Estimating aperture efficiency

It is shown that for a wide class of aperture distributions, the aperture efficiency can be related to the ratio between the beamwidth of this distribution and that of the uniform one. A heuristic rule for estimating the aperture efficiency of elliptic and rectangular tapered apertures is introduced. It is shown that, if the beamwidth is given (i.e., the aperture size is unconstrained), the maximum directivity is provided by a tapered, rather than uniform amplitude distribution.