Possibilities of Moxon Yagis

I bought and read the book HF Antennas for All Locations by Les Moxon, G6XN, over 30 years ago. I learned a lot from it but never put any of the ideas into practice. (Well, except for one time which I'll come to at the end of this article.) I must admit that I did not fully appreciate what I did read because my knowledge of antenna fundamentals was relatively poor at the time. With my interest in getting gain on 40 meters from a simple antenna I decided to have another look.

I was especially taken by the steps taken by others to exploit his work to design rotatable and fixed 2-element yagis on 40 that claim to perform favourably in comparison to other 2-element designs. Not everyone agrees. All of this was enough to grab my interest now that the weather has turned wintery and I am mostly restricted to planning for the future.

Some computer modelling is called for to investigate the matter further. There is enough conflicting information to be found in publications, including on the internet, that it becomes impossible to believe everything I read. This is not about incompetence or exaggeration on the part of others (many of whom are more skilled at this than I am). It is just that suitably comparably modelling is often lacking, or at least are not explained well. We are after all amateurs! A little bit of personal investigation can help to resolve the difficulty and set my mind at ease, and perhaps point the way to other antenna designs that are attractive.

The basic idea

The basic idea behind Moxon's strategy to improve yagi design is founded on the following sequence of ideas, which is my paraphrasing of what he has written:

• A yagi is a subtractive array that primarily achieves gain by cancellation of fields in unwanted directions. Since conservation of energy applies field reduction is one direction must show up as gain in another direction.
• Maximum cancellation, and therefore the best prospects (not a guarantee) for gain, requires equal amplitude and opposite phase. Although this is impossible to achieve over a broad range of directions with a 2-element yagi (in fact, only in one or a few points) it can be improved. Conventional yagis with parallel elements cannot achieve equal currents with element configurations that perform well in other respects.
• If the mutual coupling can be increased without reducing element spacing it should be possible to get improved results. Therefore turn the ends of the elements towards each other to increase coupling. Then tune the antenna for best results.

Before jumping into quantitative measures the above set of EZNEC current plots for an ordinary 2-element yagi (full-size wire elements) and a Moxon rectangle (adapted from a model by DF9CY) get across the basic idea. The current in the driven element is higher than the current in parasitic element (a reflector in the present case). The currents on both yagi types vary with frequency, but they vary less and remain more equal for the Moxon.

Current equalization and less variation with frequency means that the Moxon is able to improve F/B bandwidth. As we have seen before a conventional 2-element yagi does develop effective gain and F/B figures, though typically only over a narrow frequency range in comparison to yagis with 3 or more elements. There are good analytical discussions of yagis designs by W2PV (to pick a venerable example) and others, which I do not need to get into.

Conventional commercial yagis must be built to handle higher driven element current, or to advertise lower power rating. For example, the 15 meters traps on Hy-Gain tri-band yagis are different on the driven element. The higher antenna (and circulating) current is dealt with by winding that one trap coil with copper rather than the aluminum used in all other traps (same wire gauge). Otherwise there is a risk of excess heating at legal limit power.

Comparison of the Moxon and standard yagis

We'll use the same EZNEC models shown above. Both are constructed from 12 AWG copper wire, which results in a loss of about -0.3 db in both cases. This is negligible in the majority of applications. Rotatable yagis made from aluminum tubing have lower loss.

The models are in free space to remove the small skewing of results due to the presence of ground. Since the effect of ground is nearly identical for these antennas this is a good approach.

The difference in F/B is the obvious feature of the performance comparison. It is much higher across the band. Although higher peak F/B can be had with a 2-element yagi (different boom length) that does not alter the results by much.

Gain is less favourable for the Moxon which is 0.5 to 0.6 db lower than the yagi. Plotted current is that of the reflector element referenced to a source current of 10 A.

The Moxon is a Moxon rectangle, which is sensitive with respect to a few parameters:

• Element spacing, along the "boom"
• Element tip separation
• Ratio of centre segment to tip segments
• Wire (or tubing) diameter

The yagi has fewer parameters, with performance mostly related to element separation and wire (tubing) diameter. The Moxon model has element spacing of 0.13λ, centre to tip ratio of 5.4 and 36 cm tip separation. The yagi has an element separation of 0.14λ. Other parameter choices will change antenna performance. Even so the key distinctions would remain. However do keep in mind that the element tip separation in a Moxon is critical, such that a small change can have a larger than expected effect on performance.

As mentioned earlier, both use 12 AWG wire, insulated wire in the case of the yagi. If made from tubing the SWR bandwidth would increase, although that is only of advantage to the narrow-band yagi.

SWR (not shown in the plot) favours the Moxon. The Moxon achieves an SWR below 2 across the band with a direct feed with 50 Ω coax. The yagi requires a matching network (beta, λ/4 transformer, 2:1 balun, etc.) and does not match as well across 40 meters.

Tuning for Gain and F/B

In both antennas the frequency of maximum gain is close to that of maximum reflector current. Indeed the shape of the current and gain curves are similar across the band. I took the plot down to 6.9 MHz to where the current reached a maximum for the yagi. Both antennas can be tuned to shift performance higher in the band. SSB operators may prefer to make the parasite a director in order to reverse the performance curves.

Before doing the modelling I guessed that the F/B would peak where the currents peak. This is not the case. I was perhaps misled by focussing on the precise reverse direction rather than the total field outside the main lobe.

The patterns are plotted at the same frequency (in this case, where the F/B is highest on the Moxon) so that the gains are fairly compared; the yagi has maximum F/B 40 kHz higher than the Moxon. You can see from whence the yagi gets its gain with respect to the Moxon rectangle. Although the radiation off the forward lobe of the Moxon is much less than the yagi its forward lobe is wider and shallower. There's no free lunch when it comes to antennas.

Gain in the Moxon is somewhat reduced by the length of the tips, and F/B in the yagi is reduced by moderate element coupling. Although the amount of current in the Moxon element tips is low it is still high enough to account for much, if not all of the gain difference.

The intensity of the radiation of an antenna is in rough proportion to the product of element length and average current over that length. Moxon himself points this out, and finds that the trade-off is beneficial. I suspect he is largely correct with respect to what most hams want. On 40 meters especially since most who do have a 2-element yagi choose one with loaded elements and so are therefore prepared to give up the small gain difference possible with full-length elements.

Where F/B and SWR are important to an individual case the advantage becomes greater on the low bands, where the width of the band is high in relation to frequency. There is less advantage on 20 meters and above where mostly-good SWR performance can be achieved across the band with a 2-element yagi. Then it's a matter of F/B. Even there it may come down to choosing a 3-element yagi which has better SWR, gain and F/B performance. Going with a larger yagi is less challenging on the high bands.

Considering all of the above, which antenna's performance do you prefer? There is no right answer, just a matter of personal preference. My own priority is gain, with match and F/B of lesser importance if I cannot get all three. However, I suspect most hams would rather sacrifice 0.5 db of gain to get a broadband match and F/B.

High mutual coupling in other antennas

It is not only the Moxon rectangle that exhibits improved current balance and therefore improved match and F/B. We've seen examples before in this blog.

• Spiderbeam: Although the elements are vee-shaped there is substantial element coupling from bringing the parasite tips close to the driven element. Notice that the F/B and SWR bandwidth are excellent and the gain is less than a full-size or trap yagi. Gain can be improved with a trade-off in the match. The manufacturer correctly notes that performance will suffer if measurements are not closely followed since, as already mention, element tip separation is critical to performance.
• 2-element diamond vee: When I built a version of this antenna over 25 years ago (late 1980s) I had Moxon element coupling in mind. At the time I had read somewhere that this design (no unlike the more recent Spiderbeam) can work very well. The antenna did work well although I had no means to measure gain or even to do a proper comparison against a reference. What I do remember well was the excellent F/B when I switched between northeast and southwest directions. I now know that the tip separation was probably not optimally chosen. Both in free space and over ground the modelled diamond vee yagi has less gain than the two antennas discussed in this article. The diamond vee antenna in any case will do worse than a fully-horizontal antenna over real ground.

The W6NL 2-element rotatable 40 meters yagi (either in its pure form or as a modified XM-240) has some advantages. I've made my own EZNEC model of the this antenna to better understand it. You can also check out W8WWV's model analysis if you are interested. I will probably say more about this one in future. It is certainly distinctive in its use of oversized capacity hats to achieve high element coupling.

Where am I going with this?

I'm not sure. Although there are advantages with respect to F/B and SWR bandwidth I have yet to discover a model that achieves better gain than a more conventional 2-element yagi, both in maximum gain and gain bandwidth. That reduces my level of interest, even if many others would disagree. Perhaps I am being overly focussed on losing 0.5 db of gain. That is at least true for 2-element designs; 3 or more elements present additional opportunities for investigation.

Another difficulty is making a version of the Moxon rectangle reversible. This is worth some attention. It might be a superior alternative to one of the 2-element switchable wire yagis I designed in 2013. I see some possibilities to be explored.

So I'll do some modelling of alternative designs and share the results. I think it's a good idea to further my understanding of these antennas and not prematurely dismiss them. I have the luxury of time since none of these antennas will go up at my station in the near future.