In(0) in Equation 1 can be replaced by an expression involving Pt once the integral in Equation 4 is solved. Fraction of Power Received In order to detennine the size of a rectenna, the percent of the total power within a given radius must be determined. Although the power distribution is theoretically infinite in extent, most of the energy is concentrated in the main beam lobe. The outer region of this lobe may, like the sidelobes, contain power that is too dilute to rectify economically. For space applications, it may pay to capture a relatively small percentage of the total power, since size and weight are critical issues in spacecraft design, and a large rectenna in space may not be practical. It is thus important to find an expression for the fraction of power contained within a given radius at the rectenna site. A numerical solution for the power contained within a given radius may result in impractically long running times on a personal computer; therefore, an analytical solution may be valuable. If Fn(a) is the fraction of power contained within radius a, then It is therefore necessary to integrate Sn(a). This can be done by parts in a manner analogous to the untapered (n = 1) case in Reference [10] pages 397-398. Reference [11], page 177 gives the following relationships between Bessel functions:
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