OPTIMIZATION OF ANTENNA PAIRS FOR MICROWAVE POWER TRANSMISSION CHARLES E. MACK JR. and H. GARDNER MOYER Research Department Grumman Aerospace Corporation Bethpage, New York 11714 and Software Systems Department Grumman Aerospace Corporation Calverton, New York 11933 0191-9067/80/030221-20S02.00/0 Copyright 0 1980 SUNS AT Energy Council Abstract — The optimum transmitting distribution function is determined for an antenna beaming microwave power from space to a ground receiver. This is accomplished by minimizing a chosen cost function for the system using the methods of optimal control theory. It is the reverse of the usual methods of analysis wherein the distribution function is specified in advance. The distribution function calculated by the procedure developed here is the square of a finite linear sum of zero-order Bessel functions, each of which is multiplied by a constant. Very simple one-term formulas result from the analyses for the radii of the two antennas and for the minimum cost itself. For any given problem, the requisite computer runs are carried out once and for all and are only a few minutes in duration. What makes the method especially attractive is that the main results are simply a function of the ratio of the power collected to that transmitted. The optimum distribution function determined is compared to a typical Gaussian distribution. The antenna radii and relative costs for both systems are also compared. The method is applicable to any antenna pair transmitting microwave power and to any more general cost or penalty function than that used here, provided it is a monotonically increasing function of the parameters. 1. INTRODUCTION Ever since the idea of microwave transmission of power from space to a ground station was first proposed by Glaser (1) in 1968, a great many possible power distribution functions for the transmitter have been examined in considerable detail. Among others, truncated Gaussians of differing taper ratios, polynomials of assorted types, certain trigonometric functions, and various nonelementary distributions have been investigated. The overall aim is to select a distribution function that, for a given amount of power to be collected, will result in a transmitting and receiving antenna system that will be practical in the sense of being cost effective. Various environmental criteria must, of course, be met such as, for example, the power density at the center of the receiver is not to exceed a specified value so the atmosphere through which the radiation passes will not be damaged. Furthermore, each distribution function has its own characteristic pattern of sidelobes on the ground. It is important that these sidelobes decrease in such a manner that beyond a certain radius outside the receiver — the so-called fence radius — the power density will meet the predetermined low level environmental constraints. These constraints are themselves to be ascertained from consideration of the long term biological effects of the residual microwave power on people, animals, and plants.
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