Circuit Theory of Coupled Transmission Systems

Abstract

A method of obtaining an exact circuit equivalence of a class of coupled transmission systems from Maxwell's equations is described. The solution for the propagating characteristics of the coupled transmission system can be readily obtained from the circuit analog. The process of reducing field equations to circuit equations is carried out for a particular coupled structure, a coupled helix system. The circuit theory yields frequencies of the coupled modes as functions of the propagation constant, rather than the propagation constant in terms of frequency. The circuit theory has the great advantage that it is as valid for strongly coupled systems as it is for weakly coupled systems. The usefulness of the approach is demonstrated by applying the theory to several slightly different propagating systems. Expressions for the energy and the power flow derived from the circuit theory are compared to the true power flow and the energy in the transmission system. It is shown that the energy of the system in the equivalent transmission line corresponds to the true energy, if the circuit is assumed to propagate slow waves. The power flow relation obtained from the circuit analog differs from the true power flow by the factor of (vp/vg) which is attributed to the dispersive nature of the circuit. Important relationships between impedances of the transmission system defined in various ways are obtained from the power flow relation.