RC circuit: harmonic response

Control theory

This article refers to the analysis of a simple low pass filter. The circuit is made of a resistor and capacitor, connected in series. In order to keep things simple, the calculations will be carried out in the Laplace domain.


Using the voltage divider formula, we can write:


If the formula is simplified and divided by V_i, we can write:


This formula has to be compared with the more generic Bode form formula.


The two formulas have to be made equivalent to one another. This can be achieved using the following parameter values.

Parametro Valore
K 1
\tau_1 Time constant in the denominator. There is just one: RC