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

In this paper a systematic procedure is proposed to obtain the
n
-port structure appropriate to the
Y
matrix of a resistive network containing exactly
n + 1
nodes. 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 the
Y
matrix contains a few or no zero elements; A realization procedure which is particularly convenient in case the
Y
matrix contains a large number of zero elements. This procedure is also extended to the realization of
Z
matrices. It is shown that sometimes there exists more than one network with
n + 1
nodes 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.