RC circuit + leakage resistance: state space + Laplace domain model (Symbolic toolbox)

This video models a serial Resistor-Capacitor circuit whose capacitor has some leakage conductance, modelled as a second resistor in parallel with the capacitor (R+ [C|R]).
First-principle equations and Kirchoff's laws are used. Then, a normalised state-space representation is built and, last, its Laplace transform is used to obtain the transfer function and initial condition term in the Laplace domain. Computation of the time response of this circuit given some input waveforms will be addressed in future videos, see • Time response of RCR c... , • Time response RCR circ... for sinusoidal pulse time response, and • Time response, RCR cir... (sinusoidal pulse train).
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#laplacetransform #controlengineering #differentialequations
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Antonio Sala
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