Transfer Functions and Chain Parameters of SC Equivalents

Abstract

When designing SC filters, the question of charge transfer functions and chain parameters becomes very interesting. A complete analysis of this question based on standard charge conservation equations and their solution by algebraic cofactors is presented here. First, the analytic method used is reviewed (both a standard and a modified nodal voltage method are used), second, the voltage and charge transfer functions of a standard SC four-port model are discussed (including some special cases, such as SC circuits using full bilinear simulation of resistors); and, finally, a chain parameters analogy for SC circuit is derived (including special cases with non existing input/output nodes in one phase). Further possible ways to establish chain parameters are presented, and the relation between trace parameters of a chain matrix and standard transfer functions is discussed. The entire solution is demonstrated with some simple examples, and possible methods of computer-aided evaluation of the transfer functions are briefly discussed.