مرکز منطقه ای اطلاع رساني علوم و فناوري - 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. Let $G_{\\rho}$ 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 $\\rho \\geq q 2, G_\\rho$ can be realized with $8 \\rho - 11$ edges, but not with fewer edges, if the union of $G_\\rho$ and 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 $\\rho = 3$ is shown in detail, with a numerical example illustrating its application in transfer function synthesis.

Keywords :

RLC networks, constant-resistance; Synthesis; Topological methods; Attenuation; Capacitance; Equalizers; Graph theory; Impedance; Lattices; Network synthesis; Switches; Time varying systems; Transfer functions;