>
+  <p>The trends noted with respect to the 30-degree tilt model continue through the 45-degree and 60-degree models. Gain values data is summarized in <b>Fig. 7</b> and <b>Fig. 8</b> for these two cases. By the time we reach a 60-degree tilt, over Very Poor soil, the MININEC ground system shows a 3 dB advantage over the above-ground radial system, which in turn shows another 3 dB gain over the buried radial system.</p>
+  <center>
+    <img src="1603-8.gif" width="649" height="530" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 8. Gain reports over various ground qualities for a monopole tilted 60 degrees from vertical.
+  </center>
+  <p>The failure of the MININEC ground to track with the buried radial system stems from the known limitations of the MININEC ground calculation system. Any wire with a horizontal far-field component will display inaccurate results below about 0.2 wavelength from the surface. The error grows greater as we we place the wire closer to the surface. The inaccuracies show up not only in driven elements, but in any array in which one or more parasitic elements fall into the error-prone region of the MININEC ground system. Those inaccuracies affect elements with even the slightest tilt.</p>
+  <p>The "intermediate" level results obtained for the above- ground radial system are also suggestive. The departure of these results from the buried-radial system speak to the limitations of an above-ground radial system as an approximation of a buried radial system. Even in the case of the 32-radial system, the one showing the closest correlation between above-ground and buried radial systems for vertical elements, the divergence of results for tilted main elements suggest that the only good model of a buried-radial system is a buried-radial system model. Unfortunately, these results have economic consequences: since NEC-4 is the main vehicle for method-of-moments modeling of buried radial systems, serious modelers must obtain a license and then either develop their own interfaces or purchase one of the commercial implementations of the NEC-4 core. Outside the U.S., serious modelers may also encounter restrictions in licensure.</p>
+  <h3>A 2-Element Parasitic Vertical Array</h3>Lest the exercise using a tilted vertical be viewed as a Don Quixote sort of quest, let's look at an old standard sort of array using a single sloping parasitic element. We shall take a 25-mm diameter main element, 40 m long, as our driver. The choice of diameters permits us to use a simplified connection for the above-ground and buried radial systems. The parasitic reflector is a 2-mm diameter guy wire that meets the ground or the radial system and which terminates at the position specified in <b>Fig. 9</b>.
+  <center>
+    <img src="1603-9.gif" width="459" height="367" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 9. Outline of a 2-element parasitic vertical array using a sloping guy wire as the reflector.
+  </center>
+  <p>For our test runs, we shall use a MININEC ground with no radials, as is so often done in models of this and very closely similar arrays. We shall also run the model over above-ground and buried radial systems. The radial systems will be intersecting 32-radial arrays, with the line of intersection 13.5 m from each element. As always, we shall run the model over sample ground qualities ranging from Very Poor to Very Good.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 2.  2-element parasitic array:  driver = 40-m vertical
+monopole, 25 mm diameter; reflector = sloping 2-mm guy, 40.5 m
+long; intersecting 32 40.96-m (0.25 wavelength) radial system, 2
+mm diameter, tapered segmentation: 0.001 to 0.04 wavelength per
+wire (where used); NEC-4.
+
+Soil Type      Gain           TO Angle  Front-to Back       Source Impedance
+               dBi            degrees   Ratio dB            R +/- J X Ohms
+
+MININEC (no-radial) ground
+Very Poor       2.00          30        11.36               40.19 + j 53.02*
+Poor            3.34          26        14.25               *MININEC Impedance
+Good            4.62          24        17.11               is over perfect
+Very Good       6.36          18        19.50
+ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor       0.96          30        11.45               65.61 + j 43.13
+Poor            2.23          27        11.56               65.99 + j 46.27
+Good            3.29          24        11.89               65.76 + j 47.90
+Very Good       5.13          17        12.86               59.82 + j 52.06
+
+32 Radials, 0.001 wavelength below ground
+Very Poor       0.97          29        10.79               61.71 + j 41.67
+Poor            2.36          27        10.80               58.24 + j 44.17
+Good            3.51          23        11.16               56.80 + j 46.49
+Very Good       5.50          18        11.36               52.90 + j 47.48
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <center>
+    <img src="1603-10.gif" width="648" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 10. Gain reports for the 2-element array using MININEC and radial-system models.
+  </center>
+  <p><b>Table 2</b> summarizes the results of these runs. <b>Fig. 10</b> summarizes the gain data. For this system, in which the parasitic element forms an angle of about 34 degrees to the plane of the driver, both radial system gain reports are consistent for all of the soil types. However, the MININEC ground system reports gains that are about 1 dB higher for all soil types.</p>
+  <center>
+    <img src="1603-11.gif" width="644" height="526" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 11. Front-to-back ratio reports for the 2-element array using MININEC and radial-system models.
+  </center>
+  <p><b>Fig. 11</b> reveals an even greater weakness of the MININEC no- radial system for this type of array. The front-to-back figures for the two radial systems do not perfectly coincide, but are reasonably close for operational purposes. In contrast, the MININEC no-radial system shows a nearly linear increase in the front-to-back ratio as we move from one soil quality to the next better soil quality. Over Good soil (conductivity = 0.005, dielectric constant = 13), there is a full 5 dB over-estimation of the front-to-back ratio relative to either radial system.</p>
+  <center>
+    <img src="1603-12.gif" width="650" height="530" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 12. Source resistance reports for the 2-element array using MININEC and radial-system models.
+  </center>
+  <p>Similar divergences between the MININEC no-radial system of modeling vertical arrays and the two radial systems show up in the figures calculated for the source impedance. The reactances do not vary significantly among the models. However, as shown in <b>Fig. 12</b>, the source resistance values do vary considerably. The MININEC no-radial system calculates a single value over perfect ground--a value that fails to come close to the values calculated by either radial system. Interestingly, the buried-radial system shows a steadier decline in source resistance as we change soil types than does the above-ground system--another suggestion that neither one is a fully adequate approximation of the other.</p>
+  <center>
+    <img src="1603-13.gif" width="640" height="270" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    Fig. 13. Comparative elevation patterns for the 2-element array using the MININEC no-radial ground and using a 32-radial buried radial system.
+  </center>
+  <p>The different analyses of the array appear striking in elevation plots. <b>Fig. 13</b> overlays the MININEC pattern and the buried-radial pattern for Good soil. The differences are self-explanatory.</p>
+  <p>For practical modeling of vertical arrays, then, the MININEC no-radial system has serious shortcomings in approximating models of radial systems. Its use in serious modeling work is likely unjustified, given the availability of NEC facilities for modeling radial systems of any necessary size. Likewise, above- ground radial systems fail to track adequately with buried-radial systems so that the use of one as an approximation for the other becomes suspect without the modeler laying out situation-specific ground work to justify their use. Since that groundwork would necessarily involve the use of buried radials, one might as well model buried radials with buried radials.</p>
+  <p>I am well aware that 2 examples do not alone make a general case, let alone a trend. so in the final episode of this series, we shall examine a potpourri of antennas and some further antenna modeling issues related to 160-meter verticals.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 03-10-01. &COPY; L. B. Cebik, W4RNL. This item originally appeared in</i> The National Contest Journal <i>(May/Jun., 2001), pp. 3-8. 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="160v4.html"><img src="../images/fwdrd.gif" align="bottom" width="36" height="33"> Go to Part 4</a></p>
+  <p><a href="160v.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Series Index</a></p>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#mf'>MF</a>, <a href='../topics.html#vertical'>Vertical</a></p><br>
+</body>
+</html>

content/160/160v4.html

@@ -0,0 +1,300 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="MF, Vertical, Inverted L">
+  <title>Modeling 160-Meter Vertical Arrays Part 4: A Potpourri of 160-Meter Vertical Antennas and Modeling Issues</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Modeling 160-Meter Vertical Arrays<br>
+    Part 4: A Potpourri of 160-Meter Vertical Antennas and Modeling Issues</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p>So far, I have drawn some tentative conclusions about the inadequacies involved in using the MININEC no-radial system as a substitute for models employing radials, and of similar inadequacies of above-ground radial system models as substitutes for buried-radial system models. The converse of these negatively stated ideas is the following: For radial systems, (usually) only radial-system models will suffice, and for buried-radial systems, (usually) only buried radial-system models will suffice. As general propositions, these statements need further grounding. Although one might resort profitably to an examination of the mathematics of ground calculations, we shall stay with our present mode of demonstrating both the scope and the limits of these propositions by the use of demonstration models. In this way, we can also gain some appreciation of the likely properties of these antennas--or at least of these antenna models.</p>
+  <h3>The Venerable Inverted-L</h3>One of the most popular "beginners" antennas for 160 is the inverted-L. When the total length is approximately 1/4 wavelength, the inverted-L is simply a vertical monopole with the top bent over for structural convenience. The implementations of this antenna are as varied as the circumstances in which they are constructed. However, let's settle for test purposes on a 2-mm diameter wire that is 40 m long.
+  <p>Inverted-Ls vary in shape depending upon the vertical and horizontal territory and supports that are available to the builder. Some are quite tall, with only a small horizontal portion. Others are quite low, in the 10-m height range (about 33'), with the remainder spread horizontally. Therefore, let's test the three versions shown in <b>Fig. 1</b> as a reasonably fair sampling of the diverse forms of the L. As usual in this series, we shall use the MININEC no-radial ground system, the 32-radial above-ground system and the 32-radial buried system as test vehicles. The radial systems will use tapered-length techniques as laid out in earlier installments of the series.</p>
+  <center>
+    <img src="1604-1.gif" width="492" height="276" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    1. Three versions of the inverted-L to be examined over various ground systems and soil qualities.
+  </center>
+  <p><b>Table 1</b> shows the results of modeling the inverted L in its three iterations. As we saw in Part 3 when working with tilted verticals, the MININEC no-radial system results diverge from the radial systems in an ever-more radical manner as we shorten the vertical portion and extend the horizontal portion of the antenna. The pattern of the antenna is stronger away from the horizontal wire by a small amount (1 to 2 dB) so that the patterns are not perfectly circular. The table shows the maximum gain figures.</p>
+  <pre>Table 1.  Inverted-L, 40-m vertical total length, 2 mm diameter; 40.96-m (0.25 wavelength)
+radials, 2 mm diameter, tapered segmentation: 0.001 to 0.04 wavelength per wire (where
+used); NEC-4.
+
+Soil Type              Gain          TO Angle               Source Impedance
+                       dBi           degrees                R +/- J X Ohms
+
+A.  Vertical = 30 m; horizontal = 10 m
+
+MININEC (no-radial) ground
+Very Poor              -0.79         28                     31.64 - j 13.76*
+Poor                    0.38         27                     *MININEC Impedance
+Good                    1.40         24                     is over perfect
+Very Good               3.01         17                     ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor              -1.23         29                     31.18 - j 21.22
+Poor                    0.12         25                     30.91 - j 18.78
+Good                    1.09         23                     31.54 - j 17.62
+Very Good               2.80         17                     32.26 - j 16.85
+
+32 Radials, 0.001 wavelength below ground
+Very Poor              -1.12         29                     35.76 - j  7.66
+Poor                   -0.01         26                     36.34 - j  6.96
+Good                    0.86         23                     36.19 - j  7.09
+Very Good               2.60         17                     34.82 - j  8.00
+
+B.  Vertical = 20 m; horizontal = 20 m
+
+MININEC (no-radial) ground
+Very Poor               0.26         33                     20.32 - j 22.33*
+Poor                    1.01         30                     *MININEC Impedance
+Good                    1.73         25                     is over perfect
+Very Good               2.92         19                     ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor              -0.60         32                     21.04 - j 27.51
+Poor                    0.45         29                     20.64 - j 25.79
+Good                    1.22         26                     20.75 - j 24.94
+Very Good               2.61         19                     21.02 - j 24.87
+
+32 Radials, 0.001 wavelength below ground
+Very Poor              -0.61         33                     25.07 - j 14.62
+Poor                    0.17         29                     25.30 - j 14.33
+Good                    0.86         26                     24.80 - j 14.56
+Very Good               2.30         19                     23.38 - j 15.90
+
+ C.  Vertical = 10 m; horizontal = 30 m
+
+MININEC (no-radial) ground
+Very Poor               2.72         45                      7.73 - j 23.91*
+Poor                    2.54         39                     *MININEC Impedance
+Good                    2.59         33                     is over perfect
+Very Good               2.71         24                     ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor              -0.08         49                     10.22 - j 24.59
+Poor                   -0.43         41                      9.62 - j 24.11
+Good                    0.86         34                      9.23 - j 23.83
+Very Good               1.75         24                      8.78 - j 24.92
+
+32 Radials, 0.001 wavelength below ground
+Very Poor              -0.65         46                     14.57 - j 12.34
+Poor                   -0.37         39                     13.98 - j 12.95
+Good                    0.07         34                     12.86 - j 13.55
+Very Good               1.04         23                     11.09 - j 15.97</pre>
+  <p><b>Fig. 2</b> shows the maximum gain values for the shortest of the inverted-Ls over various soil qualities for each of the three modeled ground systems. The nearly level gain--and its elevated value--for the MININEC no-radial system are once more unrealistic as approximations of the gain values for either radial system. Over poor soil, the difference between the MININEC ground result and the buried radials system result is nearly 3.5 dB.</p>
+  <center>
+    <img src="1604-2.gif" width="647" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    2. Gain reports for the shortest inverted-L using 3 different ground systems.
+  </center>
+  <p>Similar divergences show up in the source resistance values. For the tallest L, the differences among all three systems are minor. However, for the shortest version, the MININEC value becomes a poor indicator of what a buried-radial system model will show. Whatever the parameter, the different models of ground once more prove inadequate approximations of each other.</p>
+  <h3>A 3-Element Parasitic Array Using Sloping Guys</h3>Since the inverted-L requires only a single radial set, models are simple to construct. In contrast, a 3-element parasitic array of the sort shown in <b>Fig. 3</b> is a far more tedious project. Again, the array is an adaptation of a fairly standard arrangement. The 40-m long driver is 25 mm in diameter. Each 2-mm diameter guy is 38.7 m long and slopes 54 degrees relative to the ground (or 36 degrees relative to the driver). In this array, a loading inductor serves to increase the electrical length of the reflector. Our interest in this particular array stems not only from the differences in reports from using different radial systems, but as well, differences that may emerge in the required value of the loading inductor to achieve maximum front-to-back ratio.
+  <center>
+    <img src="1604-3.gif" width="544" height="328" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    3. Outline of the 3-element parasitic array to be examined over various ground systems and soil qualities.
+  </center>
+  <p>Each element base is centered in a radial system for other than the MININEC no- radial test runs. <b>Fig. 4</b> is a screen "grab" of the length-tapered intersecting 32-radial system used with the model for the test runs. There are 26 intersections. The initial model with uniform segmentation required 99 wires and 1559 segments. With length-tapering, the model has shrunk to 1015 segments, but needs 619 wires. The obvious question is whether the added work of setting up the model over a radial system is worth the effort.</p>
+  <center>
+    <img src="1604-4.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    4. Sketch of 3 intersecting radial systems, 32 radials each, used with the 3- element parasitic array.
+  </center>
+  <p>The results appear in <b>Table 2</b>. The divergence in gain among the three ground systems is perfectly in parallel with results obtained for other arrays with sloping parasitic guys. Over Very Poor soil, the MININEC system shows over 4.5 dB of excess gain, although this shrinks to about 1.1 dB over Very Good soil. Interestingly, the above-ground radial system shows better gain than the buried system when over Very Poor soil, but less gain over Very Good soil.</p>
+  <pre>Table 2.  3-element parasitic array:  driver = 40-m vertical monopole, 25 mm diameter;
+reflector and director = sloping 2-mm guy, 38.7 m long; intersecting 32 40.96-m (0.25
+wavelength) radial system, 2 mm diameter, tapered segmentation: 0.001 to 0.04 wavelength
+per wire (where used); NEC-4.
+
+Soil Type              Gain          TO Angle       Front-to Back         Source Impedance
+                       dBi           degrees        Ratio dB              R +/- J X Ohms
+
+MININEC (no-radial) ground: Load = 2.87 uH, Q = 300
+Very Poor               4.85         29             20.85                 15.11 + j 32.45*
+Poor                    5.73         26             23.53                 *MININEC
+Impedance
+Good                    6.75         23             24.92                 is over perfect
+Very Good               8.15         17             27.55                 ground.
+
+32 Radials, 0.001 wavelength above ground:  Load = 2.78 uH, Q = 300
+Very Poor               1.53         28             16.74                 16.95 + j 43.54
+Poor                    2.69         26             16.02                 15.77 + j 43.78
+Good                    3.71         22             15.45                 14.98 + j 43.57
+Very Good               6.14         16             18.20                 14.56 + j 40.27
+
+32 Radials, 0.001 wavelength below ground:  Load = 1.91 uH, Q = 300
+Very Poor               0.15         27             12.23                 14.46 + j 32.44
+Poor                    2.16         25             12.99                 11.93 + j 31.72
+Good                    4.06         22             13.62                 10.12 + j 31.10
+Very Good               6.98         16             15.36                  8.62 + j 27.93</pre>
+  <p>The most dramatic differences occur in the front-to-back reports, as summarized in <b>Fig. 5</b>. Two facets of the front-to-back ratio are significant. First, the maximum obtainable ratios for the radial systems are mediocre (although operationally usable) compared to the reports of the MININEC no-radial system. The no-radial and the buried-radial systems show parallel curves, but the above-ground system curve does not join the parallel until the transition from Good to Very Good soil.</p>
+  <center>
+    <img src="1604-5.gif" width="650" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    5. Front-to-back ratio reports of the 3-element parasitic array over various grounds.
+  </center>
+  <p>It is impossible to ignore all comparisons to reality, and the front-to-back ratios of the 2-element (in Part 3) and the 3-element parasitic arrays are a case in point. The values reported by the radial system models for both cases are in line with typical 2- and 3-element horizontal parasitic beams. For the 3-element array, only the most highly optimized 3- element horizontal beams show the level of front-to-back ratio reported by the MININEC no- radial model. Yet, it would be difficult to assert that the vertical array uses dimensions that approach any degree of optimization, with the possible exception of refining the loading coil.</p>
+  <p>The loading inductor in the models is the second important area of divergence among the models. To obtain the highest values of front-to-back ratio, the loading inductors were assigned a Q of 300. In other words, the load uses a series value of resistance about 1/300 of the required inductive reactance and its associated inductance at the 1.83 MHz test frequency. The difference in required loading coil between the no-radial and the above- ground radial system represent about 1 Ohm of reactance: 33 Ohms for the MININEC ground model and 32 Ohms for the above-ground radial system. However, to obtain the best front-to-back ratio of which the model was capable with the buried radial system, the loading inductance had to be reduced to about 1.9 uH or 22 Ohms reactance.</p>
+  <center>
+    <img src="1604-6.gif" width="640" height="270" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    6. Elevation patterns of the 3-element parasitic array as modeled over a MININEC (no-radial) ground and over intersecting radial systems both above and below ground.
+  </center>
+  <p><b>Fig. 6</b> shows the elevation patterns for the three models over Good soil. The differences in the predicted patterns among the three ground systems are clearly evident. It is well to be reminded at this point that the data and patterns apply only to the modeled radial systems and that some variance will become apparent with changes in the model. For example, changing radial length and number will likely alter the reported data to some degree, in line with expectations that might emerge from our survey of system ranging from 4 to 128 radials in Part 1.</p>
+  <h3>Where the MININEC Ground System Works</h3>So far we have examined cases in which the results of using the MININEC no-radial system diverge in very significant ways from results obtained from using modeled radial systems. Not all models exhibit such large levels of deviation among models. For example, let's examine a pair of 1/4 wavelength monopoles, each 40 m long and 25 mm in diameter and positioned as shown in <b>Fig. 7</b>. We shall space them 84 m apart, which is just over 1/2 wavelength. The selected separation is intentional so that the 1/4 wavelength radials that we place under each monopole for certain tests do not overlap. Therefore, we end up with elementary though large models for the above-ground and buried radial systems--about 400 wires and 795 segments for length-tapered models. Of course, the MININEC no-radial model is simple by comparison.
+  <center>
+    <img src="1604-7.gif" width="537" height="221" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    7. Two 1/4 wavelength monopoles spaced 1/2 wavelength apart and fed in phase (with non-intersecting radial systems).
+  </center>
+  <p>We shall feed each monopole in phase with the other and examine the results, as we have for each test case so far. <b>Table 3</b> lays out the numbers. <b>Fig. 8</b> graphs the gain figures in order to show that there is little difference among the three modeling systems. In fact, for this particular antenna, the MININEC and the above-ground systems yield figures that are closer than those of the buried-radial system. <b>Fig. 9</b> compares the MININEC no-radial azimuth pattern with the buried-radial model pattern to show that there would be little or no operationally significant difference in the numbers.</p>
+  <pre>Table 3.  Two 40-m, 25-mm diameter monopoles, separated 84 m fed in phase; 40.96-m
+(0.25 wavelength) radials, 2 mm diameter, tapered segmentation: 0.001 to 0.04 wavelength
+per wire (where used); NEC-4.
+
+Soil Type              Gain          TO Angle               Source Impedance
+                       dBi           degrees                R +/- J X Ohms
+
+MININEC (no-radial) ground
+Very Poor               2.96         27                     29.05 - j  7.60*
+Poor                    4.27         25                     *MININEC Impedance
+Good                    5.37         23                     is over perfect
+Very Good               7.11         16                     ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor               2.95         27                     26.40 - j 22.70
+Poor                    4.27         25                     26.95 - j 11.40
+Good                    5.21         22                     28.00 - j 10.80
+Very Good               6.98         17                     28.90 - j 10.30
+
+32 Radials, 0.001 wavelength below ground
+Very Poor               2.36         27                     35.25 - j  2.93
+Poor                    3.84         25                     33.71 + j  1.78
+Good                    4.90         22                     32.80 - j  1.50
+Very Good               6.79         17                     31.32 - j  2.74</pre>
+  <p>The one arena in <b>Table 3</b> in which we find a difference that may be significant is the source impedance figures. Of course, the MININEC values show no variation, while the above-ground radial system figures show only small variations (with the exception of the reactance over Very Poor Soil). The values are for each of the two feedpoints of the 2- element array. As we have noted before, the buried radial system shows a wider range of variation with changes in soil quality and generally higher values than for each of the other ground systems. For this antenna, the variation carries over into the reactance column, where the array appears to be closer to resonance at 1.83 MHz than with either of the other ground modeling systems.</p>
+  <center>
+    <img src="1604-8.gif" width="647" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    8. Gain reports of the two 1/4 wavelength monopoles spaced 1/2 wavelength apart and fed in phase.
+  </center>
+  <center>
+    <img src="1604-9.gif" width="640" height="370" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    9. Azimuth patterns for the in-phase fed pair of monopoles over MININEC (no- radial) ground and over a buried radial system.
+  </center>
+  <p>Despite these differences, all three ground modeling systems would generally be adequate for analyzing the array in question. Where the elements are perfectly vertical, they do not encroach on the error-producing aspects of the MININEC ground. As well, the model lacks potential complications that might be introduced by the use of intersecting radial systems. As a result, we have a type of case in which the simplification of the ground system to a MININEC no-radial model yields reasonable results.</p>
+  <h3>A 1/4-Wavelength Monopole Over 32 Radials Buried at 3 Depths</h3>I have shown exemplary applications of overlapping radial systems, but have not yet shown an example that uses the technique of sloping the first two sections of each radial in order to model either a "fat" monopole or a shallow buried radial system. To rectify this gap, let's consider a monopole that is 250 mm in diameter. As always, we shall leave the top height at 40 m. In addition to working with the fat monopole, let's consider whether the depth of the buried radial system makes a difference to performance. With a 32-radial system, we shall use depths of 0.0005 wavelength (0.082 m or 3.23"), 0.001 wavelength (0.164 m or 6.46"), 0.002 wavelength (0.328 m or 12.91"), 0.003 wavelength (0.492 m or 19.37"), and 0.004 wavelength (0.656 m or 25.82").
+  <center>
+    <img src="1604-10.gif" width="530" height="337" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    10. The model set-up for testing a vertical monopole over a 32-wire radial system buried at 5 depths.
+  </center>
+  <p><b>Fig. 10</b> shows the general modeling set-up for the areas of the antenna nearest the junction. Only the first of the 32 radials is shown, but the separate values for the x and the Z axes appear on the sketch. The objective was to keep the shortest wire or segment length at 1 m, which is 4 times the diameter of the monopole. As well, the length of segments adjacent to the source wire are equal to its length. The models consisted of 164 wires and 460 total segments and were run over the usual span of Very Poor to Very Good Soil.</p>
+  <pre>Table 4.  Vertical monopole, top at 40 m, 250 mm diameter; 32 40.96-m (0.25 wavelength)
+radials, 2 mm diameter, tapered with interior wires slanted; depth 0.0005 wavelength to 0.004
+wavelength, NEC-4.
+
+Depth: 0.0005 wavelength, 0.082 m
+Very Poor              -1.31         28                     43.08 + j 13.11
+Poor                   -0.07         25                     44.68 + j 14.49
+Good                    0.86         22                     44.86 + j 14.64
+Very Good               2.72         17                     43.41 + j 14.34
+
+Depth: 0.001 wavelength, 0.164 m
+Very Poor              -1.30         27                     43.91 + j 13.33
+Poor                   -0.06         25                     44.71 + j 14.56
+Good                    0.87         23                     44.85 + j 14.63
+Very Good               2.72         17                     43.40 + j 14.26
+
+Depth: 0.002 wavelength, 0.328 m
+Very Poor              -1.21         27                     43.36 + j 13.66
+Poor                    0.01         25                     44.15 + j 14.68
+Good                    0.94         22                     44.24 + j 14.65
+Very Good               2.78         17                     42.79 + j 14.09
+
+Depth: 0.003 wavelength, 0.492 m
+Very Poor              -1.14         28                     43.06 + j 14.10
+Poor                    0.06         25                     43.94 + j 14.95
+Good                    0.99         22                     43.92 + j 14.88
+Very Good               2.82         17                     42.46 + j 14.07
+
+Depth: 0.004 wavelength, 0.656 m
+Very Poor              -1.09         28                     42.83 + j 14.73
+Poor                    0.11         25                     43.68 + j 15.54
+Good                    1.03         23                     43.71 + j 15.32
+Very Good               2.85         17                     42.25 + j 14.24</pre>
+  <p>The results of the runs in <b>Table 4</b> yield operationally insignificant but numerically interesting differences for any soil quality. As with the other models which we have surveyed, the results over very poor soil strongly suggest the need for more radials. See Part , which has some data for some systems up to 128 radials. For Very Good soil, 32 radials may suffice.</p>
+  <center>
+    <img src="1604-11.gif" width="651" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    11. Gain reports for a 1/4 wavelength vertical monopole over 32 radials buried at 5 depths.
+  </center>
+  <p>The gain figures represent the most interesting facet of the runs. As shown in the graph in <b>Fig. 11</b>, the radial systems at depths of 0.0005 and 0.001 wavelength are even numerically insignificantly different. The question raised by these two runs is whether the maximum 0.01 gain difference over any one soil represents a trend or a mere artifact of rounding. Deepening the radial system to 0.002 through 0.004 wavelength shows that there is indeed a trend. For the depths modeled, the deeper the radial system, the higher the gain.</p>
+  <p>What these runs do not establish is whether there is a maximum depth below which the performance of the monopole would decrease. The rate of gain increase itself decreases as we move from 0.003 to 0.004 wavelength, suggesting that there is indeed a limit. The differences are not artifacts of the changing radius of the portions of the slanting radials that are above ground. This fact was established by modeling the 25-mm monopole using a single vertical wire below ground to the radial junction. The results of model runs with the radials wholly buried and between 0.001 and 0.004 wavelength below ground appear in <b>Table 5</b>. For the thinner monopole, maximum numerical gain reports appear at different depths of the radial field for each soil type, as indicated by the "+" notations in the table. Although the results of these studies do not yield any particular construction recommendations, since the differences are very small, the trends have their own fascination.</p>
+  <pre>Table 5.  Vertical monopole, top at 40 m, 25 mm diameter; 32 40.96-m (0.25 wavelength)
+radials, 2 mm diameter, tapered with single wire to junction; depth 0.001 wavelength to 0.004
+wavelength, NEC-4.
+
+Depth: 0.001 wavelength, 0.164 m
+Very Poor              -1.61         27                     44.89 + j  7.54
+Poor                   -0.16         25                     43.44 + j  9.55
+Good                    0.86         22                     42.67 + j 10.46
+Very Good               2.79+        17                     40.48 + j 10.03
+
+Depth: 0.002 wavelength, 0.328 m
+Very Poor              -1.29         27                     42.07 + j 12.38
+Poor                   -0.04+        25                     42.48 + j 13.30
+Good                    0.91+        22                     42.36 + j 13.32
+Very Good               2.75         16                     40.87 + j 12.49
+
+Depth: 0.003 wavelength, 0.492 m
+Very Poor              -1.25+        27                     41.98 + j 15.48
+Poor                   -0.04+        25                     42.75 + j 16.20
+Good                    0.89         22                     42.75 + j 16.01
+Very Good               2.70         17                     41.48 + j 14.89
+
+Depth: 0.004 wavelength, 0.656 m
+Very Poor              -1.25+        27                     42.28 + j 18.41
+Poor                   -0.06         25                     43.23 + j 19.00
+Good                    0.85         22                     43.27 + j 18.68
+Very Good               2.62         16                     42.24 + j 17.24</pre>
+  <p>Other buried-radial questions abound and are ripe for detailed and systematic modeling. For example, we have examined only 1/4 wavelength radials: other radial lengths have been recommended for various reasons. Moreover, this set of runs was made for 1.83 MHz only. The runs do not tell us what the modeling reports would be for various depths on other amateur bands on which the use of vertical antennas and arrays is common. All of that we shall leave as unfinished business (or, as texts are fond of saying, as exercises for the reader).</p>
+  <p>There are a myriad of other modeling questions associated with verticals that we shall also have to leave unanswered. For example, there is evidence in preliminary models that the required length of phasing line required to establish a maximum rear null in 1/4- wavelength monopole spaced 1/4 wavelength apart will vary somewhat with the soil quality. How this variation itself varies with the size and depth of a radial field remains unanswered. To this question we might also add one about 1/2 wavelength near-ground verticals that are base fed. Preliminary models suggest that only minor changes in performance occur with various types of radial systems beneath the antenna, a result that is at odds with user experiential reports. However, what remains to be developed are models that adequately handle all of the aspects of the antenna system, including the usual source-matching system that places a network between the base of the antenna and the ground.</p>
+  <p>To these questions, we may add any number of others that involve the development of adequate models of various arrays. One final simplification technique remains to be treated: the use of inner and outer ground qualities to simulate a radial system. We shall examine that proposal in the final episode of this series.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 07-25-01. &COPY; L. B. Cebik, W4RNL. This item originally appeared in</i> The National Contest Journal <i>(Jul/Aug, 2001), pp. 4-9. 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="160v5.html"><img src="../images/fwdrd.gif" align="bottom" width="36" height="33"> Go to Part 5</a></p>
+  <p><a href="160v.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Series Index</a></p>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#inverted-l'>Inverted L</a>, <a href='../topics.html#mf'>MF</a>, <a href='../topics.html#vertical'>Vertical</a></p><br>
+</body>
+</html>

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="MF, Vertical">
+  <title>Modeling 160-Meter Vertical Arrays Part 5: The Use of Multiple Ground Qualities in Lieu of Radials</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/hat.gif" align="left" width="72" height="84" border="2" vspace="5" hspace="9"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">Modeling 160-Meter Vertical Arrays<br>
+    Part 5: The Use of Multiple Ground Qualities in Lieu of Radials</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p>The final technique for simplifying the modeling of radials caught me by surprise. It consists of using the facility in NEC that allows 2 ground qualities--a set radius for an inner set of values, and from that point onward, some other values. The reasoning goes that a set of radials in effect improves the ground quality. Therefore, setting the inner radius to the length of the radial system at a high conductivity value, with a lesser value from that point outward, would largely replicate the effect of a radial system without requiring the modeling of radials.</p>
+  <p>Since the practice has some currency in various quarters, it deserves an examination, even if we know in advance that the interaction of buried radial systems is quite different from a simple soil quality improvement. We need to see to what degree the modeling technique yields something useful, even by way of indicators of antenna performance. To this end, let's go back to the very beginning of our work in this series and take a further look at the classic 1/4 wavelength monopole.</p>
+  <h3>The 1/4 Wavelength Monopole Over Various Modeled Ground Systems</h3>We have come a long distance from our starting point of looking at 1/4 wavelength monopoles both over radials systems and directly connected to ground with no radials in the model. We have been using the categories of soil quality in <b>Table 1</b> as our bench marks along the way, having established the relative fairness of the spread of values in Part 2.
+  <pre>Table 1.  Soil types used in the study
+
+Soil Type              Conductivity                 Permittivity
+                       Siemans/meter                dielectric constant
+Very Poor              0.001                         5
+Poor                   0.002                        13
+Good (Average)         0.005                        13
+Very Good              0.0303                       20</pre>
+  <pre>Table 2.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001 wavelength
+below ground; NEC-4.
+
+Soil Type              Gain          TO Angle               Source Impedance
+                       dBi           degrees                R +/- J X Ohms
+
+4-radials:  32 wires; 62 segments
+Very Poor              -4.37         27                     87.04 + j 25.31
+Poor                   -2.49         25                     72.45 + j 19.47
+Good                   -0.71         23                     60.96 + j 20.42
+Very Good               2.10         17                     47.34 + j 14.52
+
+8-radials:  56 wires; 110 segments
+Very Poor              -3.11         28                     65.90 + j 18.09
+Poor                   -1.51         25                     58.63 + j 15.18
+Good                   -0.04         23                     52.43 + j 15.94
+Very Good               2.60         17                     44.34 + j 12.60
+
+16-radials:  104 wires; 206 segments
+Very Poor              -1.61         28                     52.71 + j 12.43
+Poor                   -0.16         25                     49.71 + j 12.18
+Good                    0.86         23                     46.79 + j 12.83
+Very Good               2.79         16                     42.20 + j 11.18
+
+32-radials:  200 wires; 398 segments
+Very Poor              -1.32         27                     44.89 + j  7.54
+Poor                    0.17         25                     43.44 + j  9.55
+Good                    1.12         22                     42.67 + j 10.46
+Very Good               2.94         17                     40.48 + j 10.03
+
+64-radials:  392 wires; 782 segments
+Very Poor              -1.19         27                     40.68 + j  4.11
+Poor                    0.32         25                     39.43 + j  7.08
+Good                    1.26         22                     39.73 + j  8.50
+Very Good               3.05         17                     39.06 + j  9.07
+
+128-radials:  776 wires; 1550 segments
+Very Poor              -1.12         28                     38.60 + j  2.18
+Poor                    0.17         25                     37.32 + j  5.29
+Good                    1.03         23                     37.91 + j  6.99
+Very Good               2.87         17                     37.94 + j  8.27</pre>
+  <p><b>Table 2</b> reviews the modeled values in NEC-4 of a 25-mm diameter monopole over various size radial systems and soil qualities, when the 2-mm diameter radials are buried 0.001 Wavelength below ground (about 6.5" at 1.83 MHz, our test frequency). To consolidate the numbers in a different way, <b>Fig. 1</b> graphs the gain in dBi of the monopoles, with each line representing a different soil quality and the individual lines tracing the numbers of radials from 4 to 128. The largest differentials appear in the region from 4 to 16 radials and over the poorest soils. We should not neglect the actual numbers for the gain values.</p>
+  <center>
+    <img src="1605-1.gif" width="647" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    1. Gain values for a 1/4 Wavelength monopole over various size buried radial systems and different soil qualities.
+  </center>
+  <p><b>Fig. 2</b> provides comparable curves for the source resistance calculated by NEC-4 for each of the cases graphed for gain in <b>Fig. 1</b>. As we would expect, the highest values of source resistance and the greatest rates of change occur when the radials are few and the soil is less than of Good quality.</p>
+  <center>
+    <img src="1605-2.gif" width="646" height="529" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    2. Source resistance values for a 1/4 Wavelength monopole over various size buried radial systems and different soil qualities.
+  </center>
+  <p>We have also looked at the type of model that uses no radials, but connects the 1/4 Wavelength monopole directly to ground. In earlier examinations, we looked only at the use of the MININEC ground. In <b>Table 3</b> are values for direct connection to both the MININEC and the Sommerfeld-Norton ground in NEC-4. (The values for a NEC-2 ground may differ, since there is a distinct difference in the treatment of wire approaching and touching ground in the two system. NEC-2 does not permit buried wires, although NEC-4 handles buried wires routinely so long as certain modeling conventions are met.) <b>Fig. 3</b> graphs the pair of gain curves that result from one soil quality to the next. The NEC-4 S-N curve roughly tracks the values from the 4-radial portion of <b>Table 2</b>. However, the MININEC curve reaches values not achieved by even the 64- and 128-radial portions of <b>Table 2</b>.</p>
+  <pre>Table 3.  Direct Connection Values:  40-m vertical monopole, 25 mm diameter, direct
+connection to ground (no radials), fed at the lowest segment; NEC-4.
+
+
+Soil Type              Gain          TO Angle               Source Impedance
+                       dBi           degrees                R +/- J X Ohms
+A.  MININEC ground
+Perfect                                                     37.08 + j  6.12
+Very Poor              -1.00         27
+Poor                    0.31         25
+Good                    1.41         23
+Very Good               3.16         17
+
+B.  Sommerfeld-Norton ground
+Very Poor              -2.26         27                     49.32 + j  8.11
+Poor                   -0.89         25                     48.78 + j 10.52
+Good                    0.31         22                     47.65 + j 11.48
+Very Good               2.48         17                     43.36 + j 10.21</pre>
+  <center>
+    <img src="1605-3.gif" width="651" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    3. Gain values for a 1/4 Wavelength monopole over MININEC and S-N grounds without modeled radials.
+  </center>
+  <p>The technique that we shall try to compare to these modeled results appears in <b>Fig. 4</b>. We set the monopole touching ground. Beneath the antenna and for a radius of 1/4 Wavelength (40.96 m), we set the soil quality to some higher value. In these tests, we shall use a conductivity of about 0.03 S/m, corresponding to Very Good soil. From that radius outward, we shall use Very Poor soil for the contrast.</p>
+  <center>
+    <img src="1605-4.gif" width="490" height="251" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    4. Sketch of a monopole over a dual ground-quality system as a substitute for radials.
+  </center>
+  <p>Theoretically, NEC calculates the source impedance and currents from the inner radius soil quality, and would do so even had we specified the dividing boundary radius as zero. The far field is calculated using the second or outer ground quality. For the sake of this test, I used EZNEC Pro, which permitted runs using either NEC-2 or NEC-4 and gave access to the MININEC ground as well as to the standard NEC grounds (the high accuracy Sommerfeld-Norton ground calculation system and the "fast" or reflection coefficient calculation system). The results appear in <b>Table 4</b>.</p>
+  <pre>Table 4.  Direct Connection Values:  40-m vertical monopole, 25 mm diameter, direct
+connection to ground (no radials), fed at the lowest segment; dual ground:  inner to 40.96 m
+Very Good, outer Very Poor.
+
+Ground System          Gain          TO Angle               Source Impedance
+                       dBi           degrees                R +/- J X Ohms
+A.  MININEC Ground
+NEC-4                   3.16         27                     37.08 + j  6.12
+NEC-2                   1.89         29                     37.08 + j  6.12
+
+B.  "Fast" NEC Ground
+NEC-4                   2.12         29                     35.14 + j  5.37
+NEC-2                  -5.07         29                     179.5 - j 163.0
+
+C.  Sommmerfeld-Norton NEC Ground
+NEC-4                   1.21         29                     43.36 + j 10.21
+NEC-2                   0.04         29                     56.79 + j  9.58</pre>The values shown for the NEC-2 ground calculation systems are in the table largely for reference. They are not considered usable by most modeling software experts. Tradition has used the MININEC ground as a basis for simplified modeling. However, the gain figures for both cores using a MININEC ground exceed the highest value of far-field gain found in <b>Table 2</b> for all but Very Good Soil. Note that the far-field gain is supposed to be a function of the outer soil quality, which was set at Very Poor. As well, the dual ground quality system of modeling does nothing to correct the fact that MININEC ground forces the source impedance to be calculated over perfect ground. At best, the Sommerfeld-Norton ground using NEC-4 yields values of gain and source impedance similar to those for Good soil and 32 buried radials (from <b>Table 2</b>). However, there is a significant difference in the calculated take-off angle for the two models.
+  <p>With respect to the simple 1/4 Wavelength monopole, at least, there is nothing in the data calculations to suggest that a dual ground system in any way provides usable data as a substitute for a buried radial system of any size. Since the closest correlation appeared in a NEC-4 S-N run, which presumes that one has NEC-4 at hand, one might as well model the buried radials in the first place.</p>
+  <h3>A 2-Element Sloping-Parasitic Vertical Array Test</h3>To determine whether the results for a 1/4 Wavelength monopole, as interpreted, represent a case of excessive finickiness, I went back to a model first examined in Part 3 of this series: a 2-element vertical array in which the reflector is a sloping guy wire. The outline of the array appears in <b>Fig. 5</b>. Both the 25-mm diameter driven element and the 2-mm diameter reflector guy are connected to ground--or to a radial system.
+  <center>
+    <img src="1605-5.gif" width="450" height="341" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    5. Sketch of the 2-element sloping-reflector array used as a test model.
+  </center>
+  <p>Because we wish to discover if there is a usable correlation between a dual ground quality system and a buried radial system, I extended the analysis of the array over buried radials. The 1/4 Wavelength length radial systems for the individual elements intersect--how many times being dependent on the number of radials in each system. I used 4, 8, 16, and 32 radials per element, and the resulting radial systems are sketched in <b>Fig. 6</b>.</p>
+  <center>
+    <img src="1605-6.gif" width="600" height="500" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    6. Sketches of the 4 levels of intersecting buried radial systems surveyed with the 2-element sloping-reflector array.
+  </center>
+  <p>The results of the model runs appear in <b>Table 5</b>, which provides values for each of our soil qualities for each level of radial system. <b>Fig. 7</b> provides curves for the gain values, where each line represents a different size radial system. The curves are unexceptional. We should note that the gain barely reaches 5.3 dBi with 32 radials per element over Very Good soil.</p>
+  <pre>Table 5.  2-element parasitic array:  driver = 40-m vertical monopole, 25 mm diameter;
+reflector = sloping 2-mm guy, 40.4 m long; intersecting 40.96-m (0.25 wavelength) radial
+system, 2 mm diameter, 0.001 wavelength below ground, uniform segmentation; NEC-4.
+
+Soil Type              Gain          TO Angle       Front-to Back         Source Impedance
+                       dBi           degrees        Ratio dB              R +/- J X Ohms
+
+4 Radials per element
+Very Poor              -3.03         28              5.89                 102.8 + j 53.58
+Poor                   -1.17         26              6.14                 86.89 + j 44.75
+Good                    0.88         23              7.04                 75.31 + j 47.33
+Very Good               4.03         17              8.84                 62.11 + j 46.58
+
+8 Radials per element
+Very Poor              -1.20         29              7.58                 82.12 + j 50.16
+Poor                    0.29         26              7.96                 73.99 + j 45.63
+Good                    1.94         23              8.62                 68.17 + j 47.52
+Very Good               4.54         17              9.73                 59.75 + j 47.78
+
+16 Radials per element
+Very Poor               0.25         29              9.40                 67.75 + j 49.90
+Poor                    1.49         26              9.54                 65.74 + j 48.23
+Good                    2.77         23              9.96                 63.06 + j 48.75
+Very Good               4.95         18             10.54                 57.70 + j 48.95
+
+32 Radials per element
+Very Poor               1.18         29             10.43                 60.03 + j 48.96
+Poor                    2.34         27             10.61                 59.34 + j 49.10
+Good                    3.40         23             11.04                 58.66 + j 49.77
+Very Good               5.29         17             11.26                 55.72 + j 50.06</pre>
+  <center>
+    <img src="1605-7.gif" width="649" height="528" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    7. Gain values for the 2-element sloping-reflector array over various size buried radial systems and different soil qualities.
+  </center>
+  <p><b>Fig. 8</b> graphs in a similar way the modeled front-to-back ratios achieved by the array variations. The 4-radial-per-element system benefits most from soil quality improvements. However, even over Very Good soil, the model does not achieve an 11.3 dB front-to-back ratio.</p>
+  <center>
+    <img src="1605-8.gif" width="648" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    8. Front-to-back ratio values for the 2-element sloping-reflector array over various size buried radial systems and different soil qualities.
+  </center>
+  <p>If we use a direct connection to ground and no radials, the calculated numbers derived from NEC diverge from those yielded by the buried radial systems. <b>Table 6</b> gives the modeling results of placing the two elements alone over the range of available grounds, including the MININEC ground, the "fast" NEC ground, and the S-N ground. Once more, the latter two are for reference and the general advice not to use these grounds for such purposes remains applicable.</p>
+  <center>
+    <img src="1605-9.gif" width="647" height="526" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    9. Gain values for the 2-element sloping-reflector array over MININEC, "fast, and S-N grounds without modeled radials.
+  </center>
+  <p><b>Fig. 9</b> graphs the gain values for the three sets of NEC-4 runs. Interestingly, the reflection coefficient ground in NEC-4 correlates very well to the MININEC ground. The S-N ground, when used in NEC-4 provides values that coincide roughly with a 12-radial-per- element system, if one can interpolate fairly from the data in <b>Table 5</b>.</p>
+  <center>
+    <img src="1605-10.gif" width="648" height="527" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    10. Front-to-back ratio values for the 2-element sloping-reflector array over MININEC, "fast, and S-N grounds without modeled radials.
+  </center>
+  <p>The correspondence in gain figures between the MININEC ground and the "fast" ground in NEC-4 disappears if we move to the front-to-back column. See <b>Fig. 10</b>. Although the "fast" ground curve is roughly congruent with the MININEC curve, the "fast" ground values are 5 dB lower. The S-N ground curve is much shallower, but the values are high, even when compared to the front-to-back values for the 32-radial-per-element buried radial system model.</p>
+  <pre>Table 6.  2-element parasitic array:  driver = 40-m vertical monopole, 25 mm diameter;
+reflector = sloping 2-mm guy, 40.4 m long; direct connection to ground (no radials); NEC-4.
+
+Soil Type              Gain          TO Angle       Front-to Back         Source Impedance
+                       dBi           degrees        Ratio dB              R +/- J X Ohms
+
+A.  MININEC ground
+Very Poor               2.00         30             11.36                 40.19 + j 53.02*
+Poor                    3.34         26             14.25                 *MININEC
+Impedance
+Good                    4.62         24             17.11                 is over perfect
+Very Good               6.36         18             19.50                 ground.
+
+B.  "Fast" NEC Ground
+Very Poor               2.27         28              6.37                 50.40 + j 29.73
+Poor                    3.50         26              8.63                 50.14 + j 36.48
+Good                    4.67         23             10.82                 51.25 + j 42.49
+Very Good               6.35         18             14.66                 46.64 + j 49.99
+
+C.  Sommmerfeld-Norton NEC Ground
+Very Poor              -0.63         29             10.31                 69.16 + j 38.46
+Poor                    0.85         26             10.78                 65.61 + j 42.24
+Good                    2.35         23             11.81                 62.44 + j 45.83
+Very Good               4.82         18             13.44                 53.33 + j 48.39
+
+Note:  Use of NEC-2 and the S-N ground will yield reports that differ considerably from the
+values produced by NEC-4.  The following listing is simply to display the differential:
+
+D.  Sommmerfeld-Norton NEC Ground--NEC-2
+Very Poor              -11.0         28              0.58                 342.3 - j 169.9
+Poor                   -7.06         26              1.46                 180.3 - j 77.60
+Good                   -3.60         23              3.55                 122.5 + j  4.20
+Very Good               2.94         18             10.16                 61.57 + j 38.79</pre>
+  <p><b>Table 6</b> provides S-N ground data for NEC-2, the version used by most hams. Once more, there is a very large difference in the values reported from yielded by NEC-4 under identical modeling parameter conditions. The values would hardly be useful as anything but artifacts. However, the remaining numbers in <b>Table 6</b> have equally misleading data values and should also be set aside if one is modeling a buried radial system attached to the array in question.</p>
+  <p>The final step in our test is whether using a dual soil-quality system fairs any better than the simple MININEC ground. To examine this question, I altered the model to include Very Good ground under the antenna and Very Poor ground at a distance. Since the model involves radial systems that intersect, with about 1/8 Wavelength between element bases, I chose a radius of 3/8 Wavelength for the inner ground quality (61.43 m at 1.83 MHz). The results of the modeling appear in <b>Table 7</b>.</p>
+  <pre>Table 7.  2-element parasitic array:  driver = 40-m vertical monopole, 25 mm diameter;
+reflector = sloping 2-mm guy, 40.4 m long; direct connection to ground (no radials), fed at the
+lowest segment; dual ground:  inner to 61.43 m (3/8 Wavelength from array center line) Very Good,
+outer Very Poor.
+
+Ground System          Gain          TO Angle       Front-to Back         Source Impedance
+                       dBi           degrees        Ratio dB              R +/- J X Ohms
+
+A.  MININEC Ground
+NEC-4                   6.36         18             19.50                 40.19 + j 53.02
+NEC-2                   6.82         11             18.58                 40.21 + j 53.02
+
+B.  "Fast" NEC Ground
+NEC-4                   6.03         25             14.43                 46.64 + j 49.99
+NEC-2                         No usable values
+
+C.  Sommmerfeld-Norton NEC Ground
+NEC-4                   4.45         25             14.04                 53.33 + j 48.39
+NEC-2                   3.51         11              9.58                 61.57 + j 38.79</pre>Using the normal MININEC ground for the exercise produced excessively high values of gain and front-to-back ratio relative to the buried-radial models--in both NEC-4 and NEC-2. As well, NEC-2 depressed the TO angle by 7 degrees relative to any other report. Although the "fast" and S-N numbers are provided, once more they are no more than reference reports. The end result, however, is that the dual-ground system provides no usable data or even indicators of data for the array in question.
+  <h3>Conclusion</h3>
+  <p>As expected, the dual-ground modeling technique can be as misleading as any other substitute for a direct and detailed model of a buried radial system. The calculations for the way in which radials intersect with a given soil quality when buried is quite different from the calculations for the soil alone. As a result, a radial system is not equivalent with respect to antenna performance to a simple improvement of the soil quality.</p>
+  <p>Thinking of a radial system as an improvement in soil quality may have some utility when the concern is the overall RF ground for a station and its antenna(s). However, that mode of thought can be highly misleading when it comes to calculations that yield potential antenna performance figures. We have looked in review at the results for the standard techniques of simplifying models by placing them without radials over a MININEC ground, and the result is simply that both systems of simplification are equally but separately misleading. The only type of modeling that seems adequate to a buried radial system is a buried radial model. Any suggested simplification would require that we first test the simplified model against a full model with all buried radials modeled. If a reliable correlation appears--and it might, as illustrated in Part 4--then we can use the simplification. However, once we have the full model, the rationale for simplifying seems largely to disappear.</p>
+  <p>As one step in the direction of developing more adequate models of vertical antennas and arrays for 160 meters (or any other band, for that matter), this series has tried to set forth some basics of the varied results that different kinds of models produce, as well as to give some perspective on the divergence in reports yielded by the range of ground qualities that we can model. If any theme emerges from these notes, it should be this: to the degree possible, let us model accurately and without shortcut every possible aspect of a 160-meter vertical antenna or array and begin from the ground up.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 09-25-01. &COPY; L. B. Cebik, W4RNL. This item originally appeared in</i> The National Contest Journal <i>(Sep/Oct, 2001), pp. 4-9. 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="160v.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Series Index</a></p>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Main Index</a><br></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#mf'>MF</a>, <a href='../topics.html#vertical'>Vertical</a></p><br>
+</body>
+</html>

content/a10/ant1.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <title>dB, dBi, and dBd</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/yagicad.gif" align="middle" width="125" height="62" border="2" vspace="5" hspace="10">No. 1: dB, dBi, and dBd<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>A most convenient way to compare power is as a ratio between two powers. For this purpose, we have the decibel or dB. One dB = 10 log (P1/P2), where P1 and P2 are any two powers it is relevant to compare. A power ratio of 2 is 3 dB; a ratio of 4 is 6 dB; a ratio of 10 is 10 dB. These marker points will guide you to intermediate values. Your transceiver output is 100 watts. Your linear output is 800 watts. Hence, your power gain is 9 dB to the antenna.</p>
+  <p>Antennas measure their power gain in the favored direction in dB. Since gain requires 2 powers to make the ratio, where does the second power come from? It comes from a standard reference. For most theoretical studies, the most common reference is dBi, decibels over an isotropic radiator. An isotropic radiator is a geometric point in free space with no material losses that radiates equally well in all directions. My rotatable aluminum backyard dipole at 35 feet over soils with average losses has a gain of over 7.5 dBi.</p>
+  <p>A second standard is dBd, decibels over a dipole in free space made of lossless infinitely thin wire. This theoretic dipole has a gain of 2.15 dBi. Hence, my backyard real dipole has a gain of over 5.35 dBd.</p>
+  <p>For many, if not most of the decisions you will make about antennas, neither dBi nor dBd are the real references. Suppose you wish to buy a 3- element monoband Yagi for 10. What improvement can you really expect over your dipole? Now your own antenna--an aluminum tube (with losses) antenna at a certain height over soil (with certain losses)--becomes the standard. Unfortunately, manufacturers do not rate their antennas by testing them on your mast in your yard. How can you use your knowledge of dBi and dBd to estimate the improvement the prospective antenna will make?</p>
+  <p>One way is to make antenna comparisons theoretically and extrapolate to your yard. Table 1 shows the gain figures for 3 antennas: a pretty good 3-element Yagi, a pretty good 2-element Yagi, and a dipole, all in free space. The 2-element Yagi has a forward gain of about 4.3 dB over the dipole, while the 3-element Yagi adds another 1.8 dB, for a total of 6.1 dB over the dipole. In the favored direction and in front-to-back ratio for nulling out QRM, you can expect similar performance from equivalent antennas mounted at the same height over the same terrain.</p>
+  <pre>Table 1:  Relative Antenna Gain using dBi and dBd and Antennas in Free
+Space
+Antenna        Gain           Gain over      Gain over
+               in dBi         dipole         2-element
+                                             Yagi
+Dipole          2.1           ----           ----
+2-element Yagi  6.4           4.3 dB         ----
+3-element Yagi  8.2           6.1 dB         1.8 dB
+
+Antenna        Gain           Gain over      Gain over
+               in dBd         dipole         2-element
+                                             Yagi
+Real Dipole     0.0           ----           ----
+2-element Yagi  4.3           4.3 dB         ----
+3-element Yagi  6.1           6.1 dB         1.8 dB
+</pre>
+  <p>Do not expect much more improvement than this, even if a manufacturer cites much higher numbers. The beams in this example can be tweaked for a little more gain or a little more front-to-back ratio, but not much and not both at once. And the ability of the antenna to hold its gain and front-to-back ratio over the entire 10-meter band will suffer.</p>
+  <p>As you might expect, it does not matter whether you make the gain comparison starting with figures in dBi or figures in dBd. You will get the same result. The only requirement is that you use the same reference for all your comparison calculations.</p>
+  <p>Since we started with a dipole, the charts seem to prefer dBd. That is an illusion, since we might have as easily started with a quarter-wave vertical, a 2-element Yagi (as column 3 shows), or ZL-Special. Moreover, had we placed the models over real ground, the gain numbers would have been intrinsically higher, beginning with a dipole gain of over 7.5 dBi or 5.4 dBd, but the differences would have been very similar.</p>
+  <p>Fig. 1 shows the free space azimuth patterns for the three antennas. Their relative proportions are identical no matter whether they start with dBi or dBd.</p>
+  <center>
+    <img src="ant1a1.gif" width="640" height="480" border="2" vspace="5" hspace="10">
+  </center>
+  <p>The relative gain of the 2-element Yagi over the dipole is evident, as is the relative gain of the 3-element Yagi over the dipole and the 2-element Yagi. That is what is crucial to know.<br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p><i>Updated 3-17-97. &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><br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <a href="anta.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to An-Ten-Ten-nas Page</a><br>
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+  <br>
+  <br>
+</body>
+</html>

content/a10/ant10.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <title>Notes on 10-Meter Antenna Tuners</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/yagicad.gif" align="middle" width="125" height="62" border="2" vspace="5" hspace="10">No. 10 Notes on 10-Meter Antenna Tuners<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>There are many excellent antenna tuners (ATUs) on the market that will match at 80 or 160 meters. On 10, the match may be more of an illusion than an effective reality with some designs. If you are a dyed-in-the- wool 10-meter operator and use an antenna system that calls for an antenna tuner, you may be better off building your own.</p>
+  <p>So what is wrong with the commercial tuners? (Remember, not all of them are wrong. Compare the points made here with the features you see when you think about buying one.) A number of things go wrong in designs aimed at covering 160-10 meters.</p>
+  <p><b>1. The basic design:</b> Most ATUs use a T-network with series capacitors and a shunt inductor, as schematically shown in Figure 1.</p>
+  <center>
+    <img src="ant10a1.gif" width="373" height="273" border="2" vspace="5" hspace="9">
+  </center>Figure 1. Typical Series-C T circuit.
+  <p>This design is a high-pass filter and provides little, if any, suppression of harmonic energy. One can argue that we should not rely on the ATU to do the job our rig's output circuitry should be doing. That argument is sound, but if there is a design that will also provide some harmonic energy suppression, it may be preferable. Two designs fill the bill.</p>
+  <center>
+    <img src="ant10a2.gif" width="406" height="232" border="2" vspace="5" hspace="9">
+  </center>Figure 2. Typical PI network.
+  <p>Figure 2 shows a PI network with shunt capacitors and a series inductor. It is inherently a low-pass filter.</p>
+  <center>
+    <img src="ant10a3.gif" width="428" height="213" border="2" vspace="5" hspace="9">
+  </center>Figure 3. Typical Series-L T circuit.
+  <p>The circuit in Figure 3 is also a high-pass filter: it is a T-circuit with series inductors and a shunt capacitor.</p>
+  <p>The reasons for using a series-C T are cost and size. The components for it are smaller for a given power level, since we can fit a 20+ microH coil (rotary or tapped) alongside a pair of 250 pF variable capacitors in a compact case. By contrast, the inductors for the other circuits may require up to and over 30 microH, and the capacitor for the series-L T may need values up to 1000 pF. That is, if you want to tune 80 or 160.</p>
+  <p>If you only want 10 meters, then the values drop. A 5 microH inductor (or 2) and a 250 pF air variable (or 2) give all the range anyone should need for 10.</p>
+  <p><b>2. Tapped inductors:</b> A tapped inductor may do the job you require, but for some antenna situations, you may not be able to find the 1:1 SWR point. That is not fatal if you can find a point under 2:1. However, a good rotary inductor (or 2 in the series-L T circuit) is superior, since there is no required setting that is unavailable to you. You can find some good near bargains in rotary inductors at hamfests. The same applies to capacitors.</p>
+  <p><b>3. High-value components:</b> The higher the highest value of a capacitor or coil, the higher the lowest value. The large frames of high-value rotary inductors may limit the lowest value to well over 1 microH. Capacitors are even worse, because the high maximum value does not tell the whole story. Usually, capacitors follow the rule, but you also have to watch out for construction. I have an old military capacitor with a maximum value of 35 pF. Unfortunately, its lowest value is 17 pF. It is built within a set of frame plates that surround the stators and limit how low it can go. By contrast, a 100 pF old E. F. Johnson capacitor in one of my units has a minimum value of about 10 pF. Its supporting metal work consists of two small plates on either end of the unit. If you roll your own, look for the capacitor's minimum value as well as its maximum value.</p>
+  <p><b>4. Closed tight cases:</b> On ten meters, some commercial ATUs achieve a match more with stray capacitance and inductance than with the higher Q variable components that are supposed to do the work. Steel cases that cut the inductive fields of coils and provide several pF of shunt capacitance to the other components complicate and usually hinder the basic work of the matching network. A spacious case, however much against the grain of today's stylistic fetish of ultacompactness, is a plus for an ATU.</p>
+  <p><b>5. Poor ground paths:</b> Ideally, there should be one good ground point for the ATU network. With large components, this condition is often impossible to attain. However, grounding should be as direct and compact as possible--and as near to the ground lugs of the coax sockets as possible. It should not rely on the bite of a lock washer through a painted surface. A rivet used as a ground connector is a prelude to malfunction. There are no shortcuts to good, short, wide ground paths and good mechanical and electrical connections. They are not expensive, but they do take care.</p>
+  <p>This list of difficulties is not an indictment of all ATUs. Many units have taken the trouble to be the best they can be as 80 or 160 through 10 meter units. However, you can probably do better yourself. For 10 (or realistically, 10-20 meters), a PI or series-L T circuit is achievable with parts you can obtain from hamfests. A PI might use a 5 to 10 microH inductor with a pair of 250 pF air variable capacitors of good power rating. A series-L T circuit might use a pair of 5 or 10 microH rotary inductors and a couple of 250 or 300 pF variable capacitors, with a switch to bring them into play either one or both at a time. A surplus or home brew case with plenty of room helps ensure that strays are minimized, as do well-planned ground paths. Consider a plexiglass case for the ultimate in avoidance of strays.</p>
+  <p>Remember, multiband is not always the most efficient, even if it is the most compact. The bands that take the beating are the ones at the high and low ends of the multiband range. Ten meters, unfortunately, is one of those ends. Hence, if you use a 10-meter antenna system calling for an ATU, consider building yourself a customized unit with all the advantages and none of the difficulties.<br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p><i>Updated 3-17-97. &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><br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <a href="anta.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to An-Ten-Ten-nas Page</a><br>
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content/a10/ant11.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <title>Mobile Antennas for 10 Meters</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/yagicad.gif" align="middle" width="125" height="62" border="2" vspace="5" hspace="10">No. 11 Mobile Antennas for 10 Meters<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>I was asked to do a column on mobiles. While I claim no serious expertise on mobile antennas, there are some ideas worth considering, some information worth getting, and some safety thoughts worth taking very seriously.</p>
+  <center>
+    <h4>Mobile in motion</h4>
+  </center>Inherently, a mobile-in-motion antenna system, consisting typically of a shortened, loaded vertical antenna, is a very lossy system. Most of your power goes nowhere. However, do not let that discourage you, since some truly amazing hamming has been done mobile. Let the problem be your challenge. How can you minimize the losses?
+  <p>The first step is to ensure that a mobile rig in your car will not do bad things to your car's computer and equally bad things to your car's warranty. ARRL has published some contacts with automakers and distributors where you can get some (but probably not all) of the answers.</p>
+  <p>The second step is to prepare your car for a mobile antenna system. This involves close attention to power cabling, ground cabling, and decoupling RF from the battery and other auto electrical components. Use coax that can handle the automobile's hot and cold and greasy and dirty environment. Avoid foam insulated coax cables, as well as those like RG-8 and RG-58 with older types of jackets. RG-213 generally meets the needs of the mobile environment. The very best book I know of on the subject of mobiling is Don Johnson's (W6AAQ) <i><b>40+5 Years of HF Mobiling</b></i>, which is from World Radio. Please do not just slap a rig in the car, mount an antenna on the roof, trunk lip, or plastic bumper, and try operating. Read Don's advise and carefully prepare your vehicle for a mobile set-up.</p>
+  <p>The third step is choosing an antenna. According to various sources, the bugcatchers (either Texas or California style) and the DKs (antennas that follow Don Johnson's design) appear to do the most consistent job across the ham bands. However, for 10, you can consider the Hamstick types or even an old fashioned quarter-wave whip with no loading.</p>
+  <p>Mounting brackets come in every conceivable size and shape. Brackets used by truckers for CB antennas will attach the antenna almost anywhere on the vehicle. The big question is this: where?</p>
+  <p>Since the vehicle serves as a ground plane for most mobile antennas, the best place is in the middle of the roof, which is often a bad place physically. The antenna hits every overpass (until it breaks, of course), and you have to put a hole in your new $15,000 to $30,000 car, an act to which warranty servers may not take kindly, especially if you lease your car.</p>
+  <p>Since trunks are making a comeback after a decade of hatchbacks, the trunk lip is a possibility. However, do not rely on the set screws of the trunk lip mount for a ground to vehicle metal. Add a short, wide strap from the ground of the base to a good bolt in the car metal.</p>
+  <p>Increasingly, you can find a metal bumper only on trucks and vans. However secure, the antenna base, where the highest current resides and creates the most intense part of the radiation field, is very close to ground without much of a ground plane below it.</p>
+  <p>Trucks and vans are becoming more popular as wheels for mobiles, and folks seem less fearful about making holes in them. Side-mounting mobile antennas well up the van wall or cab side is considered an acceptable alternative to roof mounting, and it lowers the tip of the antenna by a foot or so. Bumpers are strong on many of these vehicles: consider a sturdy extension to the antenna base to raise the entire assembly.</p>
+  <p>Once everything is in place, including the rig, do not just hit the road chatting away. If you have not watched a weaving car with a cellular phone in the driver's hands, you have not been paying attention. While some ham-drivers can learn to drive and talk and twiddle knobs all at once, many others are high-speed unguided missiles. Unless you are certain that you are safe, let your passenger do the operating. I learned that the semi-hard way--from a close call rather than from an accident. It was inches from being the other way around.</p>
+  <center>
+    <h4>Mobile not in motion</h4>
+  </center>The safest way for the driver to operate mobile is to stop the vehicle and operate a while. Here, the driver can select a potentially good site to maximize radiation in useful directions, as well as operate safely. Parking lots, open fields, and hilltops are all likely operating points.
+  <p>Once you stop your car, you should instantly realize that your antenna options increase dramatically. You can take a modified mag mount CB antenna, resonated for 10, and slap it on top of the vehicle so you can monitor the band while you assemble and raise some kind of antenna less dependent on the car for its ground plane.</p>
+  <p>With careful planning, you can create a dipole or a 2-element beam that breaks down into sections that store within the trunk or a similar storage space. A little tool kit with pliers, screwdrivers, and nut drivers can have a permanent place in the trunk. Here are a few tips for such antennas:</p>
+  <ul>
+    <li>1. Avoid sheet metal screws as element length connectors. Their holes will wear out just when the band opens to Asia. Use hose clamps with a nut driver (usually faster and more sure-footed than a screwdriver).</li>
+    <li>2. Protect the elements and the center connectors when not in use. A cheap golf-club bag (are there any such things any more?) or something similar is a good protective carrier.</li>
+    <li>3. Store any loose hardware in a bag with a seal inside a plastic box with a clasp. Finding all but one absolutely necessary screw is Murphy's favorite joke on you. Better yet, have no loose hardware--keep it attached to one or the other of the pieces separated for storage. Then, keep a few EXTRA pieces in that bag in a box.</li>
+    <li>4. Keep the antenna sturdy enough to store well, but as light as possible for easy assembly and raising. Remember, the antenna does not have to withstand gale-force winds in this application. Smaller diameter, thinner wall tubing will do a good job and prevent back pain.</li>
+  </ul>
+  <p>The mast can be as simple as 4 5' sections of TV mast. There are also a number of extendable aluminum poles, most never intended as masts, that will support a light antenna in very small breezes. The search for the perfect stationary-mobile mast is endless.</p>
+  <p>Guying the mast, even for a brief stop is a good safety measure. One workable system requires a little 3/16 or 1/4 inch rope and a single concrete block. The mast slips into one of the block's holes, which generally is enough to prevent the end from skidding. A side bracket attached both to the door frame (of a car and perhaps the side rail of a pickup) holds the mast a few feet up. The guy ropes go from near the top of the mast to the other side of the car and are tied to the fore and aft bumper frames with a slight tension that holds the mast in place, but still lets you turn it.</p>
+  <p>You can also make up a tubular bracket a few feet long and attach it firmly to a pickup's rear bumper. The mast slides into it and is self-supporting.</p>
+  <p>Most studies show that over flat land, low horizontal antennas do best at a 5/8 wavelength height, which is just about 20' on 10 meters. Although the take-off angle is high (above 20 degrees ordinarily), short skip operation is quite good, and dx is often only about 2 S-units down from elevations above 1 wavelength (35'). Even though the take-off angle decreases with each increment in antenna height, try to avoid heights between 3/4 and 7/8 wavelength, since ground reflections tend to cancel some of the radiation in the lowest lobe, which is the most useful lobe for skip. If the land is not flat, diffraction effects can wash out some of these phenomena.</p>
+  <p>However, a 20' mast is the most many hams can handle mechanically in the field. Those who can get above 30' up need to ensure both personal safety and the safety of passengers. Not to mention saving that big wheeled investment from damage by a $10 homebrew antenna.</p>
+  <p>Of course, nothing says you cannot use a well-installed regular mobile antenna. When the band is open, antenna efficiency only makes a difference in pileups (station pileups, not vehicle pileups).</p>
+  <p>This style of mobile operation is more leisurely than mobile on the fly. It is also safer for everyone.</p>
+  <p><b>Drive safely. The life you save may be mine.</b><br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p><i>Updated 3-17-97. &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><br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <a href="anta.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to An-Ten-Ten-nas Page</a><br>
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content/a10/ant12.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <title>Multiband vs. 10-Meter Dipoles</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/yagicad.gif" align="middle" width="125" height="62" border="2" vspace="5" hspace="10">No. 12 Multiband vs. 10-Meter Dipoles<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>If we had unlimited money and space, we could ask the following question sensibly: What is the best 10-meter antenna? The answer might be about 4 stacked long-boom, many-element Yagis from about 70' on up on a rotatable tower on a one-hill island surrounded by ocean. Even that answer might get an argument. However, for most of us, the simple question of what the best 10-meter antenna might be is an exercise in irrelevancy.</p>
+  <p>A more sensible question is usually this one: which of two alternatives is the better antenna? Each alternative might fit our yard and bank account. However, no general answer is possible. Even if one antenna does outperform another, there are always a number of other factors that affect the final decision. Can I maintain this antenna? What will my neighbors say when they see it? Is it compatible with the rose garden?</p>
+  <p>With those qualifications in mind, let's compare two antennas on performance alone just because people have asked a certain question: which is better: a multiband wire antenna like a G5RV or a center-fed Zepp on the one hand, or a dipole cut for 10 meters on the other hand? And let's presume you have the room and supports for both antennas to make this a real comparison.</p>
+  <p>If you like to work all of the HF ham bands and are limited to a single antenna, then the multiband wire is certainly an antenna to consider. An "80-meter" 135' center-fed Zepp, a G5RV 102' dipole, and a "40-meter" 67' center-fed Zepp are all long doublets, center-fed with parallel transmission lines and differ only in length. All require an antenna tuner, although some antennas show a low impedance on some bands. The 135' Zepp obviously works better on 80, although the 102' center-fed antenna does quite well there, and all three antennas can show respectable performance from 40-10.</p>
+  <p>In fact, some folks praise these longer antennas because they show some gain over a 10-meter dipole on 10-10's favorite band. Unfortunately, that kind of claim is like preferring $10 bills over $5 dollar bills. I'll take the $5s if you give me enough more of them than the $10s. The bill size is not relevant until you know how many of each are at stake.</p>
+  <p>When comparing any of the longer multiband wires with a 10-meter dipole, the extra gain is not relevant until we answer the question of where it goes and, equally, where it does not go. A lot of variables go into the answer to the "where" question, but we can give a glimpse into the answer with Figures 1, 2, and 3. Each shows the azimuth pattern of 3 antennas (2 dipoles and one multiband antenna) modeled at a height of 35' (a typical amateur backyard installation) over real ground at a 14-degree angle of maximum radiation at 28.5 MHz.</p>
+  <p>Think of these patterns as looking down on the antenna from overhead. The dipoles are the simple figure-8 double loops. For the loops reaching out to 0 and 180 degrees, the antenna runs up and down the page through the center of the diagram. For the loops reaching maximum at the top and bottom of the diagram, the antenna runs left and right across the page. Each multiband antenna also runs left and right across the page.</p>
+  <center>
+    <img src="ant12a1.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Figure 1 shows the 135' Zepp. It has four lobes that exceed the dipole limit by a good bit. However, notice how narrow they are. Notice also the nulls in the pattern. with some careful planning and some good luck in where your yard trees go, you might align the antenna so that one or more of the lobes points right where you find the stations you like to work most. Then again, you might end up aligning the antenna so that nulls point at your second and third favorite spots.</p>
+  <center>
+    <img src="ant12a2.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Figure 2 shows the dipoles with a G5RV. Again, there are higher-gain narrow lobes, but aimed more at the 45-degree point on the pattern. The shorter antenna creates fewer lobes. Again, you might use this information to hit one or more of your targets, and possibly miss a few desirable targets.</p>
+  <center>
+    <img src="ant12a3.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Figure 3 shows the same data for the 67' Zepp, about the length of a 40-meter dipole. There are only 4 lobes for this shorter antenna, but, of course, 4 nulls as well.</p>
+  <p>Each of these antennas has its place in some ham's yard, especially for working the lower HF bands (and each antenna will show a different pattern on each band). But is any really significantly better than a dipole on 10 meters? Gain is nice, but those nulls can drive you crazy.</p>
+  <p>Well, the dipole also has nulls off each side, so it too is limited. However, with an overall length of between 16' and 16.5' (depending on the element diameter), it is not too difficult to put up a rotatable dipole. You can hand-rotate the antenna mast or use a TV rotator. Then the nulls disappear. More correctly, they go where you put them, as you broadside the antenna to the desired signal. Hence, you only have to rotate a dipole less than 180 degrees to get full 360-degree coverage.</p>
+  <p>A stack of TV masting with a house clamp only roughly tight or guys in guy rings would permit you to hand turn the mast. You can attach a short level rod to the mast to make turning easier. Except in odd late afternoon shorter skip conditions, where signals seem to come from every direction, you will likely only have to change the antenna's orientation every few hours.</p>
+  <p>Am I "pushing" the rotatable dipole? Not really. Part of my point is that gain is not everything, especially if it does not point anywhere useful. Part of my point is that pointing is more simply done on 10 meters than many people believe, especially if they only look at monster 20-meter beams. Part of my point is that a multiband wire antenna is a very useful antenna for working all the bands. And part of my point is that, with a little ingenuity, a 10-meter dipole can do a lot of useful work for us without being unduly noticeable or expensive. Even if you already have that long wire, you might also consider adding a rotatable dipole to the antenna "farm." Now, if it is simple enough, you might even take it apart, toss it in the truck or trunk, and go portable with it--and put it back up when you get home.<br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p><i>Updated 3-17-97. &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><br>
+  <br></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <a href="anta.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to An-Ten-Ten-nas Page</a><br>
+  <a href="../radio.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Amateur Radio Page</a><br>
+  <br>
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+</body>
+</html>

content/a10/ant14.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <title>EDZs: Stacked and Unstacked</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/yagicad.gif" align="middle" width="125" height="62" border="2" vspace="5" hspace="10">No. 14 EDZs: Stacked and Unstacked<img src="../images/w4rnlwwr.gif" align="middle" width="99" height="83" border="2" vspace="5" hspace="10"></h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center><br>
+  <br>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>After an article on EDZs (extended double Zepps) appeared in <b><i>Communications Quarterly</i></b> in Fall, 1995 (<a href="../mu/mu3a.html">link</a>), I received some mail and phone calls on a version of the antenna I had not covered. So I thought I would bring it to your attention. The EDZ is a good fixed wire antenna for those who do not wish to fool with towers and rotators, but do wish to work some DX when the band fully reopens. It helps to have high trees or other tall poles to support the ends, and you have to like ATUs (antenna tuning units or transmatches). Even if you do not like these things, read on--they can grow on you.</p>
+  <center>
+    <h4>The Basic EDZ</h4>
+  </center>The basic EDZ is a 1.25 wavelength wire antenna fed at the center. Unlike a dipole, precision wire cutting is not required. A 10-meter EDZ needs about 44 feet of copper wire. The feedpoint impedance will be about 130 ohms with about 680 ohms of capacitive reactance. I recommend you use 450-ohm parallel feedline to an ATU. Although you can match the EDZ to 50- ohm coax at the antenna feedpoint, you would lose the ability to use the antenna on other bands. For every band 20-meters and up, the antenna is longer than a dipole and thus shows a little gain above a dipole.
+  <p>At 10-meters, an EDZ up 40' in the air shows about 3.5 dB gain over a dipole. Of course, both antennas are bidirectional. The EDZ gets its gain by shrinking the side-to-side beamwidth of its two main lobes. The dipole has a half-power beamwidth of about 78&deg; while the EDZ cuts that to about 30&deg; with two small side lobes in each direction. See Figure 1</p>
+  <center>
+    <img src="ant14a1.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Some folks view the sidelobes as QRM producers. If you agree, see the <b><i>ARRL Antenna Compendium</i></b>, Vol. 4 for an EDZ with capacitors in the elements to eliminate them. However, you may lose some performance of the antenna on other bands.</p>
+  <p>Almost any wire antenna for 10 up in the air 40' has a take-off angle of 12&deg; above the horizon. Take-off angle means the elevation of the lobe with the most power in it. The half-power points are &PlusMinus;6&deg; around that angle, so there is plenty of power in the low angles needed for efficient DXing. But perhaps we can do a little better.</p>
+  <center>
+    <h4>Stacked EDZs</h4>
+  </center>Stacking any two antennas will do two important things for you: 1. It will increase the system gain a bit and 2. it will lower the take-off angle a bit. Both those advantages are DXer delights. So let's get crackin' and stackin'. The system I shall show you derives from an article in the November, 1968, <i>CQ</i> by John Schultz, W2EEY called "The Expanded Lazy-H Antenna." (My thanks to Henry Pollock, WB4HFL, for sending me a copy of the article.)
+  <p>A vertical spacing of 5/8ths of a wavelength is about the most efficient gain producer when stacking antennas. This applies to Yagis and other arrays as well as EDZs. At 10 meters, this means a spacing of about 22' or so. Again, this number is not critical &PlusMinus;a foot. Figure 2 shows the general scheme. Assuming you have the side supports, there are only a few questions to ask about stacked EDZs.</p>
+  <center>
+    <img src="ant14a2.gif" width="454" height="467" border="2" vspace="5" hspace="9">
+  </center>
+  <p>1. What do I get for my trouble? First, you get 3 to 4 dB additional gain in both directions, depending upon which wire you set at the 40' level, where we placed our one-wire EDZ. If you can put the second wire at about 60' or so, you will get the higher gain, plus a lower take-off angle of 9&deg;. That puts the bulk of your power in the 10-meter far-DX zone. Figure 3 also shows a secondary lobe at about 28&deg; for shorter paths. If you place the lower wire at about 20' up, you will get the lower gain and a basic take-off angle of 14&deg;. That is still worth while.</p>
+  <center>
+    <img src="ant14a3.gif" width="634" height="280" border="2" vspace="5" hspace="9">
+  </center>
+  <p>2. How do I aim single and stacked EDZs? With care, since they are fixed. In much of the US, the NE-SW corridor gets you both Europe and VK- ZL-land. Or you can broadside N-S for South America and over-the-pole and back scatter. Or, you can broadside to Asia. Finally, if you have lots of trees or poles, you can build 3 EDZ stacks and switch among them (a nice wiry dream).</p>
+  <p>3. How do I feed the beast? The easiest feed system is to run 450- ohm parallel feeders from each feedpoint to a common center. At that point, you will see something like 75 ohms resistive and about 460 ohms inductive impedance. This situation gives us a choice.</p>
+  <p>a. If you wish to use the antenna on 10 meters only, you can insert on each side of the line junction a 24 pF capacitor. This is a series connection on each side, with the ends then connected to each side of a coax connector. The capacitors cancel out the inductive reactance, leaving only about the same mismatch you would get with a dipole--and that's manageable.</p>
+  <p>b. If you wish to use the antenna on all bands from 20 meters on up, just connect more 450-ohm parallel feeder and bring it to the shack and ATU. On 20 you will get dipole gain or better, with more gain on the other bands between 20 and 10.</p>
+  <p>4. What does it cost? Well, #14 wire runs about 7 to 12 cents a foot, depending on its nature, and 88' of wire is in the $8.00 range. Add some insulators and rope for supports. Then add the 450-ohm parallel feeder, which is cheaper than coax. Even if you have to erect some supports (4 sections of 10' TV mast per side, plus rope guys and tie-down ring-screws in the ground), you might run the bill to $75 to $100. That will barely buy the TV rotator, let along the tower and very light beam that goes with it.</p>
+  <p>Note that, as in all antenna work, we must compromise. The stacked EDZ requires supports and fixes your general directions to two, but saves you many dollars, pounds, yen, francs, marks, or lire. The long Yagi with the same gain gives you freedom of direction, but empties your pockets and requires constant maintenance. (Remember, Murphy's law says that when the rotator goes bad, it is always stuck in a direction with no hams in sight.) So the EDZ and the stacked EDZ array are suitable only for some people. But perhaps you are one of them.<br>
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+  <p><i>Updated 4-23-97. &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><br>
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