I am designing several small mono-band yagis to replace the TH6. The venerable tri-band yagi is fixed south at an intermediate height (~25 meters) for working the southeast US, Caribbean and South America. It's deficits are that it is narrow band (high Q), high loss (traps) and not sharable during multi-ops. It's also very very old.
A no-trap tri-band yagi like the Skyhawk fits the bill when combined with a triplexer and set of high power BPF. However that is a very expensive solution at >$4,000 if the equipment is purchased new. They are not often found on the used market. I am fortunate to have purchased a used Skyhawk far below the new price. It is rotatable at about 21 meters height.
A few small (smallish) yagis are not expensive to build since I have ample aluminum in my stock. I also do not anticipate difficulty side mounting these yagis where they can be effective without significantly interacting with the stacks for the high bands. Additional switching hardware will have to be built and fit into the station automation, but that isn't difficult. Low loss transmission lines are mostly already in place.
I decided to abandon my attempt to design a 2-element 20 meter yagi with the attributes I want. Performance of every 2-element variation, including Moxons, have been poor in some respect. These include gain, gain bandwidth, SWR or mechanical robustness. My revised objective is an ordinary 3-element yagi. I have all of the material on hand, although I'd have preferred not to use so much of it. Hopefully I can replenish my stock through more scrounging.
Even for such a simple antenna there are many interdependent parameters. For the design process I have fixed the boom length to 7 meters (23') since I can build a boom that length from available tubes and it is sufficient for good performance. I have further fixed the position of the DE (driven element) at 40 cm (16") behind boom centre: closer to the reflector than the director. It is a position that is conducive to achieving good performance that is used for most yagi designs.
Fixing certain parameters simplifies the design and optimization but can omit some high performance solutions. Based on my experience these choices are acceptable since excellent designs are readily obtainable by fixing these particular parameters.
Since this is a design exercise rather than a construction plan, all of the elements are constant diameter 25 mm wires. A taper schedule can be added later with negligible change to the yagi's performance. Using EZNEC, I compared NEC2 and NEC5 then decided to stick with NEC5 for the remainder of the design process. Gain is virtually identical between NEC2 and NEC5, with small variations in F/B and feed point impedance.
The modelled feed point matching network is a beta (hairpin) match. The length of the DE is shorter than resonance to provide series capacitive reactance. The length and impedance of the shorted stub determine the shunt inductance. These parameters are easy to adjust in the model and in the field. A beta match requires the DE to be electrically isolated from the boom, unlike the gamma matches I typically use. Mechanical complexity is traded for tuning simplicity, but either is acceptable. A CMC (common mode choke) is advisable for any feed system.
With the selected fixed parameters we have the following degrees of freedom in a 3-element yagi:
- Lengths of the director and reflector
- Ratio of director to reflector lengths
Really, that's about it. Only a 2-element yagi is simpler. Yagis with 4 or more elements are more difficult to optimize since there are so many more variables. Luckily there are numerous published and optimized yagi designs so that in most cases you can look them up in the ARRL Antenna Book and elsewhere. But beware of unverified designs based on boasting, poor methodology, old myths that refuse to die and opinions not backed up by engineering.
Even for a simple 3-element design like this one there are a several things to keep in mind:
- Maximum gain is largely determined by boom length, not the number of elements. Once a boom length is selected, we choose the number of elements needed to ensure sufficient coupling among them to enable the performance objectives to be attained.
- The length of the DE is irrelevant to performance. It only needs to be close enough to the lengths of the parasitic elements to effectively couple. Modest shortening of the DE to transform the feed point impedance to 50 Ω has negligible performance impact.
- For a 3-element yagi, gain rises with frequency and is typically maximum beyond the operating bandwidth. For 2-element yagis maximum gain is below the operating bandwidth. Yagis with 4 or more elements are similar to those with 3 elements in this respect but with more variability.
- Smaller reflector to director length ratios give higher gain and narrower SWR bandwidth. Too small a ratio can result in an antenna gain that cannot be effectively matched and requires large diameter elements (not wire) to avoid ohmic loss in the elements. This is due to the low radiation resistance where gain is maximum. That is expected and not a coincidence.
- High reflector to director length ratios can in extreme cases be fed without a matching network since their feed point impedances can be close to 50 Ω. However, that feature comes at the cost of performance.
For this design exercise I modelled a 3-element yagi with a parasitic element "spread" of 6%. That is, the reflector is 6% longer than resonance for the operating bandwidth and the director 6% shorter. I then adjusted the DE and beta match for an SWR of 1 at mid-band: 14.175 MHz. That was my baseline. From that baseline I increased and decreased the reflector to director ratio to bracket a reasonable range of performance metrics.
To demonstrate the results I will only present 3 of those spreads: 5%, 7% and 10%. Outside that range the performance metrics are not to my liking. Others could perhaps justify alternative designs for specific applications. My primary objective is as follows:
- Maximum gain for an SWR lower than 1.5 across the 20 meter band: 14.0 to 14.35 MHz.
I am not concerned with optimizing F/B, since the antenna is primarily for contests in which I am happy to hear and work stations off the main lobe. The low SWR objective is to be compatible with solid state amplifiers that have no ATU. This is an objective to enable maximum operating agility. The TH6, like any loaded or trapped yagi, performs poorly in this respect.
Well, that's a long preamble to set up what will be a brief presentation of my modelling results. So let's have a look.
From this graph it should begin to become clear why I selected the spread values that I did. Above 7% the 1.5 SWR is too narrow, and is indeed little better than the TH6. The SWR bandwidth at a 10% spread seems enticing until we consider performance.
To display F/B and gain on a single chart I expanded it vertically. The colour scheme may be a little confusing but good enough to convey the data.
There is a significant gain difference among the three designs. As already described, gain rises toward the top of the band and narrower spreads have higher gain. The range varies between 1 and 1.5 db.
Is that a significant difference for on-air performance? Many hams will say no. However, for contest use there is a demonstrable difference. It may not be immediately evident in use since QSB obscures the difference. Even 1 db will get you through the pile ups faster and when running you'll attract more callers.
For me the lower gain for the 10% spread is undesirable. At 7% gain is only 0.5 db below that of the yagi with a 5% spread, and the SWR objective is met, just barely. The parameters of the beta match (not shown) are easily achievable without compromising construction or efficiency.
While F/B is not strongly favoured for my intended purposes, the relatively poor F/B with a 10% spread is concerning. It can be somewhat improved by adjusting yagi parameters that I fixed for this modelling exercise, though not by much. A 10% is too wide. Yet it is interesting that many commercial designs within this range. Perhaps the full-band low SWR is effective marketing.
Unlike gain and SWR, the overall pattern is acutely sensitive to interactions. This is because of the exact balance of amplitude and phase to substantially cancel radiation in those many directions.
My hope is that this deliberately constrained analysis of 3-element yagis helps to clarify necessary trade offs in any yagi design. There really isn't anything new in this article. Despite this, the analysis has clarified how to proceed.
My choice is a 7% spread. I have already begun collecting the material and construction will proceed this spring. Replacement of the TH6 with the new yagi may be delayed so that I don't lose 10 and 15 meters until yagis for those bands are ready. I want all three yagis ready for the fall contest season.
I am planning construction features to achieve more than the basic objectives. For example, managing interaction with the nearby 40 meter Moxon. I'll report on those after the yagi has been completed, tuned and tested, along with a detailed description of the antenna. It was brutally cold this morning but the sun is shining and spring is not far off.
