"I have not tried to measure the antenna voltage swings. I'm not sure how to go about doing that. It seems like even a 10X scope probe would load and disturb the circuit too much to get a meaningful reading. Is there a trick to it?" - Channel Road Amps
Get a somewhat thin wire (jumper wire, wire wrap wire, coil wire, etc. it doesn't have to be super thin) 2 or 3 feet long and run it away from the Theremin and over to a capacitive divider consisting of 1pF in series with a 1000pF to ground. Measure the voltage across the 1000pF with your 10x scope probe, multiply by 1000. If the coil drive doesn't have significant resistance, I'm thinking you'll see ~300Vpp (given your 2.9Vpp drive, and your coil Q is likely ~100).
"There is one aspect of the PLL that might be a little bit uncommon. On each iteration through a PLL loop, it starts with an error measurement (phase difference from the desired 90 degrees in this case) and then derives a correction (to the oscillator frequency in this case) to reduce the error. (You understand that, of course.) To derive the correction, the software uses the known characteristics of the RLC circuit to calculate how far from resonance the frequency must have been to yield the measured error. In other words, it's not just a semi-blind correction like in a typical PID controller, but it incorporates knowledge of the circuit being controlled. I'm sure that's been done many times before, but it's probably more feasible in a theremin than it is in many other applications."
From that, it's clear you understand that the coil has a phase gain that is extremely non-linear near resonance. At resonance the gain is Q/pi, but it falls off quite precipitously to either side. PLL loop gain directly sets the bandwidth of the PLL, so when the PLL is significantly unlocked and therefore off of the LC resonance, the reduced LC phase gain will cause the PLL bandwidth to plummet. The system can be treated as linear if the PLL bandwidth is sufficient because lock will be more or less maintained, though it can cause the initial lock at startup to take longer than necessary. But it could be an issue if the locked PLL bandwidth is too low, as it could then be forced off of resonance during normal play. It sounds like you are aware of and actively compensating for this non-linearity, so the PLL bandwidth is less critical.
If the PLL has too much loop gain the bandwidth will be unnecessarily wide, and instability can result. I think 100 to 200Hz or so is a good target here.
"Initially, the scanning ranges of the oscillators were too large, so they overlapped. That is, the scan for the pitch antenna also covered the resonant frequency of the volume antenna, and vice versa. There was enough interaction to confuse the scans. But after I narrowed the scan ranges so they didn't overlap anymore, there was no problem at all with interaction."
It seems that 2:1 coil values can play rather nice together, placing the frequencies at 1:sqrt(2). This is what the Theremini does (and I do in the D-Lev).
"No doubt that is true, and I hope it didn't seem that I was claiming originality for any of my work. The article was just intended as a report on a fairly successful implementation."
Oh lord no. The only thing I believe I can claim any credit for is the linearity correction formula I finally stumbled across. The rest is a rehash of other people's ideas and some elbow grease.
John, have you tried for reduced sensitivity of the pitch field? Normally it's around 1 octave for open/closed hand. I personally find 1/3 octave more playable, but this isn't a general feature on most Theremins, so I feel rather alone in discussing the subject.
