Time response of RCR circuit to single sinusoidal pulse (1: Laplace, superposition)

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 11:49

Summary:

This video computes the time response when subject to a (single) sinusoidal pulse input of a two resistor plus capacitor circuit whose model was obtained in video [RCRmodEN], to obtain the transfer function and initial condition term in the Laplace domain.

The first minute quickly discuss the modeling phase. The sinusoidal pulse and its transform are discussed in the video [sinpulLEN], whose viewing beforehand is recommended. However, this transform is NOT going to be explicitly used here, because the same idea of delay and superposition that was used in that video will be used here with the output to a full sinusoid.

The final part of the video discusses the response to non-zero initial conditions and the same input pulse. Obviously, it is a matter of simply adding an exponential (inverse transform of initial conditions term, free response) to the previously calculated solution.

An alternative “piecewise” way of calculating the response for this same circuit is discussed in the video [sinpulRCR2EN] without resorting to “delay” concepts used here; also, the response to a train of sinusoidal pulses that repeat indefinitely is discussed in the video [trenpulRCREN].

*Link to my [whole collection] of videos in English. Link to larger [Colección completa] in Spanish.