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Quad-ridge horn antennas of various geometries are considered as possible candidates for a wideband reflector antenna feed. It is demonstrated that shaping the sidewalls of the ridge horns significantly improves the radiation characteristics of the horns. The conical quad-ridge horn with an elliptically shaped sidewall shows the most promise as a wideband reflector antenna feed. The radiation patterns are rotationally symmetric, and the 10-dB beamwidth is reasonably constant over a wide frequency range.