How do I design an Op Amp circuit that intentionally has overshoot/undershoot? What is that circuit called?

Question

As the input voltage goes up and down, the output of the circuit should jump up and down eventually settling to the same voltage as the input.

Answer 1

Maybe a differentiator is something like what you are asking for, but I'm not sure about the "eventually settling to the same voltage as the input" part, but it might be somewhere to start.



Looking at the schematic it the link below, It seems to me that if the capacitor was leaky, it would act to some extent like what you are asking for, and if the leakage (or a deliberate parallel resistor) equaled the feedback resistor...?  

Answer 2

You appear to be describing a time domain response which eventually settles on the reference but prior to that exhibits some ringing where the signal oscillates about the final value. This is called an under-damped circuit. If the signal approaches the final value without ringing it is either a critically damped signal or over damped.Critically damped is the fastest response without overshooting.

The response in an op amp circuit will be one of these three based on your selection of component values for resistors and capacitors around the op amp.

You might try a non-inverting op amp with a gain of 1 and some capacitance to provide the time domain oscillation.

See http://en.wikipedia.org/wiki/Op_amp