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A rigorous field theory method is described for the computer-aided design of a class of rectangular waveguide filters, where the cavities are coupled by irises, E-plane integrated metal inserts, broadside oriented strip obstacles, or multiple quadratic posts. These coupling elements enable low-cost manufacturing, since accurate and inexpensive metal-etching techniques, or materials with standard dimensions may be utilised. The design method is based on field expansion in suitably normalised eigenmodes which yield directly the modal scattering matrix of two appropriate key building blocks for this kind of filter, the step-wall discontinuity and the N-furcated waveguide section of finite length. The theory includes the finite thickness of the diaphragms, strips or posts as well as the immediate higher-order mode interaction of all discontinuities. The stop-band characteristic of the filter is taken into account in the optimisation process. Optimised data are given for Ku-, E-, W-, and D-band filter examples, whereby it is shown that the theory is also very appropriate for broadband designs. The theory is verified by measured results for a six resonator iris coupled Ku-band filter, with a midband frequency of 15.2 GHz and a seven-resonator metal insert D-band filter, with a midband frequency of 142.5 GHz, showing measured minimum insertion losses of 0.2 dB and 1.4 dB, respectively.