232 Radio Engineering for Wireless Communication and Sensor Applications
9.7 Horn Antennas
An open waveguide end operates as a simple antenna. It has a broad, unsymmetrical beam and a rather large impedance mismatch. A much better antenna, a horn antenna, is obtained by widening the waveguide end, as shown in Figure 9.23.
H -plane, E -plane, and pyramidal horns are fed from a rectangular waveguide. An H -plane horn is widened along the broad side of the waveguide, an E -plane horn along the narrow side. A pyramidal horn is broadened in both directions. The distribution of the aperture field follows the field distribution of the fundamental waveguide mode, TE10 . Because the amplitude in the E -plane is constant, the sidelobes are higher in this plane than in the H -plane, which has a cosine amplitude distribution tapering to zero at the edges. However, the phase in the aperture is not constant; rather it is quadratic. The H - and E -plane horns have cylindrical phase fronts, which seem to emanate from the apex. The apex is in the intersection of the slanting side planes. The phase difference between the center and edge of the aperture is in wavelengths
D = (1 − cos u 0 ) |
L |
(9.50) |
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l |
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Figure 9.23 Horn antennas: (a) H -plane horn; (b) E -plane horn; (c) pyramidal horn; and
(d) conical horn.
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233 |
where u 0 is half of the opening angle and L is the distance from the apex to the aperture.
Figure 9.24 gives the directivities DE and DH for E - and H -plane horns. Because of the aperture phase error D, it is impractical to make a horn, which has a very high directivity. For a fixed length L , the directivity increases as the aperture size increases until it collapses due to the phase error. The directivity of a pyramidal horn is obtained from the directivities
of the corresponding E - and H -plane horns: |
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D ≈ |
pDE DH l |
2 |
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(9.51) |
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32ab |
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where a is the width and b is the height of the input waveguide. Usually, the losses of horn antennas are small, and the gain and directivity are approximately equal.
A conical horn like that shown in Figure 9.23(d) is obtained by widening a circular waveguide. Although the structure is symmetrical, the fields of the fundamental mode TE11 are not. Therefore, the E - and H -plane directional patterns are different.
Figure 9.25 shows horn antennas, which produce more symmetrical beams than pyramidal and conical horns. The rectangular waveguide feeding the diagonal horn, shown in Figure 9.25(a), transforms first to a circular waveguide and then to a square waveguide, which is at a 45° angle to the feeding waveguide. The field of the aperture is a combination of the fields of TE10 and TE01 modes. The beam of a diagonal horn is fairly symmetrical,
Figure 9.24 Directivities of E -plane horns, DE , and H -plane horns, DH . Aperture size in E -plane = b 1 , aperture size in H -plane = a1 .
234 Radio Engineering for Wireless Communication and Sensor Applications
Figure 9.25 (a) Diagonal horn; (b) Potter horn; and (c) corrugated horn.
but the level of cross polarization is high in the 45° and 135° planes between the E - and H -planes.
A Potter horn or a dual-mode horn, shown in Figure 9.25(b), is a conical horn, which has a step in the feeding circular waveguide. The fundamental mode TE11 and the TM11 mode excited at the step together produce an aperture field having parallel field lines, if the modes have proper amplitudes and a proper phase difference in the aperture. The Potter horn has a symmetrical pattern, low sidelobe level, and low cross-polarization level. However, it has a narrow bandwidth because the phasing of modes depends on the frequency.
A corrugated horn, shown in Figure 9.25(c), is a conical horn having a corrugated inner wall. The number of grooves should be at least two per wavelength. The depth of grooves is about l/4. Near the throat the depth changes gradually to l /2 to ensure a good impedance match between the input waveguide and the flaring section. The mode propagating in the horn is HE11 , a hybrid of TE11 and TM11 modes. A corrugated horn has many good properties: a symmetrical pattern, low sidelobe level, low cross-polariza- tion level, and broad operating bandwidth.
9.8 Reflector Antennas
Reflector antennas are used as high-gain, narrow-beam antennas in fixed radio links, satellite communication, radars, and radio astronomy.
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A parabolic reflector antenna is the most common of reflector antennas. Figure 9.26(a) shows a parabolic antenna fed from the primary focus. The equation of the surface is
r = |
2F |
(9.52) |
1 + cos u |
where F is the focal length. The rays coming from the focal point are converted parallel by the reflector or vice versa. A more physical interpretation is that the fields radiated by the feed antenna induce surface currents, which in turn produce the aperture fields. The feed antenna is often a horn antenna. The phase center of the feed antenna should coincide with the focal point to obtain maximum gain.
The Cassegrainian antenna shown in Figure 9.26(b) is fed from the secondary focus behind the reflector. The subreflector is a hyperbolic reflector. This configuration has several advantages compared to the primary focusfed antenna: Transmitters and receivers can be placed behind the reflector; transmission lines between the feed and the radio equipment are short; positioning of the feed antenna is less critical; the phase and amplitude distribution of the aperture field can be adjusted with a shaped subreflector; and the feed pattern over the edge of the subreflector is directed toward a cold sky in satellite reception, which leads to a lower antenna noise temperature. A more complicated structure and often a larger blockage of the aperture are the disadvantages of the Cassegrainian antenna.
Figure 9.26 Parabolic reflector antennas: (a) a primary focus fed antenna; and (b) a Cassegrainian antenna.