$N$-Port T-Networks and Topologically Symmetric Circuit Theory

Abstract

N-port Pi-networks can be extracted directly from Y-parameters. Likewise, two-port T-networks can be extracted directly from two-port Z-parameters. However, it appears that N-port T-networks have not been previously identified for N > 2, a strange topological asymmetry in circuit theory. We introduce the general N-port T-network and illustrate application by synthesis of an N -port T-network lumped model from Z-parameters for a three-port microstrip via to ground on GaAs. The existence of the N-port T-network partially relieves the noted circuit theory asymmetry; however, the T-network is structurally different from the Pi-network. We show that circuit theory becomes topologically perfectly symmetric under an appropriate change of variables when we consider g-parameters and derive circuit theory from the electromagnetically symmetric form of Maxwell's equations. The perfect topological symmetry requires both electric and magnetic (i.e., magnetic monopole) current. Practical application might be possible because effects identical to magnetic monopole current and charge have recently been experimentally observed and reported.