Tuesday, April 15, 2014

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.

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