"The next post will explain why your theoretical graphs regarding the area of the antennas, do not correspond to reality (they take in consideration an antenna isolated in space and forget to consider the noise and the static capacitance of the measuring and driving electronic components)" - Livio
I hope it does, because at this time I can see almost no relevance regarding the noise of the oscillator transistor - the whole question of even moderate noise in the oscillatory circuit is, as far as I can see, of quite low importance.. (with capacitive sensors noise becomes a critical factor at the comparator and post-sensor stage, particularly if one is trying to obtain a period measurement of a high frequency - but even here, noise contribution from the oscillator is trivial compared to noise contribution from reference voltages or comparator / active components following it))
As an analogous example - you have a swing (pendulum) being pushed with a regular pulse, this is the resonant circuit - a little wind blowing on the strings on the axis of thrust of the swing aint going to change the oscillation frequency one iota! .. in fact, one could get the resonance even if one was to drive the oscillator with bursts of noise, and the frequency would still be defined by the LC as far as I can see.. Only sideways variations of wind could significantly affect the frequency, and this would be equivalent to capacitive "noise" which is entirely different to amplitude noise as I see it.
Of course, heterodyning followed by a good filter gets rid of all but the most extreme (as in, really badly designed or faulty oscillator) noise problems.
" (a radial capacitor with 20 KV isolation)."
I am interested to know where you get a 10pF 20kV NOP/COG capacitor - because at such a low value capacitance, the dielectric is important - any capacitance change due to temperature will significantly affect pitch (the N4700 dielectric common in HV capacitors has about 0.5% / degree C variation in capacitance!) .. If you were to use a couple of larger 10kV capacitors (say 1n or minimum 470pF each) in series then themperature variation will be less significant and you could probably get away with almost any dielectric (the larger the series capacitance, the less significant any changes to the value of this capacitance due to thermal effects becomes, because the antenna capacitance increasingly becomes the more significant contributor to the final sum).
20kV capacitors I have sometimes been forced to use for other projects have been horrendously expensive, and usually its far more economical to use 10kV's in series.. For theremin circuits its far more economical to put a discharge tube in the circuit (between antenna and ground), and this also gives better protection.. you can then safely use good low cost 100V NOP / COG capacitors and eliminate thermal drift from this source - this allows you to use smaller series capacitance if you need this to reduce sensitivity close to the antenna.
Once again, I dont understand the aversion to discharge tubes or other shunting type ESD protection! Trying to block an ESD spike with a series isolating component is, IMO, just insane! The cost and problems with such a component, and the extra care required in layout etc to insure that this component actually has any real use, makes this a complexity that IMO is utterly pointless!
A 12kV ESD spike can jump tracks and go routes you never expect - The only way to ensure safety from these events is to kill them at source!
Fred.