The A Matrix, New Network Description

Abstract

Both the loop and node methods of network analysis produce a system of second-order differential equations. A method of analysis is proposed which produces a set of first-order differential equations. With this method, the network equations obtained can be expressed in the formF + dy/dt = Ay, whereFandyare column matrices andAis a square matrix. The variables,y, are currents through inductances and voltages across capacitances; the forcing functions.Fare proportional to voltage and current sources. The elements ofAare inductances, capacitances, and resistances, or combinations thereof. Characteristic roots (natural frequencies) of the network are identical with the eigenvalues of theAmatrix.