Choice of a Tapered Beam As the amplitude taper of a transmitted microwave beam is increased, the sidelobe power density decreases, the percent of the power in the main lobe increases, and the main lobe becomes broader. The former two tendencies are desirable for SPS use. The latter tendency is desirable to some extent, since a lower peak beam intensity is environmentally safer. However, if the rectenna is approximately the same size as the main lobe, a larger rectenna will be necessary for increased tapers. This may be acceptable if a substantial reduction in the size of the exclusion zone is achieved. However, an excessively large rectenna may be expensive, disruptive to the environment, and may even extend past the exclusion boundary, thus partially defeating the purpose of beam tapering. Skolnik [5] presents a family of beam tapers which illustrates these tradeoffs, and may allow for improvements over untapered beam transmission. If r is the radial distance from the center of a circular transmitting antenna of radius ro, then the aperture distributions to be considered are of the form [ 1 - (p/po)2](nl), where n = 1, 2, 3, ... . Note that n = 1 refers to an untapered beam. This yields a radiation intensity pattern of the form: where Jn(u) is the n-th order Bessel function of the first kind and u is a non-dimen- sionalized distance from the center of the radiation pattern at the rectenna. Appropriate normalization constants for these intcnsitiescan be found by integrating these expressions over all two-dimensional space and setting the result equal to Pt, the total power transmitted. It will be assumed that the total power transmitted is equal to the total power received. The power intensity at the transmitting antenna is thus where D, = 2po = diameter of transmitting antenna. Thus, A, = area of transmitting antenna = trpo2 = TrDt2/4. The average intensity at the transmitting antenna is thus <Hav> = P,/A, = 4Pt/(7rDt2). The normalized intensity at the transmitting antenna is thus
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