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

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:

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}\$$)?

• Does the homework ask you to determine a transfer function, or is that your own interpretation?
– Chu
Feb 15, 2020 at 23:52
• @Chu Actually it is not really "homework". I am designing a sound localization sensor that can detect where sound is coming from. I am using 2 microphones and comparing their output signal phases and amplitudes to determine the direction of the sound. This is a small part of the circuit. For the project I'm required to derive/provide the transfer function of the designed circuit to make a prediction of how the circuit will behave. I have simulated and built the circuit succesfully and everything is working. The transfer function is the only part I'm stuck on. Feb 16, 2020 at 0:16
• These are terrible choices for your purpose. Start with good specs for transfer function. Feb 16, 2020 at 1:10
• I guess you mean input/output characteristics. ‘Transfer function’ is only defined for linear systems, and yours is non-linear.
– Chu
Feb 16, 2020 at 1:45
• @Chu, yes you are correct that is actualy what I am looking for. I will edit the post to say this instead of transfer function Feb 16, 2020 at 9:44

This is homework, so I'll help you find answers, but not directly give such – that'd rob you of anything to learn.

How can I find the transfer functions of these circuits

Vout2/Vin

This is an opamp without feedback; i.e. an ideal opamp would act like a comparator. A TL081 will likely latch up under these conditions. It's generally the most terrible Opamp you're likely to find anywhere. Don't use it.

For the ideal opamp case, I'm sure that you can just plug in a few hypothetical voltages and see how this behaves. It's easy, don't be afraid to try.

Vout1/Vin

Not at all – the diodes make this a nonlinear system (made worse by the unfortunate of opamp model, but I assume you're assuming an ideal opamp). That doesn't mean this doesn't have a transfer function – but paired with C1, the system becomes time-variant and thus doesn't have a transfer function, as the diode's I/V curve will be biased to the difference between voltage across C1 and OA1's output voltage.

So, you've got both a frequency-dependent behaviour and an amplitude nonlinearity. Vout1/Vin hence depends on Vin's "history" and can't be reduced to a single curve.

• Thanks for the tips, I actually simulated and built these circuits and they are working fine. Before using the TL081 I tried using the LM741 without succes. I think I can find Vout2/Vin. Regarding the first circuit, I think I can just say that the output represents the input signal amplitude (Vout1 = Amplitude). Also you can see my other comment where I give some context on the use of the circuits. Feb 16, 2020 at 0:40