A pattern synthesis procedure is developed for a planar aperture with a circular boundary. A (Ø-symmetric continuous distribution is assumed and required to produce a flat-topped beam with controlled ripple, surrounded by ring side lobes of controlled height. With M filled-in nulls in the shaped region, there are 2M solutions for the aperture distribution. Sampling can yield the excitation of a circular grid planar array. Linear stretching extends the results to an elliptical boundary.
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Elliott et al. (1988) studied this question.
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