The best laid plans go awry. No matter how hard we work, how careful we check and double check every step things will still go wrong. Such is the case with my recently completed stacks of 5-element yagis for 15 and 20 meters. The difficulty is only with one of the 4 antennas: the upper 20 meter yagi. This was briefly mentioned in the article about tuning and raising the yagi, and now we'll delve deeper.
Somehow along the way from successful tuning to mechanical completion, weatherproofing and tramming to the top of the tower the gamma match shifted. This was confirmed via measurements and software. For most antennas I would mutter profanities for a minute or two and then proceed to lower the antenna for repair.
Unfortunately this antenna is a monster and winter has arrived. With all attachments it weighs about 120 lb (55 kg). Lowering, re-tuning and raising are difficult jobs in good weather and definitely will not be done before spring.
A solution has now been found by means of software modelling. Although the problem has not been implemented the 20 meter stack does work, just not optimally.
In this article I'll walk through the steps from initial diagnosis to evaluation of alternative corrective measures and final design. Although few readers have stacked HF yagis there are lessons that can be applied to more common antenna projects. RF circuits are not so mysterious when you challenge yourself to take a peek under the hood.
Forensics
The problem was discovered several days after the yagi was raised. The SWR was very close to 2 across the band. Other than the high SWR an impedance analysis indicated that the yagi was performing properly.
My first step to diagnose the problem was to measure the R and X components of the impedance across the band. This was done with 22' of LMR400 coming from the feed point and a further 4' from there to the analyzer. The latter length is the equivalent length of LMR400 (VF 0.85) of a shorter length of RG58 (VF 0.66).
The measurements were transformed (using software rather than a paper Smith chart) over the 26' of LMR400 to get the impedance at the feed point. Both are plotted above. It must be done this way since the yagi has a long boom and the feed point and gamma match are well out of reach
Notice that other than about 35 Ω of inductive reactance the the feed point resistance is similar to that obtained after tuning the gamma match near the ground. It is not really that simple since R is not constant when X is changed by the gamma match capacitor.
Diagnosis
For the value of the capacitor when properly tuned the 35 Ω of excess reactance is equivalent to a few inches of the RG213 inner conductor capacitor inside the gamma rod (2.1 pf/inch). All dimensions of the gamma match were recorded after adjustment and checked during weatherproofing. At least that's my recollection. It is possible my memory of what transpired is imperfect.
After installing the stack switches and phasing harnesses I was able to sweep the yagi combinations from the shack. This is more comfortable than on a tower in winter.
Before being installed each segment of coax was tested and tested again when they were connected together. Some deviation from a perfect 50 Ω is normal and not a cause for concern. You just need to be aware of it when doing remote measurements. In this case the SWR dropped from 2 to 1.5. Sometimes the deviation is in your favour.
As previously reported the upper yagi is clearly working, as part of the stack or alone. The feed point impedance of a yagi has only a small or negligible relationship to the yagi's performance. On the basis of the evidence I am convinced that the gamma match capacitor value changed from the value it had when the yagi was tuned at a lower height.
Modelling and Implications
I developed a model of the antennas using EZNEC. First I modified the design to include a gamma match. This can be tricky although it works well when done correctly. For instructions on how to do so read my article on gamma match modelling.
Unlike other matches I used in the original model the gamma match gives a lower SWR across the band. I have not explored why that is -- there are several potential explanations. As a result the impedance at the feed point is different from that of the real antenna.
Although the modelled impedance differs from the real antenna this is only of concern to me, not you. I will deal with the actual impedance of my antenna when the time comes. The process is universal so the benefit to readers is remains valid. So let's proceed with the gamma match in the model.
I adjusted the gamma capacitor in the model to give the upper yagi about the same excess feed point reactance as the real antenna. That's as good a proxy as I can easily develop unless I can find why the gamma match model is different. I then combined the antennas with transmission lines of the actual physical length and VF into an L-network using the same design as in the actual stack switch.
- The excess reactance at the upper yagi feed point causes a phase shift. It is 20° at 14.000 MHz and declines to 10° at 14.350 MHz.
- Power division is unequal due to the unequal impedance. For the model's currents in the two yagis there is approximately twice as much power delivered to the lower yagi as to the upper yagi (65% vs. 35%). That is easily visible in the current plot to the right.
Recall that in a stack optimum gain requires that the yagis have equal power and are fed in phase. Despite the large power imbalance the stack gain reduction is only -0.4 db, with the main lobe reduced from 18.1 to 17.7 dbi. The phase shift is responsible for less than -0.05 db, in proportion to the phase shift across the band as described above.
While not a dreadful impact, and certainly less than I expected, it is worth dealing with. At the very least a low and equal SWR for the 3 modes -- upper, lower, both -- has benefits, including optimum transmission line loss and no need to fine tune amplifier tuning when switching between modes.
Impedance matching
Correcting the mismatch of the upper yagi is straight-forward. A simple L-network suffices to restore the SWR to what it ought to be. Network design depends on where it is placed in the transmission line since the impedance, not the SWR, is determined by the electrical distance from the feed point, and networks transform impedance, not SWR. To repeat: networks transform impedance and not SWR.
For an equivalent 66' of LMR400 from the modelled antenna (which is at the stack switch port) the calculated impedance plotted is to the right. Using TLW and the design match frequency of 14.1 MHz the L-network design follows:
The L-network for the modelled yagi is different that that required for the real antenna because of the aforementioned difference between the modelled and real gamma match. We'll continue with the model and the L-network required to match the upper yagi at the same electrical distance from the feed point. The upper yagi's SWR is greatly improved.
Modelling confirms that power division is equal and that the SWR is as expected for the stack. Unfortunately that is not good enough. The L-network creates a new problem: phase shift.
The plot shows the elevation pattern of the impedance corrected stack. A visual inspection alone shows that something is amiss. The gain between lobes has markedly increased. The gain of the main lobe is -0.9 db lower than it should be. Note: the gain is actually 17.2 dbi, not 14 as calculated, due to NEC2 error for the close spacing due to the gamma match models; this has been discussed previously.
Stack SWR is near perfect. Power division is almost equal, disturbed no more than 10% by the relative impact of ground and mutual coupling due to their different heights. Power loss in the L-network is not included in the model since, from the TLW tuner design (above) with a relatively poor coil Q, it is much smaller than the power imbalance.
The pattern deterioration is due to the phase shift introduced by the L-network for the upper yagi. By their nature, networks shift phase and the shift is typically greater for larger impedance transformations. Although phase shift is unimportant for an individual antenna it is critical in a stack.
The phase difference is approximately 55° at 14.2 MHz, and varies between 53° and 61° across the band. Note that these figures include the 10° to 20° phase shift imparted by the mismatched gamma match determined earlier. The upper yagi lags the lower yagi.
The phase shift is trivially corrected. The equivalent phase shift lag is placed into the phasing line coax to the lower yagi with an extra length of coax. Since the average phase shift is 55° the required additional length of LMR400 (VF 0.85) at the 14.175 MHz centre frequency is 9' (2.75 m). Inserted this into the model restores the stack pattern. The NEC2 corrected gain is 18.1 dbi.
The extra length of coax has no effect when the lower or upper yagis is individually selected, other than a negligible loss in the power delivered to the lower yagi.
With that addition the solution is complete: an L-network to correct the upper yagi mismatch and a delay line to the lower yagi to correct the phase shift due to the L-network plus that of the upper yagi's gamma match.
The design of both requires determining the phase shift in software since it cannot be measured with the tools hams typically have at their disposal and is in any case difficult to do on the tower.
For phase shifts of opposite sign the delay line goes on the other port. It is better to add coax than to cut since it is easier done and can be undone later.
Pros, cons and implementation options
Despite the mismatch the stack loses less than 1 decibel of gain. I was surprised. It goes to show how resilient yagis can be. Modest errors of phasing and power division have a small impact since gain is roughly determined by quasi-cosine functions. Look at a cosine curve near zero and you'll see what I mean (I won't get into the mathematical weeds here). In contrast, the RDF of an antenna is very sensitive to phase and current imbalance because for maximum field cancellation amplitudes must be equal and phase exactly opposite (180°).
Since my model of the gamma match doesn't match the real antenna, despite my success doing so with the 15 meter yagi, software tools other than EZNEC are required. There is little point in simply going with an L-network designed by TLW until the total phase error is quantified. Otherwise the solution will be less than optimal, and that is hardly sensible.
Besides, it's winter and it's cold up the tower. It would take a significant array deficit to motivate me to do that much tower work before spring. On the basis of my analysis of the mismatch and correction options I am not sufficiently motivated. One look out the window convinces me that tweaking of the amplifier knobs from time to time isn't an onerous task.
I'll decide on next steps when the warm weather returns. Either to correct the phase error as described here or to take the antenna down and redo the gamma match. The latter is the ideal solution. However, the cost of the less difficult corrective procedure is relatively modest at 14 MHz:
- The L-network has loss but that loss is a small fraction of a decibel. The modelled coil Q of 200 is lower than can be easily constructed so the loss can be kept even lower than that in the TLW window shown above. Of course a good quality capacitor is needed. That is easy with an air variable capacitor with modest plate spacing since in this application the voltage on the plates is only a few hundred volts with legal limit power.
- An SWR of 2 on the coax to the upper yagi has additional loss, but again it is quite low with LMR400 and not a concern. The additional loss on the 100 meters of LDF5 Heliax is more of a concern, though again the increase is quite small for an SWR of 2. Were the SWR higher I'd be concerned. When in stack mode the loss is lower since the mismatched parallel impedance results in a lower SWR of about 1.5.
Hopefully you will never have this problem should you build a large HF stack. Mistakes happen, and with all the towers and antennas I have it is inevitable that problems will arise, either when first built or later as material weathers and degrades. Perfection would be nice but never count on it!
Note: There may be one more non-technical article before 2020 closes. Regardless, I'll take this opportunity to wish everyone reading the blog a happy new year and I hope to work you on the bands in 2021. For top band enthusiasts, you can try to dig my QRP signal out of the noise in the Stew Perry contest coming up in a few days.
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