Page 171 - Satellite Communications, Fourth Edition

Antennas 151

the phase velocity of the radio wave along the wire is somewhat less than
the free-space velocity, the wavelength is also slightly less, and the
antenna is cut to about 95 percent of the free-space half-wavelength.
This tunes the antenna correctly to resonance. The main properties of
the half-wave dipole are:

Impedance: 73
Directivity: 1.64 (or 2.15 dB)
Effective aperture: 0.13 l 2
3-dB beamwidth: 78°

Assuming the antenna efficiency is unit ( 1), the power gain is
A
also 1.64, or 2.15 dB. This is the gain referred to an isotropic radiator.
As shown in Fig. 6.8b, the radiation is a maximum in the xy plane,
the normalized value being unity. The symmetry of the dipole means
that the radiation pattern in this plane is a circle of unit radius.
Symmetry also means that the pattern is the same for any plane con-
taining the dipole axis (the z axis). Thus the radiation pattern is a func-
tion of
only and is given by

2
cos a cos
b
2
g(
) (6.16)
2
sin
A plot of this function is shown in Fig. 6.8c. It is left as an exercise for
the student to show that the 3-dB beamwidth obtained from this pat-
tern is 78°.
When a satellite is launched, command and control signals must be
sent and received. In the launch phase, highly directional antennas are
not deployed, and a half-wave dipole, or one of its variants, is used to
maintain communications.

6.11 Aperture Antennas
The open end of a waveguide is an example of a simple aperture antenna.
It is capable of radiating energy being carried by the guide, and it can
receive energy from a wave impinging on it. In satellite communications,
the most commonly encountered aperture antennas are horn and reflec-
tor antennas. Before describing some of the practical aspects of these,
the radiation pattern of an idealized aperture will be used to illustrate
certain features which are important in satellite communications.
The idealized aperture is shown in Fig. 6.9. It consists of a rectangu-
lar aperture of sides a and b cut in an infinite ground plane. A uniform
electric field exists across the aperture parallel to the side b,and the