مرکز منطقه ای اطلاع رساني علوم و فناوري - On Equivalence of Resistive n-Port Networks

Abstract :

In this paper the problem of realization of a resistive $n$ -port network from its paramount admittance matrix $Y$ is considered from a geometric point of view. Augmentation of the set of $n$ ports to a linear $2n - 1$ tree on a complete graph with $2n$ vertices leads to a system of $n(n + 1)$ equations in $q = n (2n - 1)$ unknowns. All the real solutions of this system correspond to equivalent $n$ ports. They may be looked on as points of a manifold $L$ in the $q$ -space $E^{q}$ . The realization of Y in the conventional sense being constrained to non-negative resistor values is equivalent to finding a point of intersection of $L$ and the non-negative orthant $P$ of $E^{q}$ . 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 resistive $n$ -port network with $n + 1$ vertices into a unimodular congruence $Y = CGC\´$ , this paper proposes a decomposition of a general admittance matrix Y into a subunimodular congruence $Y = CGC\´$ .