Article,
The \$A\$ Matrix, New Network Description
IRE Transactions on Circuit Theory, (September 1957)
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 form F + dy/dt = A y, where F and y are column matrices and A is 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 of A are inductances, capacitances, and resistances, or combinations thereof. Characteristic roots (natural frequencies) of the network are identical with the eigenvalues of the A matrix.
