Page 192 - Satellite Communications, Fourth Edition

172 Chapter Six

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 atten-
uation, 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 result-
ing from the rainfall is calculated as shown in Sec. 4.4, and the reflec-
tor 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 cru-
cial 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 dif-
fering 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 (6.36)
l