Fig. 1. Arrangement of transmitting and receiving antennas. That is to say, the cost per unit area to erect the space transmitter is very much more than that to construct the ground receiver (including the land). Likewise, the cost of the assembled ground antenna is very much more than the cost of the raw acreage for the fence. An analysis (3) has been carried out which includes both coefficient ratios; however, with reasonable estimates for a0, «i, and aF, the absolute cost is affected only to the extent of 1 or 2% if aFla^ is disregarded in comparison to ai/u0- Thus, in the exposition below, we will neglect aFla0 in the optimization process. However, RF can be obtained from sidelobe considerations alone and so the approximate effect on the cost, C, may be calculated. It is planned, however, that a future publication will be made including aF (and some other constraints). Most of the essential features are exhibited in this simpler formulation and, as already mentioned, very manageable formulas are obtained that put the designer in the right ballpark without the necessity of a more detailed study. 3. THEORETICAL ANALYSIS Problem statement and initial equations Our problem may be stated quite simply: Consider that we have two antennas located as shown in Figure 1. Here, z represents the distance separating the planes of the antennas — in our work it will be the geosynchronous distance. We let Wo be the total power collected by the receiver and we assume that this is a given constant. If Wi is the total amount of power transmitted, we specify that the ratio /3 = Wo/Wj is known, i.e., we wish to collect a specified fraction of the power transmitted. All the power transmitted is assumed to be collected for an infinite value of Ro — losses through the atmosphere may be taken into account by increasing Wj in proportion. The wavelength, X, of the microwaves is also known. Furthermore, the power den-
RkJQdWJsaXNoZXIy MTU5NjU0Mg==