In the present paper, an iterative technique devoted to reproducing efficient footprints with arbitrary boundaries for planar arrays is addressed. The methodology here depicted is based on exploiting the nature of the continuous aperture distribution by expressing it as a Fourier series of moderately high orders. In this manner, the resulting illumination boundary is defined by a target three-dimensional flat-topped pattern composed of stretching and shrinking modified circular Taylor patterns and the maximum order of the series to obtain a good reconstruction is determined by means of the iterative process. Examples and comparisons with the previous literature were conducted by analyzing square and rectangular contoured beams as test cases. Additionally, interesting potentials regarding space applications from a geostationary satellite are outlined by means of the EuTELSAT (European Telecommunications Satellite Organization) European coverage case study. In such a way, its numerical approach was analyzed by including subarray architectures and discussing improvements about dynamic range ratio of the excitations without critical power losses within the illumination region.
Despite playing a central role in antenna design, aperture efficiency is often disregarded. Consequently, the present study shows that maximizing the aperture efficiency reduces the required number of radiating elements, which leads to cheaper antennas with more directivity. For this, it is considered that the boundary of the antenna aperture has to be inversely proportional to the half-power beamwidth of the desired footprint for each ϕ-cut. As an example of application, it has been considered the rectangular footprint, for which a mathematical expression was deduced to calculate the aperture efficiency in terms of the beamwidth, synthesizing a rectangular footprint of a 2:1 aspect ratio by starting from a pure real flat-topped beam pattern. In addition, a more realistic pattern was studied, the asymmetric coverage defined by the European Telecommunications Satellite Organization, including the numerical computation of the contour of the resulting antenna and its aperture efficiency.
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