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HARMONIC BALANCE THEORY FOR SCHEME TECHNICAL DESIGN
DOI: 10.36724/2072-8735-2020-14-11-21-32
Svetlana F. Gorgadze, Moscow Technical University of Communications and Informatics, Moscow, Russia, svetlana-gorgadze@yandex.ru
Anton A. Maximov, Moscow Technical University of Communications and Informatics, Moscow, Russia, mash2525@yandex.ru
Abstract
The analysis and generalization of the main publications on the methods of synthesis and analysis of non-linear active microwave circuits based on the use of the harmonic balance method are presented. As a result of some classification of mathematical approaches and techniques used in the context of this method, a selection and review of basic algorithms was made, the sequential application of which makes it possible to obtain the final result for a scheme of any complexity. The principles of drawing up the initial system of differential equations for electronic circuits and reducing it to a system of linear algebraic equations are considered. A detailed and, at the same time, simplified interpretation of the approaches involving the use of projection methods and Krylov subspaces is given in order to make them easier to understand. Both the complete and the restart generalized method of minimal residuals are considered, in which the desired solution is obtained in the course of an iterative process, at each stage of which subspaces of lower dimension are constructed. The possibilities of simulators and application packages intended for circuit design of electronic circuits are considered. The problem of matching a power amplifier in large signal mode using the APLAC simulator, which is NI AWR technology for designing high-frequency circuits, is discussed
Keywords: Newton-Raphson method, Jacobi matrix, projection methods, Krylov subspaces, Arnoldi orthogonalization, Hessenberg matrix, Givens rotation, matching power amplifier.
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