SOME IMPORTANT PROPERTIES OF WAVE-GUIDE JUNCTION GENERALIZED SCATTERING MATRICES IN THE CONTEXT OF THE MODE MATCHING TECHNIQUE

Some important properties for the generalized scattering matrix [S] of waveguide step discontinuities, in the context of the mode matching t echnique, are derived by considering the conservation of the complex p ower and self reaction across the discontinuities. Apart from their th eoretical significance, these properties are useful for the numerical verification of the mode matching technique when designing waveguide c ircuits. The properties are shown to apply in the general case of junc tions between lossless inhomogeneously filled waveguides, and they are proven to remain valid irrespective of the number of modes retained i n the field expansions. During the process of deriving these propertie s, the mode matching technique for a waveguide step discontinuity is r evisited and some subtle theoretical issues are resolved. In this fram ework, the selection of the appropriate testing modes for enforcing th e field continuity conditions across the discontinuity is rigorously j ustified. In addition, two distinct mode matching formulations corresp onding to the two possible orthogonality relations among the eigenmode s of lossless waveguides are proven to be equivalent. Finally, it is s hown that the correct application of the field boundary conditions acr oss the step discontinuity implies requirements on the number of modes used to represent the fields, in each waveguide, which are compatible with the relative convergence criterion.