Choosing a High-bands Yagi (Part 3) - 3-element Tri-bander

Continuing on from Part 2 of my analysis of small high-bands yagis, it is time to evaluate 3-element tri-band yagis. In this category I include those antenna with 3 elements (reflector, driven and director) that are each active on 20, 15 and 10 meters. Traps for 10 and 15 meters are employed to achieve tri-band resonance. Examples include the TH-3, TA-33, A3S, among others. They typically have a short boom, usually between 3.5 and 4.5 meters.

As with 2-element tri-banders the boom length must be a compromise since it varies by a 2:1 ratio between 20 and 10 meters, as measured in wavelengths. At a typical boom length of 4.2 meters (~14') this is 0.2λ, 0.3λ and 0.4λ on 20, 15 and 10 meters, respectively. Tri-band yagis with booms longer than 4.5 meters typically have additional elements for one or both of 10 and 15 meters since otherwise the boom is too long for effective element coupling, and therefore reduced gain. Examples of these include the TH-6 (the antenna I have stored in my garage) and CL-36, among many others.

Before we delve into the design and evaluation it is worth a moment to review the parameters which effect 3-element (and larger) yagi performance:

• Boom length: Maximum achievable gain is a function of boom length - the longer the boom the greater the gain. There is likewise an optimum boom length (in wavelengths) for a yagi comprised of a chosen number of elements. For a 3-element yagi the optimum boom length is ~0.35λ, per the reference yagi introduced in Part 1. Maximum F/B is a more complex function of boom length, but shows a periodic behaviour with peaks at odd multiples of λ/4. For a 3-element yagi there is just the one peak at 0.25λ since the next odd multiple is too long a boom for 3 elements.
• Parasitic element resonance: Maximum gain and F/B are achieved when the resonant frequencies of the parasitic elements are close together -- but not too close -- with lengths of 0.49λ and 0.47λ for the reflector and director, respectively. However this is a poor choice since the gain, F/B and SWR bandwidths are narrowest in this case. Better choices are 0.502λ and 0.463λ, where we sacrifice ~0.5 db of maximum gain and, perhaps, ~5 db of F/B in return for good performance across all 3 bands. The use of traps will further narrow bandwidth performance so we want to start with a reasonably broadband design choice. These choices help to avoid sharp radiation resistance dips at maximum gain which make it difficult to achieve a broadband match.
• Element separation: It is assumed that for the 3-element yagi the separation between reflector and director elements is equal to the boom length; that is, they are at opposite ends of the boom. The only remaining separation variable is the position of the driven element. To avoid mechanical interference with the mast clamp the driven element is typically offset from the centre position towards the reflector. As the separation between driven and reflector elements is reduced the gain increases and the impedance falls, but only to a certain point. A small offset is optimal.

Notwithstanding the above points it is not my intent to design an "optimal" 3-element trap yagi. What I am doing is creating a benchmark to serve as a proxy for the better commercial products in the category. Since there is strong market demand to optimize SWR (match) performance it is to be expected that products may have an incentive to sacrifice more gain and F/B performance than I'd prefer.

Unfortunately there is no certain way to judge yagi products for their performance. Published specs are incomplete and graphs too often look a little too perfect to be accepted as presented. This is the case even when the specs are mostly true. We can use the laws of physics (electromagnetism) to explore what is theoretically possible (and probable), knowing that no real product can exceed the performance of an ideal antenna. That is, we can use physics as a sanity test. That is one of my purposes for modelling a variety of small yagi antennas. The hope is that the best small tri-band yagis approach the ideal.

Design Process

The design process for a 3-element tri-bander is straight-forward, though more complex than for the 2-element version. Gain and F/B in the 2-element yagi is solely determined by the boom length (for a fixed style of element design). With 3 elements it is necessary to coordinate the relative resonance of the reflector and director elements to achieve a desired gain and F/B profile over the band of interest, as was described above.

Once the desired gain and F/B profiles are selected per the reflector and director tuning we can think about the match. This is done by adjusting the driven element and matching network (e.g. beta or gamma match). This matching process does not affect gain and F/B, provided the driven element does not get excessively short and the matching network is low loss.

Keep in mind that a lot of the work has already been done for us. Starting with the venerable work of the NBS many years ago, extensive theoretical modelling by W2PV around 1980, and more recent work by many others utilizing state-of-the-art software and high-speed computers. I am leaning on that work when I select design parameters. There is no need for me, or anyone, to design a yagi from scratch. It would be a waste of time. There are no undiscovered secrets left to be ferreted out by aspiring mavericks.

With all the forgoing in mind here is how I went about the design:

• Choose the resonant frequencies for the reflector and director, in relation to a centre frequency. You can either look up the performance figures or experiment with EZNEC or a similar tool. If you experiment always tune both reflector and director so that they maintain the same ratio with respect to the centre frequency. This will simplify matching. Note that as in the reference yagi it is not possible in a 3-element yagi to get the maximum gain and F/B anywhere near the same frequency, so choose the centre frequency with care.
• Develop two antenna models: one for the yagi and one for element tuning. Once an element is inserted into the yagi it is very difficult to tune it due to mutual coupling. It is better to tune it in a separate model and copy it to the yagi model. Do the element model in free space.
• For the trap elements we are using it is necessary to tune the reflector and director on all 3 bands. Calculate the target resonant frequencies on each band and get the element resonance as close to those frequencies as possible. Resonance is the frequency where the reactance is zero, not where the SWR is minimum. Don't fuss over it too since there are other factors not included in the model that affect element tuning: tubing taper schedule; element-to-boom clamps; trap dimension; coupling to other antennas, etc.
• With all 3 elements in the model the performance curves can be shifted up or down in frequency by changing resonance of both parasitic elements by the same amount.
• Alter the placement of the driven element and resonance of the parasitic elements in small increments to adjust performance (gain and F/B). Remember to do all resonance tuning in the element model and copy its parameters to the yagi model. You may want separate models for the director and reflector (as I did) to speed the design process.
• Adjust the driven element in the yagi model to place the SWR curve consistent with your design objective. Add a beta match or similar network if the feed point impedance is too low for a direct match to 50 Ω coax -- this is mandatory in the antenna we are designing. Tuning of the driven element and match has little to no affect on gain and F/B performance, which is why it is done last.

Of course I say you can do all this work but few will and will even want to do so. Since this is my project I will cut to the chase and present the antenna that I designed by this process. As with any yagi antenna it is a compromise, but one that I believe reflects the best computer-designed small tri-band yagis on the market. I will only present the performance figures since the physical dimensions and trap designs are unlikely to be an exact reflection of any commercial product. For example, my model has no boom, and that has an effect on element length. Further, the trap (load) model has no physical dimension, and although the trap performance might be similar the design is almost certainly different from all commercial products.

I chose the following centre frequencies to optimize gain and F/B for CW and lower SSB segment of each band. These frequencies require careful selection since the relationship of optimum frequency for gain and F/B are boom length dependent, and are therefore different on all 3 bands. They are derived from the models developed by W2PV.

• 20 meters: 14.000 MHz
• 15 meters: 21.200 MHz
• 10 meters: 28.600 MHz

Other design parameters:

• Boom length: 4.2 meters: 0.2λ on 20 meters, 0.3λ on 15 meters and 0.4λ on 10 meters
• Driven element spacing: 1.9 meters from the reflector, which provides enough space at boom centre for a boom-to-mast clamp but does not result in excessive torque due to wind load asymmetry
• Reflector element resonance: 13.440, 20.350, 27.450 MHz (0.960 of centre frequency, or 0.502λ length equivalent)
• Director element resonance:  14.560, 22.050, 29.740 MHz (1.040 of centre frequency, or 0.463λ length equivalent)

TH-3MK4 (from online manual)

The parasitic element lengths can be made similar on all bands despite the different boom lengths on each band as measured in wavelengths. They could be further optimized for the respective boom lengths on each band but since the potential improvements are minor I am opting to keep it simple.

The final design looks a lot like the Hy-Gain TH-3MK4, the schematic of which is shown here. Of course other 3-element tri-band trap yagis look similar and, probably, have similar performance. My choice of the TH-3 as a model is not a recommendation of this antenna. It's just that I know Hy-Gain best and their traps seem to measure well. I have never used a TH-3.

Avoiding Maximum Gain

Before getting into the modelling results for the "optimum" design it is worthwhile to explore what it means to design for maximum gain, and why this is a bad idea. Just for the fun of it I ran the model with identical elements, all being copies of the driven element. This is a symmetrical yagi that will exhibit 0 db of F/B but has bidirectional gain.

The antenna resonated at 14.140 MHz. At right is the free-space elevation pattern of the antenna. Notice that the gain is quite poor, worse than a dipole, but is reasonably directive. Where did the power go?

At resonance the impedance is 1.9 + j0 Ω. This is exceptionally low. The radiation resistance rises steeply on either side of resonance, so this is a sharp dip. Not only does this make it difficult to design an effective, low-loss matching network the low R value is an invitation to other losses. In particular the traps (modelled at 0.3 Ω ESR, the same as in Part 2) contribute -3.8 db of loss. Even with large aluminum tubing for the elements we get -0.3 db of loss. If there were no losses the bidirectional (broadside) gain would be 5.1 dbi.

There are similar losses on 15 meters, where the traps are most active. On 10 meters the trap loss is small, however the aluminum I²R losses are still present.

This demonstrates why a yagi with 3 or more elements should never be designed for maximum gain. The gain bandwidth is narrow and the target gain cannot be achieved in any case due to losses caused by the low radiation resistance. This is true even in an antenna without traps or other loads.

Trouble with traps

In the interests of sharing what I learned I will confess that the process I came up with above to tune the parasitic trap element did not work well. While I did suspect the possibility of problems, especially with director tuning, I was unprepared for the magnitude of the resulting errors. In the case of 10 meters the performance was mediocre and the performance curves were shifted 1 MHz higher. The same happened on 15 meters, although the curves shifted less than 200 kHz higher. On 20 meters the frequencies came out right but the performance was poorer than expected.

What happened? I know the design process works on yagis comprised of unloaded elements, and in fact got a textbook result with the reference yagi I developed in Part 1. To understand the source of the problem it is useful to make a brief detour to look at how yagis work.

The far-field pattern of a yagi is the superposition of radiation from all of the antenna elements (plus ground reflections). When these are in phase in a specific direction they add, resulting in gain. The amount of gain depends on how close their phases are, and their magnitudes as well. When they are exactly out of phase (180° difference) and the magnitudes are equal there is no net radiation in that direction.

The phase and magnitude of the radiation from a parasitic element depends on:

• Separation: It takes time for the field from the driven element to propagate to the parasite, a time that is proportional to distance. The phase shift is proportional to the separation measured in wavelengths of the radiation. For example, for 0.2λ separation the phase differential is 72°. That is, by the time the field reaches the parasite the phase angle at the driven element has advanced 72°. In all other directions the phase relationship differs, and therefore the field strength is dependent on the elevation and azimuth angles.
• Reactance: In general, the closer the parasite resonant frequency (where reactance is 0 Ω) is to the driven element the greater the magnitude of the induced current. When the parasite is tuned to another frequency the reactance causes the magnitude of the induced current to fall and, importantly, the phase of the induced current will be shifted. This determines the phase and magnitude of the radiation from the parasite.

The dynamics are actually more complex since it is a recursive process. Radiation from the parasites induces current in all the other elements, including the driven element, which then combine with the currents on those elements and are again radiated. This is a continuous process while the source is active and energy from the induced fields is available (not yet launched into space or dissipated by I²R losses). EZNEC shows the data for the steady-state current magnitude and phase for every wire segment in the model.

Another important facet of the dynamics is that the mutual coupling lowers system impedance and thus raises the total current in the system for a given source power. Gain is therefore not only a function of superposition but also the system impedance. (EZNEC normalizes the current to 1 A at the source by adjusting the source power unless you tell it to keep the power constant instead.)

When we specify a parasitic element by length relative to a resonant λ/2 element (or the equivalent resonant frequency) it is merely a calculation shortcut. What matters is the reactance. In a loaded element, whether done with coils, capacitance hats or traps, that shortcut is invalid. That's where I went wrong on the first try. Once again it's those traps making my task more difficult.

Because of the complex contribution to phase by the traps it is not possible to tune the parasitic elements by frequency or length. I worked around this by modelling a tube, without traps, to the target director and reflector resonant frequencies on each band (as shown above). I then read off the reactance at the centre frequency -- the X in Z = R + jX.

• 20 meters: Reflector [+41 Ω]; Director [-37 Ω]
• 15 meters: Reflector [+38 Ω]; Director [-35 Ω]
• 10 meters: Reflector [+36 Ω]; Director [-33 Ω]

I retuned the models of the reflector and director, adjusting them so that their impedances showed these reactances at the centre frequencies of all 3 bands. With some trepidation I copied these elements over to the yagi model and observed the gain and F/B across the bands. Lucky for me this worked beautifully.

Small frequency shifts were still required on 2 bands but otherwise the gain and F/B performance were per the textbook. I then proceeded to set the trap ESR to 0.3 Ω (just as in the 2-element yagi) and match the system to 50 Ω.

Performance

To avoid boring you with the processdetails, I will directly proceed to the results. These are visible in the collection of charts on the right.

I used the same chart structure as for the 2-element antenna to make comparison easier. I will do a more direct comparison at the end of this series (Part 5?) if you don't want to bother flipping back and forth as you read.

All measurements are made in free space. All of these antennas, including the 2-element version will respond to height above real ground in much the same way so this approach avoids confusing height for raw performance. We will come back to antenna height in a later article in this series.

My observations on the performance models:

• Gain and F/B bandwidth are superior to the 2-element tri-bander model. Although the maximum gain on 15 and 20 meters is only modestly better, it is available over more of each band.
• Gain on 10 meters approximates that of a full-size 3-element yagi, reaching a maximum of more than 9 dbi.
• 15 meters is, again, the worst performer. Bandwidth is narrow, both for performance and SWR (not shown). At the top end of the band the yagi reverses direction, as indicated by negative F/B. Peak F/B is excellent since the boom is close to an odd multiple of λ/4 (0.3λ).
• Loss due to trap ESR (equivalent series resistance) is, as always, highest around the frequency of maximum gain. In the case of 3-element yagis this frequency is high in the band, whereas it is low in the band for 2-element yagis. This is a general rule for 2 and 3-element yagis, and is unrelated to the use of traps.

You may have noticed that I did not plot SWR. Coming up with a beta match that would give a low SWR on all 3 bands became tedious and I gave up after working on it for a time. Surely that ideal beta match does exist -- most commercial products have done so -- but there was no point in discovering it in this model since I am not planning on building this antenna and it has no impact on gain and F/B performance.

I got close enough to the ideal by playing with beta match parameters (stub impedance and length, and driven element length) to discover the implication for match bandwidth. It is good on 10 and 20 but not good on 15 meters. Once again it is that middle band that causes problems, just as it did on the 2-element tri-bander and even the trap dipole. I do know that Hy-Gain uses different 15 meter traps on the driven and parasitic elements so they presumably have learned something that I have not.

Trap ESR Loss

That last point brings us to the impact of traps on performance. I did the same sensitivity analysis as for the 2-element tri-band yagi. You can go back to Part 2 to see what I had to say on the topic. Here I will simply present the charts that show the impact of trap ESR.

As a reminder, I used 0.3 Ω as the traps ESR for the above performance analysis since that appears to be in the range of the best commercial traps in tri-band yagis. An ESR of 0 Ω represents a lossless trap, which is useful as a theoretical benchmark but is impossible to achieve in the real world.

Loss is highest where gain is maximum since that is typically where the radiation resistance of the antenna is lowest. On 20 meters this is the high end of the band and on 10 and 15 meters it occurs mid-band. On 15 meters the loss is especially high since the radiation resistance is below 10 Ω over a large section of the band.

Apart from 15 meters the impact of trap ESR is modest. Traps are a great convenience in designing a compact tri-band yagi with good performance, but this is a cost that must be paid.

Note: The charts say the reflector tuning is 1.05 Fc, but it is 1.04 Fc as stated earlier in the design process. Or (more correctly) tuning is per the exact reactance values stated above.

Next up...

In Part 4 I will evaluate the Spiderbeam category of multi-band yagi. This is a promising antenna since it has no traps or aluminum tubing. However, as we will see, there are still compromises and trade-offs.

Choosing a High-bands Yagi (Part 2) -- 2-element Tri-bander

Having established a reference yagi in the previous article I now want to explore the first of several categories of small-sized yagis: 2-element tri-bander.

There are any number of commercial products that fall into this category. Perhaps one of the best known is the Hy-Gain TH-2MK3. I will use this antenna as a design template. This as not a product endorsement. As we will see all antennas of this type are difficult to assess with software models, or at least without knowing all aspects of the technical specifications. The traps are the major unknown.

There are several concerns I had with these antennas and were a particular focus on my modelling effort:

• Boom length: It is not possible to choose an optimum boom length (element separation) for works for all 3 bands of interest. We must learn how severe a reduction in antenna performance results from a compromise length.
• Trap efficiency: There are 8 traps in this antenna, so even small losses can add up. Their efficiency is frequency dependent and highly sensitive to electrical and physical parameters. The data for the traps is typically not publicly disclosed by manufacturers, so it is necessary to make a few intelligent guesses.
• Match: The uncorrected feed point impedance is different on each band since this parameter is sensitive to boom length (as measured in wavelengths).
• Bandwidth: These antennas can exhibit a narrow bandwidth, especially when adjusted for optimum gain. The inclusion of traps exacerbates the problem.

The above list is derived from the issues I enumerated in Part 1 since, in my estimation, they are the greatest challenges in this class of small yagis.

Traps

The first step is to design the traps for inclusion in the EZNEC model. This is an interesting challenge since there are an infinite number of L (inductance) and C (capacitance) parallel circuits that resonate at any given frequency. This is constrained to a smaller range of values by physical design, and then constrained further by impacts on efficiency and reactance on lower-frequency bands.

I modelled a dipole in free space with 4 traps (2 for 10 meters and 2 for 15 meters). As a starting point I made the dipole of similar length to the elements in the TH2, then did the same for trap placement.

Above is the current plot taken at 21.1 MHz. You can see the current "glitches" at the traps. The 10 meters traps act as inductive reactances at 15 meters, and the 15 meters traps "leak" some current since the trap is resonant above the band. The 15 meters traps have noticable loss, helping to lower the gain to 1.8 dbi, or about 0.35 db lower than a dipole.

Which brings me to the trap calculations. This is outside my area of expertise so I had to turn to other sources. One excellent resource is by W8JI (whose material I've linked to before). It was based on his measurements and theory exposition that I decided to normalize on the Hy-Gain tri-bander designs. I placed the trap resonant frequencies outside of the bands of interest, and specifically chose the frequencies that he measured for the Hy-Gain traps:

• 10 meters: 29.7 MHz
• 15 meters: 22.3 MHz

Although this worked out well in the model, I did not see the increase in trap loss near those frequencies to which he alludes. Where I did see increased losses...well, I'll come to that further along.

In a parallel resonant LC circuit the values of reactance are equal (and opposite). But what value of reactance? If we ignore physical constraints on trap design it is easy enough to choose from a wide range of values. One difference is the amount of inductive reactance the traps exhibit at lower frequencies. This affects the length of the element outside the trap. For example, with a higher value of inductive reactance contributed by the 10 meters trap the rest of the element must be shortened to compensate. Another difference can be loss: the higher the inductance the larger the ESR, and therefore the loss (all other things being equal).

Making the element too short has an effect on element gain (gain versus a dipole declines as the element gets shorter) and it can squeeze the traps together more than can be accommodated in a physical design.

Most trap calculators I've run across on the internet typically use a reactance target of 200 Ω. From my reading of related material this value correlates with achieving inductor Q of anywhere from 100 to 500 and ESR (equivalent series resistance) of less than 1 Ω. The ESR plays a key role in trap loss, so we want it to be as low as possible while not requiring an impractical coil design.

EZNEC supports loads that are configured as traps and will calculate the loss in the traps. What it will not do is tell you the ESR. You must supply that value from calculation or measurement. Not being able to do either very well in this theoretical exercise I tested what I believed would be the approximate ESR for Hy-Gain traps, which I suspect are in the range of 0.3 to 0.5 Ω. As we'll see even within this small range the results can vary quite a lot. Traps made from coax or small coils and capacitors have higher ESR.

All loads in EZNEC are distributed/centred on the segment where it is placed. Real traps have a finite width and height. In the case of Hy-Gain traps (and many others) the exterior of the trap is continuous with the element, with the outside being part of the radiator and the inside being one plate of the trap capacitor. The overall result should otherwise be similar in a realized antenna.

Boom Length

This one must be a compromise. A typical and preferred boom length for a 2-element yagi with a reflector centres on 0.14λ (3 meters long on 20 meters). This is the length I normalized on for my series on 2-element wire yagis for 40 meters. But if you select this boom length for 20 meters then the boom length is 0.21λ or 0.28λ on 15 and 10 meters, respectively. This can be a problem, especially on 10. Conversely, if the boom is optimized for 10 meters, the boom length is 0.07λ or 0.11λ on 20 and 15 meters, respectively, which can cause problems on 20 meters.

When the boom is too long the mutual coupling can be too small to achieve optimum gain. For a short boom the gain can be achieved but at the price of F/B and, more seriously, low feed point impedance. It should be no surprise that commercial products tend to choose boom lengths around 2 meters, which is midway between those extremes. For example the boom of a TH-2MK3 is 1.8 meters (6'). This is near optimum for 15 meters but workable for the other bands. The question to be answered is how severe a compromise is involved? This affects not only gain and F/B (the key performance measures) but also matching; the feed impedance (and SWR bandwidth) will vary greatly across the 3 bands.

Design Process

Once the trap dipole is adjusted to the preferred resonance on all 3 bands it is a simple matter to duplicate the element and space them apart by the chosen boom length. Remember the rule: to construct a 2-element yagi with a reflector element you make the parasitic element the same length as the original, resonant element. When I did this for the trap dipole I had a tri-band yagi that needed only small adjustments to optimize gain and F/B at the design frequencies. All of that adjustment is made to the parasitic. The driven element is only modified, later, to achieve a 50 Ω feed point impedance.

As with the trap dipole the yagi was designed in free space. Except in this case it is a good proxy for a yagi above real ground, provided it is not too close to ground. For example, the reference 3-element yagi in Part 1 maintains its gain, F/B and SWR bandwidth to heights as low as 5 meters (0.25λ). What's different is the far field pattern, in particular the performance at low radiation angles.

In the EZNEC model view notice how close together the traps must be. The inductive reactance of the 10 meters (inner) trap shortens the required length on 15 meters. With the inductive reactance contributed by the 15 meters (outer) trap only a little more tubing is needed to resonate on 20 meters. To see how this affects the current distribution on the element notice how when excited at 21.1 MHz the current jumps in the areas between and beyond the traps. On 20 meters (not shown) the current distribution curve is closer to normal, just compressed a bit between the 10 meters trap and the element end. As it turned out 15 meters was the most difficult band to adjust in the model.

The following construction diagram of the TH-2MK3 is almost identical to the yagi model, demonstrating that trap placement is no mere modelling artifact. I omitted the metal boom in the EZNEC model since other than change the resonance of the reflector element a small amount it otherwise has no performance impact I opted for simplicity. The driven element does not contact the boom.

At a separation of 1.8 meters it only takes a small change in boom length to cause significant changes in the antenna's behaviour. While the shifts in resonance are easy to correct the same is not true of the antenna's impedance profile, particularly on 20 meters where the boom length is shortest in terms of wavelength (0.9λ).

With both elements in place the next step in the design process is to adjust the centre section of tubing to achieve the gain and F/B curves for the band segment of interest on 10 meters. I followed my usual inclination of optimizing the antenna to the CW segments on all bands but ensured that there is still good performance at least up through the lower part of the SSB band segments. This proved difficult since on 20 and 15 meters the bandwidth can be narrow, whether measured by SWR, gain or F/B.

After tuning the reflector on 10 meters I did the same for the other bands, first 15 then 20. Then I did it all again since adjusting the outer parts of the element affect the higher bands a small amount.

I added a shorted transmission line to the feed point of the driven element to model the beta match on the TH2. Although its impedance is not specified it appears identical to that of the TH6. So I took a ruler out to the garage where the TH6 is stored, measured the dimensions and calculated its impedance: a little over 300 Ω. With that in the model I adjusted the driven element dimensions for best SWR in the selected segments of all 3 bands. This is, again, an iterative process, including adjustments to the beta match since my model does is not identical to that of the TH2.

Performance

I'll say up front that I was pleasantly surprised by how well this antenna performed in the model. I had to review the theory to understand what I'd missed. The main thing is that excellent gain and F/B can be achieved over a wide range of boom lengths, which allows the antenna to work well on 20, 15 and 10.

As alluded to earlier the critical items are trap ESR and low feed point impedance on 15 and 20. The first limits the achievable gain and the second limits the SWR bandwidth. On 10 meters neither item is a concern so the antenna does quite well.

Before I dwell on these concerns I will summarize the antenna performance in a few charts. For this analysis I set the trap ESR to 0.3 Ω at the resonant frequency of the trap. EZNEC does the rest.

The gain and F/B curves are typical of 2-element yagis with their respective boom lengths as measured in wavelengths. The theoretical maximum gain is a little over 7 dbi, to which we get close on 10 and 20 meters. Since in these antennas the frequency of maximum F/B is higher than that of maximum gain it helps to place the maximum gain at the low end of the desired range, which sacrifices F/B at these frequencies. The presence of the traps does not appreciably affect the performance curves, except that the trap loss limits achievable gain.

Look at the comparative gain and F/B curves for the 20 meters 3-element reference antenna (from Part 1) and the trap tri-bander on 20. The gain of the full-sized 3-element yagi is pretty flat across the band. While the gains are close together (< 2 db) where the 2-element does best they are far apart higher in the band. Expect similar results for 15 and 10 when compared to full-sized 3-element yagis. In contrast the F/B curves are not very different, although the F/B bandwith and maximum is better for the 3-element yagi.

SWR is excellent only on 10 meters. On 20 and 15 meters the usable bandwidth is narrow. The beta match can only do so much for us. This is especially true on 20 meters where the boom length is only 0.9λ, resulting in a low feed point impedance where gain is maximum with large percentage swings in radiation resistance away from that frequency. I could have fought the SWR lower on 20 meters but it would improve SWR bandwidth only a small amount. Users of this category of antenna must accept that. Use of the rig's ATU can help extend the usable bandwidth (gain and F/B are decent across all bands), but don't expect miracles at the high ends of 15 and 20.

About those traps...

Hy-Gain, Cushcraft, Moseley... the traps of all tri-band manufacturers look similar, and they are similarly placed on the elements, whether 2 or 3 element yagis. They are not the same. But how different? I can't say. In the trap article by W8JI that I linked to above there are some indications but no hard figures on the performance impact. Specifically the loss.

In the above evaluation I used an ESR of 0.3 Ω since, so far as I can tell, it is a value that is likely not to be too far from the truth. I used that value for all the traps but that isn't true. Expect different values for different traps -- even for the same band on the same antenna -- and especially across manufacturers.

This leads me to finally make a brief exploration of how trap ESR can impact 2-element tri-bander performance. I will focus on gain since it is overall antenna efficiency that is paramount. SWR is also affected by higher ESR values but (as is typical with all forms of loss) it improves SWR performance.

Perfect, loss-less traps (a useful fantasy!) are those with an ESR of 0 Ω. It tells us what can be achieved in an ideal tri-bander. We must aim a little lower. The charts show the gains at 0, 0.5 and 1.0 Ω. The value of 0.3 Ω I used in the performance evaluation is, I believe, typical of the best traps. A value of 0.5 Ω is less than ideal and 1.0 Ω is a poor trap. ESR is even higher in the worst traps, such as in many traps made from coaxial cable.

There are a few interesting things we can learn from the calculated effects of ESR on antenna efficiency (for which gain is a proxy).

• Loss is highest near the frequency of maximum gain. This is because radiation resistance is lowest at that frequency. This is I²R loss since, for a given source power, the current (I) increases as the radiation resistance decreases. Radiation resistance tends to decline as the element spacing is reduced, so this can be managed by increasing boom length. For the same reason a trap dipole has low loss even with poor quality traps since the radiation resistance is much higher than in a yagi.
• The gain of a 2-element yagi can exceed 7 dbi, but this cannot be achieved with traps. Although I don`t address the topic here, linear loading does not allow us to escape from such losses. It`s just a different manifestation of loss. There is no free lunch.
• Poor quality traps can reduce gain by several db. But even then the loss is more moderate the farther you operate from the frequency of maximum gain.
• Loss increases as antenna current flows through more traps. This is why the losses are smaller on 10 meters.
• Trap loss can shift the frequency of maximum gain. This is an artifact caused by high trap loss. It is just that the gain near the "true" maximum gain frequency is greatly reduced by trap loss.
• Managing performance on 15 meters is especially challenging. The closeness of the traps to each other has an odd effect on antenna current. This may be a necessary sacrifice in this category of antenna.

Conclusion

Performance of 2-element tri-band yagis is moderately good, but short booms and traps limit their performance. In the ideal case they compare favourably to the reference 3-element full-size yagi. Alas, we do not live in an ideal world.

In the next article I will explore 3-element short-boom yagis. Hopefully it will be shorter since the material on traps will not need to be repeated.

Choosing a High-bands Yagi (Part 1)

Big antennas are serious business. They are costly, require large (and expensive) towers and rotators, and even with all this effort they are more likely to fall to weather events than their smaller brethren.

Are they worth it? Although my 2014 objective is to a small 20-15-10 yagi (and possibly 17-12) for a small tower I intend to get the most out of whatever my choice of yagi will be. That means comparing small yagis to the best, regardless of size. Only then can we know what we're getting, or not getting, in the way of performance. Comparisons among small yagis or single-element antennas (dipoles, verticals, etc.) do not address my quest for maximum performance.

To begin, we must normalize on height. It will not do to compare a small yagi at a low height to a large yagi at a great height. They must be compared under similar conditions. Since my tower will not be more than 15 meters high that is my benchmark height. I also find it useful to do comparisons in free space to remove environmental variables.

Small, rotatable yagis come in several varieties. All are on my list of candidates.

• Standard elements lengths (with or without traps, used in tri-banders) on a short boom, typically ~4 meters (0.2λ) long (e.g. TA33, TH3, A3S)
• Fewer elements on a short boom, but where that boom length is optimized to the smaller number of elements (e.g. TA32, TH2, MA-5B)
• Wire elements on a non-conducting frame/spreaders (e.g. Spiderbeam, Hexbeam)

Since I enjoy designing antennas you might wonder why I don't choose to build one. While I can do this it can be costly in terms of time. Time to order aluminum and other material, time to design strong and effective multi-band elements, time for construction, and, finally, time to adjust the antenna to match the design. Multi-band antennas have a large number of variables and require much fussing. Single band and even multi-element wire antennas are less time consuming.

What I can do is a careful evaluation of commercial products and make a reasonable choice from among them. Some are quite good, while others are less so. Software modelling takes out much of the guesswork, so that one does not have to go by reputation or (worse) marketing literature.

To establish a basis for comparison I designed an optimum 3-element yagi for 20 meters. The boom of this antenna is 0.35λ (7.5 meters, or 24 ft.). By optimum I mean with regard to gain, F/B and bandwidth. In free space this antenna has 9 dbi gain, and it holds close to this over a wide bandwidth. The design is based on an NBS (National Bureau of Standards), and was extensively modelled by W2PV in Yagi Antenna Design, 1986.

Optimization is achieved by selection of element lengths (resonant frequency) and element spacing. Elements are constructed from aluminum tubing. So is the boom but the models ignore exclude the metal boom for simplicity. That factor can be compensated with element length adjustment later in the design process.

More gain (9.8 dbi) and F/B (>30 db) over a narrower frequency range can be achieved by selecting element resonant frequencies that are tighter together. However, I do not consider a design optimum if it maximizes one performance measure at the expense of others. Such a design looks good on paper but is deficient in actual use.

The EZNEC view of the antenna is above right (element #1 is the reflector), and the modelled performance is summarized in the following chart. In free space this antenna has a maximum gain of 9.1 dbi. 

This antenna reaches its maximum gain of 13.8 dbi at 14.350 MHz. At 14.000 MHz it is 13.4 dbi, which shows how broadband this antenna's performance can be. F/B (front-to-back) doesn't fare as well although it is still quite good. F/B peaks at better than 27 db around 13.950 MHz. There is no easy way to bring the frequencies of best gain and F/B closer together without severely compromising performance. The 2:1 SWR bandwidth is 250 kHz using a beta match, and is easy to match with a rig's ATU across the entire band.

As a further comparison, the gain of a rotatable dipole is 2.1 dbi in free space (F/B is 0 db) and a 2-element yagi is 6.9 dbi (with a narrow gain and F/B bandwidth). It may surprise you to learn that the 3-element yagi is only a little more than 1 S-unit better than the dipole and just 2.1 db better than the 2-element yagi. However the bandwidth of the optimized 3-element yagi is far better than the 2-element yagi for all performance metrics. As we'll see later, over real ground the 3-element yagi compares more favourably.

This is just Part 1 of a short series of articles. Originally I intended to do this in one article then realized it was too long and would be delayed since I have not yet done all the required work to reach a conclusion. In other words, I don't know where this exercise will take me. Of course I have a strong sense of how this will go, but there is considerable doubt. As of now I expect this will take 2, or at most 3, additional articles.

I will finish Part 1 with my reasoning for choosing the optimum 3-element yagi as my reference and the list of issues that need to be addressed by the evaluation.

I have a TH6DXX in my garage that is perfectly good. Unfortunately its wind load is too great a risk for the small, guyed tower I plan to put up this year. I want to keep the projected wind area below 4 ft². The TH6DXX wind load is high because it uses optimum element spacing on each band: 20, 15 and 10 meters. This cannot be achieved with 3 trapped elements, so there are more (actually 4 elements on 10 meters). The 24' boom (0.35λ on 20 meters) is itself a substantial wind load. However, apart from the traps and shorter elements the 3-element yagi reference I've described above, it is a good proxy for the TH6DXX which is an excellent multi-band antenna that has stood the test of time.

Speaking of traps and element length, let's finish off with the list of issues.

• Traps: Elements must be multi-band to keep the element count low (3 maximum), so traps are used. These are parallel LC circuits that are typically integrated with the element structure. Traps have loss. However not all traps are equal in this respect. Traps also reduce element length since they act as inductive loads for lower-frequencies. Achievable gain is reduced as the element length is reduced.
• Element configuration: Element in the traditional aluminum yagi are parallel to each other. This is not mandatory. They can be square sections (e.g. Moxon beam) or vee-shaped (e.g. Spiderbeam). Those bends reduce achievable gain, but they do other things well.
• Wires vs. tubing: Although aluminum (or, more often, aluminum oxide) has more resistance than copper, the size of the aluminum tubing serves to lower the losses in a yagi to negligible levels (<0.1 db for typical HF yagis). Copper wire actually has more absolute loss when used in a yagi, as we've seen before. Wire gauge and insulation become considerations.
• Resonant elements: Resonant elements can be used in order to avoid traps and to keep elements at full length. Unfortunately a straight piece of wire or tube does not resonate on more than one 20, 15 or 10 meters (unless very, very long). Therefore more elements are required. This introduces, cost, complexity and wind load.
• Element spacing: Elements that are optimally spaced on one band are not optimally spaced on the other bands. With a frequency spread of 2:1 for a tri-bander this is an important concern. Acceptable compromises must be found.

In Part 2 I will probably discuss 2-element vs. 3-element multi-band yagis. There is more to their differences than gain.

Venturing Into a SSB Contest

On a whim I decided to enter the CQ WPX SSB contest this past weekend. Since getting back on the air over a year ago I have stuck to CW, only making a handful of SSB contacts. While I generally prefer CW I have no aversion to SSB. It is just that with QRP and small antennas SSB is too difficult for my taste.

This is easy to understand with some simple arithmetic (which I think most hams already know, but is worth repeating):

• SNR (signal-to-noise ratio) is proportional to receiver bandwidth, provided that the signal is totally contained within the filter bandpass. Typical SSB transmit bandwidth is 2.4 kHz and CW bandwidth is < 10 Hz. However we rarely if ever use extremely narrow filters in our receivers. We can say, roughly, that the typical ratio of filter bandwidth (in actual use) between SSB and CW is 10. That is, for the same transmitter power the SNR of an SSB signal is -10 db in comparison to CW.
• QRM is another type of noise that affects SSB and CW differently since the activity levels and spectrum are different. In the context of a contest, which can be viewed as a worst-case scenario, we can estimate the number of stations to be twice (2x) the participants in a CW contest. However more spectrum is available (and used) for SSB, being about 2x on 20 meters, 3x on 15 meters and 4x on 10 meters. On 40, 80 and 160 the spectrum is roughly equal.

If we use the median spectrum factor of 3x we can calculate the QRM ratio (SSB:CW): 10 x 2 / 3 = 7. That is, 10x receive bandwidth times twice the number of stations, divided by triple the spectrum. The conclusion is that it is much harder to be heard in a SSB contest.

Try both CW and SSB contests with QRP and you will, like me, discover how true this is. My score in CQ WPX SSB is a great example: 454 QSOs during 18 hours of operation (20.5 hours per rules criteria), despite superb conditions on all bands. The QRM was so fierce that most stations with S9+ signals either could not hear me at all or struggled in the attempt to pull me through. The worst band was 40 meters with just 24 QSOs, only one of those from outside North America.

Let me backtrack a few days to discuss my preparation for the contest. This might seem easy enough since all that's involved is a transceiver, a microphone and a computer. My difficulty was the microphone. There were two particular challenges: compatibility with the KX3 transceiver, and quality.

Elecraft sells a handheld mic for the KX3 that reportedly works well, but that is not an option since a handheld mic is out of the question for contests; you need both hands for typing, tuning and other station operation. When I first got back on the air with the KX3 at the beginning of 2013 I used an inexpensive but reasonably good headset that I had purchased for Skype use (on the left in the above picture). It is comfortable and both microphone and headphones audio quality is not too bad. Importantly, its 3.5 mm stereo connectors are a perfect fit to the KX3.

When my SSB success didn't go so well with my QRP power I flipped the mic out of the way and only used the headphones. That is, until the foam covers over the earpieces shredded. So much for the economy PC headset. In any case the microphone worked poorly with the KX3, being unable to achieve full modulation. There was a compatibility problem, perhaps with the rig-supplied bias via the stereo connector. Fiddling with the KX3 microphone setup options didn't help. More on this below.

I next bought inexpensive headphones designed for use with portable entertainment devices (middle item above). They are lightweight and were passably effective. Since I had decided to forgo QRP SSB I could get by without a microphone.

One major problem with this unit is sensitivity, with the minimum audio gain setting already loud enough for general use. Turning the gain higher was a problem since (as with all modern digital level controls) each succeeding discrete step was too large. There were only about 4 usable settings of the AF Gain control, and no ability for fine tuning. Another problem was audio quality, which is surprising considering its intended use for music. Listening fatigue can set in after a few hours of use on a noisy band.

One last problem is the solid plastic cover over the foam pads. This is good to block ambient sound but bad for comfort. That matters in a contest. Plastic foam is better. (Of course poor quality foam on cheap headsets isn't good, as we have seen.) You can always close the shack door if there's noise from the household. That will also make your transmit audio cleaner since compressors amplify background sound.

Since I needed a headset with a microphone I decided to reach back into relative antiquity. I resurrected my decades-old Heil headset (on the right of the picture). I had no idea how it might fare after over 20 years of storage. My recollection was that it had worked very well for both receive and transmit. The reason I did not press it into service earlier was the connectors: ¼" phones (stereo) and Yaesu 8-pin mic. Since I was considering refurbishing the FT-102 I was saving it for that rig.

With WPX only one day away and no other option in sight I took the plunge and replaced the connectors. As I cut off the old connectors it felt as if I was also cutting off a piece of my past. After, with new connectors attached and tested, I plugged it into the KX3 and had a listen. It was marvelous. Receive audio quality was suddenly crystal clear, much better than either of the other headphones. Sensitivity was just about right, too. It was a joy to tune across the bands. It goes to show that quality does matter, so you should take some care in choosing what you slip on over your ears.

The microphone was a greater challenge. Elecraft had made a KX3 design decision to not support low-output microphones such as dynamics and even some bias-driven PC-compatible mics. In their defense the KX3 was intended for mobile use where a purpose-built handheld mic is most often the correct choice. So that's what they did. As it turns out the KX3 is widely used as a primary home rig, and their owners (like me) prefer to use their existing mics.

One thing I've come to really like about Elecraft is that they do listen to their customers. Plus, there is a lot of flexibility designed into their rigs that can be manipulated with firmware updates. In late 2013 they succumbed and updated the firmware, although they seemed reluctant to do so and continued to flog their own microphone even in the update notice.

This gave me confidence I could adjust the KX3 to support my ancient Heil headset. Here are the steps I went through. Much of it is standard on any SSB rig:

• I first had to configure the "3^rd pin" for PTT, mic bias or nothing. I thought about this for a moment until I remembered that the mic predates PC sound cards. It has a dynamic element. I set the pin to "nothing".
• The Heil mic element does not have a flat frequency response. It has an emphasized mid-range that is customized for DXers and contesters. The KX3 has a default mic equalization that boosts the mid-range. I therefore adjusted the KX3 mid-range equalization to flat (+0 db).
• I switched in a dummy load for the transmitter adjustments. Increase the mic gain until the ALC starts kicking when speaking as you would during a contest or in a pile-up (this usually is not a normal speaking voice). Turn on speech compression and increase it until there is a noticable effect but not more than 10 db of compression on voice peaks.
• I did not have time to wire in a foot switch so I was stuck with using VOX. This meant adjusting the VOX controls. I have a long-standing aversion to VOX since I have never found a combination of settings that I like. For contests it is important to set the VOX delay as short as possible or you'll often miss the first part of the other station's exchange. Contesters have fast reaction times and speak quickly, often responding while you're still talking! You can increase the delay for non-contest use.

The result sounded about right in the headphones using the rig's monitor function. The mic gain is set to 63, which is far above the 40 maximum in the previous firmware version. My next step was to find a station to assess my audio.

I picked 17 meters since there are many casual SSB operators to be found there. The first station I ran across that appeared ready to start a new QSO had a British accent. He told the station he was talking to that he was checking to see if the band was open. It was TX6G (Austral I.). No pile-up yet and not spotted on the DX cluster. Thirty seconds later he was in the log. But I didn't ask for an audio report. I was just happy to work him on SSB with 10 watts and a dipole. I then went to 15 meters and did solicit reports from a couple of contesters warming up before 0000Z. My audio was fine.

A couple of hours later the contest started and gave it my best shot. The QRM was fierce and almost no one could hear me. If adversity builds character I became a better person by Sunday evening. In addition to the QRP SSB challenges I mentioned earlier there are others.

• Splatter: It isn't easy to overdrive the modern generation of transmitters, though many seemed to be trying. Those using amplifiers had an easier time achieving this dubious objective. Unless the ALC is compatible and integrated with the exciter it is often easy to overdrive the amp (flat top) and cause splatter. It made for a higher basement noise level on the bands, and thus harder for me to be heard.
• Compression: For some there is no such thing as too much compression. They assume that if there is a legibility problem it's the other guy's problem, not theirs. That it slowed them down and caused many instances of miscopied exchanges (which I witnessed many times) seemingly was of no importance.
• Accents: Compression or not, the diversity of accents for non-English speakers speaking English often made copy difficult, in both directions. That doesn't happen on CW.
• Sloppiness: Let's face it, in every QSO my signal was difficult to copy. Many operators didn't let that delay them. They simply logged whatever they imagined my exchange was just so they could move on and work the next station. They will be penalized during log checking. It is better to say "sorry, no QSO, try again later" as good operators did. That works out better for both of us.

After the contest I folded the microphone out of the way. At least I now know that it is possible to operate SSB with QRP and get some results. I will stay with the Heil headset to benefit from the headphone audio quality and comfort for CW operation.

On a lighter note there are some broader benefits to venturing into SSB contests with QRP:

• We fill a psychological need on the other side of the QSO. The DX station who pulls through the weak station feels great satisfaction for having provided a needed QSO to the "little guys".
• If you have sadistic tendencies this is a safe outlet for your darker moods. Think of the pain you're causing to others as they sweat and suffer to pull you through. Focus on Sunday afternoons when the big guns have worked out the band and there are only stations like yours calling them, and they desperately need the points you represent. You can prolong the pain if the QSO is proceeding too smoothly by dialling the power back to 1 watt or less.
• Be proud that you are promoting the state of the art. One of the reasons hams build super-stations with high towers, large antennas, low-noise receiving antennas and superior, feature-rich receivers is so they can work you! This not only spurs innovation, it keeps the amateur radio economy healthy.

But above all, remember to have fun. I no longer take contests as seriously as I once did, which allows me to enjoy myself, even with QRP SSB.

Tuners Do Not Solve All Ills

I do not have antennas for 80 and 160 meters.

That may not sound like a profound statement yet, for me, it is. As far as my DXing goes it simply means I don't go there. Until I am in a position to raise effective DX antennas for those bands I stick to 40 meters and higher bands. The dilemma comes from contest operating. If I don't operate on those bands I miss out on some easily-acquired multipliers, whether it be CQ/ITU zones, countries (VE & W), ARRL sections, or states/provinces.

For my proximate need there is no need for a great antenna on those bands. It is minimally sufficient to work only a few stations to give the contest score a big boost. For example, in my report on the CQ WW CW contest in 2013 I mentioned that I used a tuner to put enough of a (poor) signal on 80 meters to work a couple of stations and add 4 multipliers (VE, W, zones 4 and 5). Yes, that really does make a difference to one's contest score and is well worth several minutes of effort to re-cable and fiddle with the tuner.

As it turns out it isn't as easy as it sounds. Certainly I have a tuner, several in fact, including one that is big enough to have only modest losses at high SWR. It has no trouble at all getting a 1.0 SWR match on 80 meters for my currently largest antennas: multi-band inverted vee (30 through 10) and delta loop (40). However the results were not at all equivalent, or even what I expected.

Neither antenna is even close to resonance on 80 meters. The SWR is high, very high. It is so high that EZNEC gives up on the calculation, only indicating that it is above 100. That is the feed point SWR, not what you see in the shack. At such high mismatches there is considerable loss due to transmission line attenuation. It may seem odd but this can be viewed as an advantage since the resulting high (not extremely high) SWR means that the tuner can achieve a match without risk of excessive loss in the tuner.

To give you some idea of how high the SWR is on 80 meters with those two antennas I used EZNEC to quantify the antenna feed point impedance at 3.525 MHz.

• Delta loop: Z = 0.5 - j80 Ω. For 50 Ω transmission line this gives an SWR of ~6700!
• Multi-band inverted vee: Z = 3 - j1000 Ω, for an SWR of ~350.

Since the true SWR is very sensitive to environment factors at these extreme impedances these are at best only rough estimates. The point is that the SWR is pretty much off the charts, and it has consequences.

The drawing of the setup gives us an idea of where to look for trouble spots.

• Tuner loss: Regardless of whether the feed point SWR is 350 or 6700 the SWR at the shack end of the coax will be much the same, since the dominant factor is transmission line loss. Since the actual value is not extreme (measured to be, very roughly, 10 or somewhat less) and is similar for both antennas I will ignore this factor in the analysis. If you like, assume a loss of -2 db, which is typical of a mid-sized tuner matching a high SWR at 3.5 MHz.
• Transmission line loss: There are two components to the loss. The first is the matched loss, when the SWR is 1 (load impedance is 50 Ω). The second is mismatch loss due to the signal reflecting back and forth between source and load, where attenuation is suffered on each reflection.
• Antenna I²R loss: The radiation resistance of an antenna rapidly declines below its resonant frequency. Since the conductor resistance is in series with the radiation resistance, as the latter gets very low more of the source power is dissipated in the conductor.
• Ground loss: As you go lower in frequency the antenna is closer to ground when measured in wavelengths. Near-field losses increase due to interaction with (typically) lossy ground.
• Pattern loss: The radiation pattern can tilt upward due to the lower height in wavelengths, especially for horizontally-polarized antennas. With more power radiating at higher angles there is less going toward low angles. If your objective is DX this factor can be viewed as "loss" even if the antenna is perfectly efficient.

Having dispensed above with the loss due to the tuner I will first turn to the radiation and ground loss. After all, the title of this blog is Pattern and Match and I often emphasize putting the priority on pattern.

In the above patterns I have normalized the gain to 25° elevation. It should be no surprise that the horizontally-polarized inverted vee directs most of its radiation straight up since it is very low to the ground on 80 meters. The pattern suffers less when using the 40 meters delta loop, remaining primarily low angle and vertically-polarized. Both antennas are close to omnidirectional on 80 meters since they are quite small in terms of wavelength.

Even with its excessive high-angle radiation the low-angle radiation (25°) is 1 db better on the inverted vee. The reason for this is due to ground loss: the modelled loss over medium ground is -1.5 db for the inverted vee versus -6 db for the delta loop.

The antenna I²R loss is low in both cases despite the very low radiation resistance. It is no more than about -0.2 db with 12 AWG insulated wire. I expected worse, so that is one positive outcome.

Now we must deal with transmission line loss. This can be difficult to model since many of the more common equations in use become increasingly inaccurate at very high SWR, and the SWR of these antennas is very high indeed.

Unfortunately the VK1OD transmission line loss calculator I've used in the past has been taken down by the author. There are other calculators on the internet but may suffer from the inaccuracy cited above. Nevertheless that is what I went ahead and did with a couple of online calculators. The true loss could be higher than the figures I am going to report.

• Multi-band inverted vee: -11 db
• 40 meters delta loop: -23 db

Both figures include the sum of matched loss and mismatch loss for ~25 meters of  RG-213 coax between the tuner and antenna feed point. I did not compensate for the λ/4 of RG-11 matching section on the delta loop since with these levels of mismatch the difference on the results is unlikely to be significant.

Gaze at those loss figures for a moment and think what they mean. If you transmit 1,000 watts on 3.525 MHz on the delta loop more than 990 watts is dissipated in the transmission line. In a way that's a good thing since at these levels of mismatch the high voltage points along the coax could otherwise punch through the dielectric and destroy the cable.

Summing all the losses, at 25° elevation the gain at 3.525 MHz on the inverted vee is -11 dbi and on the delta loop is -24 dbi, minus any tuner loss you wish to include. Most of the loss components are already included in the EZNEC model. I did not use EZNEC to model the transmission line loss. These loss calculations explain why, while both antennas performed poorly on 80 meters with a tuner, I could make a few marginal contest contacts with the inverted vee but not at all with the delta loop.

Lessons learned

Using a shack-based antenna tuner can produce far worse results than you might imagine since the SWR can be extraordinarily high. Do not be deceived by the facility with which a non-resonant antenna can be matched in this way. Tuner and other losses pale in comparison to transmission line losses for all but the shortest runs.

In retrospect this is why I was able to do so well with my eaves trough antenna, including making contacts on 80 and 160: there was no transmission line between the tuner and antenna. Although I cannot easily do an A/B comparison, I believe that the eaves trough antenna performed better on 80 meters than either the delta loop or inverted vee. This is despite its low height (6 meters), bends, corners and attachment to a conductor- and dielectric-ridden house.

The options to deal with this problem should be clear. I will list them anyway.

• Put up a resonant antenna (duh!). Even if you have to use loading coils or a matching network at the feed point it will almost always do better than a non-resonant antenna with a long run of coax and matched in the shack with a tuner. A large, efficient tuner makes almost no difference.
• Only use a shack-based tuner for small excursions from resonance for coax-fed antennas. Don't rely on the SWR you measure from the shack since transmission line losses reduce the maximum SWR you'll measure in the shack, telling you nothing about the severity of mismatch at the antenna feed point.
• You can use open-wire line to tame the transmission line losses, but is a lot of trouble to do right. Plastic-encased ladder line is not low loss; you must use true open-wire line, and you'll probably have to make it yourself. Open-wire line is fraught with difficulties, including getting through walls, preserving the differential phase between wires, corrosion, precipitation and coupling to metal obstructions.

There are other conceivable solutions to specific circumstances. For example, a switch or relay can be used to break the 40 meters delta loop into two separate arms, resulting in an asymmetric λ/2 doublet. Unfortunately it does not resonate at half the 40 meters resonance, and for anything other than QRP the switch (relay) will very likely flash over when transmitting since the voltage at the ends of a doublet can be very high.

Another possibility (one that many have tried, including myself) is to unscrew the coax connector so that only the center conductor of the coax is connected. Then ground the tuner (or transmitter) side of the outer conductor. While there is the risk of RFI, hot grounds and higher ground losses, the antenna can become much more efficient when matched by a tuner. The transmission line becomes part of the antenna. When it does work it usually only works on 160, and not so much on 80.

Final thoughts

Non-resonant antennas in typical use are poor performers, as measured by system efficiency and pattern. Unless designed for a specific purpose, a non-resonant antenna that is opportunistically tuned to make QSOs may suit in a pinch but is otherwise a bad idea. It will net a few multipliers in select contests, but nothing more.

If you want an effective signal for DX, contests or other interests, design and build an antenna that will achieve your goal. Opportunistic use of a tuner is rarely effective. You may be better off locking up or selling your tuner so that you never succumb to temptation.

Late-winter Doldrums

Too cold to work on antennas but so close to warmer weather that I can't bring myself to only plan but not do anything outside. I have pretty much convinced myself that I need to take a step up with antennas and possibly with power. QRP with small antennas has been great fun this past year, it just isn't what I want to do forever.

The spring equinox is as good an opportunity as any to look back at my DX accomplishments over the past 14 months with QRP (10 watts maximum), CW only, and simple, low wire antennas, since ending my 20-years hiatus from amateur radio. That will be a good base from which to look forward to the rest of 2014 and beyond.

DXCC

I now have over 100 countries on each of 40, 30, 20, 17, 15 and 10 meters. The last band on which I achieved this mark was 17 meters, where I now have 102 worked. I was surprised at my low country count on 17, so I had to catch up. This is most likely due to it not being a contest band. I have mostly worked 17 meters to catch some rare DXpeditions (FT5ZM, VU7AG, etc.). I have yet to work F and G on that band. Go figure.

Unsurprisingly 20 meters is my best band with 153 worked. All other bands are in between. I don't have antennas up for 6, 12, 80 and 160 meters so apart from a smattering of contacts using a tuner my efforts there are approximately nil.

My overall total countries is 193 worked. It's slow going at this point. I have heard lots of workable stations in perhaps 50 more countries but my puny signal was not heard. My objective of reaching 200 countries with my current station may not happen before I begin antenna work this year.

LoTW

Logbook of the World has proved to be a great way to confirm countries for DXCC credit. As of my last upload at the end of February I have 145 countries confirmed through LoTW. A confirmation rate of 75% is quite good.

On a per-band basis I have noticed an interesting trend. On the bands where contests are held (80, 40, 20, 15, 10) my confirmation rate is ~65%. On the other bands (30, 17) the rate is ~50%. I suspect the reason is that contesters are more likely than others to upload their logs to LoTW. Many DXpeditions delay uploads or do not use LoTW.

Contests

My DX totals were enhanced by participation in contests, both semi-serious and serious. However on deeper reflection my results mask an unpleasant truth: I am mostly working only big-gun contesters, especially on 40 meters.

It is by working the big guns on every band that my QSO totals get as high as they do. I can't run stations (sit on a frequency and call CQ or QRZ, and get answers) and I don't work many of the stations that have similarly puny signals or even those with average signals. I remember one very weak European on 15 meters that answered my CQ, and later discovering he's a regular contester in the same QRP category as myself. That's how I must sound to most stations that I call. That's why I have to call the big guns.

This is easily noticed in the logging software by the number of big guns that I've worked on every band. All it takes is working 100 of these stations across the bands to reach 500 QSOs. In DX contests where VE can work W/K there are even more of these stations to work.

Whether for purely contesting objectives or as a path to DX success I need better (bigger) antennas.

***

Looking forward to 2014 I will briefly outline the topics that are of interest to me in my pursuit of better antennas. If you follow the blog you will likely see one or several articles on each this year.

Tower

With some reservations in advance of a post-winter inspection, I believe that my opportunistically-guyed small tower passed the weather challenge quite well. This included not only cold and ice, but also some strong winds. If it checks out I plan to install a more substantial tower, though still one that would be considered light duty.

My objective is simple enough: a 3-element yagi at 14 or 15 meters height for 3 or more of the high bands will provide 10 db or more of gain over the multi-band dipole and inverted vee I currently use. Part of the improvement is antenna gain and part is greater height. If I decide to stay with QRP this change alone will make me significantly more competitive in DX pile-ups and contests. Jumping up to 100 watts would add a further 10 db gain.

My plan, if I come across something cheap and used, is a Delhi (now Wade) DMX-52. I can mount this in the same location and manner as the current Golden Nugget tower (Site C). I prefer this approach so that no concrete base is required and I stay under the municipal/federal "duty to notify" regulatory requirements that are in effect for structures higher than 15 meters above grade.

If that goes well (and I don't again lose interest in the hobby) I will consider a more permanent, stronger and higher tower in 2015. Any such tower must go to Site D in order to be clear of the septic system tile bed, yet keep a decent distance from the rear property line.

High-performance yagis for the high bands

A light-duty tower requires an antenna (or antennas) that don't stress the tower plus guying. The TH6DXX I have in storage is heavy and has more wind area that I am comfortable putting on a tower of this class. It also doesn't include 17 and 12 meters.

A rotatable wire yagi is more suitable. I am beginning to seriously look at the 5-band Spiderbeam. From people I've talked to it appears to be up to surviving our local weather and its performance claims appear to be legitimate. I found an EZNEC model of the 3-band version (20, 15, 10) and have started experimenting with it. A Hexbeam is also a possibility, except that it has a large vertical height that would easily put it over my 15 meters height limit when placed on a 14 meters high tower.

If I get ambitious I'll also put up a short yagi on 6 meters. If I don't get around to it by July I will probably not do so at all this year since sporadic-E season will have already come and gone.

Low-bands antennas

For 40 meters I may replace the delta loop with a 2-element switchable array, probably the diamond loop array I have already designed. I will need to supplement this with a dipole, possibly on the house-bracketed mast, to fill the side nodes of the array and to effectively work the northeast US in contests.

Getting an effective DX antenna on 80 meters will be difficult. Something like an inductor-loaded half-sloper might work out. However there is the potential to interfere with the performance of the 40 meters array, and there is an unknown capacitive loading due to the wire high-bands yagi. I don't need a great antenna for 80 meters, just one that will collect multipliers in contests and allow me to do some DXing.

I have no plan for 160 meters in 2014.

I have been idly playing with EZNEC to model a variety of potential 40 and 80 meters antennas for 2015, in the case that I put up a proper tower. The main challenge is getting a high-performance antenna to fit the 15 meters (50') width of my property. For instance, a rotatable 40 meters yagi cannot have elements longer than 13 meters. Managing loss in short antennas is the objective, and therefore I have started to explore in that direction.

When these models reach a suitable level of maturity I will write about them.

Antenna interactions

My immediate interests with respect to antenna interactions fall into two categories:

• Interactions among many antennas sharing one tower
• Interactions among stacked, rotatable yagis

In 2014 the first category is of most interest to me. That is why I spent some effort investigating how a vertically-polarized low-bands antenna interacts with a tower, and how to resolve problems.

The second category is more of a future concerns, but an important one. There are specific ideas I want to dig into that may shed more light on this question. Most hams go by rough, and often unverified rules-of-thumb, while other elect to ignore the issue or go to unfortunate extremes. For example, loss of structural integrity by using masts that extend far above the tower top.

Wind load

Because of my choice of tower and guying arrangement I have a renewed interest in acquiring a better understanding of wind load. In particular, the quantified wind load of antennas and other tower loads, and the behaviour and real carrying capacity of towers. This will also be useful should I erect a larger tower in 2015.

The big problems with wind load is that the marketing of antennas and, to a lesser extent, towers does not provide reliable figures. It is quite easy to find quoted square footage of popular antennas that cover an almost 2-to-1 range of values. Towers manufacturers are typically better at providing good data, if you know how to interpret and apply the data. These data are critical not only to build a robust installation but also to pass the requirements for a building permit.

This is not an unfamiliar area to me since I have put up countless towers and antennas over the decades. I have seen many towers and antennas fail as well. There is good information out there, which I have begun to collect.

Moving Into the Shack

As you might be aware the winter in central and eastern North America has been long, cold and snowy. This makes it difficult to put antenna designs into effect. At this point I am getting tired of modelling antennas. Unfortunately that's all I can do. Well, not quite. Surprising as it sometimes seems to me there is more to this hobby than antennas.

Which brings me to this article's topic -- moving into the new shack -- just for a change of pace.

I have been gradually working towards finishing my basement shack over this winter. Progress had to be gradual since I've been busy at many things, not least of which is the antenna articles I've written over the preceding months. Now that the end is near I was able to finally move back into the shack and set it up as a more permanent area for radio operation. The critical finishing pieces were the door, trim and (very important) the floor.

Once that was done all I had to do was put in an operating desk and reinstall all the equipment. The room was designed as a shack when the house was constructed in 1993 so it has all the necessary infrastructure, including dedicated electrical circuits and two 240 VAC outlets for amplifiers. It sat mostly neglected when I decided to not continue with the hobby. Now, 21 years later, I've finally moved in.

Rather than go back to a simple desk I have restored the custom operating desk that I built 30 years ago. It was used in my first station (1984 to 1992) since moving to Ottawa from VE4. I supplied the basic design parameters to my old friend and excellent amateur woodworker VE3NVM, from which he came up with a construction template. With his help and workshop the desk quickly came together.

Here it is in my new shack, already celebrated with some contacts, including one new QRP country: 5H.

The tabletop measures 84"x30", so it is an imposing presence in the modest-sized 120 ft² room. Made from plywood and seasoned maple it can not only support a lot of equipment, it is perfectly safe to stand on. The only equipment it didn't support was my old Collins 30S1 amplifier, which was meant to stand on the floor. Notice how the KX3 is dwarfed by space meant to hold an older generation of transceivers and accessories.

Let me take you through the design parameters I came up with all those decades ago so that you can get a sense of what I was attempting to accomplish with this desk. The effort I expended is more than most hams would bother with, yet the concepts are equally applicable to the selection and assembly of "off-the-shelf" products.

• Surface height is measured to fit my body. When seated in a chair, with its height set so my thighs (femur) are parallel to the ground, the desk height is such that grabbing the paddles and sending CW is almost effortless. Almost every commercial desk has a higher surface. This can lead to fatigue, especially during a weekend-long contest. One reason the surface is only ¾" thick is to provide sufficient leg clearance despite the comparatively low height. Maple is used to brace the surface due to this choice, yet still support a lot of heavy equipment.
• The lower shelf is for power supplies and other equipment which do not require operator interaction other than being turned on and off. The power bar (bottom right) is used to power them all on with one switch. Right now there is just the 4 ampere DC supply to power the KX3, and the AC power supply for the laptop. Back in the day that shelf was crowded. Its height and placement is designed to not get in the way of your feet. For SSB I had a foot switch on the floor beneath the power supply shelf.
• The rigs I used most often went into the lower bays of the upper shelf unit. I chose an antenna switch that permitted the coax cables to exit straight back. This saves space and has a clean appearance, but at the cost of some difficulty in attaching and removing those cables. The B&W switch is, regrettably, intermittent. This is a design flaw and not due to ordinary wear and tear. Worse, the unit is sealed and difficult to repair.
• The middle deck was used to hold VHF transceivers, pre-amps and amplifiers, plus an assortment of measuring devices. All I have there now is an SWR/watt meter. In the centre is a slot that held the logbook, countries list and other paper resources. All of that is now done with software.
• The upper shelf was for everything else, such as a world globe and spotlight lamp.
• On the right side is a longer open area which I used to work on equipment. It had its own power bar and lamp. When I bought my first PC in 1991 (a speedy 16 MHz) it went in this space. Thus began my obsession with antenna modelling, starting with the DOS-based of ELNEC. Even simple models could take many minutes to run on that PC.

There is one terrible lack in this otherwise functional operating desk. Do you see it? There is no place to install a flat screen PC monitor. This ought to be easy to remedy. Some of the upper shelf space will be covered by the monitor, but since today's equipment is smaller that shouldn't be a problem. Then I'll be able to put a keyboard up front and make it easy to arrange things as in any modern PC-centred ham shack.

Since this desk (less the upper shelf unit) was the centrepiece of my upstairs home office for the past 20 years I had to replace it, and fast. My new office desk is a bizarre hybrid of an old, small Ikea desk and odds and ends from Home Depot. I worked quickly this weekend to both rebuild the shack operating desk and construct and install a new office desk. Now I am not only on the air with my old and trusty operating desk but also ready to get down to work Monday morning.

Detuning a Tower from a Vertically-polarized Antenna

In my previous article on a 2-element loop array for 40 meters I issued a caution regarding the potential harm from a tower that is resonant, or just near-resonant, on the band of interest. This type of interaction can destroy the performance of a directive low-bands antenna that is vertically-polarized. Although even a single-element vertically-polarized antenna will excite a tower resonance the impact is typically not a major concern other than the effect on impedance matching. I have a particular concern with tower resonance since that may be only way I can achieve higher performance with a low-height antenna for 40 meters.

As W8JI describes it is possible to detune the tower so that, at least on one band, the tower can be made to effectively disappear. That is, become non-resonant on the band of interest. This allows the vertically-polarized low-bands antenna to meet its potential.

Of course the tower (plus ground and loading due to yagis mounted above the tower) might not be resonant on the target band and therefore there is no cause for concern. But you can only know for certain by exciting the tower with a nearby vertically-polarized antenna for that band. It would be a shame to go to all the effort of designing and building a high-performance antenna that isn't going to work out.

A better strategy is to remove the tower resonance once it is found, and ensure the antenna fulfills its potential. This is not only a one-time concern since, after all, the tower's resonant frequency will not stay fixed for all time: changes to other antennas on or near the tower will shift the resonant frequency, and we all add and remove antennas on an often yearly basis.

Since the weather is continuing to stay cold, windy and generally miserable here in Ottawa I decided to do a little more computer modelling to test methods for detuning the tower. It would be good to know this since if I erect a larger tower this year I will want to build a directive antenna for 40 meters, and due to its inevitable low height I prefer to go with a loop array rather than a yagi.

W8JI provides some general guidelines for designing and tuning what is effectively a trap on the tower. What is missing are specifics. This is understandable since there are many variables that are installation specific. However I don't want to just wing it. This is where EZNEC comes in handy, allowing us to parameterize the design so that we can succeed faster when we spring into implementation.

For the following discussion I will stick with 40 meters and the switchable 2-element narrow diamond loop array from the previous article. The lessons learned should be applicable to other bands and antenna configurations.

The basics of the trap design model are shown at right. Tom suggests a trap length of no more than 3/16-wavelength so I made my trap 5 meters long (A, wires 10 & 14), 0.5 meters wide (B, wires 12 & 13), and centred on an 18-meters tall tower (wires 9-11, with 10 as part of the trap). The 3 wires are ¼" aluminum rod, which make the trap rigid and adjustable. Heavy-gauge copper wire can be substituted for wire 14. The 18 meters tower height was selected since it is the worst case for 40 meters resonance that I previously discovered.

Currents are shown on the EZNEC plot for the case of trap resonance. Notice that the while the current in the trap is high the current in the tower segments above and below the trap are low (they decline to 0 at each tower end). In this view you cannot see the currents on the elements since EZNEC plots those at a right angle to those shown here.

A series capacitor is positioned at the lower-right corner of the trap, where it is most accessible for tuning. I assumed that the capacitor is a fixed, transmitting "door knob" capacitor or an air variable that is both low loss (small equivalent series resistance, which I inserted into the model) and can withstand the voltages present with high power. The capacitor should be protected from the weather with a cover or enclosure, and protected from mechanical strain by, for example, placing it in parallel with an antenna wire insulator.

Safety note: Place the trap high enough that it is out of arm's reach from the ground since there can be high voltages present on the trap when transmitting high power on the test antenna for which the trap is tuned.

The model was developed without doing any calculations. I simply made an educated guess at the inductor dimensions (length and width) and then adjusted the capacitor value (using an RLC load in EZNEC) until the current was maximum at the initial test frequency. This was easier than determining the trap's resonant frequency, even though in practice the latter is usually easier to measure -- I have a dip meter but not a suitable RF ammeter. Either ought to work since maximum current in the trap should coincide with the resonant frequency.

It only took about two minutes of value substitution to find the capacitor value for the test frequency: 49 pf. That's a useful value since I have several 50 pf transmitting ceramic door knobs in my junk box.

However this, as it turns out, is inadequate. I chose a test frequency of 7.02 MHz since that is the frequency at which the antenna gain is maximum. When I checked across the band I found that the F/B and higher-frequency performance were degraded. The F/B is the most valuable metric since any extraneous current will disturb the fine balance of current phase and amplitude between the antenna elements: a F/B of -20 db requires a power subtraction of 99%. Gain is less sensitive to minor phase and amplitude deviations.

Following further experimentation I found that it is possible to adjust array performance by changing the resonant frequency of the trap:

• Frequency of maximum gain (7.02 MHz, 49 pf): The result is as described above. The gain went up by a small amount, about 0.1 db, which is negligible.
• Frequency of maximum F/B (7.08 MHz, 45 pf): This gave the closest match to the gain and F/B curves for the model that has no tower, as was done in the previous article on this antenna. There is some degradation of gain and F/B at the top end of the frequency range (7.2 MHz).
• Frequency higher than maximum F/B (7.14 MHz, 35 pf): Maximum gain dropped -0.1 db (which is negligible) and the frequency of maximum F/B rose to almost 7.1 MHz. Gain and F/B improved a small amount at 7.2 MHz.
• 7.2 MHz (~30 pf): Maximum gain dropped a more significant -0.3 db and the frequency of maximum F/B rose a bit further than the preceding case. Gain and F/B made further improvements at 7.2 MHz, though not by much.

From this I conclude that precise tuning of the trap is not necessary. If you do want to eke out every decibel per my original antenna design objectives the trap should be tuned for resonance between 7.05 and 7.1 MHz. Matching is not a concern since the SWR curve shifts a managable amount as the trap is tuned across the band.

Tuning the Trap

Although this is a purely software model, one I have yet to build and use, the design must be amenable to tuning. Since it is difficult to directly measure the degree of interaction between the tower and the antenna it is best to focus efforts on the trap. Luckily this should work well, as W8JI said and as my modelling seems to demonstrate.

NOTE: If you see evidence of tower interaction during the initial setup and tuning of the loop array you must put that aside until the tower trap is installed and properly tuned. You should only continue tuning the antenna (per the procedure in the loop array article) when the trap is tuned.

Construction and configuration of the trap are the foundation of the tuning system. The horizontal arms (B) are modelled as solid aluminum rods not only for strength but to allow the inductance to be varied. I kept the arms short enough that the entire trap can be reached from the tower.

The vertical arm, A (parallel to the tower), can be wire, just take care that the copper to aluminum junction is solid and protected from corrosion. Solder lugs are a good choice, much better than clamping the wire directly to the aluminum.

The capacitor is placed at the bottom of the trap for a reason: to allow adjustment with the minimum possibility of coupling between the trap inductor and your body. It should be solidly attached to the bottom arm so that it is robust against abuse and tuning (if it is a variable capacitor). Tune it with your head below the level of the bottom arm and good insulation between your hand and the body of the variable capacitor.

If you choose to use a dip meter to tune the trap a small pickup loop should be inserted at the bottom of A. This is easier to do when vertical arm A is wire.

C vs. L -- The trap can be tuned by varying either the C or L component, although until now I've only discussed C. The L value, although not directly measured and difficult to measure in practice, increases as the A or B dimension (see above plot) increases, and vice versa. For example, if the B dimension is shortened from 50 cm to 30 cm (1 ft.) the required C value must be raised from 45 to 50 pf to counteract the reduced inductance and keep the trap resonant at 7.08 MHz.

It may be preferable for trap robustness to use a fixed C and a variable L. To vary L you slide the rods in and out of the tower or slide the taps for the A arm along B rods. Adjust both ends of A at each step so that the A wire is parallel to the tower.

If a variable capacitor is used you can opt to remove it from the trap after tuning is complete, measure its value with a capacitance meter and substitute a suitable transmitting capacitor of that value. Getting an exact match will be difficult so you should adjust the trap inductance afterwards to compensate. Whether a fixed or variable capacitor is used you must protect it from the weather to prevent damage and so that precipitation does not alter its value or breakdown voltage.

After tuning you must test the antenna from the shack. Confirm that the F/B has a sharp peak and that the SWR curve and resonance are as per the design. You can then complete tuning the of antenna, confident that the tower is no longer interfering with its performance. The trap should not need further adjustment after the antenna is tuned.

Variations on a Theme

Trap orientation -- As modelled the plane containing the trap inductor is orthogonal to the loop elements. While this is largely immaterial to the design and tuning of the trap there is a small affect on the antenna pattern. When the plane of the trap inductor is parallel to the loop elements the pattern becomes asymmetric near the pattern's nulls and rear direction. The effect isn't large so it can be ignored. However it does demonstrate how fine a balance between element currents is required to achieve a large F/B.

Vertical trap placement -- The trap can be moved up and down the tower, but does it make it difference? In my model I centred the trap on the tower, so that there is 6.5 meters of tower both below and above the 5 meters high trap section. I tested this by first moving the trap so that its bottom is 3 meters off the ground. This might be preferred to make it accessible from a step ladder.

I again tuned the trap to 7.08 MHz, and it turns out that the value of C is unchanged. I had suspected that by proximity to ground would alter the inductor value. Unfortunately the frequency of both maximum gain and F/B shifted downward by ~25 kHz and the F/B curve across the band degraded by several db. This isn't a large problem, but still. On the plus side the SWR curve improved! There is now another dip to 1.0 at 7.2 MHz (see chart). However the antenna performs almost no better than a single loop above 7.2 MHz.

Next I moved the trap higher on the tower, so that the top of the trap is 3 meters below the tower top. Interestingly the pattern and match behaviour was almost identical to that with the trap low on the tower. The significant differences are that the SWR is even better, staying below 2 even at 7.3 MHz. This time, to my surprise, it was necessary to raise the capacitor value from 50 to 63 pf.

In both cases the worse performance is visible in the currents plot. The longer section of tower outside the trap develops a higher current which interferes with the desired performance of the array. Of course if you're willing to sacrifice pattern performance (primarily F/B) for full-band matching you now have an option. However keep in mind that this is only a simple model, and once you add in the capacitive action of high-band yagis above the tower what you are likely to achieve in reality will differ, no matter which height you place the trap. My guess (which I won't bother modelling right now) is that with yagis in play the trap ought to go above the half-way point so that the electrical length of the sections above and below the trap are approximately equal.

Trap versus No Trap

Building, tuning and maintaining a tower trap requires effort, some expense and ongoing maintenance which, I believe, should only be undertaken if proven necessary. Since the resonance of the tower (plus ground and other attached antennas) is typically too difficult to predict it is best to try the vertical array (or just a single test element) first and determine whether the tower can degrade to the loop array performance. Do this by looking for anomalous SWR -- where the impedance curve and resonant frequency significantly departs from the model. Anomalies in F/B and gain are more difficult to discern.

If a trap is warranted don't hesitate to do it. When you go to all the trouble of building a large antenna to improve low-band performance it is unwise to ignore the signs that the antenna cannot perform as intended. This is too often easy to overlook (and convince yourself otherwise!) when a second antenna for the band is not available for comparison.

Even after you do build the trap you might not yet be done: solving one problem can introduce others. The placement of a trap for 40 meters in the tower could alter the performance of nearby 80 and 160 meters antennas by introducing a tower system resonance on those bands. As with any trap, on lower frequencies it acts as an inductive load which could lower the antenna system resonance to one of those bands, creating a destructive resonance that was not present before installing the 40 meters trap.

Of greater concern is any antenna for 80 or 160 meters that incorporates the tower as part of the antenna. Examples include half-slopers and shunted towers. At the very least those antennas will require retuning once the 40 meters tower trap is installed and tuned.