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For high-efficiency reflector antennas, it is important that the primary radiation pattern of the radiating feed should have complete bandwidth equalisation with low sidelobe and crosspolarisation levels. One such feed is the dual-mode circular waveguide loaded with a short dielectric sleeve. In the paper, an electromagnetic model of the dielectric-sleeve-loaded circular waveguide is developed using the modal-matching method. The numerical results thus obtained from the model are verified experimetally wherever appropriate and are then applied to the design of a suitable dual-mode radiator.