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6.12.2 Pyramidal horn antennas
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The pyramidal horn antenna, illustrated in Fig. 6.14, is primarily designed for linear polarization. In general, it has a rectangular cross section a b and operates in the TE10 waveguide mode, which has the electric field distribution shown in Fig. 6.14. In general, the beamwidths for the pyramidal horn differ in the E and H planes, but it is possible to choose the aperture dimensions to make these equal. The pyramidal horn can be operated in horizontally and vertically polarized modes simultaneously, giving rise to dual-linear polarization. According to Chang (1989), the cross-polarization characteristics of the pyramidal horn have not been studied to a great extent, and if required, they should be measured.
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Antennas
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The pyramidal horn.
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For any of the aperture antennas discussed, the isotropic gain can be found in terms of the area of the physical aperture by using the relationships given in Eqs. (6.14) and (6.15). For accurate gain determinations, the difficulties lie in determining the illumination efficiency I, which can range from 35 to 80 percent for horns and from 50 to 80 percent for circular reflectors (Balanis, 1982, p. 475). Circular reflectors are discussed in Sec. 6.13. 6.13 The Parabolic Re ector Parabolic reflectors are widely used in satellite communications systems to enhance the gain of antennas. The reflector provides a focusing mechanism which concentrates the energy in a given direction. The most
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A parabolic reflector. (Courtesy of Scientific Atlanta, Inc.)
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commonly used form of parabolic reflector has a circular aperture, as shown in Fig. 6.15. This is the type seen in many home installations for the reception of TV signals. The circular aperture configuration is referred to as a paraboloidal reflector. The main property of the paraboloidal reflector is its focusing property, normally associated with light, where parallel rays striking the reflector converge on a single point known as the focus and, conversely, rays originating at the focus are reflected as a parallel beam of light. This is illustrated in Fig. 6.16. Light, of course, is a particular example of an electromagnetic wave, and the same properties apply to electromagnetic waves in general, including the radio waves used in satellite communications. The ray paths from the focus to the aperture plane (the plane containing the circular aperture) are all equal in length.
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Figure 6.16 The focusing property of a paraboloidal reflector.
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Antennas
The geometric properties of the paraboloidal reflector of interest here are most easily demonstrated by means of the parabola, which is the curve traced by the reflector on any plane normal to the aperture plane and containing the focus. This is shown in Fig. 6.17a. The focal point or focus is shown as S, the vertex as A, and the axis is the line passing through S and A. SP is the focal distance for any point P and SA the focal length, usually denoted by f. (The parabola is examined in more detail in App. B). A ray path is shown as SPQ, where P is a point on the curve and Q is a point in the aperture plane. Length PQ lies parallel to the axis. For any point P, all path lengths SPQ are equal; that is, the distance SP PQ is a constant which applies for all such paths. The path equality means that a wave originating from an isotropic point source has a uniform phase distribution over the aperture plane. This property, along with the parallel-beam property, means that the wavefront is plane. Radiation from the paraboloidal reflector appears to originate as a plane wave from the plane, normal to the axis
P A f
0 0 S
Figure 6.17 (a) The focal length f SA and a ray path SPQ. (b) The focal distance . (b)
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