CHOICE OF A DISTRIBUTION FUNCTION Various aperture distribution functions have been used in the course of SPS system studies. The klystron reference system uses a -10 dB truncated Gaussian taper, while modifications have recently been suggested (5, 6) in which polynomial functions are used, the several coefficients being chosen according to some optimization procedure. The magnetron-powered reference system (3), makes use of a relatively new distribution function devised by Hansen (7) that has only one parameter, called h, which controls the taper and uniquely determines sidelobe levels and all other pertinent characteristics of the radiation pattern. Use of this distribution function is ideally suited to the needs of this study since, as will be seen, the cost function becomes dependent only on two variables, one being the parameter h, the other the rectenna intercept level. As a side benefit, closed form expressions exist, as functions of h, for all quantities which enter into the cost function. The Hansen distribution is given by If represents the value of u (i.e., 0) at the edge of the rectenna then it has been shown that (3) The edge taper for the Hansen illumination is given by
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