Time response of RCR circuit to a sinusoidal pulse train

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 16:44

*Enlace a Spanish version

Summary:

This video obtains the response to a sinusoidal pulse train of a circuit with 2 resistors and 1 capacitor. This video is part of the case study of a circuit with sinusoidal pulse input, constituted by the videos [sinpulLEN], [sinpulRCREN], [sinpulRCR2EN] and this one.

The development is based on the superposition of fragments of response calculated by sections, by means of the concepts of causality and state, in a way analogous to that used in the video [sinpulRCR2EN], whose previous visualization is recommended in order to better understand what it is done here.

First, it is justified that the Laplace transform of a periodic signal is that of the signal in a period divided by $(1-e^{-Ts})$, with geometric progression sum formulas.

However, this Laplace transform of the pulse train is not used in the development, because its inverse is difficult to handle. Alternatively, solving is carried out in 10 ms fragment, using the final condition of the previous one as the initial condition of the next frament.

The final part of the video discusses the steady state (not sinusoidal, because the input is not sinusoidal: there will be harmonics), computing it by solving the equation of the response that equates $y(t)$ with $y(t+0.01)$, being the initial condition an unknown variable.

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