Electric Circuits and Networks

11.4 PERIODIC STEADY-STATE IN A SERIES RC CIRCUIT

We address the issue of zero-state response to repetitive input in RC circuits in this section and consider a specific example for doing so (Fig. 11.4-1).

A symmetric square wave voltage with 1 V amplitude is applied from t = 0 to an initially relaxed series RC circuit. The period of the square wave is assumed to be equal to the time constant and the time scale is marked in terms of t/τ.

A step response starts at t = 0 and takes the output to (1 – e^–0.5) = 0.3935 V at t/τ = 0.5. Another zero-state step response starts in the negative direction at that point along with a zero-input response corresponding to an initial voltage of 0.3935 V on the capacitor. Thus, the output waveform can be expressed ...