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A Hybrid technique for the analysis of conical horn antennas is presented based on a rigorous description of the horn aperture-free space discontinuity. The transition from the feeding waveguide to the radiating aperture is analyzed by using the mode matching technique (MMT) employing a stepped-waveguide approach. The discontinuity between the horn aperture and free space is modeled by combining an offset Moment Method with the MMT for the last waveguide section. Results for the input standing wave ratio are given and compared with commercial software results which demonstrate the very good performance of the method.