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Input/output characteristics of opamp circuits involving diodes (fast peak detector and sine-to-block wave converter)

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I have these relatively simple circuits of which I need to find the transfer functions. Both circuits involve the use of an OpAmp and a diode after the output of the OpAmp. As an input I have a regular sine wave.

Finding the input/output characteristics of a simple inverting amplifier or passive filter is easy, but I get stuck when trying to find the transfer functions for these circuits:

schematic

simulate this circuit– Schematic created using CircuitLab

  • The first circuit (with output \$V_{out1}\$) is a peak detector circuit. The capacitor holds the output voltage, while the resistor is there for slowly discharging the capacitor.
  • The second circuit (with output \$V_{out2}\$) is a 0 Volt comparator for turning the sine wave into a square wave. I put a diode after the output to only allow positive voltages. The resistor to ground is to reduce the output voltage.

My question is: How can I find the input/output characteristics of these circuits (\$V_{out1} = ... * V_{in}\$ and \$V_{out2} = ... * V_{in}\$)?


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