For a given beam pattern, the maximum power unit area allowed, (PIA)h gives a relationship between grid power P and receiver area ARCV, namely; Equations (1) or (2), (3) and (4) provide three equations for the solution of the four variables C or M, PG, AT and ARCV. One more relation is needed. Two common ways of providing this are equations (5) or (6) below. Equation (5) is a transmitting antenna area to power scaling law based on a thermal limit, while equation (6) is a cost minimization condition. Photovoltaic Satellite Link Power Limited at Both Ends: Some results from the use of this equation are: PG = 5.2 x 109 w, 1.4 x 106 w and 1.1 x 106 w for the photovoltaic satellites from Table 2 using klystrons, free electron lasers, and electric discharge lasers, respectively. This is also in general the current rationale for sizing microwave power satellites. The result is not a global optimum because there is always better utilization of transmitting and receiving apertures if more power can be passed through them. For a microwave power transmission power satellite development program it may be desirable to minimize the combined purchase cost of the first satellite and rectenna while retaining the peak ionospheric power/area by increasing aperture area and relaxing transmitting array power/area. This yields a minimum purchase cost for the system as, given below. It is not, and should not be mistaken for, a minimum cost per unit delivered power optimum. For a photovoltaic power satellite using microwave klystrons with system parameters for Tables 1 and 2, the above equation gives PG = 2.52 x 10“9 w. The result is not applicable to laser link photovoltaic satellite system. Because transmitting aperture area for laser systems is so costly, purchase-cost-minimized laser systems exceed link-power-limited systems by a factor of ten for Gaussian optics. Although by choosing a different aperture power distribution this discrepancy could be rectified, it also illustrates that purchase cost minimization is hardly significant for laser power transmission power satellites. Three additional caveats apply to these simple sizing relations. The first of these is that G in the antenna link relation is fixed and the dimensions of the transmitting antenna are only scaled. In a real-world situation, what will probably happen is that the power company, which is the satellite customer, will decide what power they would like and where the receiving site should be. The antenna pattern, which is what determines G, r)B, (Avg/Pk)r and (Avg/Pk)RCF, will then be chosen to give lowest cost. Thus, the simple scaled pattern power optimizations done here are only
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