For n > 1, the intensity is thus 0 at the edge of the transmitting antenna (p = po), and is at its peak at the center of the antenna (p = 0). This peak is proportional to n. lliis may set a limit on the degree of tapering allowable, since excess power at the center may overheat the antenna. The dimensionalized intensity at the rectenna can also be found by integrating over all two dimensional space and setting the result equal to Pt (assuming no atmospheric losses). It is given by: The variables used here are defined as follows: Io = peak intensity of untapered beam at rectenna = A = wavelength h = altitude (typically geostationary, 35,786 km) Pt, Dt are the same as before r = non-dimensionalized distance from center of beam pattern at rectenna r = dimensionalized distance from center of beam pattern at rectenna. These definitions are consistent with References 1, 2, and 3. The peak intensity of a tapered beam can be found by letting r approach 0 in Equation 2, giving In(0) = Io (2n-l)/n2. For n large, I„(0) ~ 2Vn. Thus, the peak beam intensity decreases with increasing n. In order to conserve energy, the beam must therefore become broader. The case where n = 1 represents an untapered beam. For this case, Equation lb becomes Hn(p) = <Hav> = Pt/A, for all p. Equation 2 becomes:
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