Using Moxon Rectangles for WARC-Band Antennas
Part 1: Some 17-12 Meter Ideas

L. B. Cebik, W4RNL

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.

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.

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.

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. Fig. A 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).

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.

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.

The Possibility of a Dual-Band Moxon

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.

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.

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. Fig. 1 shows the outlines of the final model.

The following table shows the dimensions (in feet) for the dual Moxon with open-sleeve coupling, using the conventions of Fig. A to designate parts of the antenna.

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'

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.

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.

The projected performance of the array can be summarized in the following table, where gain is shown as free-space gain.

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

Fig. 2 shows the mid-band 17-meter free-space azimuth pattern for the array, while Fig. 3 shows the same pattern for 12 meters.

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.

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.

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.

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.

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.

A Moxon-Yagi Combination

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.

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. Fig. 4 shows the outline of the resulting design.

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.

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'

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.

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

The performance of the Moxon is altered by a small amount, as shown in Fig. 5.

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.

On 12 meters, the director-driver combination exhibits a standard Yagi pattern, as shown in Fig. 6.

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 Fig. 6 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.

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.

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.

The Simplest Dual Moxon Rectangle?

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 Fig. 7 reveals, it is actually only 1.5 Moxon rectangles, having a single driven element and two reflector elements.

The dimensions for the antenna as modeled are these:

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'

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.

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.

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 

The pattern for 17 meters holds up quite well, despite the proximity of the 12-meter reflector to the driven element, as evidenced in Fig. 8.

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. Fig. 9 tells the tale for the entire 12-meter band.

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.

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.

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

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

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

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 ARRL Antenna Compendium, 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.

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.

Updated 5-1-2000, 8-4-2000. © L. B. Cebik, W4RNL. The original item appeared in AntenneX 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.

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