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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="Moxon, HF Upper">
+  <title>Using Moxon Rectangles for WARC-Band Antennas Part 1</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>Using Moxon Rectangles for WARC-Band Antennas<br>
+    Part 1: Some 17-12 Meter Ideas</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>Many hams who wish to work the WARC bands also wish to have a compact directional antenna for the job. In the past, I have designed a number of 17 and 12 meter combinations using Yagis. Because the WARC bands have narrow bandwidths, combinations of director-driver and driver-reflector Yagis work well. A number of design possibilities appear at my web site (..) in the "upper HF" portion of the main index.</p>
+  <p>In this note, I wish to explore the possible use of the Moxon rectangle as a potential replacement for the standard driver-reflector Yagi in such combinations. The Moxon rectangle is often thought of as a wide-band antenna. However, it offers some advantages for WARC-band use. First, its side-to-side width is about 70% that of a full-size Yagi, which is a space saver. A 17-meter Yagi that would be between 25' and 26' wide becomes less than 20' wide in the Moxon configuration.</p>
+  <p>The Moxon also provides for a direct 50-Ohm feed. Although Yagis can also be set for this feed impedance, they must be about 20% wider in the front-to-back dimension than a Moxon. In addition, the Moxon is only about 0.2 dB lower in forward gain than a comparable driver-reflector Yagi, but the Moxon front-to-back ratio will be well over 20 dB--and may peak in the 30 dB range.</p>
+  <center>
+    <img src="1712m-a.gif" width="567" height="426" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The end result is that a Moxon has a number of characteristics that some operators may find desirable for WARC band use, even if the wide operating bandwidth is not one of them. Hence, it is worthwhile to see if there are multi-band designs that might use the Moxon rectangle at their core. <b>Fig. A</b> shows some conventions for describing the dimensions of a standard Moxon rectangle. Dimension A is the side-to-side length, while E is the overall front-to-back dimension, subdivided into the driver and reflector arms (B and D) and the element tip-to-tip spacing (C).</p>
+  <p>The simplest way to combine two or more bands in one array whose performance can be certified on each band is to use open-sleeve coupling. In this system (made popular by the Force 12 C-3), only the driver for the lowest band is connected to the feedline. The driver for a supplemental (higher-frequency) band is positioned so that it achieves two goals. First, it is coupled close enough to the lower-band driver that the upper band elements receive sufficient energy to provide relatively standard performance. Second, the length and position of the driver for the upper band is set so that the feedpoint connection on the lower band driver registers a desired impedance on the new band. In the case of the Moxon + supplement array, 50 Ohms for both bands is the goal.</p>
+  <p>For simplicity, I shall confine design efforts to open sleeve coupling. In this episode, we shall explore a couple of options for covering 12 and 17 meters. In Part 2, we shall explore some possibilities that include 30 meters. All of the designs will use aluminum tubing in prospect of developing a rotatable beam.</p>
+  <p><b>The Possibility of a Dual-Band Moxon</b></p>
+  <p>Since I began investigating the Moxon rectangle design, I have received numerous inquires about whether it is feasible to nest 2 or more of these antenna in the same plane. It is certainly possible to create a "Christmas tree" of Moxon rectangles, each with its own feedline. However, nesting 2 or more Moxons in the same plane presents some difficulties. G6XN did so with his wire multi-band array. However, this array used remote (antenna tuner) tuning for each element, as well as some decoupling arrangements. Although this system can be quite effective, it adds complexity to the operation of the antenna. The design goal for this effort is an antenna that requires no tuning and that can be fed with a single 50-Ohm coax transmission line.</p>
+  <p>For the harmonically related ham bands, I have modeled pairs nested Moxons using open-sleeve coupling. However, I have never recommended the designs. The high-band antenna within the lower band array displays very narrow bandwidth, both with respect to the resulting feedpoint impedance and with respect to the gain and front-to-back ratio characteristics. Hence, the designs would not have been satisfactory for these wider ham bands.</p>
+  <p>However, the WARC bands are inherently narrow, covering no more than 100 kHz maximum. Thus, the possibility for a dual-band WARC Moxon became a live possibility. <b>Fig. 1</b> shows the outlines of the final model.</p>
+  <center>
+    <img src="1712m-1.gif" width="447" height="221" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The following table shows the dimensions (in feet) for the dual Moxon with open-sleeve coupling, using the conventions of <b>Fig. A</b> to designate parts of the antenna.</p>
+  <pre>Band              Dimension         Length (feet)
+17 meters   (all elements use 0.75" diameter aluminum tubing)
+                  A                 19.46'
+                  B                  2.74'
+                  C                  0.625'
+                  D                  3.68'
+                  E                  7.04'
+12 meters   (all elements use 0.5" diameter aluminum tubing)
+                  A                 15.08'
+                  B                  1.99'
+                  C                  0.455'
+                  D                  2.13'
+                  E                  4.58'</pre>
+  <p>Dimension E may not be exactly the sum of B, C, and D due to rounding, but the numbers are in principle close enough for construction. The 12-meter driver is set 1.15' behind the 17-meter driver, which places the 12-meter reflector 1.77' ahead of the 17-meter reflector.</p>
+  <p>A caution applies here and to any other tubular Moxon rectangle. The model uses uniform diameter elements of a specified size for each band. Changing the element diameter will result in slight changes for the required spacing of the element tips. Different size tubing changes the coupling between the tips. More than slight changes in element diameter may require juggling all of the dimensions to maintain performance and still have a near-50-Ohm feedpoint impedance. Using elements with different sized tubing along the length ("stepped-diameter" elements) may also require adjustments in the dimensions, just as it does with a Yagi.</p>
+  <p>The projected performance of the array can be summarized in the following table, where gain is shown as free-space gain.</p>
+  <pre>Frequency         Gain        Front-to-Back           Feedpoint Z       50-Ohm
+  MHz              dBi         Ratio  dB              R+/-jX Ohms       VSWR
+
+18.068            6.11          24.9                  58.8 + j 0.8      1.18
+18.118            6.02          29.5                  62.9 + j 2.7      1.26
+18.168            5.94          31.8                  66.8 + j 4.3      1.35
+
+24.89             6.13          18.9                  34.6 - j11.5      1.58
+24.94             5.81          34.1                  34.1 + j 2.6      1.48
+24.99             5.47          18.5                  33.9 + j15.9      1.72</pre>
+  <center>
+    <img src="1712m-2.gif" width="640" height="300" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 2</b> shows the mid-band 17-meter free-space azimuth pattern for the array, while <b>Fig. 3</b> shows the same pattern for 12 meters.</p>
+  <center>
+    <img src="1712m-3.gif" width="640" height="300" border="2" vspace="5" hspace="9">
+  </center>
+  <p>At first sight, it would appear that the dual Moxon is a distinct possibility for home construction. With a boom just over 7' long, it would seem to make a nearly ideal compact antenna for 17 and 12. Unfortunately, I cannot recommend the array.</p>
+  <p>The main reason for not recommending the array is the exceptional finickiness of the required adjustments. The performance table gives one set of clues to this fact. Compare the rate of change for both the gain and front-to-back ratio for the two bands. On 12 meters, the rate of change is over twice as fast as on 17. The consequence of this fact is that any slight variation in construction from the model could result in very large changes in performance.</p>
+  <p>Remember, too, that any open-sleeve coupled element pair requires careful adjustment on its own. When combined with rapidly changing performance characteristics for tiny changes in dimensions, arriving at a usable match and having good performance may prove to be beyond reasonable construction methods.</p>
+  <p>An additional aspect of the difficulty is the fact that the two Moxons force on each other changes in dimensions relative to the dimensions needed for independent use. In short, the two Moxons are essentially too tightly coupled throughout their structure to make the task of finding exactly the right configuration feasible, let alone easy.</p>
+  <p>However, since the antenna is just under 20' wide (slightly narrower than a 15-meter Yagi, even though the frequency is lower), we might be willing to try a 10' boom. At this length, we may be able to develop a 17-12 combination far more easy to adjust.</p>
+  <p><b>A Moxon-Yagi Combination</b></p>
+  <p>It is much more convenient to combine the Moxon for 17 meters with a 12-meter Yagi. Unfortunately, placing a driver-reflector Yagi inside the Moxon does not work, since the required length of the reflector would overrun the side arms of the 17-meter Moxon. However, we can place a director-driver combination ahead of the Moxon.</p>
+  <p>In commercial antennas, like the Force 12 C3, the highest band (10 meters) requires several elements to achieve a combination of good operating bandwidth and gain. The WARC bands do not have significant bandwidth requirements. Hence, we can use a simple director-driver combination to achieve results that are compatible with the basic performance of the Moxon for 17 meters. <b>Fig. 4</b> shows the outline of the resulting design.</p>
+  <center>
+    <img src="1712m-4.gif" width="414" height="260" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Once more, the basic design uses 0.75" elements for 17 meters and 0.5" elements for 12 meters. Changes in element diameter will require adjustment relative to the following table of dimensions. For the Yagi portion of the design, "Space" refers to the distance from the Moxon driver to the 12-meter element in question.</p>
+  <pre>Band              Dimension         Length (feet)
+17-meter Moxon    (all elements use 0.75" diameter aluminum tubing)
+Moxon             A                 19.56'
+                  B                  2.74'
+                  C                  0.625'
+                  D                  3.68'
+                  E                  7.04'
+12-meter Yagi     (all elements use 0.5" diameter aluminum tubing)
+Driver            Length            19.40'
+                  Space              0.35'
+Director          Length            18.50'
+                  Space              3.08'</pre>
+  <p>Perhaps the first thing to notice is the set of dimensions for the 17-meter Moxon. These dimensions are unchanged from those for a design optimized for independent use. The presence of the Yagi elements ahead of the Moxon does not affect the Moxon itself to any significant degree--that is, to a degree requiring redesign. The following performance table provides the data to show this fact even more clearly.</p>
+  <pre>Frequency         Gain        Front-to-Back           Feedpoint Z       50-Ohm
+  MHz              dBi         Ratio  dB              R+/-jX Ohms       VSWR
+
+18.068            6.41          20.0                  62.9 - j 7.9      1.31
+18.118            6.34          22.6                  67.2 - j 7.3      1.38
+18.168            6.27          25.8                  71.4 - j 7.1      1.46
+
+24.89             6.78          29.2                  58.7 + j 9.3      1.26
+24.94             6.86          30.2                  52.1 + j 7.4      1.16
+24.99             6.94          28.2                  44.4 + j 7.0      1.21</pre>
+  <p>The performance of the Moxon is altered by a small amount, as shown in <b>Fig. 5</b>.</p>
+  <center>
+    <img src="1712m-5.gif" width="640" height="310" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The presence of the 12-meter elements creates a slight "director" effect on the Moxon, which lowers the front-to-back ratio a small amount and which raises the feedpoint impedance somewhat from the 50-Ohm design specification for the antenna when used independently. The amount was considered too small to require design revision. In exchange for the slightly reduced front-to-back ratio--still at least 20 dB across the 17-meter band--the director effect gives a small boost to gain--about 0.3 dB. This increase in gain will be too small to notice operationally.</p>
+  <p>On 12 meters, the director-driver combination exhibits a standard Yagi pattern, as shown in <b>Fig. 6</b>.</p>
+  <center>
+    <img src="1712m-6.gif" width="640" height="310" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The gain of the array on 12 meters is greater than the two 12-meter elements would normally provide. The "forward-stagger" effect provides a small gain increase, since the Moxon elements provide a bit of a reflector effect. The 180-degree front-to-back ratio for 12 meters can mislead the user a bit, as <b>Fig. 6</b> also shows. Although the pattern has a fine dimple directly to the rear, the rear quartering lobes are down by only about 18 dB, for an average front-to-rear ratio in the 22 dB neighborhood. In fact, the 17 meter front-to-rear performance is superior overall, despite the lower 180-degree front-to-back ratio.</p>
+  <p>The feedpoint impedance figures for 17 meters might be improved by a very small shortening of the side-to-side length (dimension A)--perhaps an inch or so. However, the reflector arms (D) should be lengthened by an equally small amount to restore and possibly center the front-to-back peak value within the operating passband on 17 meters. Indeed, it would be wise to make the reflector adjustment first to see the effect on the feedpoint impedance before adjusting the Moxon driver.</p>
+  <p>The key adjustment will be the placement and length of the 12-meter driver. Models of open-sleeve coupled elements always require subsequent field adjustment (a sophisticated way of saying "cut and try"). If the change of spacing relative to the given design is very small, then no further movement of the director will be required. If the change is more than a couple of inches, then readjust the director spacing closer to the value specified in the dimensional table in order to ensure that the array gives a satisfactory pattern. The juggling for 12-meters will have no significant effect on the 17-meter portion of the array.</p>
+  <p><b>The Simplest Dual Moxon Rectangle?</b></p>
+  <p>As an addendum to this set of design notes, I cannot overlook a deceptively simple design for a dual 17-12 m Moxon. In fact, as <b>Fig. 7</b> reveals, it is actually only 1.5 Moxon rectangles, having a single driven element and two reflector elements.</p>
+  <center>
+    <img src="1712m-7.gif" width="444" height="303" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The dimensions for the antenna as modeled are these:</p>
+  <pre>Band              Dimension         Length (feet)
+17 meters   (all elements use 0.5" diameter aluminum tubing)
+                  A                 19.46'
+                  B                  2.74'
+                  C                  0.625'
+                  D                  3.68'
+                  E                  7.04'
+12 meters   (all elements use 0.5" diameter aluminum tubing)
+                  C                  1.07'
+                  D                  2.43'
+                  E                  3.50'</pre>
+  <p>Of course, dimension C, which is normally the gap between element tails, is in this design the distance of the reflector tail from the driven element itself.</p>
+  <p>The drawback of this simplified design is the need to use parallel feedline and an ATU, since the 12-meter feedpoint impedances are not compatible with a coax feed. As well, 12-meter performance is down somewhat, as the following table shows.</p>
+  <pre>Frequency         Gain        Front-to-Back           Feedpoint Z
+  MHz              dBi         Ratio  dB              R+/-jX Ohms
+
+18.068            6.28          19.1                  40.8 - j 9.8
+18.118            6.19          22.2                  44.0 - j 6.9
+18.168            6.10          26.6                  47.2 - j 4.1
+
+24.89             5.96          14.7                  65.7 + j 425
+24.94             5.91          14.5                  69.9 + j 431
+24.99             5.85          14.2                  74.2 + j 437 </pre>
+  <p>The pattern for 17 meters holds up quite well, despite the proximity of the 12-meter reflector to the driven element, as evidenced in <b>Fig. 8</b>.</p>
+  <center>
+    <img src="1712m-8.gif" width="640" height="350" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Although the gain is slightly down and the front-to-back ratio considerably down, the pattern shape remains quite well-behaved and well within the norms for a "typical" Moxon pattern. <b>Fig. 9</b> tells the tale for the entire 12-meter band.</p>
+  <center>
+    <img src="1712m-9.gif" width="640" height="350" border="2" vspace="5" hspace="9">
+  </center>I would not necessarily recommend construction of this version of the dual Moxon. Supporting the "free-floating" reflector might be a bit of a structural challenge. Nevertheless, the design does show some of the flexibility of the Moxon rectangle design.
+  <p>As noted earlier, changes in element diameter relative to the given design will require element length (and possibly spacing) changes to account for them. For those who may wish to experiment with the designs we have looked at in model form, the following model descriptions may ease some of the entry work in modeling programs like EZNEC, NEC-Win Plus, AO, or NEC4WIN.</p>
+  <pre>17-12 m dual Moxon                        Frequency = 18.118/24.94  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1           -9.730, -2.738,  0.000  W2E1  -9.730,  0.000,  0.000 7.50E-01   7
+2     W1E2  -9.730,  0.000,  0.000  W3E1   9.730,  0.000,  0.000 7.50E-01  45
+3     W2E2   9.730,  0.000,  0.000         9.730, -2.738,  0.000 7.50E-01   7
+4           -9.730, -3.364,  0.000  W5E1  -9.730, -7.040,  0.000 7.50E-01   9
+5     W4E2  -9.730, -7.040,  0.000  W6E1   9.730, -7.040,  0.000 7.50E-01  45
+6     W5E2   9.730, -7.040,  0.000         9.730, -3.364,  0.000 7.50E-01   9
+7           -7.540, -3.139,  0.000  W8E1  -7.540, -1.150,  0.000 5.00E-01   5
+8     W7E2  -7.540, -1.150,  0.000  W9E1   7.540, -1.150,  0.000 5.00E-01  33
+9     W8E2   7.540, -1.150,  0.000         7.540, -3.139,  0.000 5.00E-01   5
+10          -7.540, -3.594,  0.000 W11E1  -7.540, -5.720,  0.000 5.00E-01   7
+11   W10E2  -7.540, -5.720,  0.000 W12E1   7.540, -5.720,  0.000 5.00E-01  33
+12   W11E2   7.540, -5.720,  0.000         7.540, -3.594,  0.000 5.00E-01   7
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+</pre>
+  <pre>
+
+17-12 m Moxon + Yagi                         Frequency = 18.118/24.94  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1           -9.779, -2.738,  0.000  W2E1  -9.779,  0.000,  0.000 7.50E-01   7
+2     W1E2  -9.779,  0.000,  0.000  W3E1   9.779,  0.000,  0.000 7.50E-01  45
+3     W2E2   9.779,  0.000,  0.000         9.779, -2.738,  0.000 7.50E-01   7
+4           -9.779, -3.364,  0.000  W5E1  -9.779, -7.040,  0.000 7.50E-01   9
+5     W4E2  -9.779, -7.040,  0.000  W6E1   9.779, -7.040,  0.000 7.50E-01  45
+6     W5E2   9.779, -7.040,  0.000         9.779, -3.364,  0.000 7.50E-01   9
+7           -9.700,  0.350,  0.000         9.700,  0.350,  0.000 5.00E-01  45
+8           -9.250,  3.080,  0.000         9.250,  3.080,  0.000 5.00E-01  45
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+</pre>
+  <pre>
+
+17-12 m dual Moxon                            Frequency = 18.118/24.94  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1           -9.730, -2.738,  0.000  W2E1  -9.730,  0.000,  0.000 5.00E-01   7
+2     W1E2  -9.730,  0.000,  0.000  W3E1   9.730,  0.000,  0.000 5.00E-01  45
+3     W2E2   9.730,  0.000,  0.000         9.730, -2.738,  0.000 5.00E-01   7
+4           -9.730, -3.364,  0.000  W5E1  -9.730, -7.040,  0.000 5.00E-01   9
+5     W4E2  -9.730, -7.040,  0.000  W6E1   9.730, -7.040,  0.000 5.00E-01  45
+6     W5E2   9.730, -7.040,  0.000         9.730, -3.364,  0.000 5.00E-01   9
+7           -7.530, -1.070,  0.000  W8E1  -7.530, -3.500,  0.000 5.00E-01   7
+8     W7E2  -7.530, -3.500,  0.000  W9E1   7.530, -3.500,  0.000 5.00E-01  33
+9     W8E2   7.530, -3.500,  0.000         7.530, -1.070,  0.000 5.00E-01   7
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space</pre>
+  <p>Of the three designs, the Moxon-Yagi offers the greater potential for being replicated in the average home shop. One Moxon construction technique (for 10 meters) appears in a piece I did for the <i>ARRL Antenna Compendium</i>, Vol. 6. Other techniques are also possible. It is wise to insulate all of the elements from a metal boom. Whatever the construction, the open-sleeve coupled Moxon-Yagi combination should acquit itself quite well during the present (and future) sunspot cycles.</p>
+  <p>The only WARC-related question left is whether there is any way to get 30 meters into the array. The answer to that question will be the subject of Part 2 of this mini-series.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 5-1-2000, 8-4-2000. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for April, 2000. 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="moxpage.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Moxon 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#hf-upper'>HF Upper</a>, <a href='../topics.html#moxon'>Moxon</a></p><br>
+</body>
+</html>

content/moxon/20moxp.html

@@ -0,0 +1,139 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="Moxon, HF Upper, Portable">
+  <title>A Truly Portable Moxon Rectangle for Nearly No-Tool Field Assembly</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>A Truly Portable Moxon Rectangle for Nearly No-Tool Field Assembly</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>Since I began development of the Moxon Rectangle as a 2-element monoband directional beam with a superior front-to-back ratio and a direct 50-Ohm feed, I have had numerous exchanges with various hams on making the antenna truly portable. Various ideas have filtered through discussions, including the use of a fiberglass support frame--alternatively stressed and unstressed--with wire elements. However, tubular elements offer a wider bandwidth for all of the main operating characteristics. So I have focused in this direction.</p>
+  <p><b>Basic Moxon Rectangle Dimensions and Performance</b></p>
+  <p>We may calculate the dimensions for any Moxon rectangle from a convenient online calculator on the <a href="moxpage.html">Moxon Rectangles and Online Calculator</a> page. The figure below gives us a set of references that will make sense of the following table of dimensions.</p>
+  <center>
+    <img src="20moxp-12.gif" width="567" height="426" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The tubing that I selected for the series of portable rectangles is 5/8" (0.625") diameter 6063-T832 aluminum, available from such sources as Texas Towers (http://www.texastowers.com) in convenient 6' lengths. Based on the use of this material, we may plug the element diameter and the design frequency into the program to derive dimensions. For 20 and 15 meters, a design frequency about 40% up from the bottom of the band provides whole band coverage. Therefore, 14.150 and 21.200 MHz are the design frequencies. On 10 meters, a frequency of 28.350 seems best for covering the entire first MHz of the band. The following chart provides the dimensions in feet.</p>
+  <pre>                       Moxon Rectangle Dimensions
+Dimension        20 Meters       15 Meters        10 Meters
+      A          25.12'          16.73'           12.49'
+      B           3.54'           2.31'            1.69'
+      C           0.95'           0.69'            0.55'
+      D           4.77'           3.19'            2.39'
+      E           9.26'           6.19             4.63'</pre>
+  <p>E, of course, is the simple sum of B, C, and D to give the overall front-to-back dimension. The constant diameter material means that the diameter as a fraction of a wavelength increases with frequency. Hence, the gap (C) at 10 meters is more than half the gap at 20 meters.</p>
+  <p>In the note that follow, I shall focus on the most difficult of the versions to make truly portable--the 20-meter rectangle. You may adapt the idea for construction with greater ease to smaller versions than you can try to scale up constructions. <b>Fig. 1</b> shows the 20-meter rectangle with dimensions and several kinds of markings that will be of significance in construction.</p>
+  <center>
+    <img src="20moxp-1.gif" width="513" height="495" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The decision to attempt construction of a truly portable Moxon depends in part on the antenna performance. <b>Fig. 2</b> shows free-space azimuth patterns for the 20-meter band edges and center for the array. The very high front-to-back ratio diminishes to about 18 dB at the band edges, while the gain decreases in a typical 2-element reflector-driver parasitic array curve.</p>
+  <center>
+    <img src="20moxp-2.gif" width="376" height="338" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The anticipated performance figures--which will be similar for all 3 wide upper HF bands--appear in the following table.</p>
+  <pre>                20-Meter Moxon Performance in Free Space
+Frequency        Gain       Front-to-Back   Feed Impedance        50-Ohm
+  MHz            dBi        Ratio dB        R +/- jX Ohms         VSWR
+14.0             6.36       18.0            39.3 - j 18.0         1.60
+14.05            6.25       21.7            43.1 - j 13.7         1.39
+14.10            6.14       27.6            46.9 - j  9.9         1.24
+14.15            6.02       38.0            50.6 - j  6.5         1.14
+14.20            5.91       29.0            54.1 - j  3.5         1.11
+14.25            5.80       23.5            57.4 - j  0.7         1.15
+14.30            5.69       20.3            60.5 + j  1.9         1.21
+14.35            5.59       18.1            63.3 + j  4.4         1.28</pre>
+  <p>The gain drops about 3/4 dB across the 20 meter band. As <b>Fig. 3</b> shows, the SWR curve is steeper below the design frequency than above it. This curve parallels the front-to-back ratio curve, and together, the two curves dictate a design frequency of maximum front-to-back ratio that is a bit below the mid-band point.</p>
+  <center>
+    <img src="20moxp-3.gif" width="583" height="200" border="2" vspace="5" hspace="9">
+  </center>
+  <p>For the average radio amateur without high towers and the finances to put a high performance set of beams into the air, the Moxon performance offers a chance for effective communications. The azimuth patterns suggest that the beam has two principle offerings. First, it is very quiet to the rear, enhancing signals from the forward direction. Second, the forward lobe is very wide, which requires less precision in aiming the antenna.</p>
+  <p>For Field Day and similar operations, the antenna can be very effective, whether constructed of wire or tubing. Wire Field-Day versions of the Moxon--including a reversible version--appear in May, 2000, <i>QST</i>. In this set of notes, we shall concentrate on making the tubular Moxon truly portable.</p>
+  <p><b>The Requirements for Portable Operation</b></p>
+  <p>A truly portable beam must meet several requirements:</p>
+  <ul>
+    <li>The array must form a compact package for storage and transport.</li>
+    <li>The array must go together using the minimum number of tools.</li>
+    <li>The array must come apart in a simple reversal of the assembly order.</li>
+    <li>The pieces must go together and come apart many times.</li>
+    <li>The array must be reasonably sturdy in light winds.</li>
+  </ul>
+  <p>The ideas that following meet all of the criteria. However, the structure must not be used for either permanent installation or for winds that are brisk or better. 15 knots represents the highest recommended wind load for the antenna.</p>
+  <p>The key to the ideas sketch in these notes is to assemble in the shop those pieces that form permanent subassemblies or pieces. Shop construction will require stainless steel hardware (bolts, sheet-metal screws, or clamps) for any junction of metals. In the field, a freshly made junction will provide electrical continuity for the duration of an operating session. Therefore, the only task for hardware will be to securely hold in place the junctions created in the field. Screws, clamps, and bolts are unnecessary for this purpose.</p>
+  <center>
+    <img src="20moxp-11.gif" width="244" height="68" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The only hardware needed for field junctions appears in the figure above: the hitch pin clip (otherwise knows as the hitch pin, the hairpin cotter pin, or the spring retainer). When properly sized, these pins will more than suffice to keep the pieces of a portable Moxon in place. Hitch pins are available in many sizes. Although stainless steel pins are the most durable, they cost twice as much for half the number of zinc-plated steel version, according to McMaster-Carr catalog pages (page 2971 of the on- line catalog at http://www.mcmaster.com.</p>
+  <p>Effective use of the hitch pin requires careful shop work. Drill the junction pieces of tubing together with the junction tightly in place. Use a hole size just barely large enough for the straight side of the pin. The tighter the fit, the more durable the junction. However, if a pin hole becomes loose and sloppy after a few uses, then a redrill at a nearby location with fix the problem.</p>
+  <p>Hitch pins come in many sizes. For 5/8" diameter tubing, the pin rated from 1/2" to 3/4" service is suitable. The pin wire diameter is 1/8" (0.125"), which dictates the shop drill bit size. Unless you have a precision shop, it is unlikely that similar pieces will be interchangeable at junctions. Therefore, it is wise to use tape on both side of a junction with a coding that allows you to join the correct pieces in the field.</p>
+  <p>Hitch pins are one of those items most likely to become lost in the grass. Therefore, be sure to obtain and store with the antenna parts a sufficient over-supply. As well, you might obtain brightly colored tape and add a tab through the top ring of each pin. These cautions fall under the basic principle that the more worst-case thinking you do in the shop, the fewer worst-case events will occur in the field.</p>
+  <p><b>Designing the Portable Moxon</b></p>
+  <p>Making a portable Moxon rectangle for 20-meters is our goal. The design effort begins by breaking the antenna into many sub-assemblies. The dimensions for these assemblies emerged from the dimensional requirements, shown in Fig. 1 and the available materials. Tubing comes in 6' lengths from many mail-order sources in order to fit with the UPS limits above which special shipping charges apply. Since the 20-meter version of the antenna is 12.56' (150.7") each side of the center line, we can use two sections between 5' 9" (69") and 6.0' (72") for each element's long portion. (A 10-meter version would require only one section per element per side of center line, and a 15-meter version might use two shorter sections.) The corner assembly will make up the remaining few inches. The tail pieces are well under 6', so they can be independent parts. The junctions consist of 0.5" tubing inside the main 0.625" tubes.</p>
+  <p>The array for 20 meters will need about 70' of tubing, which weighs less than 7.5 pounds in the 0.58" wall size. The boom and other hardware, if carefully chosen and constructed will about double to total weight, for a 15-pound package. Because the hardware needs--including the boom, boom-to-element mounts, and boom-to-mast mount--will not substantially change for the smaller versions of the antenna, expect a 10-pound 10-meter Moxon and a 12-pound 15-meter version.</p>
+  <center>
+    <img src="20moxp-4.gif" width="612" height="518" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The first stop along our examination of details consists of the corner assemblies. The 9" lengths of tubing will be variable according to the exact lengths of the tubing from the center-line (boom) to the element end. A 6" 0.5" diameter tube is permanently attached with stainless steel hardware to the linear section of the element--both to the long element and to the tail piece. Hitch pins position the junctions and also hold down a length of non-conductive strap or bar that holds the corner square during use. Two small plates make up the corner hinge that allows the piece to fold for storage and transport. The folding corner's chief advantage is storage compactness.</p>
+  <p>The drawback of the folding corner is the need for tools to tighten the corner. You might well replace the type of corner shown with a section of bent 0.5" diameter aluminum. If you choose this route, be certain that the straight and curve sections of each element add up to the correct overall element length shown in the chart of dimensions. The total driver length is A + (2 x B), while the total reflector length is A + (2 x D). Bending aluminum tubing to 90 degrees requires some care. Fill a piece longer than the final dimensions with play sand, the finer the better. Many benders warm the aluminum and sand to the point where they can just handle the piece with gloves. Make up a form (or use a suitable solid circular piece among the "found-objects" in the shop). Pin down one end of the tube. Bend slowly in small increments until the piece reaches a slightly tighter angle than the 90 degrees. It is easier to slightly unbend the cooled piece than to add to the curve later on.</p>
+  <p>The bent corner requires no brace. Hitch pine holes aligned with the inserted junction pieces are the final step in shop work--except for the labeling. Four corners with hitch pin holes of slightly different alignments can become a frustrating field exercise if not labeled for easy selection.</p>
+  <center>
+    <img src="20moxp-5.gif" width="573" height="442" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Detail 2 shows the general junction scheme used throughout the portable design. 0.5" diameter tubing forms each junction piece. The inward section of the long element portions and that tail pieces use appropriate hardware for permanent connection. The more outward tubing or the corner section gets a hitch pin hole. Create the hitch pin holes by first ensuring a tight butt joint at the ends of the 5/8" tubing section to be joined. Then drill carefully through both the inner and outer tubing all the way through the "top" and "bottom" of the junction. If the drill bit will pass though both holes, the hitch pin straight side will also fit.</p>
+  <center>
+    <img src="20moxp-6.gif" width="497" height="288" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Detail 3 shows the tail assemble, although not to scale. For the 20-meter Moxon, obtain about 36" of rigid or nearly rigid tubing with a true outside diameter of 0.5". (Measure any tubing that lists its dimensions as "nominal," since such materials tend to use pipe dimensions and only a measuring device will show the true outside diameter.) 18" per tail will hold the ends of the 20-meter Moxon tails the correct distance apart while maintaining alignment. Since the driver tail will be shorter, the permanent hardware goes on that side, with the hitch pin applied to the reflector tail portion. Since you need a similar assembly on each side of the array, good labeling is important.</p>
+  <center>
+    <img src="20moxp-7.gif" width="498" height="331" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Detail 4 reveals that the Moxon requires a split feed mount that insulates and isolates the elements from the boom. A 1/4" thick polycarbonate plate provides the strongest plate for this service. It can be any length and width that will fit the need. For the feedpoint plate, be sure there is room for a small aluminum bent piece to hold a coax connector and leads to the tubing on each side of the plate.</p>
+  <p>Since the plate shown uses U-bolts, obtain a polycarbonate or fiberglass rod to fit within the tubes. Such a rod keeps the tubes aligned, thus reducing the number of U-bolts required. It also prevents the tubing from collapsing under the pressure of tightened U-bolts.</p>
+  <center>
+    <img src="20moxp-7a.gif" width="620" height="334" border="2" vspace="5" hspace="9">
+  </center>
+  <p>For storage, the system shown in Detail 4 and repeated in the alternative figure has a disadvantage. It requires tools to loosen at least one side of the assemble so that you can disassemble one of the 69" element sections. (Remember that 69" is approximate and depends on how you apportion the subsections of the parallel element portions.) The alternative construction shown in the lower portion of the figure uses a shorter length of non-conductive rod. Its function is to align the tubing ends and to provide a base for hardware that allows connection to the coax receptacle.</p>
+  <p>The alternative center mount uses portions of the first long-element section with a cut-off just beyond the feedpoint plate. To strengthen the inner portion of the 20 meter elements, a full 6' length of 0.5" tubing runs the entire length of the element and forms the junction inside the feedpoint assemble as well as the junction with the next outward section of tubing. The long tube holds the permanent hardware, with hitch pins on the other side of each junctions. The sketch shows the positions of the pins, but not their orientation. The hitch pin at the feedpoint plate should be parallel to the face of the plate.</p>
+  <p>Although somewhat more complex to construct, the alternative feedpoint plate assembly can now remain fully constructed with no need for tools at the field site. Hitch pins do the work.</p>
+  <center>
+    <img src="20moxp-8.gif" width="489" height="329" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Detail 5 shows the corresponding reflector plate. As shown, the plate will require tools to loosen one of the element U-bolts. For a no-tool assembly job at the field site, revise the sketch to resemble the alternative feedpoint plate, but with a 0.5" junction tube instead of the fiberglass or polycarbonate rod. Of course, the coax connector is irrelevant to the reflector.</p>
+  <center>
+    <img src="20moxp-9.gif" width="503" height="311" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The final detail (6) concerns the boom and the boom-to-mast mount. I recommend nested sections of 1.25" and 1.125" aluminum if the wall is 0.58" thick. Single thickness tubing might work, but is subject to distortion under the pressure of U-bolts. For 20 meters, we need 9.5 to 10 feet of boom. To create such a boom, use a 6' length of each size tubing and a shorter (3.5' to 4') length. Alternate their placement and position with hitch pins. The pins allow disassembly for storage as lengths no more than 6' long--roughly that same as the longest element pieces. The boom-to-mast plate can be either 1/8" thick aluminum or 1/4" polycarbonate. U-bolts should be stainless steel. Saddles are useful in preventing slippage and tubing distortion.</p>
+  <p><b>Storage, Transport, and Use</b></p>
+  <p>There is nothing magic in the suggested construction of the portable Moxon rectangle. Feel free to adapt and revise as you wish--and you may well have ideas to improve the techniques suggested here. The two key goals are these:</p>
+  <p>1. Keep to an absolute minimum the number of tools needed at the field site to assemble and disassemble the antenna. Murphy's Law dictates that you will forget to bring the one key tool you need to complete the assembly. Keep Murphy at bay by developing the antenna so that it needs no tools at all--or only a small steel rod (sometimes called a screwdriver) to free the hitch pins after use.</p>
+  <p>2. Keep the storage package as short and small of girth as possible. The 6' tubing lengths, plus fixed extensions for junctions, dictates one dimension. The stack of well-labeled tubes has a certain girth when bound together. The folding corners add least to the girth of a round stack, but bent tubes might well be accommodated with a flatter storage scheme.</p>
+  <p>Develop some sort of storage container. Canvass or similar material works well. Be certain that the hardware fits in a well-marked and hard-to-lose bag or box--with extra pins. If your assembly needs a few tools, purchase a few inexpensive tools especially for the antenna and store them with the aluminum and hitch pins.</p>
+  <p>I have made no comments on the mast assembly, since the options are too many and often are site-specific. However, try to raise the Moxon rectangle as high as safely feasible. For 20 meters, the approximate minimum recommended height is about 3/8 wavelength or 26' above ground. At this height and above, the SWR curve will be very stable.</p>
+  <center>
+    <img src="20moxp-10.gif" width="376" height="338" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 10</b> shows the band-edge and band-center azimuth pattern at the take-off angle for the array at a height of 26' on 20 meters. At 3/8 wavelength, the TO angle is 35 degrees, but drops to about 26 degrees when the antenna is 1/2 wavelength up. The lower height, however, is often satisfactory for field use, since the vertical lobe of the far-field pattern is very broad, with usable radiation down to 10 to 15 degrees elevation. As well, at 3/8 wavelength height, as the figure shows, the front-to-back ratio is excellent for a two-element array.</p>
+  <p>These notes are only a set of ideas on the construction of a truly portable Moxon array for 20 through 10 meters. The hitch pin is a much overlooked fastener that can simplify field assembly and disassembly. However, it requires the tubing itself to make the electrical contact at the junctions. If you clean the tubing (with a plastic abrasive pad, not steel wool or other scarring materials) before each use, electrical contact should pose no problems.</p>
+  <p>For permanent installations involving long term exposure to weather and the chemical soup called the atmosphere, use other connection methods and a stronger basic design.</p>
+  <p>However, for short-term field operations, the construction ideas shown here and supplemented by your own knowledge of materials and hardware can produce a truly portable Moxon rectangle--or almost any other type of array you wish to carry into the field.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 02-01-2003. &COPY; L. B. Cebik, W4RNL. This item appeared in</i> AntenneX<i>, January, 2003. 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" width="591" height="3">
+  </center>
+  <p><a href="moxpage.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Moxon Index</a></p>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Amateur Radio Page</a></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#moxon'>Moxon</a>, <a href='../topics.html#portable'>Portable</a></p><br>
+</body>
+</html>

content/moxon/3017m.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="Moxon, Yagi, HF Lower, HF Upper">
+  <title>Using Moxon Rectangles for WARC-Band Antennas Part 2</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>Using Moxon Rectangles for WARC-Band Antennas<br>
+    Part 2: Some 30-17-12 Meter Ideas</h1>
+  </center>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p>Last month we looked at the Moxon rectangle, cut for 17 meters, as the basis for a very compact dual-band Moxon-Yagi for 17 and 12 meters. The design used open-sleeve coupling between the physically driven 17-meter driver and the slaved 12-meter driver. The Yagi portion was a standard driver-director design with about 0.07 wavelength spacing. The result was a two-band array about 10' long and 20' wide that provided over 6 dBi free-space gain, better than 20 dB front-to-back ratio, and a direct feed with 50-Ohm coax (with, as always, a recommended choke or 1:1 balun to attenuate common-mode currents).</p>
+  <p>Compactness: this goal was one of the good reasons for using a Moxon as the basis for the dual band beam. The width of a Moxon is only about 70% that of a full size Yagi with a driver and reflector, and the Moxon uses no loading to achieve the shortening. Instead, it bends the elements around to point toward each other. By selecting the correct proportions and tip-to-tip spacing, one can obtain a parasitic driver-reflector array with nearly the gain of the full size Yagi and considerably improved front-to-back ratio over the Yagi. Part of the reason for the excellent front-to-back performance lies in the current magnitude and phasing on the rear element relative to the front element: they are close to what one might obtain with each element driven to perfection for maximum rearward rejection.</p>
+  <center>
+    <img src="3017m-a.gif" width="567" height="426" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. A</b> provides an outline sketch of a basic Moxon, a refresher. As well, the portions of the Moxon structure are identified, since we shall once more provide some design ideas involving this antenna. However, this month, we shall include 30 meters.</p>
+  <p>A 30-meter Yagi with unloaded elements would be about 48' to 49' side-to-side. A Moxon rectangle for 30 meters requires only 35' of side-to-side space, and about 13' front-to- back. These dimensions are close to those for a common 20-meter beam. The structure of a 30-meter Moxon might have to be a bit beefier than that of a 20-meter Yagi, since the parallel element must support the "tails" (B and D in <b>Fig. A</b>). Nonetheless, for those with space limitations, 35' elements are usually easier to sustain than 48' elements.</p>
+  <p><b>A 30-17 m Combination</b></p>
+  <p>When we examined the possibilities for 17 and 12 meters, we reached two practical conclusions. First, a dual Moxon array may be too sensitive to minor variations to be truly practical for home building. Second, placing a full size 12-meter Yagi of driver- reflector design inside the 17-meter Moxon was not feasible due to the length of the 12- meter elements--especially the reflector.</p>
+  <p>Therefore, we shall bypass a dual Moxon for 30 and 17 meters. However, we shall not forego the possibility of a full-size 17-meter Yagi placed within the frame of a 30-meter Moxon. The longest element of a driver-reflector Yagi for 17 meters is 27' and that should be no problem within the 35' dimension of the 30-meter Moxon. <b>Fig. 1</b> shows the general outline of the combination.</p>
+  <center>
+    <img src="3017m-1.gif" width="444" height="231" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The following table of dimensions uses the designators of <b>Fig. A</b> for the Moxon. The Yagi element spacing entries are distances from the Moxon driver. All dimensions are in feet. The Moxon elements are 1.25" aluminum tubing, while the Yagi elements are 1" diameter aluminum tubing.</p>
+  <pre>Band              Dimension         Length (feet)
+30-meter Moxon    (all elements use 1.25" diameter aluminum tubing)
+Moxon             A                 34.91'
+                  B                  4.89'
+                  C                  1.12'
+                  D                  6.56'
+                  E                 12.57'
+17-meter Yagi     (all elements use 1.0" diameter aluminum tubing)
+Driver            Length            25.80'
+                  Space              1.30'
+Reflector         Length            27.00'
+                  Space              8.00'</pre>
+  <p>The spacing between the Yagi elements is 6.7' or about 1/8 wavelength. The spacing of the Moxon elements is about 0.13 wavelength. The Moxon dimensions are unchanged from those optimized for maximum front-to-back and a 50-Ohm feed when used independently. Of course, changes in material dimensions or the use of stepped-diameter elements will require readjustment of the design to yield satisfactory performance. As I did last month, I shall place model descriptions at the end of these notes for those who wish to experiment with other material combinations.</p>
+  <p>However, once the basics are established, the only post-construction adjustment will be to the slaved 17-meter driver. Its exact length and spacing from the Moxon driver will determine the feedpoint impedance on 17 meters at the physical feedpoint.</p>
+  <p>The Moxon-Yagi combination is a very well-behaved. The following performance table, listing the gain in terms of free-space gain, gives a good general picture.</p>
+  <pre>Frequency         Gain        Front-to-Back           Feedpoint Z       50-Ohm
+  MHz              dBi         Ratio  dB              R+/-jX Ohms       VSWR
+
+10.100            6.21          22.9                  47.6 - j 3.6      1.09
+10.125            6.13          27.0                  50.7 - j 1.4      1.03
+10.150            6.05          33.4                  53.7 + j 0.6      1.07
+
+18.068            6.37          10.8                  52.4 - j22.5      1.55
+18.118            6.26          10.9                  49.9 - j 5.4      1.11
+18.168            6.16          10.9                  47.5 + j10.9      1.26</pre>
+  <p>As we saw last month, the addition of a closely-spaced parasitic beam slightly detunes the Moxon in terms of moving the peak front-to-back ratio upward in frequency. However, the gain and the source impedance are mostly unaffected. <b>Fig. 2</b> provides a free-space azimuth pattern of the 30-meter Moxon performance at mid-band. One of the side-benefits of the Moxon rectangle design is that it tends to hold its high front-to-back ratio even down to a height of 3/8 wavelength--about 36' on 30 meters. Of course, the old rule that higher is better still applies. Nevertheless, even a modest installation can expect quite reasonable results on 30 meters.</p>
+  <center>
+    <img src="3017m-2.gif" width="640" height="300" border="2" vspace="5" hspace="9">
+  </center>
+  <p>On 17 meters, we must expect the lesser front-to-back ratio associated with the driver- reflector Yagi design. <b>Fig. 3</b> shows the mid-band free-space azimuth pattern for the array at 18.118 MHz.</p>
+  <center>
+    <img src="3017m-3.gif" width="640" height="370" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Because the upper band Yagi is behind and within the Moxon rectangle, there is no significant forward-stagger effect. Hence, the Yagi gain and front-to-back ratios are virtually identical to those one might obtain from an independent driver-reflector Yagi for 17 meters. However, with 1/8 wavelength spacing, the feedpoint impedance of an independent Yagi would be closer to 35 Ohms. The near-50-Ohm match is obtained by virtue of the open-sleeve coupling, which can be set for virtually any desired impedance by changes in the length and/or spacing of the driver relative to the physically fed element. As we saw last month, the impedance changes more rapidly on a slaved element than on a directly fed element. In the case of the 17-meter Yagi, it is the reactance that undergoes the most rapid change, while the resistance remain quite stable.</p>
+  <p>Although the 17-meter Yagi does not gain anything from being inside the Moxon, it does not lose anything either. Moreover, it does not take up an additional space on a supporting tower. The two-band array has identically the same outside dimensions as the 30-meter Moxon itself. Except for the additional weight and wind load of the 17-meter elements, there seems little reason not to add the upper band if one seriously plans a 30-meter Moxon.</p>
+  <p><b>A 30-17-12 m Combination</b></p>
+  <p>Suppose we might be willing to extend the boom of the Moxon-Yagi from 12.6' to about 16 feet. For the additional 3.4' of boom length, we add one more band to the array--with virtually no change in the design work done so far. A driver-director Yagi with an element spacing of about 0.07 wavelength can be added ahead of the Moxon driver to arrive at a WARC 3-band array of considerable compactness. <b>Fig. 4</b> shows the general outline of the arrangement.</p>
+  <center>
+    <img src="3017m-4.gif" width="446" height="262" border="2" vspace="5" hspace="9">
+  </center>
+  <p>For the lower bands, the design once more uses 1.25" diameter elements for 30 and 1" diameter elements for 17. The 12-meter elements are 0.5" in diameter, and everything is aluminum. With these materials we can uses the dimensions in the table below. For the 17-meter elements, the spacing entry indicates the distance behind the Moxon driver. For 12 meters, the spacing entry indicates the element spacing forward from the Moxon driver.</p>
+  <pre>Band              Dimension         Length (feet)
+30-meter Moxon    (all elements use 1.25" diameter aluminum tubing)
+Moxon             A                 34.91'
+                  B                  4.89'
+                  C                  1.12'
+                  D                  6.56'
+                  E                 12.57'
+17-meter Yagi     (all elements use 1.0" diameter aluminum tubing)
+Driver            Length            25.80'
+                  Space              1.30'
+Reflector         Length            27.00'
+                  Space              8.00'
+12-meter Yagi     (all elements use 0.5" diameter aluminum tubing)
+Driver            Length            19.46'
+                  Space              0.70'
+Director          Length            18.70'
+                  Space              3.43'</pre>
+  <p>For the Moxon and the 17-meter Yagi, nothing has changed. The dimensions of the 12-meter Yagi are very slightly different from those used with the 17-meter Moxon last month. However, that Moxon used elements with a smaller diameter than the 30-meter Moxon in this design. The major change is in the spacing from the Moxon to the 12-meter slaved driver--somewhat wider than in the 12-17 design.</p>
+  <p>If we see little difference in dimensions, we should also expect little difference in performance. The following performance table provides the numbers.</p>
+  <pre>Frequency         Gain        Front-to-Back           Feedpoint Z       50-Ohm
+  MHz              dBi         Ratio  dB              R+/-jX Ohms       VSWR
+
+10.100            6.23          22.5                  48.5 - j 4.9      1.11
+10.125            6.15          26.3                  51.7 - j 2.8      1.07
+10.150            6.07          32.1                  54.9 + j 0.9      1.10
+
+18.068            6.40          11.3                  53.3 - j16.3      1.38
+18.118            6.31          11.4                  51.3 - j 1.2      1.04
+18.168            6.21          11.4                  49.4 + j13.6      1.31
+
+24.89             6.57          25.3                  59.4 - j 9.9      1.28
+24.94             6.67          22.1                  48.7 + j 3.4      1.08
+24.99             6.76          19.2                  38.9 + j18.5      1.62</pre>
+  <p>On 30 meters, performance only shows insignificant changes in the last decimal places of the performance figures. On 17 meters, the performance values are numerically up, but again, not in a way that makes a difference that one could detect in use. The numeric increase is due in part to the forward stagger effect that gives the 12-meter elements a slight director effect during 17-meter operation.</p>
+  <p>On 12 meters, the 2-element driver-director array performs normally for an antenna of this type, although the independent feedpoint impedance of about 20 Ohms is overcome by slaving the driver to the 30-meter Moxon driver. Last month we saw higher gains on 12 meters. However, the 30-meter driver is farther removed from the 12-meter elements and provides some isolation of them from the interior 17-meter elements. Hence, forward stagger effects are minimal.</p>
+  <p>Nonetheless, for a beam with a 16' boom length, the tri-band Moxon-Yagi offers excellent potential. <b>Fig. 5</b> shows the free-space azimuth pattern at 10.125 MHz.</p>
+  <center>
+    <img src="3017m-5.gif" width="640" height="300" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    <img src="3017m-6.gif" width="640" height="370" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In <b>Fig. 6</b>, we see essentially the same pattern as in <b>Fig. 3</b> for the middle of 17 meters. The 12-meter free-space azimuth pattern for 24.94 MHz (<b>Fig. 7</b>) is similar to the one shown for 12 meters last month. The same rear quartering lobes are present to moderate the 180-degree front-to-back ratio.</p>
+  <center>
+    <img src="3017m-7.gif" width="640" height="320" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The exact spacing and length of the slaved drivers will require field adjustment to arrive at a final setting to achieve a good 50-Ohm match on each band. However, those adjustments are about the only critical matters related to construction--once you decide on and design for the precise set of materials you will use. Essentially, you can design an independent Moxon for 30 meters and adjust it to perfection. Then, you can add the 17-meter elements and perform driver adjustments until you are satisfied. Rechecking the 30-meter impedance should show no significant change. Finally, add the 12-meter elements and adjust its driver for a good match on that band. Because element spacing is a bit more critical for driver-director arrays than for driver-reflector Yagis, recheck the element spacing for 12 meters before concluding the adjustment procedure. Once more, the impedances for 30 meters and 12 meters should not have significantly changed by adding the 12-meter elements.</p>
+  <p>I have good luck in adjusting Moxons and simple Yagis close to the ground by pointing the array as close to straight up as possible, with the reflector anywhere from 4 to 12 feet off tghe ground. The adjustments have held true at heights from 20 to 35 feet up. This technique is not applicable for all beams, but it is worth a try for those who do not relish adjusting beam elements from the top of a tower.</p>
+  <p>In 2006, Charles Johnson, K4ZRJ, built a version of the 3-band antenna. <b>Fig. 8</b> shows the antenna mounted above his tribander. Charles used parts originally designed for the Hy-Gain 203BA for his version of the antenna. He reports good results with the antenna, and his workmanship is very evident from the photo that I have included with his permission.</p>
+  <center>
+    <img src="3017m-8.JPG" width="640" height="435" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Charles used a taper schedule for the aluminum tubing that required him to modify the design somewhat. The EZNEC listings show his model for the design that he produced. If you use different materials, you may have to redesign the element sections to suit those materials.</p>
+  <p>For those who wish to do further design work on models of the two basic antenna designs, here are model descriptions that should ease wire coordinate entries for most NEC modeling software.</p>
+  <pre>30-17 m Moxon-Yagi                           Frequency = 10.125/18.118  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1          -17.457, -4.888,  0.000  W2E1 -17.457,  0.000,  0.000 1.25E+00   7
+2     W1E2 -17.457,  0.000,  0.000  W3E1  17.457,  0.000,  0.000 1.25E+00  45
+3     W2E2  17.457,  0.000,  0.000        17.457, -4.888,  0.000 1.25E+00   7
+4          -17.457, -6.005,  0.000  W5E1 -17.457,-12.569,  0.000 1.25E+00   9
+5     W4E2 -17.457,-12.569,  0.000  W6E1  17.457,-12.569,  0.000 1.25E+00  45
+6     W5E2  17.457,-12.569,  0.000        17.457, -6.005,  0.000 1.25E+00   9
+7          -12.900, -1.300,  0.000        12.900, -1.300,  0.000 1.00E+00  33
+8          -13.500, -8.000,  0.000        13.500, -8.000,  0.000 1.00E+00  33
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+
+30-17-12 m Moxon-Yagi                        Frequency = 10.125/18.118/24.94  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1          -17.457, -4.888,  0.000  W2E1 -17.457,  0.000,  0.000 1.25E+00   7
+2     W1E2 -17.457,  0.000,  0.000  W3E1  17.457,  0.000,  0.000 1.25E+00  45
+3     W2E2  17.457,  0.000,  0.000        17.457, -4.888,  0.000 1.25E+00   7
+4          -17.457, -6.005,  0.000  W5E1 -17.457,-12.569,  0.000 1.25E+00   9
+5     W4E2 -17.457,-12.569,  0.000  W6E1  17.457,-12.569,  0.000 1.25E+00  45
+6     W5E2  17.457,-12.569,  0.000        17.457, -6.005,  0.000 1.25E+00   9
+7          -12.900, -1.300,  0.000        12.900, -1.300,  0.000 1.00E+00  33
+8          -13.500, -8.000,  0.000        13.500, -8.000,  0.000 1.00E+00  33
+9           -9.730,  0.700,  0.000         9.730,  0.700,  0.000 5.00E-01  25
+10          -9.350,  3.430,  0.000         9.350,  3.430,  0.000 5.00E-01  25
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+Version designed and built by Charles Johnson, K4ZRJ:
+
+                      EZNEC/4 ver. 4.0
+
+30,17,12 M Moxon Yagi Combo                   Frequency = 10.125/18.118/24.94  MHz.
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs       Insulation
+          Conn.      X       Y       Z       Conn.      X       Y       Z                   Diel C  Thk(in) Loss Tan
+1          W8E1     -222,  196.9,    816      W2E1     -189,  196.9,    816     0.438   7       1        0        0
+2          W1E2     -189,  196.9,    816      W3E1     -109,  196.9,    816     0.875   13      1        0        0
+3          W2E2     -109,  196.9,    816      W4E1   -2.925,  196.9,    816      1.25   17      1        0        0
+4          W3E2   -2.925,  196.9,    816      W5E1    2.925,  196.9,    816      2.14   3       1        0        0
+5          W4E2    2.925,  196.9,    816      W6E1      109,  196.9,    816      1.25   17      1        0        0
+6          W5E2      109,  196.9,    816      W7E1      189,  196.9,    816     0.875   13      1        0        0
+7          W6E2      189,  196.9,    816      W9E1      222,  196.9,    816     0.438   7       1        0        0
+8          W1E1     -222,  196.9,    816               -222,  117.1,    816     0.438   13      1        0        0
+9          W7E2      222,  196.9,    816                222,  117.1,    816     0.438   13      1        0        0
+10                -173.5,  138.5,    816     W11E1     -106,  138.5,    816     0.438   13      1        0        0
+11        W10E2     -106,  138.5,    816     W12E1      -49,  138.5,    816     0.875   13      1        0        0
+12        W11E2      -49,  138.5,    816     W13E1   -2.925,  138.5,    816         1   9       1        0        0
+13        W12E2   -2.925,  138.5,    816     W14E1    2.925,  138.5,    816      2.14   3       1        0        0
+14        W13E2    2.925,  138.5,    816     W15E1       49,  138.5,    816         1   9       1        0        0
+15        W14E2       49,  138.5,    816     W16E1      106,  138.5,    816     0.875   13      1        0        0
+16        W15E2      106,  138.5,    816              173.5,  138.5,    816     0.438   13      1        0        0
+17                  -162,   57.1,    816     W18E1     -106,   57.1,    816     0.438   13      1        0        0
+18        W17E2     -106,   57.1,    816     W19E1      -49,   57.1,    816     0.875   13      1        0        0
+19        W18E2      -49,   57.1,    816     W20E1   -2.925,   57.1,    816         1   9       1        0        0
+20        W19E2   -2.925,   57.1,    816     W21E1    2.925,   57.1,    816      2.14   3       1        0        0
+21        W20E2    2.925,   57.1,    816     W22E1       49,   57.1,    816         1   9       1        0        0
+22        W21E2       49,   57.1,    816     W23E1      106,   57.1,    816     0.875   13      1        0        0
+23        W22E2      106,   57.1,    816                162,   57.1,    816     0.438   13      1        0        0
+24        W31E1     -222,   41.5,    816     W25E1     -189,   41.5,    816     0.438   7       1        0        0
+25        W24E2     -189,   41.5,    816     W26E1     -109,   41.5,    816     0.875   13      1        0        0
+26        W25E2     -109,   41.5,    816     W27E1   -2.925,   41.5,    816      1.25   17      1        0        0
+27        W26E2   -2.925,   41.5,    816     W28E1    2.925,   41.5,    816      2.14   3       1        0        0
+28        W27E2    2.925,   41.5,    816     W29E1      109,   41.5,    816      1.25   17      1        0        0
+29        W28E2      109,   41.5,    816     W30E1      189,   41.5,    816     0.875   13      1        0        0
+30        W29E2      189,   41.5,    816     W32E1      222,   41.5,    816     0.438   7       1        0        0
+31        W24E1     -222,   41.5,    816               -222, 103.25,    816     0.438   13      1        0        0
+32        W30E2      222,   41.5,    816                222, 103.25,    816     0.438   13      1        0        0
+33                  -122,   33.1,    816     W34E1      -73,   33.1,    816     0.438   9       1        0        0
+34        W33E2      -73,   33.1,    816     W35E1   -2.925,   33.1,    816     0.875   13      1        0        0
+35        W34E2   -2.925,   33.1,    816     W36E1    2.925,   33.1,    816      2.14   3       1        0        0
+36        W35E2    2.925,   33.1,    816     W37E1       73,   33.1,    816     0.875   13      1        0        0
+37        W36E2       73,   33.1,    816                122,   33.1,    816     0.438   9       1        0        0
+38                  -117,      0,    816     W39E1      -73,      0,    816     0.438   9       1        0        0
+39        W38E2      -73,      0,    816     W40E1   -2.925,      0,    816     0.875   13      1        0        0
+40        W39E2   -2.925,      0,    816     W41E1    2.925,      0,    816      2.14   3       1        0        0
+41        W40E2    2.925,      0,    816     W42E1       73,      0,    816     0.875   13      1        0        0
+42        W41E2       73,      0,    816                117,      0,    816     0.438   9       1        0        0
+
+Total Segments: 446
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       27       50.00      50.00    2        1           0         V
+</pre>
+  <p>The 30-17 or the 30-17-12 combination arrays offer some interesting potentials for small WARC band beams. These design notes aim to whet your appetite for further and improved designs. However, you will have to go some to improve performance on all bands while shrinking the size of these arrays. However, if you do manage the trick, I'd be first in line to find out how.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 06-01-2000, 07-04-2006. &COPY; L. B. Cebik, W4RNL. The original item appeared in</i> AntenneX <i>for May, 2000. 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="moxpage.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Moxon 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#hf-lower'>HF Lower</a>, <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#moxon'>Moxon</a>, <a href='../topics.html#yagi'>Yagi</a></p><br>
+</body>
+</html>

content/moxon/4030.html

@@ -0,0 +1,136 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="Moxon, Yagi, HF Lower">
+  <title>Moxon Rectangles for 30m and 40m</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <img src="../images/moxbut.gif" align="left" width="119" height="61" border="2" vspace="5" hspace="10"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">
+  <center>
+    <h1>40 + 30 = 50 (Not 70)<br>
+    The Rudiments of a Design Idea</h1>
+  </center><br>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center>
+  <center>
+    <img src="../images/colorbar.gif" width="591" height="3">
+  </center><br>
+  <br>
+  <p>A number of requests over the years have taken this direction: can you design a combination 40 meter and 30 meter beam on a single boom--making everything give full-size performance but still be compact--relative to the bands involved?</p>
+  <p>That request is a tall order. Full size Yagi elements for 40 meters run over 70' in length. Most commercial Yagis for 40 meters use various methods of element shortening to reduce the raw physical load created by full size elements. Linear and inductive loading are the two most popular approaches. However, there are a number of 3 and 4 element full size Yagis on the job. (Very often, the 4th Yagi element functions less to increase gain and more to permit a wide operating bandwidth.)</p>
+  <p>30-meter elements are more modest at lengths approaching 45-50'. As well, the band is narrow enough (50 kHz) to permit the use of narrow-band, high performance driver-director Yagis. A beta match usually suffices to bring the low feedpoint impedance up to standard coax levels. (Of course, we should not overlook the relatively compact phased array for 30 meters developed by N7CL.)</p>
+  <p>It would be nice if a combined 40 and 30 array could have elements that extended no further outward than the +/-25' required for 30-meter elements. There is a way of achieving this goal, but it is not likely to be an easy one to implement in a physical design. There are some adjustments that require field implementation, and they can be a bit daunting. As well, supporting the number of elements in the final array, along with their peculiarities, will also require engineering beyond the scope of this design exercise. However, for whatever it may be worth, here is a design that will cover all of both bands with only a 50' side-to-side width.</p>
+  <p>These note can only be the rudiments of a design and not a finished product. Because I do not have the facilities or tower to build and test the array, I cannot complete all of the mechanical details that will also have an impact on the electrical design. At best, I can only locate some of the many points where the individual designer and builder will have to make decisions and refine the outlines given here.</p>
+  <p>The basic design consists of a Moxon rectangle for 40 meters with a 2-element driver-director Yagi for 30 meters. The 30-meter driver is slaved to the 40-meter Moxon fed element. <b>Fig. 1</b> shows a general outline sketch of the array.</p>
+  <center>
+    <img src="4030-1.gif" width="636" height="392" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The maximum side-to-side width of the array is 50'. The boom length is 26' (plus whatever excess is necessary for proper element support). There are a total of 4 elements, with the Moxon elements having end tails that point toward each other. The Moxon element arrangement will present physical problems that we shall take up later.</p>
+  <p><b>Fig. 1</b> labels each dimension, and the following table provides numbers that go with the labels. However, the dimensions are based on NEC-4 models of the array using 1" diameter aluminum elements throughout. I chose the modeling diameter based upon the equivalent uniform diameter of elements from a number of 40-meter arrays on file. Although such arrays begin with large diameter tubing--sometimes up to 3"--they step downward rapidly and end up with 0.5" and even 0.375" element diameters at the outer ends. We shall go into the meaning of this situation for practical antenna construction before we are done. First, some basic dimensions.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                 40-30-Meter Moxon-Yagi Combination Dimensions
+
+Note: all dimensions are in feet and correspond to designations shown in Fig. 1.
+
+            Dimension         Length in Feet
+                  A           50.00'
+                  B            7.21'
+                  C            1.73'
+                  D            9.47'
+                  E           18.41'
+                  F            0.64'
+                  G            6.95'
+                  H           26.00'
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Before we look into the dimensions and their implications for refinement and construction, let's first see if this is a design in which you would be interested by virtue of its performance. The 40-meter performance is strictly Moxon-rectangle standard. One of the reasons for using fatter elements (instead of wire) is to increase the operating passband width, not just in terms of SWR, but as well, to include a spreading of the gain and front-to-back profiles.</p>
+  <center>
+    <img src="4030-2.gif" width="600" height="300" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 2</b> provides azimuth and elevation plots for the 40-meter array at the edges and middle of the band. The antenna height is 70' or about 1/2 wavelength on 40. I would not recommend using the array below 70' or else you will have to make some adjustments to center the SWR curve. Like every Moxon rectangle, the beamwidth tends to be wider than that of most Yagis.</p>
+  <center>
+    <img src="4030-3.gif" width="600" height="300" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 3</b> provides band edge and center patterns for 30 meters, which are mostly a function of the forward two elements. However, the 40-meter elements also function in a minor way as reflectors to increase the overall performance. (We determine this in part by the current levels on the Moxon elements and also by the increase in performance over a stand-alone 2-element driver-director Yagi of the same spacing.) A 2-element driver director Yagi with closely spaced elements (less than 0.08 wavelength) yields quite high gain and a good front-to-back ratio, but only over a narrow bandwidth. Being "slaved" to the Moxon rectangle (or any other fed array) tends to further reduce the operating bandwidth. Only the narrowness of 30 meters permits good performance (for an array of this type) across the entire band.</p>
+  <p>To translate the patterns into more definite numbers, the following table gives the principal operating predictions from the model.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  40-30-MHz Array Operating Potential at 70'
+
+Freq.       Gain        180-Deg/Worst-Case      Feedpoint Z       50-Ohm
+ MHz        dBi         Front-to-Back dB        R +/- jX Ohms     SWR
+40 Meters:  TO/Elevation Angle of Maximum Radiation:  26 degrees
+ 7.0        11.29       13.32--13.32            41.3 - j22.1      1.68
+ 7.1        11.14       20.37--20.37            67.3 - j12.9      1.49
+ 7.2        10.90       15.99--15.73            85.3 - j16.8      1.80
+ 7.3        10.66       12.17--12.17            91.7 - j21.2      1.97
+30 Meters:  TO/Elevation Angle of Maximum Radiation:  19 degrees
+10.0        11.50       16.35--14.25            84.0 + j10.4      1.72
+10.125      12.05       24.76--18.18            42.9 + j 3.1      1.18
+10.15       12.17       22.47--19.43            32.3 + j 8.7      1.63
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The take-off angles for the two bands, of course, are functions of the fact that, with respect to a wavelength, the antenna is higher on 30 meters than on 40 meters. Only part of the extra 30-meter gain is attributable to the increased height. Most of it stems from the fact that a closely spaced driver-director Yagi in fact has more gain than the Moxon rectangle or a comparably spaced driver-reflector Yagi.</p>
+  <p>The key influences of the arrays on each other show up in the impedance reports. The slaved 30-meter driver keeps the Moxon feedpoint reactance capacitive in this array, when an independent Moxon might well show a shift from capacitive to inductive reactance across the band. The slaved 30-meter driver also affects the feedpoint impedance on the 40-meter element during 10-MHz operation, creating a dip in the inductive reactance at mid-band, but not going into the capacitive region. Expect impedance curves in an actual antenna that may even vary from these, according to the finally selected dimensions used in the array.</p>
+  <center>
+    <img src="4030-4.gif" width="583" height="210" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 4</b> provides both 50-Ohm SWR curves on one graph. It is unlikely that one can change the 30-meter curve much, except to move it a bit up and down the narrow band. The Moxon 40-meter curve might well show improvement with careful adjustment of some of the dimensions.</p>
+  <p>One cannot simply buy a batch of 1" diameter tubing and construct this array. The first task for any builder is to determine the stepped-diameter schedule to be used. For the 4 elements, the first portions up to 25' from center can all be identical, assuming that the smallest diameter tubing used allows sufficient strength to support the tails.</p>
+  <p>Once you have selected a mechanically sound element taper schedule, the best procedure is then to convert the uniform 1" diameter element lengths into lengths suitable for the stepping schedule. It is very likely that you will have to lengthen all side-to-side dimensions with the tubing that you use. Elements that taper downward from center to outer end usually require greater length than uniform diameter elements. The differential may amount only to a few inches, but it will be enough to detune both portions of the array considerably if not taken into account.</p>
+  <p>There are handbook formulas for making the transformation of element lengths. However, one of the most convenient methods is to create a model on a NEC program and adjust the element tip lengths until you arrive at uniform-diameter equivalents that match the initial design. If the equivalent uniform element diameter is between 0.8 and 1.2 inches, the original dimensions will not require much adjustment. However, feel free to customize the design to your own desires. Both EZNEC and NEC-Win Plus have provisions for creating uniform-diameter substitute elements for unloaded symmetrical elements using a tapering schedule.</p>
+  <p>In the Moxon portion of the array, perhaps the most critical dimension is the gap between element tails. The Moxon makes use of 2 forms of elements coupling to achieve its patterns and impedance: mutual coupling between the element portions parallel to each other and end coupling between the tails. The degree of end coupling depends upon 2 factors: the space between the tail ends and the diameter of the elements at that point. The initial design makes use of 1" diameter tail ends, but a tapered-element schedule is likely to use smaller diameter tubing for the tail ends. Therefore, to achieve the same coupling with smaller tubing, the tails will need to be brought closer together--without significantly changing the overall final design length of the reflector element (including the parallel and tail sections). Incidentally, one cannot use the tapered-diameter correction facility in NEC-2 programs with the Moxon rectangle, since the elements are not linear. However, one can use sundry work arounds to arrive at adequate construction guidance (including obtaining a NEC-4 program).</p>
+  <p>To keep the tails aligned, it is very useful to use a section of non-conductive tubing that just fits inside the two tail end tubes. Since the goal is alignment rather than mechanical support, the tubing can be relatively light, such a CPVC or similar. We shall turn to mechanical support soon.</p>
+  <p>The slaved 30-meter driver must be very close (0.64' in the model) to the 40-meter Moxon driver to achieve the desired feedpoint impedance. Several factors suggest that the element spacing will not be identical to the initial model used here. First, using a tapered diameter schedule will alter the coupling slightly along the length of both elements. Second, the model is reaching the limits for giving accurate reports with closely spaced elements of different lengths, even though the segment ends are closely aligned throughout the mode. This is a NEC limitation. Therefore, expect to make adjustments to the spacing of the slaved driver and to its length as well. At 30 meters, one can make several inches worth of adjustment without having to restore the director to the initial design spacing from the driver. However, finding the right combination of element spacing and length to achieve an acceptable 50-Ohm SWR curve on the main driver from 10.0 to 10.015 MHz can be laborious. Adjustments work best when the initial setting is somewhere close to ideal. When the elements are spaced too far apart, the progression of results for small adjustments seems to move in the opposite direction than when inside the ballpark. Hence, once can work for hours, being led all of the time in the wrong direction. When adjustments only seem to make matters worse, return to the starting point and begin again, but in the opposite direction as used during the first run.</p>
+  <p>Elements as large as those used in the array will tend to oscillate in the wind. Because the Moxon elements, with their tails, are constrained by the non-conductive tail links, the 40-meter assembly will have wind-motion characteristics quite unlike the 30-meter elements, with their free ends. Collisions between the 30-meter slaved driver and the 40-meter fed driver will be inevitable. Therefore, some means of holding the 30-meter slaved driver and the 40-meter Moxon driver in alignment is likely more a necessity than something merely desirable.</p>
+  <p>Besides holding the drivers in alignment, we also need a means of supporting the 40-meter tails. The tail assemblies on a large Moxon rectangle place significant strain on the two elements supporting them. One method of support is to use tubing sizes large enough that the weight of the tails is no especial problem. Alternatively, one might develop a supplemental support system for the entire array that can reduce element stress and keep the elements aligned.</p>
+  <center>
+    <img src="4030-5.gif" width="497" height="479" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 5</b> shows the basic outline of such a scheme. Somewhere (sensible, from a mechanical perspective) above the main boom, install a shorter stiff boom on the mast. This boom will be used to hold one end of a series of stays, that is, non-conductive support lines for the elements.</p>
+  <p>At a mechanically sensible point outward on each side of center, place a non-conductive support arm (tube?) so that it is beneath each element. By a series of notches and/or ties, fastened to each element to the arm. Because there will still be differences in the way elements react to the wind, the tie system should be set to fix the spacing but to let the individual elements slide a bit. On one or more elements, fix the arm in both directions so that the stay-system does not pull the arm inward.</p>
+  <p>At points near the out ends of the arms, connect and fasten the stays. If the arm material is too flexible, you may add a third set of stays perpendicular to the mast. The support system then depends on the equalization of tension on the stays.</p>
+  <p>Without a set of specific load figures, derived from a program like YagiStress and customized to the particular element diameter schedule chosen for the array, it is impossible to recommend any particular set of dimensions for the support-arm-and-stay system. Indeed, there are many variations on this theme that one might apply to the array. However, the basic message is that this is a major collection of aluminum tubing that has considerable weight and wind area. Adequate support is a necessity if the design and construction effort goes for naught during the first stiff breeze.</p>
+  <p>As we noted at the beginning, these notes only begin the design process; they do not complete it. I have tried to locate many of the areas that will need detailed attention before one can begin to gather materials, let along start actual construction.</p>
+  <p>Nonetheless, the design principle is sound, having been applied to light arrays for the upper HF region. It does show that a combination 40-30-Meter array is possible with quite decent full-band performance for a 26' boom. Until I have facilities and space to try out the design with an actual set of elements on a tower that will give me the minimal height for adequate performance, these notes will have to do. Unfortunately, I do not have time at present to customize the design for specific taper schedules, but you can do the job yourself with any of the low-end NEC-2 programs with a facility for providing uniform-diameter equivalents. Even when the customizing has been completed within the design system, expect to do considerable adjustment on the physical product of this work.</p>
+  <p>For those who wish to model the array, the following EZNEC model description should suffice to create a model in any of the leading programs.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+40-30-M Moxon-Yagi Array                     Frequency = 7.1  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+(40-meter elements)
+1          -25.000, 11.200, 70.000  W2E1 -25.000, 18.406, 70.000 1.00E+00   7
+2     W1E2 -25.000, 18.406, 70.000  W3E1  25.000, 18.406, 70.000 1.00E+00  45
+3     W2E2  25.000, 18.406, 70.000        25.000, 11.200, 70.000 1.00E+00   7
+4          -25.000,  9.472, 70.000  W5E1 -25.000,  0.000, 70.000 1.00E+00   9
+5     W4E2 -25.000,  0.000, 70.000  W6E1  25.000,  0.000, 70.000 1.00E+00  45
+6     W5E2  25.000,  0.000, 70.000        25.000,  9.472, 70.000 1.00E+00   9
+(30-meter elements)
+7          -24.000, 19.050, 70.000        24.000, 19.050, 70.000 1.00E+00  43
+8          -22.900, 26.000, 70.000        22.900, 26.000, 70.000 1.00E+00  41
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <center>
+    <img src="../images/colorbar.gif" width="591" height="3">
+  </center><br>
+  <br>
+  <p><i>Updated 10-20-2001. &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" width="591" height="3">
+  </center><br>
+  <br>
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content/moxon/6m.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="Moxon, VHF / UHF">
+  <title>Moxon Rectangles for 6 Meters</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1><img src="../images/moxbut.gif" align="middle" width="119" height="61" border="2" vspace="5" hspace="10"> Moxon Rectangles for 6 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>
+  <center>
+    <img src="../images/colorbar.gif" width="591" height="3">
+  </center><br>
+  <p>I have had numerous requests over the last few years for the dimensions and construction plans for Moxon rectangles designed for the 6-meter band. The Moxon rectangle is a quite broad-band antenna, but it is not quite broad enough to cover the entire band. As well, the lower end of the band is the major arena for horizontal polarization using CW or SSB. The upper portion of the band sees most of the FM activity, with vertical polarization being standard.</p>
+  <p>Hence, for full band coverage--or for selected use of one or the other mode of activity--we really need 2 Moxons. The first will be a horizontally oriented beam designed for 50.5 MHz with coverage of the first MHz of the band. The second will be a vertically oriented version designed for 53 MHz, with coverage from 52 to 54 MHz. After looking at the characteristics of these two versions of the same basic design, we shall make a few construction suggestions. Finally, we shall show how to combine them into a single array--but with separate feedlines.</p>
+  <center>
+    <img src="6m-1.gif" width="317" height="438" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 1</b> shows the general outlines of the two types of Moxons. The Moxon is a driver-reflector type of parasitic array. Unlike standard Yagi designs that employ only the coupling between parallel lengths of element conductor, the Moxon folds back its elements to provide a second form of coupling. The coupling of the driver and reflector tails that face each other provides a second form of coupling, and the combination of the two gives us an array that we can design for very good front-to-back performance, about as much forward gain as a 2-element Yagi, and a 50-Ohm feedpoint impedance for direct connection of a standard coaxial cable feedline.</p>
+  <center>
+    <img src="6m-2.gif" width="371" height="275" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Since we need a way to refer to the parts of a Moxon when giving dimensions, <b>Fig. 2</b> supplies what has become a set of default designations. Dimension A is the total side-to-side dimension of the array. B is the driver tail or fold-back portion, and D is the reflector fold-forward portion or tail. C is the most critical dimension, the gap, and tends to vary as a direct function of the element diameter. E is simply the sum of B, C, and D, and gives us the total front-to-back dimension of the array.</p>
+  <p>All 6-meter Moxons will be about 7' wide or about 3.5' each side of the center line. The front-to-back dimension with be about 2.5', plus or minus a little. Hence, the Moxon makes a very compact array, suitable for enhancing repeater communications or for SSB operation in local nets.</p>
+  <p>In fact, the precise dimensions for a 50-Ohm Moxon for any frequency and element diameter have been developed into several computer programs, ranging from a GW Basic utility in the <a href="../radio.html#HAMCALC">HAMCALC</a> suite to a NEC-Win Plus model to a stand-alone Windows program developed by AC6LA and available for free download from his site (<a href="https://www.ac6la.com/moxgen1.html" target="_blank"><b>www.ac6la.com/moxgen1.html</b></a>). Since all of them are based on the same modeling and regression analysis that I performed some time back, all will give the same dimensions for the same design frequency and element diameter.</p>
+  <p>Let's start our foray into 6-meter Moxons with the low-end horizontal version.</p>
+  <h4>A Horizontal Moxon Rectangle for 50.5 MHz.</h4>The materials that folks have access to will vary from region to region. Therefore, let's make a chart of dimensions. All of the dimensions will presume that we are using some form of aluminum tubing, ranging from 1.0" down to 0.25" in diameter. As we shall see in the construction section, aluminum tubing is an optimal choice for a 6-meter Moxon.
+  <p>In the following table, all dimensions refer to <b>Fig. 2</b> and are in inches.</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Dimensions for a 50.5-MHz Moxon Rectangle
+
+      El. Dia.        A          B          C          D          E
+      1.0             83.61      10.40      4.58       16.22      31.20
+      0.875           83.68      10.53      4.46       16.21      31.20
+      0.75            83.76      10.69      4.32       16.19      31.20
+      0.625           83.86      10.86      4.16       16.18      31.20
+      0.5             83.97      11.07      3.97       16.15      31.19
+      0.375           84.12      11.32      3.74       16.12      31.19
+      0.25            84.31      11.65      3.44       16.08      31.18
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>Note that the dimensions change only a small amount from one tube diameter to the next. Moreover, the front-to-back dimension (E) changes almost not at all. However, the differences are important to centering the performance curve of the Moxon on the design frequency, which then has consequences for performance at the band edges. So using the dimensions that apply to the element diameter that you will use does have significance.</p>
+  <p>Let's set the antenna 25' above ground, which is just over 1.34 wavelengths up. The forward gain will be about 11.4 dBi at 50.5 MHz, with a 180-degree front-to-back ratio of about 30 dB and a 78-degree beamwidth between -3-dB points. The feedpoint impedance of 50 Ohms, plus or minus 1 to 2 Ohms reactance.</p>
+  <center>
+    <img src="6m-3.gif" width="376" height="345" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 3</b> overlays the design frequency and the passband edge azimuth patterns of the Moxon rectangle when oriented horizontally. As you can see from the patterns, taken for a version using a 0.5" diameter element set, as we move lower in frequency, the gain increases very slightly (too slightly to ever be measured in operation), and the rearward radiation begins to increase. Above the design frequency, the gain decreases by an equally slight amount, and, again, the rearward radiation pattern shows growth.</p>
+  <p>The performance of the antenna is virtually unchanged at the design frequency for any tubing size. However, the band-edge performance does change (in this case, using a 1-MHz passband). The fatter the tubing, the slower the rate of forward gain change. More significantly, the fatter the tubing, the slower the growth of rearward radiation lobes both above and below the design frequency. However, those changes are not so great as to override considerations such as the most convenient tubing size for constructing a Moxon rectangle.</p>
+  <center>
+    <img src="6m-4.gif" width="583" height="217" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Tubing size also makes a difference in the 50-Ohm SWR for the final antenna, as measured at the antenna terminals, as shown in <b>Fig. 4</b>. For a 1-MHz passband, almost any size tubing will do, and the SWR at the shack end of the coax is likely to be too low to get a definite frequency for the lowest value.</p>
+  <h4>A Vertical Moxon Rectangle for 53.0 MHz.</h4>The design principles do not change at all when we flip the Moxon rectangle for upper 6-meter service. However, the dimensions will change, since we are now using a design frequency of 53.0 MHz in order to cover the 52-54-MHz range. The following table provides dimensions, again in inches and again using <b>Fig. 2</b> as a reference.
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Dimensions for a 53.0-MHz Moxon Rectangle
+
+      El. Dia.        A          B          C          D          E
+      1.0             79.64       9.86      4.41       15.46      29.73
+      0.875           79.71       9.99      4.29       15.45      29.73
+      0.75            79.79      10.14      4.16       15.44      29.73
+      0.625           79.88      10.31      4.00       15.42      29.73
+      0.5             79.99      10.50      3.82       15.40      29.72
+      0.375           80.13      10.75      3.60       15.37      29.72
+      0.25            80.31      11.07      3.31       15.33      29.71
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>The last decimal place in column E, the overall front-to-back dimension, may be a digit or two off the sum of B, C, and D due to rounding of the individual values. However, I doubt that any builder will be constructing the elements to a hundredth of an inch tolerances. In fact, in the construction section, we shall be slightly altering the dimensions to take account of the fact that we shall bend the tubing at the corners.</p>
+  <p>Once more, let's place a 0.5" diameter version of the antenna at a height of 25' above ground. At the design frequency, we shall obtain a 50-Ohm feedpoint impedance accompanied by a front-to-back ratio well above 30 dB. (Vertical orientation affects the front-to-back ratio less than horizontal orientation for an antenna within about 2 wavelengths of ground.) However, unlike the horizontal version of the array, the peak gain is only about 7.6 dBi. Let's see why.</p>
+  <center>
+    <img src="6m-5.gif" width="376" height="345" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 5</b> overlays the azimuth patterns of the antenna at the design frequency and at 52 and 54 MHz. In all cases, we see a very wide beamwidth, over 142 degrees between -3-dB points. That increased beamwidth--about twice the value for the horizontal version--spreads the radiated power over a much wider area and thus reduces the peak gain. This is inherent in any parasitic array with all of the elements in a single plane. Nevertheless, both the horizontal and the vertical versions of the array have almost 4 dB gain over their counterpart dipoles at the same height.</p>
+  <p>As the patterns show, the increased bandwidth that we require of a vertical Moxon increases the rearward radiation at the band edges. Once more, the fatter the elements, the less growth to the rearward radiation for any change in frequency relative to the design frequency.</p>
+  <center>
+    <img src="6m-6.gif" width="583" height="217" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In <b>Fig. 6</b>, we have the 50-Ohm SWR curves for the array at selected element diameters. The SWR increases more rapidly below the design frequency than above it. The antenna feedpoint impedance for the thinnest tubing actually is above 2:1, although at the shack end of the coax, where we usually measure SWR, it may seem lower than that value. Hence, one might well think in terms of at least an intermediate tubing size for the vertical Moxon.</p>
+  <p>The SWR climbs more slowly above the design frequency, suggesting that we might choose a lower design frequency and extend the coverage from 51 to 54 MHz. This tactic is possible, but at a cost. The forward gain and the front-to-back ratio degrade continuously as we move above the design frequency. Hence, with a design frequency of, say, 52 MHz, the array performance would not be very good at 54 MHz.</p>
+  <h4>Building a Moxon Rectangle for 6 Meters</h4>There is an unfortunate tendency among newer antenna builders to see a design they like and then to grab almost any materials close at hand and slap together a version that almost works. Many a good antenna design has gotten a bad name in some regions because builders did not exercise the same care in construction as the original builder. To obtain performance that agrees with the design notes above, acquire the right materials and then build the antenna with all the care possible.
+  <p>A good tubing size for a 6-meter Moxon--whether horizontal or vertical--is 0.5". This size is useful, since we can use #8 or #10 hardware for fastenings. Of course, the hardware will all be stainless steel, both for rust prevention and to avoid bi-metallic contact problems.</p>
+  <p>For a 6-meter Moxon rectangle, we shall need 4 6' lengths of 1/2" diameter tubing. This size tubing can be shipped from suppliers like Texas Towers by UPS. (Yes, we shall have some scrap left over for use as garden stakes.) Use 6061-T6 or 6063-T832. Hardware depot tubing has an unknown vintage, so good quality antenna tubing is highly desirable. Do not use aluminum electrical conduit or copper tubing. The conduit is too heavy, and so is the copper in any form rigid enough not to gradually fold over on its own accord.</p>
+  <p>We shall also require a short (under 6") length of 3/8" aluminum tubing and a similar length of 3/8" diameter fiberglass or similar rod. We shall be constructing the elements in halves, so we need to join and align them. The short length of 3/8" aluminum tubing will join the two halves of the reflector, making them electrically one. The fiberglass or equivalent rod will align the driver halves, but allow a gap for connecting the feedline. Finally, we shall require some 3/8" outer-diameter fairly rigid tubing, something light but straight. These tubes will fit inside the ends of the driver and reflector tails to hold the spacing constant under all conditions.</p>
+  <p>For hardware, we shall require some #8 nuts and bolts, along with some locking washers. We can use sheet metal screws to fasten the tail junction tubes in place. However, all hardware must be stainless steel, including the washers. Since some of this falls outside what home warehouse hardware bins contain, consider locating a hardware supplier or use an on-line ordering source like McMasters-Carr. From such sources, you can also obtain a small sheet of 1/4" thick UV-protected polycarbonate (trade-name Lexan) to use as boom-to-element plates. Polycarbonate cuts nicely with woodworking saws and drills cleanly with standard bits.</p>
+  <p>The needs for a single Moxon rectangle are small, so you may wish to combine orders with others interested in the antenna in order to make up the minimum order requirements for a given supplier. Since we have vowed to be careful, we need not rush to get parts, but can go slowly and get everything we need.</p>
+  <p>For a boom, you can use either metal or Schedule 40 PVC (if the PVC in your area is adequately UV protected--this varies around the U.S.). In the southeastern US, white PVC gives me about 10 years of service before becoming brittle.</p>
+  <center>
+    <img src="6m-7.gif" width="586" height="406" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 7</b> shows some of the suggested construction methods that I use. you may have better ones, in which case, use them. There are 4 keys areas of construction concern.</p>
+  <p>1. <i>The reflector junction</i>: A 3/8" section of tubing a little longer than the boom-to-element plate joins the two halves. If we use polycarbonate plates about 4" long and 3" wide, we have plenty of room for the elements and the nuts/bolts for boom fastening. A 1" nominal PVC pipe is actually about an inch and a quarter in diameter and is very rigid for a boom that is less than 3' long. For the plate-to-boom bolts, #10 hardware is very secure, using only 2 bolts per plate. However, use a compression lock washer against the plate or obtain self-locking nuts (with a nylon insert).</p>
+  <p>Since a #10 bolt requires a larger hole, you may wish to fasten the elements to the plate with #8 hardware, again with compression lock washers against the plate. (Toothed lock-washers may gradually loosen by gouging the polycarbonate.) For all drilling of the boom and the elements, make up a jig from scrap wood to pin the material in place while you drill. If you can gain access to a drill press--even a small device designed to hold an electric hand drill--by all means use it. Align all holes before drilling instead of widening holes later to bring parts into alignment.</p>
+  <p>2. <i>The driver gap</i>: By using a 3/8" fiberglass rod to align the driver halves, we can fasten the driver and the rod to the plate using #8 hardware. Note that there are two sets of hardware at the driver: an outer set to pins the element to the plate and an inner set to which we shall connect the feedline. If you prefer, you can set the connection hardware at right angles to the element-to-plate hardware to keep the coax more in line with the boom.</p>
+  <p>The sketch shows direct connections between the element and the coax, with no connector. I have found that from 6 meters on upward, connectors and their associated leads contribute reactance to the feedpoint impedance. A direct connection and a short length of coax taped to the boom for strain relief simplifies feedpoint construction. Once everything is complete, seal the connections, especially since solder terminals may not be available in stainless steel. Plasti-Dip or similar materials provide a weather-secure coating.</p>
+  <p><i>A note on the gap</i>: The gap at the feedpoint is part of the overall element length (or dimension A), NOT an addition to it. Whether you start with a 1/4" gap or a much wider one, let the driver side-to-side dimension remain constant. In effect, the coax leads make up the seemingly missing tubing. The driver gap is not critical from 1/4" to over 3/4", but closer is always better in this type of antenna.</p>
+  <p>3. <i>The tail separation</i>: Because we must keep the tail ends at a specified distance and aligned, we need a short piece of non-conductive tubing to lock their relative positions. Almost anything will do here, if it is 3/8" in outside diameter and relatively rigid. We shall need only about 4-4.5 inches exposed, so even flexible nylon tubing will work, although rigid plumbing CPVC is superior. You may use sheet metal screws to fasten the tube inside the tail pieces--after careful measurement, of course.</p>
+  <p>4. <i>The element bends</i>: Bending aluminum tubing requires care to prevent crimping that will eventually result in a metal crack and break. The radius of the corner bends will depend on the tubing size used. A plumber's tubing bender is applicable only up to about 1/4" diameter tubing. Larger tubing requires larger bend radii, and that means a home-made jig.</p>
+  <center>
+    <img src="6m-8.gif" width="375" height="254" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 8</b> shows a simple jig: a circle mounted on a base plate. The circle can be cut from plywood or be a pulley wheel. For larger radius bends, I have used such materials as a worn-out power mower wheel.</p>
+  <p>Mark a point on the 6' length of tubing that marks the center of the bent corner and leaves excess on both the tail and the parallel sections. Try to keep this mark at the center of the bend. As well, mark the tubing to indicate the parallel length (1/2 of dimension A) and the tail (B or D, as applicable). Fill the tube with the finest sand available and tape the end shut. If you prefer, warm the tube until it can just barely be handled with gloves. Pin one end of the tube (a nail in the base board will do) and slowly bend the tubing. The fatter the tubing, the more important it is to bend a few degrees and pause. Continue the bend until it is at least a 90-degree bend. A little more will not hurt, since a slight unbending of the tube does no harm.</p>
+  <p>Bend the tubing before you drill any mounting holes to make sure that all such holes are at right angles to the mounting plates. In fact, let's delay any drilling and do some work on the floor.</p>
+  <p>From the dimensions that apply to your tubing size, draw out the Moxon on the floor (or on paper taped to the floor). Be sure to mark the center or boom line as well as the points where the tails end. Next, lay the untrimmed bent pieces on the drawing. Because the corners are "clipped" by the bending, the pieces will just exceed the lines on the floor.</p>
+  <p><i>NOTE</i>: For the adjustment of positions, be sure that the gap is constant and does not change!</p>
+  <p>With a constant gap distance as specified for the tubing size and measured against the marks made on the tubing, adjust the tube position to equalize the amount by which the tubes fall outside the original lines. At the same time, align the tubes. Now trim the tubes. Remember to trim a bit (1/8" or so per tube) off the driver to leave a gap for the coax connection. Smooth all cuts. Aluminum oxide sandpaper is best so that you do not leave residues of other metals on the aluminum. Clean the outer and inner edges of the tubes, since you will be inserting rods or tubes inside the main elements.</p>
+  <p>Now return to the assembly process and complete the Moxon rectangle. If you have used sufficient care, it should be right on target on the first try. However, you can always trim a bit more from the reflector and driver tubes at their centers--and a little expansion that leaves a little inner reflector tube showing and widens the driver gap a small amount should do not harm.</p>
+  <p>I assume that you have a boom-to-mast plate and stainless steel U-bolt hardware. As well, I assume that the coax from the feedpoint has a connector and a double-female in-line connector. If those assumptions are correct, you are ready to put the Moxon rectangle into service.</p>
+  <h4>Crossed Moxons</h4>Suppose that you have both SSB and FM operations on 6 meters and that you decide that the Moxon has characteristics that are suitable for each job. Then you may wish to think about <b>Fig. 9</b>.
+  <center>
+    <img src="6m-9.gif" width="426" height="441" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The outline sketches crossed Moxon rectangles. Since the low-end horizontal version is a bit larger than the vertical high-end version, let's place the horizontal reflector slightly ahead of the vertical reflector. Actually, it will make no difference if the two reflector join at the center. However, we shall need physically separate feedpoints--and separate feedlines as well. However, the assembly will fit on a single boom.</p>
+  <p>Crossing Moxons and operating them separately makes no difference at all to the performance of either one.</p>
+  <p>One precaution applies to either a single vertical Moxon or to crossed Moxons: we shall need a non-conductive boom if we attach the mast at the center of the boom. (6-meter arrays are heavy enough where I do not recommend extending the boom rearward for attachment to a mast without a further extension and counterweight.) Schedule 40 PVC has two sizes that nest reasonably well for stiffening the material for mast use: 1" inside 1-1/4" nominal (closer to 1.25" and 1.5" actual outside diameters). You will need about 3.5' to go from the boom to the edge of the vertical Moxon and perhaps another 2' above any metal structure (like a tower), plus a few more feet to reach a rotator. (An old TV rotator is more than sufficient to handle even the crossed Moxons). However, do not use more PVC mast than you need to do the job.</p>
+  <h4>A Wire Moxon for 6 Meters?</h4>As a final note, we should address the question of making a wire Moxon. A #12 or #14 copper wire Moxon is feasible for the horizontal version only. However, the thin wire will narrow the passband severely. If you operate within a very narrow spread of frequencies at the low end of the band, then you may consult one of the design aids and set up a wire version. It will perform well--as well a the tube version. As well, it may be easier to make sharp corners and trim to length.
+  <p>However, a wire version of the vertical Moxon is likely to prove unsatisfactory for repeater hopping. It will work well for monitoring a single repeater--or a couple that are within a half-MHz of each other (allowing for the frequency split). However, for general coverage of the FM region of 6 meters, a version with fatter elements is strongly advised.</p>
+  <p>We can illustrate the opportunities and the limitations of a wire Moxon for 6 meters with a simple example. Let's design a wire Moxon for horizontal use around the design frequency of 50.5 MHz. The dimensions will be as follows:</p>
+  <pre> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Dimensions for a 50.5-MHz Moxon Rectangle
+
+      El. Dia.        A          B          C          D          E
+  AWG #14 (0.0641")   84.86      12.53      2.61       15.95      31.09
+      0.25            84.31      11.65      3.44       16.08      31.18
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .</pre>
+  <p>I left the figures of the quarter-inch version for comparison. As shown in <b>Fig. 10</b>, the wire Moxon has a steeper gain curve and a sharper front-to-back curve than the tube version of the same antenna. However, for local and net operations, these figures may be very adequate.</p>
+  <center>
+    <img src="6m-10.gif" width="744" height="473" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The SWR curve, while steeper than the ones for the tube versions of the antenna, guarantees coverage of the first MHz of the band. See <b>Fig. 11</b>. You may note in the two graphs that the front-to-back ratio peaks just below the design frequency, as does the 50-Ohm SWR curve.</p>
+  <center>
+    <img src="6m-11.gif" width="744" height="473" border="2" vspace="5" hspace="9">
+  </center>
+  <p>You can make the frame from 1/2" or 3/4" CPVC. By passing the frame through carefully aligned holes in a central Schedule 40 PVC mast, you can cement the structure together. Each cross arm will need to be just over 7.5' long (3.75' each side of the mast). As well, you will have to plan your angles for the holes carefully to get the correct shape between corners. However, if you are only a little off, you can stress the arms with Nylon line (1/8" to 3/16") to perfect the shape of the ultimate support structure. If you adjust the holes in the mast, then add through bolts to finalize the positions of the support arms. The details of a suggested construction for the frame, line, and wires appears in <b>Fig. 12</b>.</p>
+  <center>
+    <img src="6m-12.gif" width="655" height="419" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Even if you get the angles between supports correct, you may still run a length of nylon or similar line from the corners along the line of the tails. Then, tape the tails to this line, and the ends (raw cut and not looped) will stay in alignment and maintain their spacing. (I tend to prefer to use a full perimeter line to pre-stress the frame so that it maintains its shape under all conditions.) The resulting wire Moxon very likely will be considerably cheaper then any of the tube versions, since we can make it from PVC and household wire, along with a little hardware at the feedpoint.</p>
+  <p>Whether the Moxon is the right antenna--and which version is the one to build--depends on your own analysis of operating needs. Do not build one unless it will do the job that you need. But if you do build one, build it carefully, and it will work correctly without further field adjustment.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p>Updated 02-03-2003. &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.</p>
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+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
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content/moxon/c3m.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="Moxon, HF Upper, Yagi">
+  <title>Moxon-Modifying the C3-Type Tri-bander</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <center>
+    <h1>Moxon-Modifying the C3-Type Tri-bander</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>The Force 12 C3 tri-band Yagi has become a very popular compact beam for the general operator. Nevertheless, its 35' wing-spread has prevented some would-be owners from purchasing the antenna because their available space is not sufficient for full-size 20-meter elements. I have over the years received a number of inquiries as to whether the 20-meter elements could be shortened by various types of loading.</p>
+  <p>In general, but not absolutely, the answer has been negative. Most forms of loading--except element-end loading--disrupt the current phase relationships between the fed driver and the slaved drivers, destroying the feed system.</p>
+  <p>However, the 2-element 20-meter portion of the array can in principle be replaced by a Moxon rectangle without disturbing the other elements of the array. The result is not only a beam with only a 25' side-to-side spread, but as well a boom length nearly 2' shorter than the original.</p>
+  <p>The following notes are designed only as a feasibility study to validate the replacement in principle. I developed the foundations for these notes in late 1999, but have not had the opportunity to implement them with an actual beam. Hence, I can only provide the information suggested by extensive modeling in NEC-4. However, as we shall see at the end of the article, reality has caught up with design theory.</p>
+  <p>Our first step is to understand something of how the C3-type array is designed. For that purpose, I shall not present a detailed model of the Force 12 C3. To obtain an authorized computer model of the antenna, one should contact the company directly. My model makes use of uniform-diameter elements and hence represents only a C3-type antenna, not the actual commercial version.</p>
+  <p>As well, many facets of the actual C3 are protected by patents and other proprietary considerations, for example, the open-sleeve feed system. Therefore, these notes are intended only as a design study for individual use and not for any commercial purpose whatsoever.</p>
+  <p><b>The C3-Type Tri-Band Antenna</b></p>
+  <p>The C3-type tribander consists of three antennas: a 20-meter 2-element driver-reflector Yagi, a 15-meter 2-element driver-reflector Yagi, and a 3-element driver-director Yagi. The general arrangement is sketched in outline in <b>Fig. 1</b>.</p>
+  <center>
+    <img src="c3m-1.gif" width="640" height="380" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The following model description from EZNEC provides details of the element lengths and spacings.</p>
+  <pre>C-3-Type 20-10-m tribander                   Frequency = 14  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -138.50, 34.000,  0.000       138.500, 34.000,  0.000 7.50E-01  43
+2          -132.35,119.000,  0.000       132.350,119.000,  0.000 7.50E-01  43
+3          -101.00,134.500,  0.000       101.000,134.500,  0.000 5.00E-01  33
+4          -97.000,146.500,  0.000        97.000,146.500,  0.000 5.00E-01  33
+5          -89.000,212.500,  0.000        89.000,212.500,  0.000 5.00E-01  33
+6          -195.00,130.250,  0.000       195.000,130.250,  0.000 1.00E+00  61
+7          -209.00,  0.000,  0.000       209.000,  0.000,  0.000 1.00E+00  61
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          31     6 / 50.00   (  6 / 50.00)      1.000       0.000       I</pre>
+  <p>The elements are organized in the order 15 meters, 10 meters, 20 meters. My placement of the 20-meter elements at the end results from the fact that we shall eventually replace them with a Moxon rectangle. Note also that I have used 1" diameter elements for 20 meters, 0.75" for 15, and 0.5" for 10 meters.</p>
+  <p>The most central feature of the C3-type multi-band Yagi is the drive system. It makes use of open-sleeve coupling such that only the 20-meter element is driven, whatever the band in use. The 15-meter driver is slaved to the 20-meter element on the side of the fed-driver closer to the corresponding reflector. Likewise, the 10-meter slaved driver is on the side of the fed driver closer to the 10-meter directors.</p>
+  <p>I should note that the spacing and lengths of the slaved drivers relative to the fed driver may differ from the actual spacings used in a C3. Both NEC-2 and NEC-4 have some limitations when wires of different lengths and diameters are brought into close proximity. Even with great care in aligning segment junctions among the elements, the closer the spacing, the more the potential error in the model. Hence, the actual required slaved driver lengths and spacings may be different from those used in the model. However, the model is sufficiently accurate to establish the principles involved in the operation of a C3-type antenna.</p>
+  <center>
+    <img src="c3m-2.gif" width="640" height="380" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The 20-meters driver and reflector together form a 2-element beam of relatively standard design and performance. <b>Fig. 2</b> shows the free-space azimuth patterns of the NEC-4 model at the ends and center of 20 meters. The following table summarizes 20-meter modeled performance.</p>
+  <pre>Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+14.0        6.44        10.48       68.8        44.7 - j 4.4      1.16
+14.175      6.13        10.90       69.6        55.4 + j 6.8      1.18
+14.35       5.84        10.51       70.2        65.9 + j16.6      1.49</pre>
+  <p>As the table shows, the performance is everywhere normal for a 2-element Yagi. The gain descends with frequency increases. The element spacing to achieve a 50-Ohm match reduces the front-to-back ratio slightly relative to that obtainable with closer spacing and a lower feedpoint impedance. However, the SWR curve for a direct feed system is outstanding.</p>
+  <center>
+    <img src="c3m-3.gif" width="640" height="380" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Placing the 15-meter driver and reflector between the corresponding 20-meter elements results in close to optimal coupling, something that is more difficult to obtain had the 15-meter slaved driver been placed forward of the fed driver. However, a slaved driver generally has a narrower operating passband with respect to impedance than a directly driven element. The narrowing tends not to show up in terms of pattern shape, as evidenced by <b>Fig. 3</b>. However, the &lt;2:1 SWR passband on 15 meters is only about 360 kHz, somewhat less than the whole band. However, the peak SWR of about 2.8:1 is well within the range of antenna tuners built into modern transceivers. As well, the SWR curve will be noticeably shallower at the shack end of any common coaxial cable if the cable is over a wavelength long. The following table shows the modeled performance of the subject antenna on 15 meters.</p>
+  <pre>Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+21.0        6.55        10.78       67.2        52.9 - j36.0      1.99
+21.225      6.20        11.19       68.6        44.1 + j 4.9      1.18
+21.36       5.99        10.92       69.6        39.3 + j28.5      1.96
+21.45       5.84        10.59       70.4        36.2 + j44.2      2.83</pre>
+  <p>The band-edge patterns of the 20-meter and 15-meter sections of the antenna are quite similar, as is the front-to-back level. Only the SWR curve reveals the presence of the open-sleeve coupling system, and it is still a highly workable set of values.</p>
+  <p>The 10-meter section of the antenna differs considerably from the 20-meter and 15 meter sections. Beginning with a slaved driver forward of the fed driver, there are two directors. Although there is no tuned 10-meter reflector, the 15-meter elements (especially) fulfill part of that function in a system known as forward-stagger design.</p>
+  <p>Note that the first director is quite closely spaced to the slaved driver. Although this director does not lose all of its gain-enhancing function, its chief role is in setting the impedance and the operating passband of the 10-meter section. It bears more than a small resemblance to the spacing that would be used in OWA designs. The result is a 900 kHz SWR passband with usable patterns above 29 MHz. <b>Fig. 4</b> shows the 28, 28.5, and 29 MHz free-space azimuth patterns for the modeled array.</p>
+  <center>
+    <img src="c3m-4.gif" width="640" height="380" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The following tables shows the reported properties of the 10-meter section across the first MHz of the 10-meter band.</p>
+  <pre>Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+28.0        6.34        15.12       66.8        55.7 - j35.1      1.94
+28.5        6.55        16.65       68.8        45.0 + j 0.2      1.09
+28.9        6.80        17.68       70.4        36.0 + j26.6      2.00
+29.0        6.87        17.86       70.8        32.7 + j33.0      2.44</pre>
+  <p>Once more, the SWR curve at the shack end of a coaxial cable will likely be shallower than the one at the feedpoint terminals, and any remnant SWR in excess of 2:1 is easily handled by a built-in ATU in the transceiver. More significantly, the performance curve reflects a typical Yagi with directors, as the gain increases with increasing frequency. The use of two directors provides a bit higher gain across the operating passband than the driver-reflector sections used on 20 and 15 meters.</p>
+  <p><b>Replacing the 20-Meter Section with a Moxon Rectangle</b></p>
+  <p>If we replace the 20-meter elements with a Moxon Rectangle, we obtain an array with a smaller footprint: 10' narrower and almost 2' shorter. <b>Fig. 5</b> shows the outlines of such an array.</p>
+  <center>
+    <img src="c3m-5.gif" width="640" height="380" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The following model description permits a direct comparison of element length and spacing between the Moxon-ized version of the C3-type antenna and the basic model just examined.</p>
+  <pre>Moxon-C3-type tribander                      Frequency = 14  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -138.50, 34.000,  0.000       138.500, 34.000,  0.000 7.50E-01  43
+2          -131.90,119.000,  0.000       131.900,119.000,  0.000 7.50E-01  43
+3          -101.00,134.500,  0.000       101.000,134.500,  0.000 5.00E-01  33
+4          -97.000,146.500,  0.000        97.000,146.500,  0.000 5.00E-01  33
+5          -89.000,212.500,  0.000        89.000,212.500,  0.000 5.00E-01  33
+6          -150.00, 88.250,  0.000  W7E1 -150.00,130.250,  0.000 1.00E+00   7
+7     W6E2 -150.00,130.250,  0.000  W8E1 150.000,130.250,  0.000 1.00E+00  51
+8     W7E2 150.000,130.250,  0.000       150.000, 88.250,  0.000 1.00E+00   7
+9          -150.00, 78.650,  0.000 W10E1 -150.00, 22.250,  0.000 1.00E+00  10
+10    W9E2 -150.00, 22.250,  0.000 W11E1 150.000, 22.250,  0.000 1.00E+00  51
+11   W10E2 150.000, 22.250,  0.000       150.000, 78.650,  0.000 1.00E+00  10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          26     7 / 50.00   (  7 / 50.00)      1.000       0.000       I</pre>
+  <p>If you examine wires 1-5, you will notice that the only change is to the 15-meter driver length--a slight adjustment needed to bring all of the SWR passbands back into alignment. I have left these elements at there original marks to facilitate the comparison. However, the Moxon reflector is 22.25" forward of the position of the former Yagi reflector.</p>
+  <center>
+    <img src="c3m-6.gif" width="640" height="380" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Perhaps the most significant change in performance occurs on 20 meters, as the typical Moxon pattern replaces the 2-element driver-reflector pattern of the original array. <b>Fig. 6</b> shows the increased beamwidth, increased front-to-back ratio, and slight decrease in forward gain. The numbers associated with these patterns appear in the following table.</p>
+  <pre>Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+14.0        6.40        16.56       77.2        43.0 - j11.4      1.33
+14.175      6.03        31.51       77.8        60.9 - j 3.3      1.23
+14.35       5.67        19.94       78.4        75.6 - j 1.1      1.51</pre>
+  <p>While the gain differential is unlikely to be detectable in operation, the increased front-to-back ratio will be readily noticed. The 10-degree wider beamwidth may or may not be useful, depending upon the type of operation. In a contest, it reduces the need for re-aiming the beam so often.</p>
+  <p>However, the key benefit of using the Moxon is the reduction in the side-to-side dimension of the array. However, every benefit is usually accompanied by a challenge. In this case, the difficulty lies in building element corners and a means of keeping the element ends in alignment. As well, unless good construction is used, the forward and rear elements may react to winds in differing rhythms, thus stressing the element tail assemblies. In short, Moxon rectangle construction for 20 meters may require a bit more careful planning than the usual 2-element Yagi.</p>
+  <center>
+    <img src="c3m-7.gif" width="640" height="380" border="2" vspace="5" hspace="9">
+  </center>
+  <p>On 15 meters, the chief feature to notice is that there is no significant change in performance compared to the basic array from which this one is derived. The <b>Fig. 7</b> free-space azimuth patterns are virtually identical to those for the basic array, and the following table of modeled values confirms the appear of the patterns.</p>
+  <pre>Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+21.0        6.63        11.08       67.0        61.9 - j37.3      1.99
+21.225      6.22        11.75       67.8        50.1 + j 8.4      1.18
+21.36       5.99        11.25       68.2        44.0 + j33.2      2.01
+21.45       5.84        10.74       68.4        40.3 + j49.4      2.91</pre>
+  <p>Gain values, where they differ at all, do so only in the meaningless hundredths column. All of the other values a mere smidgens apart from the numbers reported for the basic array. In short, confining the 15-meter elements within the Moxon rectangle results in no significant interactions in addition to those one might find when the elements are between Yagi elements for 20 meters.</p>
+  <center>
+    <img src="c3m-8.gif" width="640" height="380" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In similar fashion, the 10-meter performance--as sampled in the free-space azimuth patterns of <b>Fig. 8</b>--also replicates closely the performance on 10 meters by the original array. The following table, when compared with the corresponding table for the original antenna, confirms how closely the two perform.</p>
+  <pre>Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+28.0        6.32        15.14       67.0        57.4 - j34.7      1.92
+28.5        6.61        16.51       67.4        46.8 + j 0.7      1.07
+28.9        6.90        17.38       68.0        36.5 + j26.8      1.99
+29.0        6.99        17.51       68.2        33.0 + j33.2      2.43</pre>
+  <p>In principle, then, it is possible to replace the 20-meter elements in a C3-type antenna with Moxon Rectangle elements with no loss of performance and only a change in the nature of the 20-meter patterns that reflect the differences between a 2-element Yagi and a Moxon Rectangle. In principle, one obtains a smaller array that might fit in spaces in which a full-size C3-type antenna might not fit.</p>
+  <p><b>The Differences Between Principles and Practice</b></p>
+  <p>The design exercise has established a principle, but there may be numerous problems to overcome in translating the principle into practice. Although I have mentioned a few along the way, let's review what they might be in one place.</p>
+  <p>1. <b>Modeling limitations</b>: I have called attention to the fact that NEC-2 and NEC-4 have limitations associated with closely spaced wires having different lengths and diameters, even when one is careful to set up those wires so that the segment junctions align as closely as possible. The closeness of the slaved drivers to the fed driver, especially on 10 meters, suggests that the element dimensions and spacing are only suggestive. They will require considerable adjustment in practice. For the 10-meter slaved driver forward of the fed driver, here is the guideline.</p>
+  <blockquote>
+    <p>A. Increasing the element length decreases the feedpoint resistance and makes the reactance more inductive (or less capacitive). Decreasing the element length does just the opposite, increasing the feedpoint resistance and making the reactance more capacitive (or less inductive).</p>
+    <p>B. Closing the spacing decreases the feedpoint resistance and makes the reactance more capacitive (or less inductive. Opening the spacing increases the resistance and makes the reactance more inductive (or less capacitive).</p>
+  </blockquote>
+  <p>If this is your first open-sleeve coupled beam, be extra patient. It is easy to forget the guidelines and adjust the wrong parameter. If that happens and the feedpoint values appear to be going awry, return the slaved element to its original length and spacing and start the procedure again. Make very small changes between feedpoint measurements until you get a good feel for how much each increment of change affect the feedpoint impedance.</p>
+  <p>2. <b>Element diameter taper and other construction points</b>: the models use uniform-diameter elements, which is normally impractical on the HF bands. For a practical antenna, one must first reconstruct the model using the element taper schedule that reflects proposed construction. The linear elements can be re-sized using Leeson correction factors. However, these corrections only apply to linear elements. Hence, the Moxon elements may require either the use of NEC-4 to obtain a reasonably reliable model or considerable experimentation during construction.</p>
+  <p>However, all is not thrown into a murky bog by this limitation. The Moxon elements can be built and tested independently. Once established, the remaining elements have almost no effect upon them. (Similarly, the 20-meter elements of the original array are almost wholly unaffected by the addition of the elements for 15 and 10 meters.)</p>
+  <p>There have been many techniques used for the construction of Moxon corners. One can bend aluminum around various forms by first filling the tubing with sand and then--if possible--warming it. However, numerous Moxon builders have found pre-bent sections of aluminum in many places. Among the most original was the use of leg-sections from lawn chairs that had been placed on a pile of discarded items. CPVC (thin-wall PVC) makes a cheap and reasonably rigid separator for the element ends. Polycarbonate tubing would be superior from a UV and RF perspective, but CPVC is quite serviceable.</p>
+  <p>Finally, it is wise to develop a simple bracket to keep the fed driver and the two slave drivers well aligned. Sheets of acrylic, Plexiglas, or polycarbonate placed about 6-7 feet outward from the boom and "trapping" all three drivers will reduce SWR excursions created by winds that wave the elements out of step with each other.</p>
+  <p>This design exercise is, in the end, only a proof of principle and an invitation to those who wish to experiment further. I have no wish to reduce sales of the original C3 antenna. However, for those with too little space for the original, the Moxon version may--with considerable construction care--prove to be a feasible alternative.</p>
+  <p><b>The OptiBeam OB6-3M</b></p>
+  <p>Since developing the models for the modified C-3-type antenna, I have encountered a new beam that resembles on the surface the C-3. OptiBeam of Germany makes a line of multiband Yagis that differs from the Force 12 line in 2 respects: the OptiBeams use a method of directly feeding all drivers and the beams themselves are somewhat heavier in construction.</p>
+  <p>I suggested to the makers indirectly that they might consider Moxon-izing their smallest model, and they have done so. Below is a photo of the OB6-3M, a 6 element, 3-band beam using a Moxon rectangle for 20 meters. Relative to the C3-type antenna, the OptiBeam small model uses only 2 elements on 10 meters, placing the driver behind the 20-meter element with only 1 director. The makers claim a wider operating bandwidth for this arrangement.</p>
+  <center>
+    <img src="c3m-9.gif" width="628" height="587" border="2" vspace="5" hspace="9">
+  </center>
+  <p>For those who do not wish to experiment but instead directly purchase a finished version of the beam, the OB6-3M and the other beams in the OptiBeam line are available from <a href="https://www.optibeam.net/" target="_blank">OptiBeam</a>. Since I do not have a version of the antenna on hand, I cannot vouchsafe for the claimed specifications, but they are quite similar to those noted in the study above.</p>
+  <p>Reality sometimes does catch up with antenna modeling.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p><i>Updated 06-08-2002. &COPY; L. B. Cebik, W4RNL. This item first appeared in</i> antenneX <i>for June, 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>
+  <p><a href="moxpage.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Moxon Index</a></p>
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+  <p class="topics-footer">Topics: <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#moxon'>Moxon</a>, <a href='../topics.html#yagi'>Yagi</a></p><br>
+</body>
+</html>

content/moxon/dd.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="Moxon, HF Upper">
+  <title>The Double-D Antenna</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <img src="../images/moxbut.gif" align="left" width="119" height="61" border="2" vspace="5" hspace="10"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">
+  <center>
+    <h1>The Double-D Antenna</h1>
+  </center><br>
+  <center>
+    <h3>L. B. Cebik, W4RNL</h3>
+  </center>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  Peter Dodd, G3LDO, developed the Double-D antenna as an improvement on the VK2ABQ square. Between 1980 and 1990, he evolved several versions of the antenna, as described in his book, <i>The Antenna Experimenter's Guide</i> (Chapter 8 of the first edition). Actually, the antenna is a slightly revised version of the Moxon rectangle, with "tails that either go up or down and inward toward the mast for easier assembly.
+  <p>As a reference point, <b>Figure 1</b> reviews the structure of a Moxon rectangle, while <b>Figure 2</b> provides a free space pattern for a 20-meter Moxon rectangle. No dimensions are given here for the Moxon, but there are other notes at this site for wire Moxons from 10-40 meters. The sketch is from that note. Also note that the parts of the sketch with letter labels do not coincide with the parts of the Double D shown below.</p>
+  <center>
+    <img src="dd1.gif" width="567" height="426" border="2" vspace="5" hspace="9">
+  </center>
+  <center>
+    <img src="dd2.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The Double-D has a somewhat more complex geometry due to its elevated tails. <b>Figure 3</b> illustrates the basic structure, with identification of the arms. The antenna forms a horizontal square, 28' from corner-to-corner for 20 meters. Dodd has preferred to make both Ds equal in overall length, although he reports one version with a very small difference in tail length between the driven element and the reflector.</p>
+  <center>
+    <img src="dd3.gif" width="600" height="344" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The best modeled performance I have been able to derive from a 20-meter version of the Double-D has required that the reflector tails be significantly longer than the driven element tails. Here are the dimensions of the best modeled version:</p>
+  <pre>Table 1.  Dimensions for a bare-copper wire Double-D.
+
+Designator     Item                     Length
+A, B           Length/Width             19.8'
+C              Arm length (from mast)   14.0'
+D              Junction elevation        2.3'
+E              Tail length, DE           7.9'
+F              Tail length, Ref          8.2'
+
+All element #14 copper wire.</pre>
+  <p>Notice that these dimensions use a very conservative elevation of the tails. More radical elevation changes, as well as shorter dimensions for the length and width, yield lower performance figures. Even so, the best free space gain obtained from the antenna has been about 4.1 dBi, with a front-to-back ratio just over 15 dB. As Figure 4 shows, the beamwidth is nearly 90 degrees, and the rear quadrant is well-behaved, that is, the rear quadrant shows a smooth pattern of rejection.</p>
+  <center>
+    <img src="dd4.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The Double-D is designed for compact yards or gardens and modest installations. The arms are nonconductors. The wires and cords from the arm ends to the mast serve double duty: as tails and as supports for the arm ends. A perimeter cord is recommended to keep the arms properly positioned laterally.</p>
+  <p>Over level average terrain, at a height of 1/2 wl (about 35' on 20 meters), the antenna exhibits a broad forward lobe and an equally broad rear lobe. The front-to-back ratio increases to about 22 dB, while the forward gain is in the neighborhood of 9.5 dBi. Figure 5 overlays a Moxon and a Double-D pattern for relevant comparison.</p>
+  <center>
+    <img src="dd5.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Although the two patterns look similar, there is a major difference: the elevation angle of maximum radiation for the Moxon is 26&deg;, while the Double-D's take-off angle is 4&deg; higher. The double-D falls considerably short of Moxon rectangle performance. However, it lends itself to somewhat easier construction, especially if one contemplates rotating the antenna by hand or rotor. For some types of operation, the front-to-back ratio may be of more utility than raw forward gain. A convenience is the fact that the feedpoint impedance is in the neighborhood of 50-55 ohms, a good match for coaxial feed systems.</p>
+  <p>In the end, however, Dodd's claims of 3-4 dB gain over a dipole do not fully materialize. At best, I have been able to model about 2 dB over a similarly situated dipole, and my models have been optimized. The end result is an antenna with somewhat less gain than a properly tuned X-beam, but with a superior rear pattern. It also has less gain than a 2-element Yagi shortened to about 2/3rds full size using linear or inductive loading at the feedpoint, although shortened Yagis are capable of quite good front- to-back ratios. These comparisons are intended neither to compliment nor condemn the Double-D, but only to place it relevantly within the cluster of antennas to which it belongs.</p>
+  <p>The dimensions have been altered by Dodd for the 2nd Edition of his excellent book, <i>The Antenna Experimenter's Guide</i> (RSGB), with some improvements in performance. However, compared to a standard Moxon Rectangle, which takes up very little more room for any given band, the high performance region occurs over a very narrow portion of the band. The newer version has a peak gain a little more than 3 dB better than a dipole. Because Peter's book is such a good reference volume for the antenna experimenter, I shall leave further details of the improvements "as an exercise for the reader."</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p><i>Updated 3-18-97, 5-4-99. &COPY; L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center><br>
+  <br>
+  <p><a href="moxpage.html"><img src="../images/rtnhome.gif" align="bottom" width="40" height="40"> Return to Moxon Index</a></p>
+  <p><a href="../radio.html"><img src="../images/return.gif" align="bottom" width="40" height="40"> Go to Amateur Radio Page</a></p>
+  <p class="topics-footer">Topics: <a href='../topics.html#hf-upper'>HF Upper</a>, <a href='../topics.html#moxon'>Moxon</a></p><br>
+</body>
+</html>

content/moxon/mbm.html

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+<!DOCTYPE html>
+<html lang="en">
+<head>
+  <meta charset="UTF-8">
+  <meta name="keywords" content="Moxon, HF Upper">
+  <title>Multi-Banding the Moxon Rectangle</title>
+  <link rel="stylesheet" href="../styles.css">
+</head>
+<body>
+  <img src="../images/moxbut.gif" align="left" width="119" height="61" border="2" vspace="5" hspace="10"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">
+  <center>
+    <h1>Multi-Banding the Moxon Rectangle</h1>
+  </center><br>
+  <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>I have had a number of inquiries into multi-banding the Moxon rectangle. The compact antenna seems to beg for nesting. However, to the present time, I have had no success in developing a workable model of the antenna for any HF band combination in the nested configuration.</p>
+  <p>In Moxon's book, <i>HF Antennas for All Locations</i>, G6XN notes a detuning system that he uses with his wire version. However, the wire spacing required by the system makes for a bad model. Consequently, I cannot say whether or not the system would work with aluminum rectangles, each of which has been optimized for its band.</p>
+  <p>One solution is to create a "Christmas Tree" of rectangles, each well spaced from the one below it. Such systems have been used with ZL-Specials and HB9CVs, both of which are phased arrays. 10-12 feet of spacing should provide ample separation. The system would require separate feedlines, with switching done either at the mast or on the ground.</p>
+  <p>Most inquiries have indicated a preference for a single array boom on which to mount all elements. Within this constraint, a solution of sorts may be possible--in fact, two solutions. Let's examine them one at a time.</p>
+  <h3>Back-to-Back Moxons</h3>For some potential Moxon users, the pattern is the most important aspect of the antenna. The near cardioidal pattern with a very high front-to-back ratio in a 2-element beam has a niche in the operating needs of hams. We can obtain that pattern on two bands by placing a pair of rectangles back- to-back.
+  <p>To see how well this would work, I modeled 10-meter and 15-meter rectangles in a back-to-back configuration, drawing the two reflectors as close together as possible without severely damaging the overall pattern. A practical limit of about 2' of separation emerged for the 10-15 combination. <b>Fig. 1</b> shows the general outlines of the array.</p>
+  <center>
+    <img src="mbm-1.gif" width="439" height="437" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The overall boom length is about 12.7' with a little extra needed for element-to-boom mounting. The following table shows the values used in constructing the model:</p>
+  <pre>10-15-meter Moxons back-to-back             Frequency = 21.225  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+1         -8.417, -4.930,  0.000  W2E1  -8.417, -7.007,  0.000 1.01E+00   7
+2   W1E2  -8.417, -7.007,  0.000  W3E1  -8.249, -7.175,  0.000 1.17E+00   1
+3   W2E2  -8.249, -7.175,  0.000  W4E1  -2.685, -7.175,  0.000 1.01E+00  15
+4   W3E2  -2.685, -7.175,  0.000  W5E1   2.685, -7.175,  0.000 1.17E+00  15
+5   W4E2   2.685, -7.175,  0.000  W6E1   8.249, -7.175,  0.000 1.01E+00  15
+6   W5E2   8.249, -7.175,  0.000  W7E1   8.417, -7.007,  0.000 1.17E+00   1
+7   W6E2   8.417, -7.007,  0.000         8.417, -4.920,  0.000 1.01E+00   7
+8         -8.417, -4.222,  0.000  W9E1  -8.417, -1.168,  0.000 1.01E+00   9
+9   W8E2  -8.417, -1.168,  0.000 W10E1  -8.249, -1.000,  0.000 1.17E+00   1
+10  W9E2  -8.249, -1.000,  0.000 W11E1  -2.685, -1.000,  0.000 1.01E+00  15
+11 W10E2  -2.685, -1.000,  0.000 W12E1   2.685, -1.000,  0.000 1.17E+00  15
+12 W11E2   2.685, -1.000,  0.000 W13E1   8.249, -1.000,  0.000 1.01E+00  15
+13 W12E2   8.249, -1.000,  0.000 W14E1   8.417, -1.168,  0.000 1.17E+00   1
+14 W13E2   8.417, -1.168,  0.000         8.417, -4.222,  0.000 1.01E+00   9
+15        -6.270,  3.920,  0.000 W16E1  -6.270,  5.575,  0.000 7.50E-01   5
+16 W15E2  -6.270,  5.575,  0.000 W17E1  -6.145,  5.700,  0.000 8.75E-01   1
+17 W16E2  -6.145,  5.700,  0.000 W18E1  -2.000,  5.700,  0.000 7.50E-01  11
+18 W17E2  -2.000,  5.700,  0.000 W19E1   2.000,  5.700,  0.000 8.75E-01  11
+19 W18E2   2.000,  5.700,  0.000 W20E1   6.145,  5.700,  0.000 7.50E-01  11
+20 W19E2   6.145,  5.700,  0.000 W21E1   6.270,  5.475,  0.000 8.75E-01   1
+21 W20E2   6.270,  5.475,  0.000         6.270,  3.920,  0.000 7.50E-01   5
+22        -6.270,  3.400,  0.000 W23E1  -6.270,  1.125,  0.000 7.50E-01   6
+23 W22E2  -6.270,  1.125,  0.000 W24E1  -6.145,  1.000,  0.000 8.75E-01   1
+24 W23E2  -6.145,  1.000,  0.000 W25E1  -2.000,  1.000,  0.000 7.50E-01  11
+25 W24E2  -2.000,  1.000,  0.000 W26E1   2.000,  1.000,  0.000 8.75E-01  11
+26 W25E2   2.000,  1.000,  0.000 W27E1   6.145,  1.000,  0.000 7.50E-01  11
+27 W26E2   6.145,  1.000,  0.000 W28E1   6.270,  1.125,  0.000 8.75E-01   1
+28 W27E2   6.270,  1.125,  0.000         6.270,  3.400,  0.000 7.50E-01   6
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1 (15 M)    8     4 / 50.00   (  4 / 50.00)      1.000       0.000       I
+or
+1 (10 M)    6    18 / 50.00   ( 18 / 50.00)      1.000       0.000       I
+
+Ground type is Free Space</pre>
+  <p>One slight peculiarity of this model is that the corners use a sloping wire to simulate tubing bends. However, in actual construction practice, this nicety of modeling has proven unnecessary: results with or without the corner sloping wire are well within the normal home shop construction variables.</p>
+  <center>
+    <img src="mbm-2.gif" width="470" height="135" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Performance on each band is quite normal. <b>Fig. 2</b> shows the 50-Ohm VSWR curve for 15 meters, while <b>Fig. 3</b> shows the 10-meter 50-Ohm VSWR curve. The slightly higher values of SWR across the band on 10 meters suggest that the 15-meter rectangle influences the 10-meter rectangle more than the other way around. As with monoband Moxon rectangles, forward gain varies from about 6.2 dBi at the low end of the band to about 5.7 dBi at the upper end in free space models. Relative to other 2-element designs, the front-to-back ratio is superior across the band.</p>
+  <center>
+    <img src="mbm-3.gif" width="472" height="198" border="2" vspace="5" hspace="9">
+  </center>
+  <h3>A Hybrid Tri-Band Moxon-Yagi</h3>One of the features of the Moxon rectangle that appeals to many builders is the reduction in side-to-side width of the antenna relative to linear elements. On 20 meters, the normal 36' elements are reduced to 25' side-to-side--a value not much greater than the width of a 15-meter beam. Since small tri-banders tend to use short booms, the reduction in the side-to- side dimension also means a significant reduction in the antenna turning radius.
+  <p>I have received a number of notes wondering if parasitic elements might be added to a 20-meter Moxon to produce a tri-band beam. The addition of a 10- meter director and a 15-meter reflector yields some forward gain, but the feedpoint impedance makes large excursions, forbidding the use of coax.</p>
+  <p>These initial steps into developing a tri-band antenna around a 20-meter Moxon tend to stop short of something truly satisfactory. What is required for easy use is a system that permits a 50-Ohm feed for each band. The result will be more elements, but not a major increase in the footprint over and above the initial addition of a reflector and director.</p>
+  <p>To develop a beam of this order, one might well adapt some of the principles underlying the Force 12 C3. This popular antenna uses a 2-element 20 meter driver-reflector Yagi at its core. It also places a 15-meter driver-reflector combination behind the 20-meter driver. The two drivers are close enough to permit open-sleeve coupling. Ahead of the 20-meter driver are 3 10-meter elements--a driver (also open-sleeve coupled to the 20-meter driver) and two directors. The furthest director provides the essential pattern shaping function, while the closely-spaced first director functions much like the added director on the NW3Z/WA3FET OWA designs: it helps form a wider band feedpoint impedance than a single director could provide. Performance remains essentially the same as a 2-element driver-director Yagi, but over a larger portion of the band.</p>
+  <p>It is possible to replace the 20-meter elements with a Moxon rectangle and obtain tri-band performance on a 16' boom. <b>Fig. 4</b> shows the general outline.</p>
+  <center>
+    <img src="mbm-4.gif" width="438" height="400" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The following table presents some element data used in the models testing this idea. The elements are of uniform diameter for each band. Consequently, adjustments would be required for any element diameter tapering schedule used in an actual antenna. Likewise, none of the dimensions should be taken to be those of an actual C3.</p>
+  <pre>Hybrid Moxon-Yagi                                 Frequency = 29  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -138.50, 11.750,  0.000       138.500, 11.750,  0.000 7.50E-01  21
+2        -132.00, 96.750,  0.000       132.000, 96.750,  0.000 7.50E-01  21
+3        -101.00,112.250,  0.000       101.000,112.250,  0.000 5.00E-01  15
+4        -97.000,124.250,  0.000        97.000,124.250,  0.000 5.00E-01  15
+5        -89.000,190.250,  0.000        89.000,190.250,  0.000 5.00E-01  15
+6        -150.00, 66.000,  0.000  W7E1 -150.00,108.000,  0.000 1.00E+00   3
+7   W6E2 -150.00,108.000,  0.000  W8E1 150.000,108.000,  0.000 1.00E+00  25
+8   W7E2 150.000,108.000,  0.000       150.000, 66.000,  0.000 1.00E+00   3
+9        -150.00, 56.400,  0.000 W10E1 -150.00,  0.000,  0.000 1.00E+00   4
+10  W9E2 -150.00,  0.000,  0.000 W11E1 150.000,  0.000,  0.000 1.00E+00  25
+11 W10E2 150.000,  0.000,  0.000       150.000, 56.400,  0.000 1.00E+00   4
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          13     7 / 50.00   (  7 / 50.00)      1.000       0.000       I
+
+Ground type is Free Space</pre>
+  <p>For this exercise, the 20-meter elements were set at 1" diameter, the 15- meter elements at 0.75" diameter, and the 10-meter elements at 0.5" diameter. Since the design uses open-sleeve coupling, a single feedpoint suffices for all bands.</p>
+  <p>Here is a band-by-band run-down of potential performance. These figures are generated on MININEC (AO 6.5), since the close spacing of the drivers produces excess gain estimates in NEC-2. The error is an especially large overestimation of gain on 10 meters. Hence, MININEC is the core of choice for this exercise.</p>
+  <p><b>20 Meters</b>: On 20 meters, the Moxon rectangle performs normally, with a typical Moxon pattern, as shown in the free-space azimuth pattern in <b>Fig. 5</b>.</p>
+  <center>
+    <img src="mbm-5.gif" width="640" height="300" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The following table summarizes the performance across the band.</p>
+  <pre>Freq.     F-S Gain        F-B           Feed Z         50-Ohm
+MHz       dBi             dB            R+/-jX         VSWR
+14.0      6.46            15.6          38-15          1.55
+14.175    6.09            32.4          55- 6          1.15
+14.35     5.72            21.0          69- 1          1.38</pre>
+  <p><b>Fig. 6</b> demonstrates the anticipated SWR curve on 20 meters.</p>
+  <center>
+    <img src="mbm-8.gif" width="464" height="167" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Relative to a Yagi driver-reflector combination, the Moxon shows a gain decrease of about 0.25 dB, but an increase in front-to-back ratio that exceeds 10 dB on average.</p>
+  <p><b>15 Meters</b>: On 15, the pattern is that of a 2-element driver-reflector, as illustrated in the free-space azimuth pattern in <b>Fig. 7</b>.</p>
+  <center>
+    <img src="mbm-6.gif" width="640" height="370" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The modeled free space performance figures across 15 meters are these:</p>
+  <pre>Freq.     F-S Gain        F-B           Feed Z         50-Ohm
+MHz       dBi             dB            R+/-jX         VSWR
+21.0      6.63           10.8           61-40          2.01
+21.225    6.21           11.6           50+ 6          1.13
+21.35     5.99           11.2           44+29          1.87
+21.45     5.82           10.7           40+47          2.82</pre>
+  <p>Note that the effective 2:1 SWR bandwidth is about 350 kHz or just a little bit more on 15 meters. One consequence of a simple open-sleeve coupling feed system is a more rapid rise in reactance as one moves away from resonance. At the upper end of the band, the reactance controls the SWR figure. One may, of course, reset the driver length to favor the upper end of the band. In addition, a broader operating bandwidth may exist at the ground end of a standard 50-Ohm coaxial cable--the exact width depending upon the line's length and losses.</p>
+  <center>
+    <img src="mbm-9.gif" width="469" height="260" border="2" vspace="5" hspace="9">
+  </center>
+  <p><b>Fig. 8</b> shows in graphic form the SWR curve on 15 meters, as modeled in free space.</p>
+  <p><b>10-Meters</b>: <b>Fig. 9</b> shows a free-space azimuth pattern for the hybrid antenna at 28.5 MHz. Again, it is a typical 2-element Yagi pattern, with a slightly better front-to-back ratio due to the use of directors.</p>
+  <center>
+    <img src="mbm-7.gif" width="640" height="370" border="2" vspace="5" hspace="9">
+  </center>
+  <p>In tabular form, here are the AO predictions of performance, as referenced to free space.</p>
+  <pre>Freq.     F-S Gain        F-B           Feed Z         50-Ohm
+MHz       dBi             dB            R+/-jX         VSWR
+28.0      6.31           15.0           57-37          2.00
+28.5      6.59           16.4           46- 0          1.08
+28.9      6.89           17.4           36+26          1.98
+29.0      6.98           17.5           33+32          2.42</pre>
+  <p>The gain and front-to-back ratio are typical for a 2-element driver- director design with one exception. The standard driver-director design has a narrow operating bandwidth for both the performance and the impedance characteristics. Something as narrow as 100 to 150 kHz is not unusual. The first director that is close to the driver provides the builder with the ability to tailor characteristics in a couple of ways. First, it forces the second director to a considerable distance from the driver so that characteristics change more slowly across the band. Second, it allows the builder to achieve a stable feedpoint impedance over much of the band--in this case, about 900 kHz between 2:1 SWR points, as illustrated in <b>Fig. 10</b>.</p>
+  <center>
+    <img src="mbm-10.gif" width="470" height="206" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Undoubtedly, one can improve on this hybrid design. Indeed, the requirement for adjusting element lengths and spacings to account for element diameter taper schedules would enforce an exploration of possible improvements. As with all models of open-sleeve coupling, considerable adjustment may be needed in the slaved drivers to achieve the correct impedance and bandwidth. Moreover, although home construction of single antennas for personal use requires no special attention to any legalities, any other use of the non-Moxon-rectangle techniques noted in the design should involve consultation with Force 12 to ensure compliance with any proprietary or patent rights held by that company.</p>
+  <h3>Conclusion</h3>The two designs shown here are simple illustrations that multi-band designs involving Moxon rectangles are possible. The back-to-back design is "pure rectangle" and makes use of the very high front-to-back ratio in order to closely space two independent antennas. The hybrid design makes use of a number of techniques to maximize performance within each element group of a multi-band antenna with a single feed system.
+  <p>In both cases, the antennas use no loading devices, but instead employ full size elements. Any compacting of the overall size relative an antenna with only linear elements is a function of geometry. If I discover additional multi-banding techniques, I shall certainly add them to this note.</p>
+  <center>
+    <img src="../images/colorbar.gif" width="591" height="3">
+  </center>
+  <p><i>Updated 8-12-99. &COPY; L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.</i></p>
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+  <title>2-Element Moxon Rectangle 10m</title>
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+</head>
+<body>
+  <center>
+    <h1><img src="../images/moxbut.gif" align="left" width="119" height="61" border="2" vspace="5" hspace="10"><img src="../images/w4rnlwwr.gif" align="right" width="99" height="83" border="2" vspace="5" hspace="10">An Aluminum 2-Element Moxon Rectangle 10m<br></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>
+  I often receive inquiries from folks who cannot quite support the width of a 10-meter Yagi (either 2 or 3 elements) because obstructions give them less than the 16.5' needed. Is there an antenna with decent performance that will fit in a space about 12-13' wide? If it can be home built to save money and require no fancy tuning or matching system, so much the better.
+  <p>In fact, there is an antenna that fits this category almost perfectly. Imagine an antenna with the gain (over real ground) of a 2-element Yagi (11+ dBi), the front-to-back ratio of a 3-element Yagi (&gt;20 dB from 28.3 to 28.5 MHz), and an SWR of below 2:1 from one end of 10 to the other. In fact, imagine that the antenna has better than 15 dB front-to-back ratio all the way down to 28 MHz and still has about 12 dB front-to-back ratio at 29.7 MHz. (All figures are free space modeling estimates, except gain.) Imagine also that the antenna can be directly connected to 50-ohm coax with no matching system whatsoever (even though I always recommend a 1:1 choke balun). Imagine also that you can make it yourself from hardware store materials, that it will weigh about 10 pounds including the boom (under 5 pounds without the boom), and that you can make it in your garage with no special tools. Imagine also that when it is done, you will still have change from a $50 bill.</p>
+  <p>The antenna is the Moxon rectangle. Past versions that I built using wire elements required lots of PVC to support them. See "Modeling and Understanding Small Beams: <a href="../mu/mu2a.html">Part 2: VK2ABQ Squares and Moxon Rectangles</a>," <i>Communications Quarterly</i> (Spring, 1995), 55-70. Those versions were to prove the principles of the Moxon rectangle, not to produce an easy-to-build antenna.</p>
+  <center>
+    <img src="mox-1.gif" width="796" height="420" border="2" vspace="5" hspace="9">
+  </center>
+  <p>However, if we translate the antenna into hardware store aluminum tubing, we can easily build a 1-boom version. Now peak at the sketch of the pieces. (Note: to get the detail into the figure, I had to make it a bit too large for 640-wide screens. Hence, it may not print well unless you download it and print it out landscape.)</p>
+  <p>Some 7/8" and 3/4" diameter aluminum tubing form the main elements, with 3/4" tubing for the side elements. The corners can use radius-bent tubing or be squared by making some corner supports from L-stock. Cut the straight tubing at 45-degree end angles and use 1/16" thick L-stick to fashion over and under supports. About 1-2" length each way with stainless steel sheet metal screws or pop rivets will solidify the corners with minimal weight. I even tried 1/2 inside conduit Ls, but had to ream out the ends to accept the 3/4" tubing.</p>
+  <p>The corners I used were 7/8 aluminum radius-bent sections sent to me by N6BT (of <i>Force 12</i>) to speed up the experimentation. You can bend your own by filling the aluminum tube with sand (or cat litter in a pinch) and bending around a 6" or larger wheel or pulley. Work slowly. Keep the sand well packed in the tube to prevent pinch bends.</p>
+  <p>The combination of 7/8" and 3/4" aluminum tubing lets you telescope the ends into the center for a precise fit or a center frequency adjustment. A similar advantage accrues from using 1" and 7/8" hardware store aluminum tubing.</p>
+  <p>The side-to-side length is the key to centering the SWR curve for lowest reading at about 28.4 to 28.5 MHz. The center frequency changes about 150 kHz for every 1" of length adjustment. Hence, using the U-shaped outer ends as trombone slides will let you center the antenna anywhere in the 10 meter band. If you use slightly larger stock, say 1" and 7/8" hardware store aluminum tubing, performance will change very little. With 7/8" tubing for the outer main elements and the sides, you can weld or otherwise fasten (with Penetrox or another bi-metal conductor/protector between metals) 3/8" copper plumbing pipe Ls as the corners.</p>
+  <p>Since the end spacing and alignment is critical to make the antenna give its full performance, you can slide a piece of CPVC or similar lightweight, durable tubing either inside the ends or over the ends and lock them in place with sheet metal screws. The rigid spacer is also a good idea to limit the twisting force placed on the curved or right-angle corners. Sheet metal screws also connect the 3/4" and 7/8" tubing together. Be sure that all hardware screws are stainless steel. "Pop" rivets will also do well, if you use the sturdiest kind.</p>
+  <p>The feedpoint assembly is not shown in the sketch. I used a very simple system. I cut one side of the driven element tubing 1" short at the feedpoint. I then cut a 2" section of 1/16" thick L-stock, and cut a 5/8" diameter hole at one end. A chassis-mounting female coax connector (with a lock washer) fits into the hole, with the plug-side pointed at the mast. stainless steel sheet metal screws attach the "extra-inch" side of the L-stock to the cut-off tube. A #14 copper wire (tinned the entire length) goes from the center pin to the other side of the feedpoint, where it is fastened under another sheet metal screw. You can devise your own more durable set of feedpoint connections. After testing but before committing the antenna to permanent installation, be sure to waterproof the rear of the coax connector as well as the coax plugs.</p>
+  <p>For element-to-boom plates, you can use any durable material. Spar varnished 3/8" plywood or LE plastic make good plates. About 3" by 9" (or longer) plates give ample room to U-bolt the elements to the plate and have room for U-bolts that go over the mast. My test model used 1/2" PVC electrical conduit U-straps fastened in place with #8 stainless steel hardware. Since 7/8" tubing stresses these straps a bit too much, I placed an extra washer between the U-strap and the plywood plate. The object is a very firm grip, but not a broken strap. Two straps hold the reflector center tube in place, but the driven element requires two on each side of the feedpoint.</p>
+  <p>As with all good antenna structure, let the elements hang under the boom. What boom? Well, almost anything, from 1-1/4" nominal diameter PVC (which I had on hand) to a good grade of aluminum tubing (thicker-wall than the usual 0.55" hardware store variety--or two pieces nested) to a 5' length of spar varnished 1.25" diameter closet rod. Make up a boom-to-mast plate similar to the boom-to-element plates, only a bit more square, and you are in business. PVC is the heaviest; aluminum the lightest, but at 5', the boom weight is not a significant issue.</p>
+  <p>The dimensions of the antenna in the drawing are too fussy, being direct translations of the computer model used to generate the antenna. Just try to keep the dimensions within about 1/4" of the drawing, and no one will be able to tell any difference in performance. Squaring the corners or missing the dimensions by a half inch will shift the performance centers by about 100 kHz at most. In most cases, you will not be aware of any difference at all. To assure that the assembly is neatly squared and close to the prescribed dimensions, you can draw the outer dimensions and center line on the shop/garage/basement floor with a marker pen and then assemble the pieces within those boundaries. As "they" always say, measure twice, cut and assemble once.</p>
+  <p>Note that the antenna is just about 12.7' wide and under 5' front-to-back, for a turning radius of about 6'8" or so. Strapped up on the side of the house, the antenna is unlikely to overhang the neighbor's yard line. The antenna is light enough for hand rotating, but an old TV rotator might come in handy. Because of the antenna's characteristics, you may not need to rotate it much.</p>
+  <center>
+    <img src="mox-2.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The free-space azimuth patterns for 28.1, 28.5, and 28.9 MHz show the possibilities for the Moxon rectangle. Note the very broad forward lobe that is almost a cardioid, giving reception and transmission as wide as your peripheral vision. Behind you is silence--or at least a large dose of silencing. Les Moxon, G6XN, uses a wire version of the antenna with both elements remotely tuned: that way he works the world just by electrically reversing front and rear elements with a fixed mounting. Note also that the performance characteristics promise to hold up well across the most active part of 10-meters.</p>
+  <p>But what about performance at real heights above ground?</p>
+  <center>
+    <img src="mox-3.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>At 35' up, about 1 wavelength, the antenna provides most of its free space performance across the band. At higher mounting levels, the performance moves closer to free-space patterning. The elevation angle at 35' for maximum gain is 13-14 degrees.</p>
+  <center>
+    <img src="mox-4.gif" width="640" height="480" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Even at 20' up, a typical portable antenna height at 10 meters, the antenna continues to display excellent front-to-back characteristics with the gain of a 2-element Yagi (which does not have good front-to-back characteristics at this height--perhaps 9-10 dB or so). The elevation angle of maximum radiation is about 23 degrees at the 5/8 wavelength height.</p>
+  <center>
+    <img src="mox-5.gif" width="646" height="517" border="2" vspace="5" hspace="9">
+  </center>
+  <p>The Moxon rectangle is quite stable with respect to feedpoint characteristics as the antenna is raised and lowered. The curves actually flatten some over real ground. Therefore, setting up the antenna for operation is simple.</p>
+  <p>My own initial procedure was to fasten the antenna to a 20' mast propped up by a sturdy tripod. The reflector was no more than 5' above ground. I then adjusted the side-to-side length to minimize SWR at 28.45 MHz, sing the trombone-slide end sections. After fastening down the sections and raising the antenna, there was no detectable difference in SWR performance from the adjustment position pointing at the sky.</p>
+  <p>A view of the completed all-aluminum (and a little PVC) Moxon for 10 meters atop its test mast. The CPVC element-end separators and corner pieces should be visible with reasonable clarity for comparison with the sketch.</p>
+  <center>
+    <img src="moxon1.gif" width="476" height="286" border="2" vspace="5" hspace="9">
+  </center>
+  <p>A close-up view of the test model feedpoint assembly and element mounting scheme. The PVC half-clamps should be replaced every 2-3 years before they grow brittle (about 4-5 years average in my climate in East Tennessee). The rear of the female coax connector and the coax junction should be weather sealed if the antenna is to be used for a permanent installation.</p>
+  <center>
+    <img src="moxon2.gif" width="500" height="284" border="2" vspace="5" hspace="9">
+  </center>
+  <p>Contrary to claims made for the VK2ABQ, these antennas do not like to be nested for a multiband array. Even stacking requires a minimum of 10' or more between 10 and 15 meter models. However, you might consider back-to-back 10 and 15 meter antennas. A 13' boom would hold both antennas, reflector-to-reflector with minimal interaction.</p>
+  <p>It is unlikely that anyone will ever produce this beam commercially, since it is a monobander without the super gain that avid DXers and contesters crave. You can only get that kind of performance from many Yagi elements. However, you can build your own compact antenna with a pretty good chance of success on the first try. It will beat a fixed wire dipole or a dry-land vertical hands down at 20 meters and up. It also makes a dandy Field Day antenna. So if you need a compact 10-meter beam for your compact home site, then you might roll your own version of the aluminum Moxon rectangle.</p>
+  <p>So why am I placing this item at the web site rather than sending it off to a magazine? My usual outlets have a backlog of items, and the article would not appear for over a year. Sunspots are approaching for 10 meters, and a year would perhaps force some folks to wait too long. Antenna-building season is upon us. In short, this seemed the best way to disseminate the information in the shortest time. If you have a friend who needs a shortened, but full performance 2-element antenna, and who does not have web access, pass along a copy.</p>
+  <center>
+    <img src="../images/colorbar.gif" align="middle" width="540" height="4">
+  </center>
+  <p><i>Updated 4-6-98. &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>
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