Symbolic modeling of periodically time-varying systems using harmonic transfer matrices

Abstract

This paper presents an algorithm for generating symbolic expressions for the harmonic transfer functions of linear periodically time-varying (LPTV) systems, like mixers and PLLs. The harmonic transfer functions characterize the up- and downconversion behavior of the wanted and unwanted signal components. The algorithm, which the authors call Symbolic HTM, is based on the organization of the harmonic transfer functions into a harmonic transfer matrix. This representation allows one to manipulate LPTV systems in a way that is similar to linear time-invariant systems, making it possible to generate symbolic expressions relating the overall harmonic transfer functions to the building block parameters. These expressions can be used as design equations or as parameterized models for use in simulations or synthesis. Comparison of the symbolic models with numerical data shows them to be accurate, even for small numbers of modeling terms.