Topological Considerations in the Realization of Resistive n-Port Networks

The topological implications of irreducibility of the admittance or impedance matrix of an n-port network are studied. Special attention is given to the cases when in
(n - 1)
rows of such a matrix of order
n
the main diagonal elements are equal to the absolute values of some off-diagonal elements. It is shown that the conditions of realizability of a
Y
or
Z
matrix of this type reduce to the known conditions of realizability by means of a network with
(n + 1)
vertices or exactly n independent circuits. Some examples show realizable
Z
matrices which cannot be realized as
Y
matrices and vice versa. Other examples give nonrealizable, paramount
Y
and
Z
matrices showing that paramountcy is not a sufficient condition for realizability.