Differentiator: harmonic response

Control theory

This article deals with a simple differentiator circuit, using an operational amplifier.


If we use the generic formula of the transfer function of a generic operational inverting amplifier, we can write:


Where Z_f is the feedback impedance, while Z_i is the impedance connected to the input.

The transfer function has just one zero in the origin and, for that reason , it behaves like a differentiator. If we compare the final expression with the Bode form of the transfer function,


it’s easy to see that there are just two meaningful parameters: K and n.

Parameter Value
n -1