Maximum off-axis gain of elliptical beams

Antenna beams of elliptical cross-section are analysed to determine the maximum gain that can be achieved over any particular elliptical cross-section. The analysis is concerned with maximising the gain at specified off-axis angles in the principal planes of the antenna. The maximum achievable gain is completely determined by the specified beam cross-section. Since the analysis applies to a lossless (100%-efficient) antenna, it establishes an upper bound to the off-axis gain of elliptical-cross-section beams. The analysis is based on scalar diffraction theory for a rectangular aperture antenna with a cosN aperture-field distribution. The gain of a 3.5° × 7° beam is derived to show the effect of the aperture distribution on the gain. From a knowledge of practical antenna efficiencies, one can derive realistic values for the gain of elliptical beams produced by array, horn and reflector antennas. The analysis has particular application to communication satellites that radiate beams of elliptical cross-section for regional coverage on the surface of the earth.