Junction Admittance between Waveguides of Arbitrary Cross-Sections

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.