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Circular waveguide dual-mode (CWDM) filters have been widely employed in the manifold-coupled output multiplexer (OMUX) for satellite payloads. In this paper, a deterministic electromagnetic (EM) design technique for fast and accurately computerized prototyping a general CWDM filter is presented. By introducing a generalized K impedance inverter using the generalized scattering matrix of the tuning screw section, the insertion phase and the coupling of the two degenerate modes in a CWDM cavity can be determined by a most effective way. To handle the asynchronously tuned cases, the theoretical formula that relates a self-coupling to its corresponding phase offset is derived. The design technique is based on modal analysis at the center frequency and is deterministic without using optimization or curve fitting. The presented technique enables the full-wave EM design of CWDM filters as easy and accurate as designing conventional single mode waveguide filters. To validate the design technique, practical design of eight-pole symmetric and asymmetric CWDM filters have been studied theoretically and experimentally. An EM design of a complete Ku-band 15-channel contiguous OMUX is also demonstrated.