As expected, Fgood(°) = 0 and FgOod(°°)= 1Note that the expression for Pt in Equation 38 contains an integral which is equal to SgOod(°°) or 74/7. Thus, Equation 38 can be rearranged to give: The main lobe of Igood(u) *s similar in amplitude and shape to 12(0), but the sidelobe structure is different (see Reference 5). Equations 37, 56, and 2b can be combined to give: where the factor of n/2 has been suppressed in the argument of the function Ig00d(F). Results of Integration of Beam Intensity Figure 1 shows beam the beam intensity functions In (with n = 1, 2, 3, and 4, from Equation 36) and Igood’ plotted as a function of dimensionless distance from the center of the beamF, and normalized to the peak intensity of the n = 1 case. Note that the main beam lobe broadens with increasing transmitted taper; the transmitting antenna gain thus decreases with increasing transmitted taper. The n = 2 and "good" cases have similar main lobe intensities, although their sidelobe structures differ. For the purpose of wireless power transmission, a certain degree of tapering is desirable, since the sidelobes are reduced and the power in the main lobe is distributed more evenly. A transmitted beam that is too sharply tapered may not be desirable, since the received main lobe will become too spread out and dilute. Reference 5 discusses beam tapering issues in detail. Figure 2 shows the fraction of power enclosed within a given dimensionless distance from the center of the microwave beam. The curves were obtained by plotting Fn(a) (equation 33, with n = 1, 2, 3, and 4) and Fg00(i(a) (equation 55) parametrically
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