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Conventional Approach
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Conus beam example: 56 feed horns 84 pounds 1.0 dB loss
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Single feed example: 14 pounds 0.3 dB loss
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Figure 6.25 Shaped-beam reflector, showing ray paths. (Courtesy of Hughes Space and Communications Company. Reproduced from Vectors XXXV(3):14, 1993. Hughes Aircraft Co.)
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until the model produces the desired coverage. On a first pass the computer analyzes the perturbations and translates these into surface ripples. The beam footprint computed for the rippled surface is compared with the coverage area. The perturbation analysis is refined and the passes are repeated until a satisfactory match is obtained. As
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an example of the improvements obtained, the conventional approach to producing a CONUS beam requires 56 feed horns, and the feed weighs 84 pounds and has a 1-dB loss. With a shaped reflector, a single-feed horn is used, and it weighs 14 pounds and has 0.3-dB loss (see Vectors, 1993). Shaped reflectors also have been used to compensate for rainfall attenuation, and this has particular application in direct broadcast satellite (DBS) systems (see Chap. 16). In this case, the reflector design is based on a map similar to that shown in Fig. 16.8, which gives the rainfall intensity as a function of latitude and longitude. The attenuation resulting from the rainfall is calculated as shown in Sec. 4.4, and the reflector is shaped to redistribute the radiated power to match, within practical limits, the attenuation. 6.17 Arrays Beam shaping can be achieved by using an array of basic elements. The elements are arranged so that their radiation patterns provide mutual reinforcement in certain directions and cancellation in others. Although most arrays used in satellite communications are two-dimensional horn arrays, the principle is most easily explained with reference to an in-line array of dipoles (Fig. 6.26a and b). As shown previously (Fig. 6.8), the radiation pattern for a single dipole in the xy plane is circular, and it is this aspect of the radiation pattern that is altered by the array configuration. Two factors contribute to this: the difference in distance from each element to some point in the far field and the difference in the current feed to each element. For the coordinate system shown in Fig. 6.26b, the xy plane, the difference in distance is given by s cos . Although this distance is small compared with the range between the array and point P, it plays a crucial role in determining the phase relationships between the radiation from each element. It should be kept in mind that at any point in the far field the array appears as a point source, the situation being as sketched in Fig. 6.26c. For this analysis, the point P is taken to lie in the xy plane. Since a distance of one wavelength corresponds to a phase difference of 2 , the phase lead of element n relative to n 1 resulting from the difference in distance is (2 /l)scos . To illustrate the array principles, it will be assumed that each element is fed by currents of equal magnitude but differing in phase progressively by some angle . Positive values of mean a phase lead and negative values a phase lag. The total phase lead of element n relative to n 1 is therefore 2 s cos l (6.36)
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y s s cos
Array
An in-line array of dipoles.
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(Imaginary) j
ER E E 0
Figure 6.27 Phasor diagram for the in(Real) line array of dipoles.
The Argand diagram for the phasors is shown in Fig. 6.27. The magnitude of the resultant phasor can be found by first resolving the individual phasors into horizontal (real axis) and vertical (imaginary axis) components, adding these, and finding the resultant. The contribution from the first element is E, and from the second element, E cos jE sin . The third element contributes E cos 2 jE sin 2 , and in general the Nth element contributes E cos(N 1) jE sin(N 1) . These contributions can be added to get: ER E
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