for our final nondimensional form. Thus, in normalized form, the optimum distribution function only depends on the power ratio = WofWi since X is also a function of p. In order to compare these optimum distribution functions with those of the truncated Gaussian, etc., it is of interest to compute the taper ratio of our transmitter. By definition, the taper ratio in db is given by j=i <=i The taper ratio is seen to depend only on the fraction /3 of power collected. It thus is a result of our calculations and is not normally specified in advance. Distribution function of the ground antenna A very simple relationship exists between the optimum power distribution function of the transmitter pfr) and the resulting power distribution of the receiver po(p)t This relationship is of considerable importance in numerical work so it is set forth here but in the interests of brevity, inasmuch as it is not directly required for the optimization process, we will merely outline how the results are obtained. By using equation (41) for u(r) and eliminating the X/s by means of equation (28) and further replacing a0/XWi by its equal 1//3, we arrive at an alternate expression for u(r). When we replace the summation in this expression with an integral by passing to the limit, the result is tThis was first noticed by Dr. R. Kopp of Grumman Research who analyzed this problem from an integral equation point of view. Let us compute the value of the distribution function at the center of the transmitter where
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