Differentiator: harmonic response

Control Theory

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

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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

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