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.