Sunday, August 28, 2016

Perils of Chasing Yagi Performance: A50-6

Ever since a friend loaned me a 6 meter rig in the mid-1970s I've been intrigued with the magic band. That brief experience led to construction of a simple yagi and the addition of the FT-650B transverter for my FT-101E. When I had the opportunity to build a proper tower and station in 1985 I purchased an FT-726R and a Cushcraft A50-6 yagi. With a 150 watt amplifier I worked hundreds of grids, 6 continents and 70 countries, well before 6 meters was as popular as today and before many countries had a 6 meter band.

By the time I tore down my station in 1992 I knew that the A50-6 as originally designed is a poor performer. Computer modelling was just then going mainstream in the ham community and helped the vast majority without the means to range test antennas to evaluate antenna designs. I did the same, purchasing the MiniNEC-based ELNEC, the forerunner of today's EZNEC product from W7EL.

That was a long time ago and my model is long lost on a forgotten floppy disk. But I do remember that the antenna gain fell short by several decibels from what was theoretically achievable with 6 elements on a 1λ boom. Getting the model right, I recall, was difficult because of the long run times on a 16 MHz 386 processor without a math co-processor. Not only that but the lack of stepped diameter correction (SDC) resulted in telescoping tubing elements to have an incorrect resonance.

As I consider what antenna I will use for 6 in my next station I am revisiting this antenna. The boom is being reconstituted from its component pieces, from what had been its interim usage as a mast or for fishing wires through my backyard foliage. One section of boom needs to be replaced due to damage it suffered. All the elements are in excellent condition. A couple of them were used in the 2-element yagi I constructed for use in 2015.

Computer modelling has come a long way over the past 30 years. There really is no excuse for poor antenna design nowadays. What design best fits my operating objectives? To this end I have come back to the A50-6 to see what I can do with it. After all, I have the components of a high-performance antenna, if only I can decide how to best use them.

The original A50-6

VE3VN tower and antennas in 1985
Unfortunately I cannot easily redo a model for this old antenna. I dug up the manual for this antenna (see cover above) and discovered it had no information on element length. There isn't even a dedicated manual for it: it rates only a set of errata in the manual for the A50-3 and A50-5. It simply instructs you to insert the tubes for the tips up to the black marks painted on them, order them from longest to shortest and space them 47" on the boom. Since those marks are long since faded away and the elements difficult to retrieve from storage I have no dimension data at hand.

No matter. Other than curiosity there is no good reason to model this antenna. I know that its deficiencies.

The equal spacing may seem odd yet it is not a dreadful idea.  W2PV in his studies during the 1970s (documented in his book Yagi Antenna Design) used equal spacing, using which he created excellent designs. That is not the problem with the A50-6; rather, it is the element tuning.

For your interest I've included a picture of my tower in 1985 just as antenna construction is being completed. At the bottom is a TH6 (19 meters high), with the A50-6 at the top (22 meters high) and a Cushcraft long-boom yagi for 2 meters in between. You can see the equal spacing on the A50-6, so different from a modern yagi. You can also see that I did not use a common mode choke, which while not uncommon back then is surely a bad idea. Each yagi was fed with 40 meters of brand new LDF4-50A Heliax. The attenuation is -0.6 db at 50 MHz. That small loss was confirmed; it was not responsible for the poor performance.

Today's A50-6S

Performance of the current antenna of this name is nothing like the original. The design has been rigourously optimized, by, as I understand it, W1JR. Yet the boom length is the same (with a different taper schedule) and the elements similarly constructed. The improved performance is easily verified in EZNEC or YW, including the Leeson SDC for tapered tubing elements. I used EZNEC to model the antenna. Since the manual has the measurement details if you are interested so I won't list them here.

A50-6S wire model with the current profile at 50.5 MHz

How not to model a yagi

My first attempt to model the A50-6S did not go well. I wrote the following paragraph before realizing just how badly I messed it up.
When tuned for the range 50 to 51 MHz (per the manual) the free space gain is 13.1 dbi at 50 MHz and peaks at just over 13.5 dbi at 51.5 MHz. F/B is best toward the higher end of this range, consistently better than 20 db. Feed point resistance between 50 and 51 MHz is approximately in the range of 16 Ω to 18 Ω and the reactance is similarly stable. I didn't need to model the matching network to know that SWR would be very good and within reach of the supplied gamma match.
If you are an experienced antenna modeller you may be able to make some good guesses at what went wrong. But first I'll discuss a few points that gave me pause, evidence that led me to the answer. There are lessons here for anyone contemplating antenna modelling, and especially for yagis.

Ultimate gain

I knew that 13.5 dbi gain is high, and maybe too high. I was lulled by the Cushcraft manual that claims a gain for the antenna of 11.6 dbd, which is equivalent to 13.7 dbi. But this is 2 db more than the theoretical maximum gain for a 1λ boom.

The A50-6S gain would therefore be ~2 db better than the similar design in the ARRL Antenna Book (and other respected reference designs) and up to 2 db even better over equal spaced elements like the original A50-6 I purchased.

Alas, this was not to be. If something looks too good to be true it probably is. Take a look at the following chart from W2PV's classic book Yagi Antenna Design. There are other references that generally agree with these figures, as W2PV discusses in his book.

The maximum achievable gain for a 6 element yagi on a 1λ boom is ~11.3 dbi. More is possible with some fine tuning of the design, at the expense of difficult matching and reduced F/B. Even so the maximum gain will fall below 12 dbi. The 13.5 dbi figure I modelled is clearly impossible.

Perils of NEC2 modelling

EZNEC features will warn you about some problems in your model. The one that is proved especially useful in this case was average gain. When you do a 3D pattern plot EZNEC calculates the total field versus an isotropic radiator. The ratio between these -- average gain -- should be exactly 1. Here is what I saw:

Now we know where that extra 2 db came from! We have only to determine why. This is where close attention to detail pays dividends. The EZNEC manual has all the information you need and is an excellent resource. But if you don't know what you're looking for how can you find it?

I had a strong suspicion of the cause of the error. It turns out my suspicion was correct. But rather than jump to the answer let's look at how I diagnosed the problem. That procedure is more important than the conclusion.

The yagi's radiation resistance was quite low: ~16 to 18 Ω. While this is entirely possible it did not look right in the context of the wide spread in resonant frequencies of the elements. So I took the driven element and isolated it. At its resonant frequency the radiation resistance was 44 Ω. A dipole in free space ought to be 73 Ω. Fat elements lower the value somewhat but not even close to that degree.


EZNEC didn't raise any segmentation warnings (too long, too short, etc.) yet therein lay the problem. I had made the segment lengths of the main tubing sections approximately equal but perhaps fairly large for a VHF antenna. I used a 1 segment wire equivalent for the U-bolt clamp and boom crossing, 5 segments for the next 24" tube and a variable amount for the outside tube, the length of which varied with the element length. All my choices caused problems.

The biggest problem was that centre section. I had to make it 1 segment since its length is quite short at only 1" or 2", with a diameter of ~1"; I experimented with various dimensions to determine what seemed most realistic. (Note: A 1-segment wire is not unusual and serves well when a source or transmission line connects to that wire.) The impedance dramatically changed as I varied the length and diameter. At 4" long the radiation resistance got very to the proper value: 71 Ω.

It isn't sufficient to do just that. So I reduced its length to a more sensible 2" then made the segment lengths of the tubing sections equal to that, or as close as I could get. This increased the segment count in the total antenna by quite a lot which slowed calculation. However it was worth it when the average gain came in at precisely 1.000 and the yagi's feed point impedance rose to 29 Ω. The forward gain was exactly where it ought to be, between 11.1 and 11.3 dbi, and overall good performance in its specified operating band between 50 and 51 MHz.

More perils: using the Leeson SDC

Having overcome one modelling peril I came to a more subtle matter: the reliability and correct usage of SDC (stepped diameter correction). With NEC4 the correction is not necessary so you are already one step ahead in the game. But with NEC2, which the vast majority of us use, some kind of SDC is required. It is not without its pitfalls. The NEC2 model can only be as accurate as the Leeson SDC used in EZNEC. It has numerous constraints, many of which you can read about further in the EZNEC manual (circa page 64).

The references I've checked show that the SDC for telescoping tube elements is less than 0.2%, often no worse than 0.1%, compared to NEC4. Field tests seem to confirm the model results. My own small experiment worked pretty well when putting the EZNEC model into practice.

Since in the present case I am shifting the yagi down in frequency by 1% (500 kHz) even a 0.2% (100 kHz) error is perfectly acceptable. Accumulated errors from construction technique and interactions with adjacent antennas and wires almost certainly are at least of of similar magnitude. Perfection isn't possible, and you will not notice a gain difference of 0.2 db! Even a degraded F/B due to interactions can be a poor correlate to gain loss.

The next source of error in using SDC is the centre section of the element, which is where the element crosses and attaches to the boom. The boom and clamp together make for a wider electrical diameter, though one without a well-defined translation to an equivalent wire diameter. Most formulas for this purpose assume a flat plate for an element-to-boom clamp, while the A50-6 uses a U-bolt. If we get it wrong how large an error can we expect?

I experimented with the centre section in EZNEC, varying the section diameter and length to see how sensitive element resonance is to changes. Once again I used the isolated single element model and adjusted the element tips to resonate the element at 50.5 MHz. Its impedance is approximately 44 + j0 Ω. The centre section baseline is a 1" diameter wire equivalent with a length of 1". The 1" diameter seems justifiable for a U-bolt clamp across a boom tube of 1.5" to 1.75", but I could be wrong.

Estimating the equivalent diameter and length of the centre section is important since it affect both the radiation resistance (and average gain) and the resonant frequency of the full element. There may also be interactions between segment length and the SDC algorithm, though this is not so easy to determine and isolate. I didn't try.

What I did instead was a sensitivity analysis of the centre section. The simple test I performed in the model was to double the wire diameter and length, going through their allowable combinations in the model and measuring the change in resonance. I varied the wire diameter while keeping the wire length constant (2" segment length) to avoid the segmentation error discussed above.

The first case is my baseline, with the centre section being a continuation of the ¾" tube; that is, no wire diameter increase due to the U-bolt and boom crossing. Notice that the resonant frequency is more sensitive to larger diameters. At my original 1" estimate the shift is negligible. Although not shown I did some trials with a 4" centre section (with adjusted segmentation) and determined that the length was significantly less of a factor than the wire diameter.

Based on this analysis I went with the 1" wire diameter that is 2" long and 1 segment. It really isn't the equivalent of 2" long but making the length shorter reintroduced the segmentation error. The segmentation I settled on was 1, 11 for the centre 2" long section and  the ¾" section. The segments in the ⅝" section (element tip) varied from 12 to 17, selected to keep the segment length as close to 2" as possible. This brought the feed point resistance of the test dipole to ~71.5 Ω, about where it ought to be.

Lowering resonance to capture more of the available gain

The maximum gain of yagis with 3 or more elements typically falls at the high end of the usable band width, and sometimes higher. Despite the gain being close to the ultimate there is some more that could be milked from the antenna. This is in part due to the new A50-6S design is being more broadband than I require. Getting that additional gain will almost certainly narrow the SWR bandwidth due to a lower radiation resistance where the gain is maximum; that is, at the high end.

Changing the element lengths to capture this gain runs into a conundrum: I don't know the precise frequency range of the stock antenna. Modelling is not so reliable that I can assume that my model, which includes SDC and estimated centre wire parameters, is sufficiently accurate, and I don't know how reliable the manual is. I reviewed the cleaned up model and compared it to similar 6-element designs but I still cannot be certain the model is accurate. This matters since I will not only be adjusting element length but also shifting the yagi down in frequency so that the maximum gain is closer to the bottom end of the band.

Since the best performance of the antenna is skewed toward the upper end of its ~2 MHz optimum bandwidth and I am only interested in the first 500 kHz of the band a first step to optimizing the antenna to my personal interests is to lower the range. This is easily done by shifting resonance of all the elements downward by 500 kHz, or 1%. Each element half is lengthened by ½".

Gain at 50.1 MHz is improved, which is where most of my activity takes place. The difference may be small -- incremental gain of 0.2 db and F/B reduction of ~5 db -- but why not take it if we can?

One danger is that towards the upper end of the original range the feed point resistance begins a rapid rise. Another is that the gain, typical of optimized multi-element yagis, drops steeply above a critical frequency. However in this case the gain is 11.5 dbi at 51 MHz with a F/B of almost 30 db. This is excellent.

The SWR with a suitable matching network is also excellent, though it does show signs of a high end rise.
We could lower resonance even further to capture a little more gain and F/B but perhaps at the expense of an optimum match.

There is some benefit in keeping the SWR below 1.5 to satisfy the need of legal power broadband amplifiers, if that is what you want. For that reason alone it's worth the tuning effort. Gamma matches can be tedious to tune so some time must be spent to get that perfect match. Since the feed point is so far along the boom this is an ideal situation for adjusting the gamma match with the yagi in a vertical orientation.

Perils of increasing gain

We can push the gain higher if we dare. To do so will necessarily narrow the SWR bandwidth since the radiation resistance will drop, thus increasing antenna Q, and almost certainly reduce the F/B. I am willing to risk both because my target band segment is narrow and F/B is not much of an issue on 6 meters, and can be deleterious by making it less likely that you'll notice an opening in other directions. This is a personal choice, and you may feel differently.

Yagi tuning for maximum gain is in general achieved by reducing the ratio of the resonant frequencies of the reflector and director(s). Since we have 4 directors the critical one is most often the last director. In the case of the A50-6S that is director 4. Per the manual's dimensions the resonance spread of the yagi based on the two outermost elements is ±11.5%. This is quite wide. That the gain is near the theoretical maximum is evidence of how good the performance of the redesigned A50-6S is.

As with the 15 meter yagi from an earlier article I tightened the tuning by shifting the reflector resonance up and the director 4 resonance down by an equal amount. The other directors were not changed. In the A50-6S the length of director 4 is significantly less than director 3, so we have some room to play with it without ruining overall performance.

The change was made in small increments of ¼". At each step the yagi performance was checked. Where necessary the array's frequency range was shifted up or down by adjusting all elements the same amount.

As expected the gain crept upward while the F/B declined and the variability of the feed point impedance increased. When I had about as much gain as I could eke out without overly degrading the match and F/B I stopped.

My optimization quest garnered only an additional 0.3 db gain. It ranges from 11.6 dbi at 50.0 MHz to 11.65 at 50.5 MHz. This is pushing hard against the theoretical maximum. F/B degraded to no a little less than 20 db. The free space azimuth plot show how it fares at 50.2 MHz, which is the near the centre of its most useful range.

The feed point impedance was difficult to tame. It can be kept below 1.5 between 50 and 50.5 MHz, but rises to 2 before again dipping above 51 MHz. The antenna's gamma match should be able to deliver the above SWR curve with careful adjustment.

The dimensions of the half element (boom centre to element tip) are as follows, using the A50-6S hardware without other modification:
  • Reflector: 59 ½"
  • Driven: 55 ¼"
  • Director 1: 54 ¾"
  • Director 2: 53 ¾"
  • Director 3: 53 ¼" [Corrected June 24, 2021, thanks to reader John N5TEE]
  • Director 4: 51 ¾"
The frequency spread between the reflector and director 4 has been reduced to ±7.2%.

Was it all worthwhile?

When I began writing this article I intended to exclude my errors and false starts to exclusively focus on the A50-6S performance. Since that turned out to be the least interesting aspect of my experiment I changed the primary focus to modelling challenges and gave the results less prominence. I believe this is more useful to you and to me.

My final judgment on whether I ended up with a better design for my A50-6 than the already excellent A50-6S remains open. An interesting point is that I got more incremental gain by shifting the antenna down in frequency than I did by tightening up the tuning for more gain. That is, even at the lower frequency range in the Cushcraft manual the gain peaks too high in the band to be useful for my operating preferences. Your situation might or might not mirror my own. Perhaps all I ought to do is lengthen the elements by ½" and not risk the F/B and SWR performance

My hope for this article is that the lessons learned can be applied to any antenna project, whether the antenna is designed from scratch or a modification of a commercial product. W7EL has done a good job of documenting common errors in modelling with the NEC2 engine, and the tools to diagnose those errors. You need only learn to understand NEC2's peculiarities and EZNEC's model testing features.

Don't hesitate to play with commercial products! Be reasonable in your expectations and proceed with caution.

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