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To sense the capacitance value of a sensor, I found the following circuit.
My knowledge on analogue electronics isn't that great, so I'm not sure how I'd determine the gain of this circuit.
Vo is the output voltage I need, the peak value detector and Vdc can be ignored.
So what is the gain, Vo/Vs, in this circuit?
If you pick Rf to have a high resistance relative to the impedance of Cf at the input frequency, the gain before the peak detector will be approximately -Cs/Cf.
That's a consequence of the feedback impedance being XCf || Rf ~= XCf and the normal equation for the closed-loop gain of an inverting op-amp amplifier.
One would normally pick the resistor in such a way- typically the purpose of Rf is to provide a path for the bias current of the op-amp. At very low frequencies the gain will be less as the resistor influence manifests, and you can easily write an equation for the gain including the resistor and including the op-amp open-loop gain too, if you want.
