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An accurate and efficient method for analyzing circular to multiple off-center rectangular side-coupled waveguide T-junctions is developed based on a rigorous mode-matching technique. The method is very general and not limited by symmetry or other dimensional constraints to the junction. A new way to match fields on the curved interface between subregions is described in detail. The computer code developed based on this theory is highly efficient. The numerical results match with the results obtained by other methods including experimental ones. The method is used to design a side-coupled circular waveguide dual-mode filter.