I was playing with Falstad’s simulator and managed to rig up an analog oscillator with a single op-amp and a phase-delay network.
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The big issue here is that the waveform is not very controllable; it spontaneously starts oscillating in what is at first a nice exponentially growing sinusoid, but rapidly hits the opamp rails, at which point it continues to oscillate nicely but no longer sinusoidally. So I was thinking I could maybe rig up a peak detector and use that to control a MOSFET to control the loop gain. I was scared to use a low-impedance peak detector, since the impedances in the rest of the circuit are kind of high, but now I realize that was silly since the peak detector is directly connected to the op-amp output... so even 100Ω and 1μF don’t load the simulated circuit.
So the idea is to decrease the amplifier gain when the peak detector voltage is too high, and increase it when it’s too low. An N-MOSFET in the ohmic region decreases its resistance when its gate voltage goes high, and increases it when it's low. So if I add an N-MOSFET into the negative feedback path for the op-amp, I would want to add it where the gain goes up when its resistance goes up, which is to say, between the inverting input and the output. This has the complicating factor that the source of the MOSFET won’t be at ground but rather somewhere near the input, which could result in modulating the gain with the waveform.
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At startup, this version of the circuit oscillates between the rails until the peak detector charges up enough to push the AGC MOSFET into its linear region. But this leaves the gain slightly too low, and the gain stays too low until the oscillations die away (the Q is about 2 I think). The gain then rises so that over two or three oscillations the wave grows from 10 mV to 15 V peak amplitude and saturates again, at which point the cycle starts over.
There are different things I could try to improve this situation. When it’s oscillating successfully, the channel resistance is about 50–900Ω, and 900Ω is about the point where it explodes and saturates again; I could try to make the gain respond more rapidly to changes in the channel resistance by ensmallening the fixed resistors in the feedback path. I could try to reduce the AGC control loop delay, although it seems like it would be difficult to solve the problem entirely that way. I think I’ll try the ensmallening approach first; instead of 1kΩ and 8.2kΩ I’ll try 100Ω and 820Ω. That does reduce the problem a bit but doesn’t eliminate the problem.
The particular way that the problem manifests is that, as the waveform is growing, at some point the MOSFET is carrying so much current (about 6.5 mA) that it goes past its linear region into saturation. At this point, just as surely as in cutoff, the opamp can raise its output voltage with no effect on the voltage it sees on its inverting input — and so its voltage immediately shoots to the positive rail.
Further tweaking doesn’t solve the problems:
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