SECTION 6 TRANSMITTING ANTENNA 6. 1 APERTURE ILLUMINATION AND SIZE The optimum transmitter aperture distribution is one that places the most power within the angle subtended by the receiving antenna. Beam efficiency is defined as the fraction of power radiated into a cone with half angle 9, for , where is the normalized transmitting antenna radius, X is the wavelength, and is the angle through which the power is radiated. The beam efficiency is given by where is the aperture illumination over a circular aperture of radius a, and p and are circular coordinates. The optimum illumination is the that maximizes . This function is known as a hyper spheroidal or generalized prolate wave function and satisfies the integral equation The maximum value of r is , where is the asso- dated equation. Figure 6-1 is a plot of beam efficiency. Figure 6-2 is a plot of beamwidth and first sidelobe level.
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