N can be found by setting this expression equal to 1. Thus, The increase in total main lobe area for the system, compared to the untapered 2.45 GHz case, can be found by multiplying N by the square of the relative position of the edge of the main lobe from Table 1 and then dividing by m2. Since the nr dependence drops out, frequency scaling will not affect the total main lobe area or total 83.8% capture area of the system; it will, however, affect the area of each individual main lobe (as per Equations Ila and lib), as well as the number of SPS units, and the power level of each. Thus, Relative total area of main lobes = (relative radius of individual main lobes for case n)2. Similarly, Relative total area for 83.8% capture (relative radius of individual 83.8% capture regions for case n)2. The change in total exclusion zone area will depend on the value of Is, as well as other parameters in Equations Ila and 11b. In addition, since these equations do not apply to regions near the main lobe, the change in total exclusion zone area must be computed numerically. The frequency will be increased from 2.45 GHz to 9.8 GHz, as mentioned earlier, so that m = 4. The effect of this frequency increase, combined with beam tapering, is shown in Table 3. Note that there is no net change in total main lobe area or sidelobe area if the frequency is increased without tapering the beam. Beam tapering is actually disadvantageous if the effect on the main lobe alone is considered; N times as many SPS units, each with 1/N as much power will have a greater total main lobe area for a tapered beam than for an untapered beam. This is due to the broadening of a tapered beam. The relative position of the individual main lobes increases with increasing n at a rate slightly faster than (2n-l)/n2 decreases. Thus, the relative total main lobe areas (compared to the untapered 2.45 GHz) will increase slowly with increasing n. As seen in Table 3, the relative total 83.8% capture areas are all about 54% smaller for a tapered beam, compared to an untapered beam. In addition, if the tapered beam patterns
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