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I am looking at an analog synthesizer circuit the design of which incorporates several "ringing oscillators", which look like this:

Ringing Oscillator Schematic

I understand that this is a resonant system that enters oscillation whenever the input transitions from low to high or vice versa, which fades in amplitude over time to zero, until another impulse is received. I'd like to understand what exactly is happening in the op-amp circuit to accomplish this, so if anyone could provide a scientific analysis I would greatly appreciate it.

In case it is helpful, this is the larger circuit I am looking at: https://www.cgs.synth.net/modules/v8.html

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It can be analyzed for gain/phase response. The theory is defined by the Barkhausen Criteria where the midpoint between;

  • stable decaying oscillations and
  • growing saturated oscillations and defined by unity gain with 180 deg using inverting an additional inverted (180 phase shift) making it positive feedback

  • ,stimulated by any energy in that narrow spectral bandwidth such as an impulse or step pulse after which, it is sustained for a long time.

This settling time can be measured in cycles and is also defined by a frequency response coefficient called zeta or dampening factor which is inverse to Q the shape of the resonant bandpass filter peak Center f / difference frequency of bandwidth when inputs are attenuated -3dB.

The higher the Q , the more sensitive to changes it becomes.

These are fundamental concepts studied in Electrical Engineering.

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There are free circuit simulators such as LTSpice that can help you analyze the circuit fully. This is a really good way to learn about circuit topologies and how they respond. In fact I challenge that you would learn more about this circuit from that activity than any amount of explanation that you could get here or from reading a book about the subject.

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