These grating lobes are regularly spaced and coincide with the subarray pattern nulls of a single beam antenna. Multiplication of the array pattern and subarray pattern enhances the main beam and greatly attenuates the grating lobes as shown in Fig. 2. For multiple beams, the array peaks occur at each beam location and at the grating lobes of each beam. The main beam peaks no longer coincide with the maximum of the subarray pattern as given in Fig. 3. This misalignment results in a slight degradation in the main beam magnitude and, hence, a small efficiency loss, and in an increase in the grating lobe peaks. For example, if rectenna sites are located ±75 km from the antenna boresight, the subarray pattern, as given by Eq. 9, predicts a decrease in electric field intensity of 0.84% using 4.2 m subarrays and 7.5% with 12.6 m subarrays (Xg = ± 75 km, Y„ = 0). The corresponding rectenna collection efficiencies (where rectenna collection efficiency is the percentage of power transmitted by the satellite antenna which is incident upon the rectenna) are 94.2% and 82.1% for the 4.2 m and 12.6 m subarrays, respectively. A limitation is imposed upon the maximum separation of rectenna sites because of these degradations in collection efficiencies. The allowable separation are determined by subarray (or power module) size as discussed in the next section. The SPS grating lobes are environmentally constrained to a 0.01 mW/cm2 power density limit. In order to meet this constraint, the single beam reference satellite had an allowable antenna tilt of one arcminute for phase control to the subarray level and
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