Details on Matching the 20 Meter Mult Yagi 6 Elements; 48’ Boom, December 2021

After the antenna model was completed for the 20 meter mult antennas and the first antenna was built, we matched it to 50Ω using a hairpin or beta match. The beta match can be a conventional shunt coil, or in our case a parallel shorted transmission line (or hairpin). The beta match requires the antenna have a series resistance of <50Ω, and a negative, or capacitive, reactance. This can often be achieved by adjusting the length of the driven element; then the shunt inductor transforms it to 50+j0Ω.

In the past, while watching the series impedance with an antenna analyzer, we had adjusted the lengths of the tips of the driven element and the location of the shorting bar on the hairpin to decrease the SWR. A change of either variable changes both the series resistance and the series reactance, and this becomes a trial-and-error exercise. Though we didn’t abandon this technique, we also tried another method which we expected would make it easier to decide which type of adjustment was needed. The idea was to first adjust the tip lengths of the driven element until the parallel resistance was 50Ω. At that point, the hairpin length is adjusted, by changing its shunt location, to transform (or to move up the parallel impedance arc on a Smith Chart) the impedance and reduce the SWR to about 1:1. We collected data in both series and parallel-impedance format, using an AA-54 antenna analyzer, at 14.050 MHz (focusing on the CW sub-band). Data is presented below on a Smith Chart, which made it easier for us to visualize. Note that the SWR circles on the plots go from 1.1:1 to 1.5:1 by 1/10's.

Using parallel impedance allows for the driven element tip length and the hairpin length to be easily adjusted separately as independent variables. Using series impedance, the driven element tip length and hairpin length are not independent and are more difficult to adjust properly.

For each data point described below, we lifted the antenna to about 80’ using a rope off of a pulley at the top of a 160’ tower. The length of the coax from the antenna analyzer to the feed point was an integral of λ/2. We started with the hairpin attached, and with the shorting bar at 24”. The many lifts of the antenna were completed by a great crew!

Note in the plot below that the arc which is labeled “50 ohm parallel resistance” is the same arc which a shunt impedance must start from if it will transform the load to series 50+j0Ω. Our first objective is to intersect that arc by changing tip lengths of the driven element.

From point #1 to #2, we shortened the tips of the driven element – and found that they needed to be lengthened instead! So we progressively lengthened tips until we got to point #5. At that point we started adjusting the hairpin, but it might have been easier to finish adjusting the tip lengths first.

The next plot starts at point #5, from the last plot. We lengthened the hairpin from 24” to 24.5" at point #6, shortened it to 23" at point #7, and then lengthened it to 25.5 at point #8 – and it looks like it needs to be even shorter. NOTE that points #7, #6, #8 are in order of INCREASING hairpin length. I don't see an explanation for point #5, but when you see that the scale is greatly expanded, it looks like points #7, 6, 8 are at an average of about 53Ω parallel resistance. Point #7 had a 23" hairpin and point #8 had a 25.5" hairpin. So we SHORTEN the hairpin to move counter-clockwise up the "parallel-resistance" arc.

Now look at the path from #8 to #9. This occurred when tips of the driven element were increased by 1" to 58.25". The path cuts right across that "50 ohms parallel" arc that we need, so... we went too far! If we had next shortened the tips by 1/2”, then the remaining moves would have been only adjustments of the hairpin length as we proceeded up the 50 ohm shunt inductance arc.

This last plot shows two of the last points from the previous plot, and the remainder of the data. From points #9 through #12 we shortened the hairpin. Note that those 4 points are roughly on a "parallel resistance arc", but they are inside the desired "50Ω parallel arc". From points #12 to #13 we shortened the tips of the driven element by 1/2", which is just about perfect. The moves from #9 to #12 include shortening the hairpin by 1.5", then 1" more, then 1.5" more. The resulting match is very good... but it looks like we could improve it even more by shortening the hairpin another 1"!

If you’re wondering why we went to this effort, it’s because this antenna is the template for the other two antennas which will be the 3-stack on the new tower. They are all at different heights, and there is a lot of work involved in building, hoisting and maintaining them, so we wanted this match to be as good as we could get it.

To save time, we didn't start with an impedance measurement with the hairpin removed – but this would have let us know how actual tuning compares to the model that we worked on. That could, for instance, help us better select hairpin lengths in the future.

We didn’t always make efficient tuning adjustments while we were evaluating the two tuning methods. The early use of larger adjustments to the tip lengths, to bracket the "50 ohms parallel" arc, would have reduced the number of tuning steps.
 
Smith Charts are not necessary for tuning an antenna with a hairpin, but they are helpful if you choose not to use parallel-impedance data; it lets you see your target 50Ω parallel inductor arc. Impedances need to be in series format to enter into SimSmith. SimSmith has a few other peculiarities in order to have the plots show icons at data points.

Though we did many lifts while tuning and comparing tuning methods, here is a summary of what we learned:

1. Moving the tip lengths of the driven element first, to get to the target 50Ω parallel reactance arc, should be done first and is easy to do when observing the impedance in parallel format.
2. Adjusting the shorting bar on the hairpin to transform to an acceptable SWR should be done last. You can watch for low SWR, or low series reactance, or high parallel reactance which may be positive or negative.
3. Though using parallel impedances for tuning shunt circuits is not novel, recent availability of antenna analyzers which easily provide parallel impedance information makes this method much easier to use than in the past.
4. Using two tuning methods at the same time made the tuning process more time-consuming.
5. A Smith Chart does not need to be used when using parallel-impedance readings, but is helpful if you’re only using series-impedance readings.