Electric Circuits and Networks

15.1 CIRCUIT RESPONSE TO COMPLEX EXPONENTIAL INPUT

Let the n^th order differential equation describing a n^th order linear time-invariant circuit be

 

 

y(t) is some circuit variable identified as the output variable and x(t) is some independent voltage/current source function. Let x(t) = 1 e^st be a complex exponential function of unit amplitude and complex frequency s = σ + jω Let y(t) = A e^st be the trial solution where A is a complex number to be determined. Substituting the trial solution in Eqn. 15.1-1, we get,

 

 

Thus, when the input to ...