Constructing Symbolic Models for the Input/Output Behavior of Periodically Time-Varying Systems Using Harmonic Transfer Matrices

  • Authors:

  • P. Vanassche;G. Gielen;W. Sansen

  • Affiliations:

  • Katholieke Universiteit Leuven, Department of Electrical Engineering, ESAT-MICAS, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium;Katholieke Universiteit Leuven, Department of Electrical Engineering, ESAT-MICAS, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium;Katholieke Universiteit Leuven, Department of Electrical Engineering, ESAT-MICAS, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium

  • Venue:
  • Proceedings of the conference on Design, automation and test in Europe
  • Year:
  • 2002

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Abstract

A new technique is presented for generating symbolic expressionsfor the harmonic transfer functions of linear periodicallytime-varying (LPTV) systems, like mixers and PLL's. The algorithm,which we call Symbolic HTM, is based on the organisationof the harmonic transfer functions into a harmonic transfer matrix.This representation allows to manipulate LPTV systems in away that is similar to linear time-invariant (LTI) systems, making itpossible to generate symbolic expressions which relate the overallharmonic transfer functions to the characteristics of the buildingblocks. These expressions can be used as design equations or asparametrized models for use in simulations. The algorithm is illustratedfor a downconversion mixer.