Necessary Conditions for the Realizability of n-Port Resistive Networks with more than (n + 1) Nodes

A new set of necessary conditions are presented for an nth-order square symmetric matrix Y with real entries to be the
n
-port admittance matrix of a network containing positive resistors and
(n + 2)
nodes. The so called "supremacy" conditions represent a symmetric set of inequalities among products of pairs of elements in a matrix S obtained in a simple manner as a linear combination of entries in Y. The conditions are derived by augmenting the given matrix Y with an additional port to form a connected port structure, transforming the port structure until it is linear, applying the "uniform tapering conditions" and then eliminating the augmenting port. Extensions are given to the case of
n + p
nodes with
2 <P \leq n.