Zero state response of linear circuits to exponential inputs

In this paper an efficient method for calculating the zero state response of linear time invariant circuits is given. The input, in general, is a complex exponential function of time, of which step and sinusoidal functions are special cases. The method gives an algebraic relationship between the response due to two arbitrary exponential inputs. If the transient response due to one input is known, then the response due to the other input can be computed by the solution of a system of linear equations. No approximation is made in the derivation, and they are valid for all time and all exponential inputs. The method is useful in reducing the computational costs of analyzing periodically switched linear networks, such as, switched capacitor and switched current circuits