That is exactly the way it works in all Moog Etherwave theremins built after 2008.
Moog Etherwave - Problem with Pitch Oscillator Variable Inductors
I've made my theremin from scratch using a prototyping bread bored, instead of the PCB bored that comes in the kit. Do you think the capacitance of the bored has anything to do with the oscillators not working? If the capacitance of the board is larger than the capacitance of the circuit it will dampen the signal, correct? I did put the output of the oscillators to an oscilloscope, and the signal produced is incredibly fuzzy. Other than changing the bored, is there a way to make the signal more clear?
I am building my theremin for an electronics class, so buying a kit is forbidden. I might ask about this one though, because I would still be able to test signals and voltages on it since the components are exposed to the user. I was just wonder on an scientific stand point if using a breadboard would add parasitic capacitance to the overall circuit.
The answer is: it depends on the bread board. If it's one with copper stripes, the risk of parasitic capacitance troubling the function is elevated. If it's one with small copper spots, there is less risk, but in ever case, you have to respect common RF circuit guidelines when creating your circuit layout.
Since a theremin must basically react to capacitance changes of 1/100 of a pF, it is obvious that whatever parasitic capacitance might potentially be problematic, but an experienced electronics engineer can estimate the impact depending on where in the circuit it becomes active.
If you wanted to do a school project, why did you choose such a complex and tricky (and outdated) circuit like the EM theremin? There is a circuit which I have developed just for that purpose and which is much simpler and less critical: http://www.thereminworld.com/Forums/T/29231/my-new-year-gift-to-tw-a-new-theremin-circuit
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