ALGORITHM OF ELECTRIC CIRCUIT STATE MATRIX TRANSFORMATION USING THE MODIFIED NODAL ANALYSIS

Abstract

The article proposes the algorithm of electric circuit state matrix transformation obtained by the modified nodal analysis. The algorithm is aimed at reducing the system of electrical circuit differential equations to Cauchy problem form for the purpose of subsequent solution. Application of the modified nodal analysis to an electric circuit with energy inertial elements leads to a system of ordinary differential equations, which contains a singular matrix before the derivatives vector in matrix form if there are ungrounded capacitors in a circuit. For this reason, direct reduction of this equations system to Cauchy problem form is impossible. The idea of solving such systems is to pass from equations with potentials to equations with voltages and subsequent division of the equations system into two pieces: containing derivatives and without them. An important step in the transformation to equations with voltages is the elimination of linearly dependent rows of the singular matrix. The algorithm of that transformation is based on the analysis of the adjacency matrix compiled for the capacitors of the electrical circuit, and is the subject of this work. The algorithm can be used for topologically arbitrary connection of an unlimited number of capacitors. For the purpose of demonstration, an example of using the algorithm is given in the article.