where Z is the distance between the transmitter and receiver. For example, with an rms phase error of 10° on the transmitter, a wavelength of 0.122 meters (2.45 GHz), 18 meter subarrays, and 2400 subarrays (1 km circular transmitter), the rms beam displacement would be about 10 meters. Since the receiver in a microwave power transmission system would be on the order of 8 km in diameter (references 5-8), such a beam displacement would be insignificant. Further, since the pointing error has a Gaussion distribution (reference 20), the 99.99% confidence limits on beam displacement for the above conditions would be 37 meters, again a relatively insignificant displacement. Since the transmitter size and number of subarrays are fixed by other conditions (references 5-8), one concludes that beam pointing errors in an MPTS would be insignificant provided the transmitter rms phase error is less than 10°. CONCLUSIONS Closed form relations can be developed which allow quick determination of statistics of key parameters of space-to-earth microwave power transmission systems. Relations are provided for the mean power pattern at the receiver, the variance of this pattern and variance of the beam pointing. For 10° rms phase error and 10% amplitude error on the transmitter the peak power density at the receiver would be degraded by only 3%. For the same conditions, the first sidelobe level is within 1.5 db of the zero error pattern with a confidence of 99.99%. The rms pointing error would be no more than 10 meters and the peak displacement would be less than 37 meters with a confidence of 99.99%.
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