End-Fed Half Wave Tuner

Origins

This project originated from a some messages posted on qrp-l.org regarding polyvaricons available from an eBay vendor and their use in an end-fed half wave antenna tuner. I ordered a batch of 10 of these from the vendor for $15.00 plus shipping (an excellent value, and a great purchasing experience from this vendor). Once the caps arrived, I asked the list about the design of these tuners, and received a very excellent, detailed reply from VK2ZAY:

I generally use any old box I have hanging around that will fit the polyvaricon and the toroid with room for banana sockets/binding posts and a BNC. I like to pick the biggest toroid that I can, and use fairly thick wire in an attempt to reduce the losses. I don't go smaller than a T68-6.

Polyvaricons are likely not the highest Q capacitors, so this may be not that important. Measuring capacitor Q is pretty hard, but some swaps between a silver mica and a polyvaricon across a coil suggest they might be significantly worse than the silver mica cap - if nothing else the leads are pretty thin.

Anyway, I pick an inductive reactance that gives me a loaded Q of at least 10-20 (assuming a load resistance of about 4000 ohms). Hopefully this works out to enough turns that link coupling to the low-Z feedline is at least two turns, otherwise I need another cap in series with the low-Z side to transform it up to something that can be implemented in a few turns. (On HF this is generally easy, on VHF it can be far more difficult to simultaneously achieve without a series cap. The two-cap approach is quite useful on HF however. I have also tapped down on a air-spaced coil on VHF and 10 metres with pretty good results - resonant autotransformer matching. Above 20 metres the radiator capacitance becomes a very significant fraction of the resonating capacitance if you try to get a good loaded Q, this may be considered a good thing and you can, with some fiddling, dispense with the resonating cap all together and achieve a fixed match covering entire bands. No idea about the losses of this approach however, I've never modelled it.)

I then lash up the prototype on the bench and try matching some 3k6-4k7 resistors looking into the low-Z side with a return-loss bridge fed from the signal generator. I tweak the turn count on the link to get a good match and play with the load side (using a 10k pot) to see what kind of matching range it offers. These tests generally bear out the rough maths I used to design the matching network, but sometimes Nature suprises me and I need to go back and work out what I forgot to consider.

I've only built one (my original 40/80 metre one) with a resistive VSWR bridge in the box for easy tuning up. For my others I just rely on the VSWR reading in the FT-817 (although it is extremely generous according to my tests and should only be used as a guide of "hopeless" vrs "ok" load).

Initial Design

Based on Alan's criteria and the capacitance measurements (about 7 to 270 pF) of the polyvaricons provided by others who purchased them, I worked up the math for an initial iteration of a tuner that could cover 10 to 40 meters.

20 Meters

Based on a desired loaded Q of 20 for 14 MHz, we first need to find the desired reactance of the tank circuit:

$X={R_L \over Q_L} \rightarrow X={4\,\text{k\Omega} \over 20} \rightarrow X=200\,\text{\Omega}$

This means that the inductance of the secondary winding of the transformer is:

$L={X_L \over {2 \pi f}} \rightarrow L={200\,\text{\Omega} \over {2 \pi(14\,\text{MHz})}} \rightarrow L=2.27\,\text{\mu H}$

Using a T68-6 toroid, we need 22 windings to get this amount of inductance.

Since

$X_L=X_C$ at resonance:

$C={1 \over {2 \pi f X_C}} \rightarrow C={1 \over {2 \pi(14\,\text{MHz})(200\,\text{\Omega})}} \rightarrow C=56.8\,\text{pF}$

This is well within the range of the polyvaricon.

40 Meters

Now we need to see how well the design will scale to the extreme ends of the tuning range that is desired. We know the inductance on the transformer secondary is 2.27 uH, so let's find out the inductive reactance at 40 meters:

$X_L=2 \pi f L \rightarrow X_L=2 \pi (7\,\text{MHz}) (2.27\,\text{\mu H}) \rightarrow X_L=100\,\text{\Omega}$

Now we need to calculate how much capacitance it takes to resonate 100 ohms at 7 MHz:

$C={1 \over {2 \pi f X_C}} \rightarrow C={1 \over {2 \pi(7\,\text{MHz})(100\,\text{\Omega})}} \rightarrow C=227.3\,\text{pF}$

It looks like our polyvaricon can tune to 40 meters as well. Let's find the loaded Q at 40 meters to see if it's acceptable:

$Q_L={R_L \over X} \rightarrow Q_L={4\,\text{k\Omega} \over 100\,\text{\Omega}} \rightarrow Q_L=40$

It's a bit high, so the tuning will be sharp, but it should be good enough for our purposes.

10 Meters

Finally, let's see how the numbers look at 28 MHz. First, the inductive reactance calculation for 10 meters:

$X_L=2 \pi f L \rightarrow X_L=2 \pi (28\,\text{MHz}) (2.27\,\text{\mu H}) \rightarrow X_L=400\,\text{\Omega}$

OK, now the capacitance required to resonate 400 ohms at 28 MHz:

$C={1 \over {2 \pi f X_C}} \rightarrow C={1 \over {2 \pi(28\,\text{MHz})(400\,\text{\Omega})}} \rightarrow C=14.2\,\text{pF}$

This is pretty low, but according to the measurements made by multiple owners of the polyvaricons, it can be reached. Finally, let's see how the loaded Q looks:

$Q_L={R_L \over X} \rightarrow Q_L={4\,\text{k\Omega} \over 400\,\text{\Omega}} \rightarrow Q_L=10$

The tuning might be a bit "mushy", but it still should work fine.

Transformer

Now we need to figure out how many turns on the primary are required to match a 50 ohm input impedance to the estimated 4000 ohm antenna impedance:

$N_P=N_S \sqrt{Z_P \over Z_S} \rightarrow N_P=22 \sqrt{50\,\text{\Omega} \over 4\,\text{k\Omega}} \rightarrow N_P=2.46$

We can't have a fractional number of turns, so let's try 2 turns on our primary to start with.

Build

Digging around in my junk box, I discovered that I didn't have a T68-6 handy, but I did have a T68-7, which should work in a pinch. I wound 22 turns on the secondary with 26 gauge magnet wire and a 2 turn primary with solid hookup wire. I had a nice little Radio Shack project box laying around that worked quite nicely as an enclosure. A BNC jack was placed on one end of the box and banana jacks on the other end to accept the end-fed half wave antenna.

The polyvaricons took a bit more work to enable them to be mounted. They come with no mounting hardware and essentially no shaft. I took one of the caps down to the local Ace Hardware to see if I could find a match. After about a half hour of searching, I found that 2.5 mm hardware seemed to work (although the fit was slightly loose). I used 2.5 mm x 6 mm countersunk machine screws for mounting the polyvaricon to the enclosure. To create a 1/4" shaft, I purchased 1/4" diameter by 1/2" length nylon spacers. A 2.5 mm x 16 mm machine screw was passed through the spacer and secured to the shaft. I later on found out that the actual hardware size required by these polyvaricons are 2.6 mm, which would explain the slight amount of slop. However, I have found that the 2.5 mm works just fine in practice. I know that some of you may cringe at this, but it works for my purposes and I don't have to try to special order 2.6 mm screws.

I mounted the polyvaricon about 1 inch from the top of the project box, so that it was off-center from the BNC and banana jacks. Next, the toroid was installed into the enclosure. Since I knew that I would be tinkering with the design, I didn't secure it to the box. Once I'm happy with a "final" design, I'll use some hot glue to keep the core in place. The primary winding was wired to the BNC jack, while the banana jacks were wired to the secondary winding. One section of the polyvaricon was wired in parallel with the secondary, and all of the ground points were wired together.

First Test

Now that the tuner construction was completed, it was time to test the thing. I very roughly measured out a half wavelength antenna for 20 meters (approximately 33 ft.) and a 1 meter counterpoise (see AA5TB's most excellent web page for the reasons behind this choice of counterpoise). I'm fortunate enough to have a LP-100 vector wattmeter in the shack, which enabled me to make some measurements on the impedance that the tuner presents to the rig. I tossed the antenna wire out my second story shack window to a tree limb about 20 ft. away, letting the rest of the antenna length hang down. There was a definite SWR null and noise peak on 20 meters when I tuned the polyvaricon. However, the best SWR that I could achieve was 2.0. According to the LP-100, the rig was seeing a Z of 100 Ω, with a resistance of 97 Ω and a reactance of 22∠13Ω.

Redesign

The first test didn't seem too bad, but I thought I could do better. After thinking about the initial design a bit more, I realized that I made a mistake in rounding down my primary winding to 2 turns. This gives a turns ratio of 1:11, which would give an impedance ratio of 1:121. This means that 50 Ω is transformed up to 6.05 kΩ. This is a bit too far out of the range of expected end-fed half wave antenna impedances. I decided to re-wind the toroid to achieve an integer turns ratio. Since a lot of the other resources on end-fed half wave antennas suggest that their impedances tend to be a bit lower than 4 kΩ, I decided to settle on a turns ratio of 3:24 (or 1:8). This would match 50 Ω to a much more reasonable 3.2 kΩ.