Gain and beamwidth of a uniformly excited aperture

The uniformly excited aperture has high sidelobes that have a minor effect on gain.  This serves as a good first approximation to a high gain antenna.

A tapered amplitude excited aperture has its gain lower by the Amplitude Taper Loss (dB) for each taper distribution in both planes.  For example, a cosine distribution has ATL = 0.91 dB.  To achieve a desired gain, the aperture length has to be increased by the amplitude taper efficiency: 10ATR/10.   The beamwidth is increased by the HPBW factor.  The cosine distribution has a 1.342 HPBW factor.  Factors for other distributions can be found in text books.