Small signal transient stability of periodically switched circuits

A method of small signal analysis for a class of switching circuits is presented and is demonstrated using a single phase bridge rectifier circuit. This method may be used in any switching circuit in which the switching is periodic. The state equations for the circuit are written and shown to be a set of linear differential equations with periodic coefficients. The periodic transition matrix is determined and the characteristic roots of this system are shown to determine the transients around a steady state operating point.