Thursday, February 29, 2024

Reversible 40 Meter Moxon: Initial Model

I would like to retire the XM240 this year. It is not just because of its low efficiency due to the loading coils. When I side mounted it last fall, I did it with the full knowledge that I was impairing my flexibility on 40 meters since it can only be rotated through about 130°. It works well for working most of North America, and DX further afield to the south and west. But I miss having two antennas with full rotation.

I prefer to keep the limited-rotation side mount rather than replace it with a swing gate. The latter would allow 300° rotation, which is more than adequate for my needs. There is a 60° arc between 100° and 160° bearing that I can omit without serious loss of station effectiveness. When that direction is needed for long path contacts (e.g. Asia) and southern Africa, the high 3-element yagi is a superior choice, and it is fully rotatable. The offset mount of a swing gate requires robust construction and a strong rotator for the mechanical load of a 40 meter yagi.

After consideration of alternatives, I returned to an antenna design that I chose against several years ago: the W6NL 2-element Moxon. It's relatively small, has good F/B and broad SWR bandwidth, at the expense of modest gain and the narrow gain bandwidth inherent to every 2-element yagi, Moxon or not. However, it does not suit my application without one major modification: making it reversible. 

Reversibility on the side mount would permit 260° coverage and instant switching between, say, Europe and the US. The gaps are between 95°-145° and 275°-325°. There are few stations to work in those directions and, as already mentioned, there is the big 3-element yagi for those directions. The Moxon is small enough that my ancient (and multiply refurbished) Ham-M rotator can handle it.

The actual W6NL design works pretty well but it has a few unusual characteristics. The modelled SWR bandwidth appears to be narrower than a traditional Moxon rectangle, gain is slightly less and I worry about the capacitance hats striking each other when it's windy and their inconstant separation. The latter is a critical parameter of the Moxon design.

For these reasons I decided to explore and compare alternative approaches. I hoped to gain insights into their relative performance, both electrical and mechanical. Any 40 meter rotatable yagi is a large antenna and there may be good reasons to compromise electrical performance in favour of mechanical robustness.

The baseline model I developed is a symmetrical Moxon rectangle. It is not novel since others have made similar antennas, but I didn't have a model in hand that I was comfortable with. 

I proceeded by keeping the symmetric rectangle dimensions close to those of the traditional (asymmetric element) Moxon rectangle and placing a coil at the centre of the reflector. The coil lowers element resonance so that it has the proper reactance (phase shift) to be a reflector at the operating frequency.

In a real antenna the coil and feed point are switched to reverse the yagi but this is not necessary in a model since the switching system does not affect the antenna when properly implemented.  The switching system can introduce coupling and stray reactance that are not part of the model but must be dealt with during construction and testing of the antenna.

To meet my criteria the antenna must have these features:

  • Symmetrical: two identical elements
  • Critical coupling: element tips are placed near each other
  • Switchable: driven element and reflector; the reflector has a coil at the centre
  • Switching system: method for selecting which element is driven and which is the reflector

Exploration is a multi-step process. The first model uses constant diameter elements -- 25 mm in this instance -- with each element tuned to 7.0 MHz. That allows NEC2 to handle the antenna reasonably well since SDC (stepped diameter correction) is avoided, and EZNEC's SDC does not support bent elements well. Element dimensions and coil value were varied until the performance was approximately equal to that of a traditional (asymmetric) Moxon rectangle. 

When this reversible Moxon rectangle is optimized to this very good SWR, it looks as follows:

  • 5.6 meter boom
  • 14.5 meter elements and 2.65 meter inward legs
  • 30 cm (12") gap between element tips
  • 1.5 μH reflector loading coil
  • Peak gain of 6.6 dbi at 6.955 MHz; Peak F/B of 23 db at 7.1 MHz

There may be slightly better solutions, but this is pretty typical for a Moxon rectangle. Every 2-element yagi with a reflector as the parasite, Moxon or not, has the maximum gain placed below the band edge so that the F/B and SWR are good across the band. This symmetric Moxon has the same attributes, which will be shown further below. This was a promising beginning.

There are commercial antennas similar to this, but they're rare due to their size. For example the one from Optibeam is electrically shortened. The performance penalty is modest, but there is one. It is rotatable but not reversible. 

Take note of the mechanical connection between the element tips. Sagging over the span of the boom length can be significant. Wind and ice demand a robust design for these large elements. I'll return to this later since it's an important structural consideration.

The W6NL design eliminates the sag problem by making each element horizontally balanced. The inner legs, that make it a type of Moxon, are one half of each capacitance hat. The element tips are extended which moves the hats inward. There is less stress at the ends of the elements. It is possible to design this style of yagi without element trusses if the elements are made sufficiently strong (and heavy).

However, the W6NL Moxon (whether built from scratch or as a modified XM240) is not symmetrical and it is therefore not reversible. For this modelling exercised I instead explored modifications of the basic design that are symmetric.

The diagram comes from Cebik's article that does a deep dive into the Moxon rectangle. The critical parameters are shown. There is the ratio of the length to the width and the gap between element tips. There is a dependence of k (ratio of wire diameter to wavelength) which I will skip over in this article since it isn't particularly relevant. Also, I use symmetric elements with loading rather than element length to tune them.

Element topology contributes to gain. The greater the length of the parallel element sections, the greater the gain; the tip radiation cancels in the far field due to their symmetry. The gap, C, determines the coupling, for which we need the best value to achieve the Moxon's particular advantages with respect to impedance, SWR bandwidth and F/B.

I explored these three variants. The one on the right is the most similar to the Moxon rectangle. On the left is the one most similar to the W6NL design; the element tips are short since I did a screen capture while I was playing with the model. In the centre is a hybrid where the capacitance hats are at the ends of the elements; it looks like a Moxon rectangle with outward arms at the 4 corners.

I found that the critical gap between element tips was around 30 cm (12") for all of these 40 meter variants. Moving away from that value in either direction had a large effect on the 50 Ω match, and a more gradual effect on the F/B bandwidth. In all cases the wire diameters are 25 mm (1") along their entire lengths. The choice is justified since this is a design exploration, not a construction article.

The symmetric Moxon on the right has a few interesting features. It works best when the boom length (width) is 5.6 meters (18'-4"), with respect to gain and F/B. After many trials, the same was found for the other two designs. The surprised me since the W6NL Moxon has a longer boom. Shortening the boom had the effect of making the elements longer and the capacitance hats shorter to compensate. When the booms are 5.6 meters, the capacitance arms are identical for all three: 2.65 meters. The outer arms for the two with T-hats are also 2.65 meters for mechanical balance.

Notice that the length to width ratios for the two on the left are lower than that on the right. The maximum gains are a little lower due to the shorter elements. That is due to loading by the hats. 

The element tips on the symmetric version of the W6NL Moxon proved to be a problem. The longer they were the worse the gain and match (I didn't closely monitor the F/B during the process). The problems mostly vanished when the tips were reduced to zero length, which is the T-hat version in the middle diagram. I can't give a definitive reason based on a cursory inspection of the models other than to say that the coupling between elements is less than critical due to the greater distribution of high-impedance points where capacitive coupling is under-utilized. 

I therefore discarded the design on the left and focussed on the remaining two. After coarse optimization I compared their performance.

Gain and F/B are sufficiently similar that we can declare them to be effectively equal. The gain of both is a little less than that of a traditional 2-element yagi with a reflector element and slightly longer boom. Both plots are continued below the band edge to demonstrate that gain increases, which is typical of all 2-element reflector yagis, Moxon or not.

The impedance matches are also very similar and quite good right across the band. The Moxon rectangle is on the top and the T-hat on the bottom.

Since their electrical performance is about the same we turn to the mechanical parameters. These can be as critical as performance considering the large size of 40 meter yagis. Regarding the electrical and mechanical performance of the W6NL Moxon, I suggest reading this paper by W8WWV.

There are several parameters to consider:

  • Element length
  • Element balance
  • Weight
  • Wind & ice load
  • Maintaining the distance between element tips

First, let's compare the total linear lengths. For the symmetric rectangle, each half element is 7.25 meters and the inward sides are each 2.65 meters, for a total length of 19.8 meters. For the T-hat version, each half element is 5.9 meters and each T-hat arm is 2.65 meters, for a total length of 22.4 meters. The elements of the latter are shorter but the arms at the ends of the elements, where they are weakest are double that of the rectangle.

The T-hats are balanced on the element ends while the inward arms of the rectangle are not. The torque on the end of the element is a concern with the rectangle. It can be partially mitigated by a fibreglass rod to fix the gap distance and mechanically couple the arms of the opposing elements. However, the long span of 5.6 meters of, hopefully, lightweight tubing requires more mechanical strength than for the similarly coupled arms of the balanced T-hats.

The arms of the rectangle design require a stronger design than for the T-hats, and that may be a greater threat than the nominally lighter rectangle. Element trusses do not solve the problem. The T-hat design might not even need element trusses if the elements are made sufficiently strong. Since the T-hats are weight and load balanced, the 5.6 meter inner span between the elements might only need attention with respect to stress caused when the elements experience unequal loading in a strong wind.

It's a dilemma and I have no good answer at the moment. You could say the electrical performance is the easy part of the antenna design. Although I have enough aluminum in my stockpile to increase the strength of the elements, there is a greater risk of breakage at the centre since both elements must be split for feeding and for switching in a series coil. The elements must also be electrically isolated from the boom. The mechanical design is challenging.

That will be my next step. Until I have a robust mechanical design I will not make a final determination on whether to proceed with a rectangle or T-hat design. The basic mechanical design is common to both. 

There are alternatives like the NW3Z 3-element yagi and yagis with two V-shaped elements that do away with the high load at the ends of the elements, but those come with an additional performance penalty: they are not true Moxons and gain is reduced by the smaller effective element spacing.

I'll end with an additional concern for both designs: potential for interactions. The XM240 is not resonant on the third harmonic which would otherwise fall within the 15 meter band. I included capacitance hats on the 3-element yagi to accomplish the same. It was therefore important to know how the reversible T-hat and rectangle designs fare in that respect.

The SWR sweep of the rectangle is at the top and the T-hat is on the bottom. Both meet my objective of avoiding resonance on any contest band, and especially 15 meters. I was not really concerned since loaded elements (which includes the non-linear element profile of the Moxon rectangle elements) shift the third harmonic away from its simple arithmetic value.

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