where In(u) has the dimensions of power per unit area and In(0) is the peak power density for case n. The parameter u is related to the dimensionalized radial distance r by where Dt is the diameter of the transmitting antenna array, X is the wavelength, and h is the distance between the transmitting antenna and the rectenna. Papers on wireless power transmission often use nF/2 instead of u in Equation 1; therefore If a rectenna is constructed whose radius is r, then its diameter will be given by Dr = 2r. Thus, Thus, r is equal to the expression in the brackets in Equation 2c, and is also equal to the powerlink parameter in Reference 2. Total Power Transmitted In order to choose an amplitude distribution appropriate for a given application, it is necessary to relate the peak power density In(0) to Pt, the total power transmitted. This can be found by using the following integral, where 0 is the azimuthal angle: Note that In(u) is azimuthally symmetric, so that the integral with respect to 0 yields 2n The integration variable must now be changed from r to u, using Equation 2a. This yields:
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