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A stepped circular waveguide dual-mode (SCWDM) filter is fully investigated in this paper, from its basic characteristic to design formula. As compared to a conventional circular waveguide dual-mode (CWDM) filter, it provides more freedoms for shifting and suppressing the spurious modes in a wide frequency band. This useful attribute can be used for a broadband waveguide contiguous output multiplexer (OMUX) in satellite payloads. The scaling factor for relating coupling value M to its corresponding impedance inverter K in a stepped cavity is derived for full-wave EM design. To validate the design technique, four design examples are presented. One challenging example is a wideband 17-channel Ku-band contiguous multiplexer with two SCWDM channel filters. A triplexer hardware covering the same included bandwidth is also designed and measured. The measurement results show excellent agreement with those of the theoretical EM designs, justifying the effectiveness of full-wave EM modal analysis. Comparing to the best possible design of conventional CWDM filters, at least 30% more spurious-free range in both Ku-band and C-band can be achieved by using SCWDM filters.