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

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 impedance
Z(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 impedances
Z(p)
having either a pole or a zero at
p = \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.