On Equivalence of Resistive n-Port Networks
Israel Cederbaum · IEEE Transactions on Circuit Theory · 1965
In this paper the problem of realization of a resistiven-port network from its paramount admittance matrixYis considered from a geometric point of view. Augmentation of the set ofnports to a linear2n - 1tree on a complete graph with2nvertices leads to a system ofn(n + 1)equations inq = n (2n - 1)unknowns. All the real solutions of this system correspond to equivalentnports. They may be looked on as points of a manifoldLin theq-spaceE^{q}. The realization of Y in the conventional sense being constrained to non-negative resistor values is equivalent to finding a point of intersection ofLand the non-negative orthantPofE^{q}. In this paper the theory of equivalence is studied and some properties of L are defined. Similarly to the known method of the decomposition of the admittance matrix Y of a resistiven-port network withn + 1vertices into a unimodular congruenceY = CGC', this paper proposes a decomposition of a general admittance matrix Y into a subunimodular congruenceY = CGC'.