Analysis of nonlinear RF and microwave circuits using harmonic balance and system identification methods

Abstract

The use of harmonic balance standard simulations and system identification methods to analyze the nonlinear behavior of high-frequency circuits is reported. In order to illustrate the technique, two circuits are analyzed and measured: an oscillator and a monolithic digital frequency divider by two. Both circuits show different operating modes.

Variable-ratio digital frequency dividers: Analogue design methodology and phase noise analysis based on harmonic balance

“…Another method uses an auxiliary sub-harmonic circuit (ASC) [6] to initialize the frequency components of the circuit variables to nonzero values. Other techniques are: Transient Assisted Harmonic Balance [7], Envelope-Transient [8] (no application to digital frequency dividers has been published yet, to our knowledge), closed loop techniques, originally developed for oscillators [9,10], also applied to analogue frequency dividers [11], conversion matrix techniques [12] and system identification methods to map the operation modes, depending on the evaluation of zeros and poles [13].…”