A computational method for solving a wide range of transverse and longitudinal waveguide discontinuity problems is described. Results are obtained by the simultaneous solution of matrix equations, generated by Fourier analysis, which relate the complex amplitudes of orthogonal electric and magnetic field components. In some cases the solution is found to be sensitive to the way in\ud which infinite series of field functions are truncated, and it is shown how the optimum form of truncation can be determined for many configurations of practical importance.\ud \ud Several examples showing the application of the method are\ud given, and comparison of results with those obtained by experiment, and by other analytical techniques, confirms its accuracy.\ud \ud The application of the method in the design of discontinuities for higher-mode generation in multimode antennas is considered, particularly in connection with a multimode monopulse feed for a satellite-communication reflector antenna. Primary and secondary characteristics are determined theoretically for various modeconverter\ud configurations, allowing those giving satisfactory allround\ud performance to be selected. Comparison with conventional\ud feeds shows the multimode feed to be superior in many respects. A prototype multimode feed is constructed, and theoretical primary radiation patterns are compared with those obtained experimentally
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