Page 182 - Satellite Communications, Fourth Edition

162 Chapter Six

and containing the directrix (see App. B). Although the characteristics of
the reflector antenna are more readily described in terms of radiation, it
should be kept in mind that the reciprocity theorem makes these appli-
cable to the receiving mode as well.
Now although there are near- and far-field components present in the
reflector region, the radio link is made through the far-field component,
and only this need be considered. For this, the reflected wave is a plane
wave, while the wave originating from the isotropic source and striking
the reflector has a spherical wavefront. The power density in the plane
wave is independent of distance. However, for the spherical wave reach-
ing the reflector from the source, the power density of the far-field com-
ponent decreases in inverse proportion to the distance squared, and
therefore, the illumination at the edge of the reflector will be less than
that at the vertex. This gives rise to a nonuniform amplitude distribu-
tion across the aperture plane, which in effect means that the illumi-
nation efficiency is reduced. Denoting the focal distance by and the
focal length by f as in Fig. 6.17b, then, as shown in App. B,
2
sec (6.27)
f 2

The space attenuation function (SAF) is the ratio of the power reach-
ing point P to that reaching point A, and since the power density
is inversely proportional to the square of the distance, the ratio is given by
f 2
SAF a b

(6.28)
4
cos
2
For satellite applications, a high illumination efficiency is desirable.
This requires that the radiation pattern of the primary antenna, which
is situated at the focus and which illuminates the reflector, should approx-
imate as closely as practical the inverse of the space attenuation factor.
An important ratio is that of aperture diameter to focal length.
Denoting the diameter by D, then, as shown in App. B,

f 0
0.25 cot (6.29)
D 2
The position of the focus in relation to the reflector for various values
of f/D is shown in Fig. 6.18. For f/D 0.25, the primary antenna lies in
the space between the reflector and the aperture plane, and the illumi-
nation tapers away toward the edge of the reflector. For f/D 0.25, the
primary antenna lies outside the aperture plane, which results in more