20 Meter 2-element Yagi With Bent Reflector: First Models

More than a few times I've mentioned that I am not happy with the TH6. Since I have it I use it but now only as a "multiplier antenna" pointing south. Yet it still has and causes problems. These include: narrow bandwidth and loss due to the traps; interaction with the 40 meter yagi beneath it; high SWR when wet; and, high coupling to the Europe pointing 15 and 20 meter stacks. And, it's very old, leading to questions about its future durability. But after 40 years I've certainly gotten my money's worth!

Its replacement doesn't need to be a tri-band yagi, nor does it need to have high gain. A group of several small yagis for each of 10, 15 and 20 meters could suffice, and might offer more flexibility than one tri-band yagi that either can't be shared, or can be shared at high expense (high power triplexer and filters). I see no need to spend a lot for what is really just a multiplier antenna. It only has to perform well enough to punch through the pile ups.

I've temporarily set aside 10 and 15 meters since, being smaller, those are easier yagis to design and build. A 20 meter yagi can be quite large, with 3 elements typically placed on an 8 or 9 meter boom. While that will easily give me more than 8 dbi across the band, considering its size I decided to look at smaller antennas. I can live with 7 dbi and perhaps even 6 dbi if it has other positive attributes.

These are the criteria I came up with:

• Lightweight: I'd like it to be reasonably small and light. Since it won't be rotated, I want to see how little aluminum I can do this with.
• Simple: The design and construction should be straight forward.
• Performance: Low SWR across the band (better for solid state amps); good but not great F/B and F/S; and (per above) within 1 to 2 db of a full-size 3-element yagi.
• Isolated element: By insulating the elements from the boom the interaction with the nearby 40 meter yagi can be eliminated. 

My first attempts focussed on 2-element yagis. This category includes Moxon rectangles, hex beams, and other element configurations. Each has its advantages and disadvantages. The following are the configurations considered in this study:

From the right are a conventional yagi, Moxon rectangle, "spider" beam style yagi and a yagi with a half-bent reflector. All of these yagis are unidirectional to the right. The latter two use wire for the bent bits, and indeed the reflector for the vee-shaped reflector is all wire.

A conventional 2-element yagi has poor F/B, good F/S, reasonable gain and SWR with a matching network. The bandwidth over which these metrics are best is narrow, perhaps 100 kHz on 40 meter. Outside of that it quickly gets worse. This is not a popular style of yagi for the low bands.

When we double the frequency to 20 meters that's still barely half the 350 kHz band. If you operate CW or SSB, but not both, perhaps that's sufficient. But not for me. We can do better with one of the other designs, so I'll say nothing more about the conventional 2-element yagi in this study except as a baseline for comparison.

The Moxon rectangle has excellent SWR and F/B across 20 meters, and even on 40 meters where it has to stretch farther due to the much larger bandwidth (by percent). I put this to good effect on my 40 meter reversible Moxon. However a Moxon's peak gain is worse than a conventional yagi due to a portion of the elements turned inward. 

As with all four of these 2-element designs, peak gain occurs at or below the band of interest. That's simply the nature of 2-element yagis due to the phase relationship between the elements. With more adjustable yagis of 3 or more elements there is more latitude on where to place peak gain and F/B. Not infinite latitude since, due to the nature of passive, close-spaced parasitic elements, there are constraints on the phase and amplitude relationships.

The Moxon rectangle, while not overly large on 20 meters, requires tubing for all element components. The designs on the left use less aluminum by using wire for the element tips. Cost, weight and wind/ice load are reduced. On the other side of the equation, tuning these designs for optimum performance requires precision in the tip spacing and interior angle. NEC2 does poorly at this so I used NEC5 for my models. 

I chose wire tip angles that allow a cord or rigid insulation to fasten the wire to the more rigid tip of the driven element. That required multiple iterations to optimize performance and mechanical layout. While I can't claim that I achieved the best possible performance, I believe I've come close. Close enough, that is, to evaluate and compare these designs.

The 3 designs are primarily evaluated for SWR (direct feed, no matching network) and gain. F/B and F/S are not major objectives considering its intended use as a fixed direction multiplier antenna -- work the mult and move on, no running or rag chewing.

Before diving into the modelling results, here are my motivations for looking at these particular 2-element yagi designs:

• Conventional yagi: Simple and well understood, with the maximum gain but relatively poor F/B and SWR bandwidth. It also uses the most aluminum.
• Moxon rectangle: Again, a well understood yagi design with relatively good F/B and excellent SWR bandwidth. But it's an awkward antenna to build and raise. Recall what I went through with raising the 40 meter reversible Moxon. 
• Vee-shaped reflector: It is, in a way, half of a Spiderbeam 3-element yagi. It is lightweight, but at the cost of gain and F/S, with SWR not as good as a Moxon rectangle.
• Reflector with bent tips: It is intermediate between the conventional yagi and the one with a vee-shaped reflector with respect to weight and cost. It is also intermediate with respect to gain and F/B, with still good F/S and excellent SWR bandwidth.

Although I knew all of this before the modelling study, there is value in confirmation and spending time to optimize performance; there is no need for hasty reasoning. After presenting the results of the modelling I'll come back to explaining why they perform as they do.

First, the free space azimuth patterns in 100 kHz steps from 14.0 to 14.3 MHz. I skipped the upper 50 kHz since I rarely operate there and performance is little different from that at 14.3 MHz. Rather than tables (as I've often done in the past), I'll present the data as overlaid traces. Pay attention to the outer ring gain on each chart since those differ for each antenna.

It is no surprise that the conventional yagi has the most gain. The greater the parallel portion at the centre of the elements the greater the sum of the currents. However, inter-element coupling is poor in a conventional yagi so that the gain bandwidth is not great. That said, the gain bandwidth isn't all that different for the others, except for the relatively poor gain performance of the yagi with a vee-shaped reflector. Gain is pretty good across 20 meters for 3 of the 4 designs.

F/B is not very good for the conventional yagi and for the vee-shaped reflector. Surprisingly, the Moxon rectangle is not as good as the yagi with the bent wire tips reflector. At least it was a surprise to me. 

F/S is relatively poor for the yagis with full or partial wire reflectors. This is expected. You can gain an insight by imagining yourself in space some distance directly off the side of each yagi. When you look at the conventional yagi you see almost nothing since the elements are pointing at you; an ideal dipole has no collinear radiation. For the other antennas, the amount of reflector that you can see is non-zero, with the least for the Moxon rectangle and the most for the vee-shaped reflector. Hence the relatively poor F/S.

Again, these are not fully optimized designs. It is likely possible to squeeze out a little more performance, in particular the yagis with a vee-shaped or bent wire tips reflector. The distance to and angle with the driven element are critical since small differences cause large performance changes. Critical coupling is called critical for a reason!

Next, let's look at the SWR across the 20 meter band. The conventional yagi uses a beta (or hairpin) match and the others are directly fed at the centre of the driven element.

The Moxon SWR could be improved with more fussing. I didn't bother since small changes will have little effect on the pattern. The same is likely true for the vee-shaped reflector. That said, the SWR at the band edges will be almost the same when the SWR is optimized to dip 1 at one mid-band frequency. 

All designs other than the conventional yagi do very well. Few transmitters would complain. Keep in mind that environmental factors (interactions with the tower, guys and other antennas) will in most cases cause deviations from perfection more than what you see on these plots.

At this point it was time to stop. I have time over winter to mull over the possibilities. At the moment the reflector with bent wire tips looks attractive: <1 db gain below that of a conventional 2-element yagi with good F/B, F/S and SWR bandwidth. Other than the conventional yagi these antennas are a little complicated to raise onto a tower, just as it was for the 40 meter reversible Moxon.

A 3-element design would be better, especially mechanically since the driven element will be pulled equally from both sides; the wire tips and cords of the parasitic elements "guy" the DE. But the antenna is larger, more complex and with only modest performance improvement. But only about 1 to 1.5 db gain improvement can be expected.

Due to interactions that I am likely to encounter in my station I did not attempt to make this a multi-band antenna. It is likely that I'll have a 20 meter mono-band yagi and a separate 10 & 15 meter yagi to replace the TH6. The latter may very well be a multi-element two-band conventional yagi with interlaced elements. Again, these are early thoughts not a definite plan. I'll develop models when the time comes.

Note: Dimensions are not shown for any of the modelled antennas since I used constant diameter tubing and bare wires rather than tapered tubing and insulated wires. These can be adjusted when and if it comes time to build the antenna that I settle on. Dimensions were selected to be approximately average element diameters. Booms are between 3 and 3.2 meters (~0.15λ), with variations made to make the wires fit the space while being connected to the DE tips.