Time Domain Analysis of Steady State Response in Linear Periodic Systems and Its Application to Switching Converters

Abstract This note discusses the steady state response of a linear periodic system with a periodic input, especially for linear systems with periodic and piecewise continuous coefficients. The first order approximation of the steady state response with respect to the period of time is obtained for general linear periodic systems. This result is then applied to analyze the buck-boost converter operating in continuous conduction mode. This mathematically clarifies conventional results of switching converters which have been deduced under physical inspections or assumptions.