Gain and beamwidth of a uniformly excited circular aperture
A tapered amplitude distribution excited has its gain lowered by the Amplitude Taper Loss (dB). Examples: TE11 mode horn 0.77 dB, Resonant mode corrugated horn 1.60 dB, Truncated Gaussian distribution (-12 dB) 0.60 dB with other distribution values found in text books. To achieve a desired gain, the aperture radius is increased by the square root of the amplitude taper efficiency 10ATR/20. The beamwidth is increased by the HPBW factor. Examples: TE11 mode horn 1.616 E-plane (S=0) and 2.038 H-plane (S=0), Resonant mode corrugated horn 2.078 (S=0), Truncated Gaussian distribution (-12 dB) 1.14 (67° to 70° for parabolic reflector) with other distribution values found in text books.
