An Approximate Analysis of a Periodically Switched Filter

A rapid means of analyzing linear networks containing a periodically operated switch is presented. It is assumed that the switch closure time is very short compared to the network time constants and the switching period. The method is based on obtaining an approximation for the pulse transfer function (ptf) of an arbitrary minimum reactance impedance by approximating the real part of the impedance as a sum of triangular elemental real part impedances. The approximate ptf is used in the analysis of a specific resonant transfer filter and the transmission response is computed. The approximate result is compared with the result based on more exact calculations. A table of normalized values for the ptf corresponding to elemental triangles is included so that the approximation can be used generally for other applications.