A Unifying Approach to Electrical Network Analysis Based On a Complete Model

In this paper the problem of defining and building-up a model of an electrical network is considered. The whole electrical network, here called the active network, is considered to be a pair of interacting but autonomous structures: 1) the nonenergized or “dead” network, which is associated with passive, zero-state elements and 2) the excitation, which represents external inputs and/or initial conditions. Axiomatic definitions are given for both the dead network and the excitation and, starting from these definitions, the topological structures of both the excitation and the dead network are drawn and discussed. A general topological reference frame is described and a procedure is given for obtaining it on the basis of the graph associated with the active network, as well as on the basis of the graph associated with the dead network. Starting from this topological reference frame, a network model is set up, which is said to be “complete” (not reduced) as it consists of as many equations as the number of passive elements which are contained in the active network. Finally, it is shown how such a complete model contains, as special cases, all the models usually employed in the so-called traditional methods of network analysis (nodal, cut-set, mesh, loop).