A hybrid mode-matching/compact 2-D finite-difference frequency-domain (MM/compact 2-D FDFD) method is proposed for the analysis of rectangular ridged waveguide discontinuities. In order to apply MM technique, mode spectrum of the ridged waveguide is determined by an improved compact 2-D FDFD method with only two transverse field components at the cutoff frequencies which lead to two independent sets of real symmetric eigenvalue problems for TE and TM modes. Solving these two separate eigenvalue equations, cutoff wave numbers and discrete mode field functions can be obtained respectively from eigenvalues and eigenvectors. Finally, the generalized scattering matrix (GSM) of the rectangular-ridged waveguide step discontinuity can be easily calculated through the transverse field matching procedure. The method is demonstrated at the examples of two waveguide structures, and results are shown to be in excellent agreement with those by the commercial CAD software HFSS.
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