To achieve full collection of the main power beam requires a value of U* approximately equal to 3.7 (producing an 87% collection efficiency for an ideal, error-free uniform antenna). Fundamental beam characteristics (beamwidth, average intensity, distribution of sidelobes) are determined primarily by the U* argument. Its mathematical form (Eq. 1) indicates a beam spreading effect with increases in wavelegnth (X) or transmission distance (/?„), and a beam concentrating, enhanced collection effect with increases in antenna and rectanna radii (R, and rK). Finer structuring of the microwave power beam is determined by the specific taper shape used. Collection efficiency curves for both uniform and optimal tapers for the case of satellite-space station power transmission are given in Fig. 10. The uniform taper produces maximum power densities along the antenna boresight and gives the best efficiency performance up to 70-80%. The optimal taper provides lower peak intensities but a wider, flatter and more power intensive mainbeam, giving superior high efficiency performance. In the following discussion of alternative configurations for microwave systems, use of the optimal taper for high efficiency is assumed. SIZING TRADEOFFS The performance capalities of power transmission systems are limited by certain geometrical constraints of the microwave beam. The efficiency requirement to maintain the beam parameter 2tt Rt rR/XR0 = 3.7 has already been mentioned. Using a 20 m diameter antenna, 30 m rectenna, and a frequency of 5.8 GHz (X = .0517 m), the effective transmission range (/?„) is about 5 km. Increased range is possible only
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