A generalized form of Tellegen´s theorem

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.