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A Topological Method of Generating Constant Resistance Networks

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1 Author(s)

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.

Published in:

IEEE Transactions on Circuit Theory  (Volume:14 ,  Issue: 2 )