Steady-State Analysis of Circuits Containing a Periodically-Operated Switch

Abstract

The exact conversion functions are calculated for networks containing one periodically operated switch, using familiar pole-zero and Fourier methods of analysis. It is first assumed that the switch is alternately open and closed during equally long time intervals. Circuits whose driving-point impedanceZ(p)seen from the switch has neither pole nor zero at infinity are treated in detail. The analysis is then extended in order to allow for impedancesZ(p)having either a pole or a zero atp = \infty. Complete results are also given for circuits whose switch is alternately open during time intervals of duration,T_1, and closed during intervals of duration,T_2 \neq T_1. The general analysis is applied to a series modulator and the realization of a given function of frequency as conversion function of such a modulator is investigated. Throughout this paper, the impedance Z(p) is assumed to have only simple poles and simple zeros.