Approximation of the Jacobian in Solving Harmonic Balance Equations

Abstract

A new algorithm is presented to reduce computational costs in solving harmonic balance equations obtained by separating state variables. The harmonic balance method is widely used in RF electronics CAD systems. In the author's previous works, an approach was proposed where the vector (matrix) of unknowns is replaced by two matrices of small dimension, which leads to two systems of balance equations that are solved iteratively. The first equation reduces the number of harmonics in the balance equations, the second equation reduces the number of circuit nodes. Equations with reduced dimension are solved sequentially by Newton's method. This algorithm made it possible to reduce computer memory for storing model equations and reduce computational costs when solving high-dimensional problems. In this paper, it is proposed to further reduce computational costs by approximating part of the elements of the balance equations using the decomposition procedure based on singular values. It is proposed to construct a matrix of sets of responses of nonlinear dependencies of circuit models before solving the problem by an iterative method. This matrix reflects all the main changes in nonlinear dependencies with changes in the amplitudes of the input effect and over time. The resulting matrix is then approximated by applying decomposition based on singular values. The matrix of averaged values reduced in this way is substituted into the balance equations. Comparison of the proposed algorithm with the standard harmonic balance method and algorithms developed by the author earlier showed its high efficiency. #CSOC1120.