# Inverting a (voltage-) transfer function using opamp

If we have a circuit that - given some input voltage $$\U\$$ - produces an output voltage $$\f(U)\$$ (where $$\f\$$ is continuous, monotonic descending), we can construct a new circuit that behaves like the (negated) inverse $$\f^{-1}\$$ of $$\f\$$ (meaning the function-inverse) as follows: simulate this circuit – Schematic created using CircuitLab

Now I've tried applying that with a funtion $$\f\$$ that roughly looks like a $$\\arctan\$$-function (up to a scaling factor) where $$\f\$$ is implemented using following circuit. I have tested this circuit and it works fine. simulate this circuit

To check if that worked I built this on a breadboard with a NE5532 op-amp (with bypass cap with +-12V supply) used a 20Hz saw-wave and hooked up an oscilloscope. It seemed to work fine but the output was quite noisy. This was especially noticeable in the flat part (so I'm not sure if it's actually particularly strong there or it is just particularly noticeable to the flat slope).

Now I was wondering, where does this noise come from, and how can I reduce it? Below is the circuit I actually used (can be simulated, see "DC Sweep") simulate this circuit

Here's the simulation output that works as desired: • You made an attenuator , the inverse of your feedback gain = - 10 until the diode compresses the feedback and thus amplifies the input signal into a quadratic expander with less phase margin and more noise., with unity gain where the diode voltage/current= impedance = 10k What results did you get? What did you expect? Feb 20, 2021 at 16:40
• I'm not sure I understand: Do you say that reducing the gain (by setting R2 to e.g. 10k) would decrease the noise? I have played around with various values of but none seemed to alleviate the issue. Feb 20, 2021 at 16:53
• Does my answer make sense yet? Feb 20, 2021 at 19:55
• @TonyStewartSunnyskyguyEE75 I don't know enough yet to understand all the details. But your answer helped me see the issue when thinking about the situation of a constant output. Thanks a lot! Feb 20, 2021 at 21:04