New method and solution algorithm for harmonic balance equations

Abstract

Harmonic balance (HB) method is widely used for modeling nonlinear electronic circuits in CAD electronics. The main problems of CAD algorithms and programs based on various modifications of HB methods are significant requirements for computing machine memory and huge computational costs when modeling complex circuits having thousands of electronic components and hundreds of thousands of model equations. Reduced-order model methods, which became popular lately, can significantly reduce size and memory required for electronic circuit models to analyze dynamic behavior. The main problems of reduced-order methods for modeling electronic circuits are due to very small reductions in computational costs (with significant reduction of dimensional equations and model required memory). A new method and solution algorithm for harmonic balance equations that are used in electronics CAD is presented. The new algorithm is based on applying concept of reduced-order model methods to harmonic balance equations. Vector (matrix) of unknown equations is replaced by two matrices of small dimension, which are solved iteratively (as in the standard method of harmonic balance) if compared to previously developed method of joining concepts for reduced-order  models and harmonic balance. The first equation reduces harmonics number in balance equations, the second equation reduces circuit nodes’ number. Equations with reduced dimension are solved sequentially and so this algorithm can significantly reduce computing machine memory to store model equations and to reduce computational costs. The simulation program was developed in Matlab/Simulink system. The results of modeling circuits differing in number of electronic circuit nodes and of considered harmonics made it clear that the gain was obtained only for problems of dimensions more than a hundred (the nodes’ number and considered harmonics’ number).