Algebraic reduction of electrical multiterminal networks

Abstract

An electrical dc network consisting of m edges with given conductances and of n points, n 1 of which are marked as terminal points, can be reduced to an equivalent network with connections between the n 1 terminals only (terminal network). In the special case n 1 = 2, rduction of the given network results in one single conductance. The computation of the n 1 2 replacement conductances as functions of the given conductances requires the inversion of matrices with variable coefficients. 1. A theorem (forest theorem) is proved which reduces the algebraic calculation to a combinatorial problem, and 2. a recursive algorithm (ec algorithm) is developed which simplifies stepwise the given network, thus leading to terminal networks. For the sake of simplicity all considerations have been formulated in the terminology of Ohmic networks with conductances. Generalization to passive ac networks and admittances should be obvious.