A Topological Method of Generating Constant Resistance Networks

Abstract
Zadeh has shown that any self-dual network, fixed or linear time varying, is a constant resistance network. To date, the only known constant resistance networks with self-dual structures are the classical lattice and bridged-T networks. In this paper, we investigate the topological aspect of the problem, with the aim of obtaining new constant resistance network configurations. LetG_{\rho}be a self-dual one-terminal-pair graph with respect to vertices (i, j), and with the degrees of (i, j) both equal to\rho. It is proved that for\rho \geqq 2, G_\rhocan be realized with8 \rho - 11edges, but not with fewer edges, if the union ofG_\rhoand an edge joining (i, j) is to be 3-connected. Using these graphs as the basis, a class of constant resistance networks are generated, which include the classical lattice and bridged-T networks as special cases for\rho = 2. The generation of a constant resistance network for\rho = 3is shown in detail, with a numerical example illustrating its application in transfer function synthesis.

This publication has 7 references indexed in Scilit: