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For a project, I built a theremin using an LM311N as the basis for my fixed and variable oscillators. I wanted to find the period of the variable oscillator by finding the systems of diff eqs associated with it but I'm having trouble deriving them. I applied KCL at the inverting node to get one but that gave me two variables, the current and the voltage. I'm not sure how to get another diff eq. This feels really similar to doing circuit analysis with an op-amp where since we're treating it as a black box, we have to make assumptions about its behavior in order to define the circuit. But I guess with the comparator, I'm not sure what assumptions I can make. I think the comparator is op-amp based so in the ideal case, no current can go into the input pins but that only lets me get one of the equations. Is there something I'm missing?

Circuit Diagram of Variable Oscillator

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  • \$\begingroup\$ Is there a specific reason why the four separate series inductors cannot be merged into a single inductor? Or do they represent some kind of transducer? \$\endgroup\$
    – jonk
    Dec 11, 2021 at 22:56
  • \$\begingroup\$ @jonk Just wild guessing, but they could be the separate coils that are then coupled by the "player" when he moves his hands near those rods protruding from the instruments. I guess they are physically separate coils. \$\endgroup\$ Dec 11, 2021 at 23:01
  • \$\begingroup\$ @jonk I think it's supposed to be better to have 4 of them instead of one equivalent inductor because it reduces the capacitance between the wires in the coil. But for the purposes of analyzing the circuit, if we assume that the inductors are ideal then I think it should be ok to just combine them together. \$\endgroup\$
    – NaiveCoder
    Dec 11, 2021 at 23:02
  • \$\begingroup\$ The comparator work as a strongly non-linear device. The diff eqs. you are going to get won't be easy to solve. You won't get those nice diff eqs. you get for linear systems that are amenable to Laplace transformations and all the usual linear system techniques. \$\endgroup\$ Dec 11, 2021 at 23:04
  • \$\begingroup\$ Could the missing item be a pull-up resistor (to VCC) from pin 7? This will make the LM311 work more like an op-amp. \$\endgroup\$
    – glen_geek
    Dec 12, 2021 at 3:51

1 Answer 1

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I wanted to find the period of the variable oscillator

Just use a simulator like this: -

enter image description here

And note that R4 is needed as a pull-up resistor for the LM311.

  • For C2 = 20 pF, the oscillation frequency is 72.117 kHz (a period of 13.8663 μs).
  • If I changed C2 to 15 pF, the period drops to 13.7082 μs (72.949 kHz).

Is there something I'm missing?

Possibly a method that gives you a real taste for solving near-practical values.

  • At 10 pf for C2, the period is 13.8458 μs (72.224 kHz) and,
  • As you can see, the oscillator is now starting to lower its frequency.

Interesting circuit and maybe with this information, you can establish a formula based on just analysing L, C2 and C1. However, the big killer is the parasitic capacitance of the 4 x 10 mH inductors and what it brings to the party. If I make an assumption that each 10 mH has maybe 25 pF parallel parasitic capacitance then I would consider using a lump of 40 mH in parallel with 100 pF. If I did an AC analysis on the components in the negative feedback circuit (R3, L1 || 100 pF and C2) I can see this making sense now.

$$\color{red}{\text{So, you must take into account the non-ideal parasitic components in the circuit}}$$

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