Electric Circuits and Networks

15.4 THE s-DOMAIN SYSTEM FUNCTION H(s)

We saw in Sect. 15.1 that when an input e^st is applied to a linear time-invariant circuit described by an n^th order differential equation

 

 

the forced response is given by H(s)e^st where

In Sect. 15.2 we observed that a right-sided function x(t) can be expressed as a sum of infinitely many complex exponential functions of frequency between σ – j∞ and σ + j∞ with the line Re(s) = σ falling within the ROC of Laplace transform of x(t). We combine these two facts along with superposition principle to arrive at the zero-state response of a linear time-invariant circuit to a right-sided input function.