On the Synthesis of Resistive N-Port Networks

A new approach to the problem of the synthesis of resistive
n
-port networks with
(n + 1)
nodes is given. First it is shown that, given a conductance matrix
G
of order
n
, the signs of its elements define the complete tree of the n port uniquely (if it exists). The case of two (or more) ports in "series" is exceptional: the order of such ports in the complete tree can be found by comparing the absolute values of a couple (or more couples) of elements of
G
. Once the complete tree has been determined, the synthesis becomes very simple, since the
G
matrix can be transformed into another matrix Go referred to a set of node-to-datum independent voltages, whose conditions of realizability are well known.