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The A Matrix, New Network Description

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1 Author(s)

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 = Ay , 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. F are 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.

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Circuit Theory, IRE Transactions on  (Volume:4 ,  Issue: 3 )