A Frequency-Domain Theory for Parametric Networks

This paper presents a frequency-domain method for analyzing the transient and steady-state behavior of a class of linear, variable parameter networks defined as follows: A "lumped, linear, parametric network" (LLPN) consists of a finite number of lumped circuit elements, R's, L's, and C's, whose values vary periodically with time, imbedded in a network of fixed R's, L's, C's, and sources. In any particular LLPN, the frequencies of all the time-variant elements are comensurable. The method of analysis, based upon the theory of linear difference equations, is exact. There are no approximations which restrict the analysis to networks containing sharply tuned filters. For a single sinusoidally varying element, a precise numerical method that is readily performed by a digital computer is presented. In addition, some interesting properties of single-element linear parametric amplifier networks are presented.