A New Algorithm for Solving of Harmonic Balance Equations by Using the Model Order Reduction Method

The harmonic balance method (HB) is widely used for modeling nonlinear radio circuits in electronic CAD systems. The main problems of CAD algorithms and programs based on various modifications of HB methods are significant requirements for computer memory and huge computational costs when modeling complex circuits containing thousands of electronic components and hundreds of thousands of model equations. Methods of model order reduction have become popular in recent years, and can significantly reduce the dimension and memory required for electronic circuit models for dynamic mode analysis. The main problems of low-order methods for modeling electronic circuits are associated with very small reductions in computational costs (with a significant reduction in the dimension of the equations and the required memory for the model). A new method and algorithm of solving the equations of harmonic balance method used in electronic CAD systems is presented. The new algorithm is based on applying the ideas of model order reduction methods to harmonic balance equations. In comparison with previously developed method of usage the ideas of model order reduction for harmonic balance method, the new method replaces the vector (matrix) of equation unknowns by two matrices of small dimensions that are solved by iteratively (as into the standard harmonic balance method). The first system of equations reduces the number of harmonics in balance equations, and the second system of equations reduces the number of circuit nodes. These equations of small dimensions are solved sequentially, so this algorithm allows significantly reduce the size of computer memory for storing of model equations and reduce of computational costs. The simulation program was developed in the Matlab/Simulink system. The results of modeling test circuit with different number of electronic circuit nodes and the number of considered harmonics showed that the gain was obtained only for dimensions of problems more than one hundred (the number of nodes and the number of considered harmonics).