as a function of r , where a = n r /2. The fraction of power received can be thought of as reception efficiency and F can be thought of as the powerlink parameter DtDr/(Xh) discussed in Reference 2. The curves in this figure are the integrals of the functions shown in Figure 1 multiplied by the dimensionless distance, normalized so that the integral over all two-dimensional space is 1. The figure further illustrates the advantage of beam tapering. The n = 1 (untapered) case initially levels off at a lower level than the others, since its main lobe contains only 83.8% of the total energy, while the main lobe of the tapered cases contain between 98.2% and nearly 100% of the total energy. A moderate amount of beam tapering is thus advantageous. Figure 2 shows that the higher the degree of taper, the greater the distance it takes for the curve to level off, but the leveling off is at roughly the' same plateau. Thus, increasing the taper beyond n = 2 adds little more power to the main lobe and causes that lobe to spread out. Thus, higher tapers are desirable mainly in applications where sidelobe intensities must be kept very low. FIGURE 1. Microwave beam intensity (Infor n = 1, 2, 3, and 4, and I good) as a function of dimensionless distance from the center of the beam (x ), normalized to the peak intensity of the case where n = 1. The main lobes for the n = 2 and "good” cases are virtually indistinguishable at this scale. Conclusions Bom and Wolf [10] show that the intensity of energy projected from a uniformly illuminated circular aperture can be integrated analytically. A generalization of this work which includes tapered illumination patterns has been shown. Although only one family of beam tapers (out of a virtually limitless number of different types of
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