Derivation of Thevenin's and Norton's Theorems Using Two-Port Network Analysis

Abstract

In this paper, a novel and simple method for deriving Thevenin's and Norton's Theorems using z-parameters of two-port networks has been developed. In a most general way, electrical networks with dependent and independent voltage sources as well as current sources, connected to a load impedance have been considered. It is shown that, the voltage at a given set of terminals can be calculated by using the z-parameters of all the possible two-port networks that can be formed from the given network by taking one independent source at a time using superposition theorem. All the steps and corresponding expressions for the currents and voltages in the derivation of the theorems have been methodically presented. It is also shown that by employing z-parameter method, it is easy to explain the fact that, for certain networks only Thevenin equivalent circuit exists but not Norton equivalent circuit. Several examples in solving electrical circuits by including equivalent circuits of electrical machines and power systems have also been worked out, to illustrate the proposed method. The approach presented in this paper will also serve as a useful exercise for tutorial sessions in electrical circuits.