A generalized form of Tellegen's theorem

Abstract

Among the theorems of circuit theory, Tellegen's theorem is unusual in that it depends solely upon Kirchhoff's laws and the topology of the network. The theorem therefore applies to all electrical networks that obey Kirchhoff's laws, whether they be linear or nonlinear, time-invariant or time-variant, reciprocal or nonreciprocal, hysteretic or nonhysteretic; the excitation is arbitrary, and the initial conditions are also immaterial. When specific assumptions are made concerning the network elements, the excitation, and the initial conditions, Tellegen's theorem reduces to many useful network theorems. In this paper a generalized form of Tellegen's theorem that allows the efficient derivation of new results is presented. A special formthe "difference form"-of this theorem is shown to be of particular value, and also capable of simple expression in terms of wave variables. The application of the generalized form of Tellegen's theorem is illustrated by an example.