Constructing symbolic models for the input/output behavior of periodically time-varying systems using harmonic transfer matrices

A new technique is presented for generating symbolic expressions for the harmonic transfer functions of linear periodically time-varying (LPTV) systems, like mixers and PLL´s. The algorithm, which we call Symbolic HTM, is based on the organisation of the harmonic transfer functions into a harmonic transfer matrix. This representation allows to manipulate LPTV systems in a way that is similar to linear time-invariant (LTI) systems, making it possible to generate symbolic expressions which relate the overall harmonic transfer functions to the characteristics of the building blocks. These expressions can be used as design equations or as parametrized models for use in simulations. The algorithm is illustrated for a downconversion mixer