Frequency-Domain Nonlinear Behavioral Modeling Using The Arithmetic Operator Method

Abstract

A behavioral modeling environment for the rapid, high-dynamic range analysis of steady-state systems is presented. The Arithmetic Operator Method (AOM) is extended an cast in a solid mathematical framework. AOM is implemented as the AOM Toolbox with the Matlab environment. The AOM Toolbox operates entirely in the frequency domain using behavioral modeling to permit large-signal nonlinearities and handling input signals consisting of one hundred or more distinct input tones with arbitrary spacing of the tones. Frequency domain analysis techniques have been applied previously to nonlinear circuits with multitone inputs, but in environments limited to a few tones processed by transfer functions with low orders of nonlinearity.

Among the contributions brought forward by the development of the enhanced AOM method are the decomposition of the frequency domain into an underlying vector space that permits easy separation of correlated and uncorrelated spectral components after nonlinear processing, an algorithm for computing the underlying vector space decomposition of the frequency domain, algorithms for sparse matrix construction of convolution matrices, and the discovery of properties of the double-sided complex matrix and vector forms that facilitate the use of eigendecomposition as an alternative path to solutions. Validation of the AOM Toolbox is achieved by comparing the time-domain expansion of AOM Toolbox output to results produced purely in the time domain by two other means. Several applications the AOM Toolbox are given, including the prediction of the response of an amplifying device to correlated and uncorrelated multitone inputs, the response of an amplifying device to a broad-band linear FM chirp, and the response of a broadband television broadcast amplifier to a multicarrier input.