On the representation of electrical networks

Abstract

By integrating in the representation of electrical circuits the properties of the physical laws which govern their functioning, we propose a way to construct a representation such that two circuits which "function in the same way" have the same representation. In this article, we show that the bond graph representation is a good candidate for such a functional representation because its formalism deletes a piece of information which is useless for analyzing the circuit's functioning. However, the existing algorithms which transform a circuit into a bond graph are not fully adapted to this formalism. A more suitable algorithm is proposed, based on the Tutte decomposition of graphs. This algorithm associates a unique bond graph with a given circuit and it formalizes the "inspection method" suggested by Karnopp [1975]. With this new algorithm, the gap between the bond graph representation and the functional representation is reduced.