The resulting grating lobe peak power density is the main beam maximum density (all elements in phase) reduced by the subarray field term squared and can be written using Eq. 23 as For the SPS reference system parameters (1 km antenna, 10 dB Gaussian taper, Lx = 10.43 m, Ro = 36,000 km, Pden(ant) = 23 kW/m2), the peak power density for the first X-axis grating lobe is 0.0158 mW/cm2 for one arc-min antenna tilt and 0.1424 mW/cm2 for 3 arc-min tilt. These peaks are virtually unchanged when power amplifier failures, amplitude and phase errors, and subarray misalignments are included. Summarizing, the on-axis grating lobe intensities increase as the antenna tilt angle squared. On the 45° axis, Xg = Yg, and the normalized subarray pattern can be written for a square subarray as An antenna tilt in the 0r = 45° direction shifts the subarray pattern by Zotan </>T/ V 2 in the X and T directions. Assuming small tilt angles, the grating lobe peak power density along the = 45° axis is Since 0T is very small (on the order of a few arc-minutes or less), fourth power scaling means the 45° axis grating lobes are much lower than the axial lobes. For the SPS reference system, the first 45° grating lobe occurs at Xg = Yg = 423 km with a peak
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