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 rows of such a matrix of order 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 or matrix of this type reduce to the known conditions of realizability by means of a network with vertices or exactly n independent circuits. Some examples show realizable matrices which cannot be realized as matrices and vice versa. Other examples give nonrealizable, paramount and matrices showing that paramountcy is not a sufficient condition for realizability.