Gain and beamwidth of a uniformly excited square aperture
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.
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