A Topological Method of Generating Constant Resistance Networks

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. LetGρbe a self-dual one-terminal-pair graph with respect to vertices (i, j), and with the degrees of (i, j) both equal toρ. It is proved that forρ 2, G_ be realized with8 ρ - 11edges, but not with fewer edges, if the union ofG_ 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 forρ = 2. The generation of a constant resistance network forρ = 3is shown in detail, with a numerical example illustrating its application in transfer function synthesis.