simplifies the antenna design at the cost of decreased collection efficiency at the rectenna. The steps are quantized in equal power increments according to the relationship (ref. 1), The collection efficiencies for the 5, 8, and 10 step quantizations are compared to the continuous distribution in Figure IV.A.2-9. There are only small differences between the collection efficiencies of these three step approximations, which is in contrast to previous results (ref. 1). However, since the revenue return over the 30-year lifetime of the SPS is $524 X 10° per 1% collection efficiency (based upon a charge rate of 40 mils per kilowatt-hour), the model configuration will have a 10 step approximation. The 10 step function gives about 1% greater efficiency than the 5 step and the extra $524 X 10° revenue justifies the slightly greater complexity of the antenna. The configuration of the 10 step taper is shown below in Figure IV.A.2-10. The amount of power radiated per subarray is lowered progressively outward from the center of the total array by reducing the number of klystrons per subarray. There is a maximum of 42 klystrons/subarray at the center of the array and a minimum of 6 klystrons/subarray at the edge. A diagram of the normalized power density at the array as a function of radius is shown in Figure IV.A.2-11. There are equal power increments between each step except at the center and end of the array. This is the configuration used in the design of the DC power distribution for the antenna. IV.A.2(g) SUBARRAY SIZE TRADEOFFS The 1 km transmit array is composed of smaller subarrays, each phased together with a feedback reference signal from the ground. Each subarray can be considered an individual antenna, the gain and beamwidth of which is determined by its size. The previous work (ref. 1) used an 18m X 18m subarray. However, the 18m X 18m subarray had such a narrow beamwidth that active positioning devices, i.e., motor-driven screwjacks, were needed in order to mechanically compensate for small misalignments in the antenna. These misalignments were caused by thermal warping of the antenna, tilting of the individual subarrays, etc. Smaller subarrays have the advantage of wider beamwidths, and hence, reduced mechanical alignment requirements. However, the phase control costs increase since each subarray has its own receiver and phasing electronics.
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