# Differentiator: harmonic response

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:

$$G(s)=-\frac{Z_f}{Z_i}=$$
$$=-\frac{R}{\frac{1}{sC}}=RCs$$

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,

$$K\frac{(1+T_1s)+...(1+\frac{2\zeta_1s}{\rho_{n1}}+\frac{s^2}{\rho_{n1}^2})+...}{s^n(1+\tau_1s)+...(1+\frac{2\xi_1s}{\omega_{n1}}+\frac{s^2}{\omega_{n1}^2})+...}$$

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

 Parameter Value K $RC$ n -1