I am building a Theremin based on the Moog EMTheremin/Etherwave circuit for a final-year undergraduate physics project. I'm currently trying to understand the following passage from the "Understanding, customising, and hot-rodding your Etherwave” document. It describes the interaction of the signals generated by the variable pitch oscillator when they are near the resonant frequency of the (passive) pitch antenna circuit. Both are LC circuits with well-defined resonant frequencies determined by their respective capacitance and inductance values.
Interestingly, this is completely separate to the beat frequency signal (which is the actual pitch of the Theremin) which is derived from the mixing of the variable pitch oscillator and another similar but separate oscillator not mentioned above."When the variable pitch oscillator is tuned properly and the player's hand is away from the pitch antenna, the resonant frequency of the pitch antenna circuit is slightly lower than that of the variable pitch oscillator. Now, when the resonant frequency of the antenna circuit is lower than that of the oscillator circuit, the oscillator frequency is pushed higher. (The mathematics for this interaction is somewhat technical, but you can visualize it by imagining a car being pushed forward when a force is applied from the back.) In the case of a properly-tuned Etherwave, the 'loading' by the antenna circuit when the player's hand is away from the pitch antenna raises the frequency of the variable pitch oscillator by about three kHz. Then, as the player brings his hand near the pitch antenna, the difference between the resonant frequencies of the antenna circuit and the oscillator circuit increases, the loading of the oscillator circuit by the antenna circuit decreases and the oscillator frequency falls to its 'natural' (unloaded) frequency."
Additionally, this interaction seems to be different from “frequency/injection locking”, which is where coupled oscillators tend to synchronise their frequencies especially when their respective frequencies are close. In this case, it seems that when the antenna circuit’s resonant frequency is close to the pitch oscillator’s, the pitch oscillator’s frequency is moved away, or is repelled by the resonant frequency of the antenna coil circuit. Indeed, this is the analogy that Moog uses after the quoted paragraph.
Given that I am doing this for an undergraduate Physics thesis, I would very much like to get at the actual fundamental electronic/theoretical basis for this interaction. I would not be surprised if I’m just missing something very simple but if this system is indeed nontrivial then - if anyone knew of relevant search terms that describe this specific interaction or even research papers/books that describe a similar fundamental interaction between oscillators (or if one was capable of a quick back-of-the-envelope electronics/physics derivation
) - that would be much appreciated!