where the variables are defined above. The subscript "ideal" should not be taken too literally. The beam intensity at the center of the rectenna (r = 0) is 28/37 Io ~ 0.757 Io. This is nearly identical for the peak beam intensity for the n = 2 case, which is 3/4 Io. Suddath derives the transmitted power intensity function which yields this beam pattern. It is given in non-dimensionalized units by: If this is dimensionalized, it becomes: Equation 1 (with n = 1, 2, 3, and 4) and Equation 4 are plotted in Figure 1 for P, = 5 gigawatts. Equations 2 and 3 are plotted in Figure 2 for these same cases and power level, for a geostationary SPS beaming power to a rectenna at the equator. The axis calibrations without brackets in Figure 2 refer to the 2.45 GHz frequency, while the calibrations in brackets refer to the 9.8 GHz (= 4 x 2.45 GHz) frequency. Note that distance scales as the inverse of frequency. This follows from the definition of r since a fourfold decrease in A requires a fourfold decrease in r to maintain the same value of r. In addition, intensity scales as the square of the frequency. This follows from the definition of Io given above. The 2.45 GHz frequency is taken from the NASA/US Department of Energy reference design [4]. The 9.8 GHz frequency is used to show the effect of frequency scaling on the beam pattern and sidelobe levels. The author and M. Kadiramangalamhave determined that 9.8 GHz is a frequency worth considering for SPS use. It allows for a simple fourfold scaling, without crossing into a frequency regime that is vulnerable to rain and air attenuation. The intensity pattern at the transmitting antenna is unaffected by frequency, since A is not present in Equations la and 4. The tapers for various values of n, as well as the "ideal" taper will be further examined, and their suitability for SPS microwave power transmission will be assessed.
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