geous. For the 1.0 mW/cm2 case (Figure 6), beam tapering is advantageous at the higher frequencies (roughly 7 to 15 GHz), but not the lower frequencies; furthermore, all of the tapers considered have roughly equal exclusion zone radii. In Figures 7 and 8 (5 and 10 mW/cm2, respectively), it is seen that beam tapering may actually be a disadvantage, at least at the lower frequencies. These latter two cases represent exclusion zone boundaries that are within the main lobe, since tapering the beam broadens the main lobe (see Figure 9). The n = 2 case may represent the best overall taper, since, compared with the other tapers, it causes the least increase in peak intensity at the transmitting antenna (Figure 1), while allowing for some reduction in peak beam intensity at the rectenna (Figure 2 and Table 1), without unduly broadening the rectenna (Figure 2 and Table 1). In addition, it provides roughly the same exclusion zone reduction as the "higher" tapers (Figures 4, 5, and 6). The "ideal" taper is quite similar to the n = 2 case, but its peak transmitted power is somewhat higher. However, since the aperture illumination function for these two cases is different (Figure 1), a heat transfer analysis of the transmitting antenna is needed to provide a more complete comparison. Effect of Beam Tapering on the SPS System The size of the exclusion zone of an untapered beam is not very sensitive to frequency (Equation 11b and Reference 2). In addition, the peak beam intensity at the rectenna varies as the square of the frequency. An m-fold increase in frequency will allow for an m2-fold decrease in the area of a given part of the beam pattern (such as the main lobe or 83.8% capture region), but only an m2/3-fold decrease in exclusion zone area. If the m2 increase in intensity is compensated for by an m2 decrease in Pt, then m2 times as many SPS units will be needed. 'Hiere will be no net change in the total area of the either the main lobes or the exclusion zones. However, the use of a tapered transmission beam may make frequency scaling more feasible. It was seen earlier that the peak intensity at the transmitting antenna is proportional to n, while the peak beam intensity at the rectenna is proportional to (2n-l)/n2. Furthermore, for an m-fold increase in frequency, the peak beam intensity at the rectenna is proportional to m2, while the peak intensity at the transmitting antenna is unchanged. A goal can be set to hold the peak beam intensity at the rectenna to the same level as in the untapered 2.45 GHz case, while not letting the peak intensity at the transmitting antenna increase beyond that case. This can be accomplished by increasing the frequency by a factor of m, using the n-th taper, and decreasing P, by a factor of N, where N is the factor of increase in the total number of SPS units needed. Since the peak beam intensity at the rectenna is proportional to
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