Метод топологического анализа электрических цепей с изменяющейся топологией

Abstract

In this article we propose a method of topological analysis of electric circuits with variable topology based on the new version of the modified Gaussian elimination for solving systems of linear algebraic equations. We describe the algorithms of both the original and re-topological analysis of electric circuits taking into account the characteristics of the matrices used. The described method significantly reduces the computational cost of the redefinition of the tree of a graph and the formation of the fundamental circuit matrix and the fundamental cut set matrix, and also allows you to detect qualitative changes in the circuit, such as the emergence of CE-circuits and LI-cuts. The proposed method significantly simplifies the re-topological analysis after various changes to the circuit topology such as adjunction an element in the circuit, removal of an element circuit, changing the priority of the element circuit, transition branch from a tree of a graph in complement and transition from complement in the tree of a graph, which is typical for structural synthesis of electronic devices. The examples demonstrate that the use of the proposed approach to typological analysis provides advantages over using traditional approach.