Graph based inversed matrix in electric circuits solutions

Abstract

The matrix calculus is very frequently used in electrical engineering to calculate the different parameters of (but not only) electric circuits. One of the most important points of mathematical background of this analysis is the calculation of inverse matrix. This can be realised by numerous well-known algebraic methods (unit/identity matrix, different algebraic supplements, etc.) or numerical techniques. Inverting of matrixes is a well-known method; nevertheless, idea of alternating paths (presented in the paper) is completely new and unpublished. The electric circuit can be represented in the form of a graph and this graph structure rewritten into the form of matrixes. The paper shows the inverse matrix acquisition without using any algebraic technique - directly from graph structure. The presented technology can further be used as an input for any numerical method used for circuit parameters analysis or on- and off-line simulation. Practically, this is based on the following steps: the electric circuit is transformed into the graph structure. A new graph structure is created using the presented algorithm. The matrix system describing this graph structure, obtained without use of any conventional technique, is the inverse matrix of the original graph. The proposed utilization of alternative paths essentially differs from work of other authors.