Synthesis of Resistive N-Port Networks with N + 1 Nodes

Abstract

In this paper a systematic procedure is proposed to obtain then-port structure appropriate to theYmatrix of a resistive network containing exactlyn + 1nodes. The method presents: A set of necessary conditions which may eliminate quickly a large class of matrices from further consideration for realization; A simple procedure for the determination of a port structure in the case theYmatrix contains a few or no zero elements; A realization procedure which is particularly convenient in case theYmatrix contains a large number of zero elements. This procedure is also extended to the realization ofZmatrices. It is shown that sometimes there exists more than one network withn + 1nodes realizing a given matrix Y with different port structures. An evident application of the method presented in this paper is the realization of fundamental circuit matrices and fundamental cut-set matrices of oriented graphs.