Flat-topped antenna beams with maximum gain-area product

Most antenna applications require maximum gain in a single direction resulting in a pencil beam solution. For some applications antennas are required to provide service with some minimum gain over an angular beam area. Gain-area product (minimum antenna gain within the beam area times the beam area in square degrees) is a useful figure of merit for beams designed to cover an area. Maximizing the minimum gain over the area is obviously beneficial. An aperture of infinite size can achieve the ideal gain-area product (GAP) value of 41,253 square degrees. This paper develops the maximum achievable GAP for finite apertures. We start with the one- dimensional case to find the best line-source distribution to maximize the minimum gain over a specified angular beamwidth. This result can then used with separable distributions to provide an optimal gain over a rectangular area. The approach is then extended to a circular beam shape. Coverage of these simple shapes offer useful bounding results on achievable gain as well as the onset of diminishing returns in gain with increasing reflector size. In all cases the maximum available GAP is shown to be a function of the beamwidth times the aperture diameter in wavelengths. The results provide a useful tool to select antenna size for particular applications.