FREQUENCY-ANALYSIS OF TIME-VARYING PERIODIC LINEAR-SYSTEMS BY USING MODULO-P TRANSFORMS AND ITS APPLICATIONS TO THE COMPUTER-AIDED ANALYSIS OF SWITCHED NETWORKS

This paper introduces a theory of modulo p Laplace and Z-transforms which can adequately analyze any time-varying periodically switching system in frequency domain, in particular, switched-capacitor SC networks with nonideal operational amplifiers. Formulae for inverse and direct modulo p transforms are included. Since the regular Laplace and Z-transform fail to be adequate for a nonideal sampled system, this new tool can be effectively used instead. An extremely efficient and fast program is developed based on the general theory. This program has been used by the author for the analysis of SC networks with nonideal operational amplifiers and requires less time for calculations compared with conventional time-domain methods. Furthermore, closed-form solutions for the nonideal transfer functions are given. The presented algorithm permits us to calculate the transfer function in partial fraction form and thus stability can be verified immediately. © 1990 Birkhäuser Boston Inc.