Junction admittance between waveguides of arbitrary cross-sections

Abstract

A general formula for the admittance of the junction between two waveguides of arbitrary and different cross-sections, coupled end-to-end by an aperture of arbitrary shape, is derived by the application of Schwinger's variational procedure. It is shown that, if the dominant modes of either waveguide have similar patterns over the coupling aperture, the junction may be represented approximately by a 2-terminal network. A general and simple definition of characteristic impedance is introduced which enables us to regard the junction as an “impedance mismatch” together with a “junction effect” owing to shunt susceptance. The restrictions required for an exact 2-terminal description are discussed. Simplified formulae, applicable when the waveguides have similar cross-sections, are derived. The symmetrical junction is also considered. The approximate 2-terminal theory is applied to the junction between two rectangular guides of different E-plane dimensions and the results obtained are compared with those derived elsewhere by a more rigorous method. In this way some idea of the accuracy of the theory and the limits of its applicability is obtained. The 2-terminal theory is also applied to a circular-to-rectangular transition, and the results are shown to be in favourable agreement with experiment. The behaviour of a waveguide of hexagonal cross-section is analysed. Finally, various aspects of the impedance definition are discussed.