Page 189 - Satellite Communications, Fourth Edition

Antennas 169

where e is the eccentricity of the hyperboloid (see App. B) and f is the
h
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 with-
out 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 subre-
flector, 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 Reflector 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 reflec-
tor is made smaller than that required for the paraboloid. This compen-
sates 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 wave-
length, which makes them rather difficult to see, especially at the Ka
band. Reflections from the uneven surface reinforce radiation in some