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The illumination efficiency is usually a specified number, and it can range between about 0.5 and 0.8. Of course, it cannot exceed unity, and a conservative value often used in calculations is 0.55. A fundamental relationship exists between the power gain of an antenna and its effective aperture. This is Aeff G l 4
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where l is the wavelength of the TEM wave, assumed sinusoidal (for practical purposes, this will be the wavelength of the radio wave carrier). The importance of this equation is that the gain is normally the known (measurable) quantity, but once this is known, the effective aperture is also known. 6.10 The Half-Wave Dipole The half-wave dipole is a basic antenna type which finds limited but essential use in satellite communications. Some radiation occurs in all directions except along the dipole axis itself, and it is this nearomnidirectional property which finds use for telemetry and command signals to and from the satellite, essential during the launch phase when highly directional antennas cannot be deployed. The half-wave dipole is shown in Fig. 6.8a, and its radiation pattern in the xy plane and in any one meridian plane in Fig. 6.8b and c. Because
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The half-wave dipole.
Antennas
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 l2 3-dB beamwidth: 78 Assuming the antenna efficiency is unit ( A 1), the power gain is 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 containing the dipole axis (the z axis). Thus the radiation pattern is a function of only and is given by cos2 a cos b 2 sin2
g( )
(6.16)
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 pattern 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 reflector 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 rectangular 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
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y a Perfectly conducting infinite ground plane x
An idealized aperture radiator.
aperture is centered on the coordinate system shown in Fig. 6.3, with the electric field parallel to the y axis. Radiation from different parts of the aperture adds constructively in some directions and destructively in others, with the result that the radiation pattern exhibits a main lobe and a number of sidelobes. Mathematically, this is shown as follows: At some fixed distance r in the far-field region, the electric field components described in Sec. 6.4 are given by E( , ) E ( , ) C sin sin X sin Y X Y sin X sin Y C cos cos X Y (6.17) (6.18)
Here, C is a constant which depends on the distance r, the lengths a and b, the wavelength l, and the electric field strength E0. For present purposes, it can be set equal to unity. X and Y are variables given by X Y a sin cos l b sin sin l (6.19) (6.20)
It will be seen that even for the idealized and hence simplified aperture situation, the electric field equations are quite complicated. The two principal planes of the coordinate system are defined as the H plane,
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