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6.15.1 Cassegrain antenna
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The basic Cassegrain form consists of a main paraboloid and a subreflector, which is a hyperboloid (see App. B). The subreflector has two
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Figure 6.22 A 19-m Cassegrain antenna. (Courtesy of TIW Systems, Inc.)
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focal points, one of which is made to coincide with that of the main reflector and the other with the phase center of the feed horn, as shown in Fig. 6.23a. The Cassegrain system is equivalent to a single paraboloidal reflector of focal length fe eh eh 1 1 f (6.35)
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Main reflector (paraboloid)
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Subreflector (hyperboloid) S2 S1
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Main reflector (paraboloid)
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Figure 6.23 Ray paths for (a) Cassegrain antenna. (b) Gregorian antenna. (b)
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Antennas
where eh is the eccentricity of the hyperboloid (see App. B) and f is the focal length of the main reflector. The eccentricity of the hyperboloid is always greater than unity and typically ranges from about 1.4 to 3. The equivalent focal length, therefore, is greater than the focal length of the main reflector. The diameter of the equivalent paraboloid is the same as that of the main reflector, and hence the f/D ratio is increased. As shown in Fig. 6.18, a large f/D ratio leads to more uniform illumination, and in the case of the Cassegrain, this is achieved without the spillover associated with the single-reflector system. The larger f/D ratio also results in lower cross-polarization (Miya, 1981). The Cassegrain system is widely used in large earth-station installations.
6.15.2 Gregorian antenna
The basic Gregorian form consists of a main paraboloid and a subreflector, which is an ellipsoid (see App. B). As with the hyperboloid, the subreflector has two focal points, one of which is made to coincide with that of the main reflector and the other with the phase center of the feed horn, as shown in Fig. 6.23b. The performance of the Gregorian system is similar in many respects to the Cassegrain. An offset Gregorian antenna is illustrated in Fig. 6.24.
6.16 Shaped Re ector Systems With the double-reflector systems described, the illumination efficiency of the main reflector can be increased while avoiding the problem of increased spillover by shaping the surfaces of the subreflector and main reflector. With the Cassegrain system, for example, altering the curvature of the center section of the subreflector to be greater than that of the hyperboloid allows it to reflect more energy toward the edge of the main reflector, which makes the amplitude distribution more uniform. At the same time, the curvature of the center section of the main reflector is made smaller than that required for the paraboloid. This compensates for the reduced path length so that the constant phase condition across the aperture is maintained. The edge of the subreflector surface is shaped in a manner to reduce spillover, and of course, the overall design must take into account the radiation pattern of the primary feed. The process, referred to as reflector shaping, employs computer-aided design methods. Further details will be found in Miya (1981) and Rusch (1992). With the Hughes shaped reflector (Fig. 6.25), dimples and/or ripples are created on the surface. The depth of these is no more than a wavelength, which makes them rather difficult to see, especially at the Ka band. Reflections from the uneven surface reinforce radiation in some
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Figure 6.24 Offset Gregorian antenna. (Courtesy of Radio Electr. Eng., vol. 54, No. 3, Mar. 1984, p. 112.)
directions and reduce it in others. The design steps start with a map of the ground coverage area desired. A grid is overlaid on the map, and at each grid intersection a weighting factor is assigned which corresponds to the antenna gain desired in that direction. The intersection points on the coverage area also can be defined by the azimuth and elevation angles required at the ground stations, which enables the beam contour to be determined. The beam-shaping stage starts by selecting a smooth parabolic reflector that forms an elliptical beam encompassing the coverage area. The reflector surface is computer modeled as a series of mathematical functions that are changed or perturbed
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