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The theoretical directional patterns of circular apertures are only rough approximations of real patterns. Aperture field distribution depends on the radiation pattern of the feed antenna and on the ratio of the focal length and diameter of the reflector, F /D. A constant aperture field gives the highest gain but also the highest sidelobe level. A high edge illumination leads also to a high feed radiation over the edge of the reflector. Tapering the aperture illumination toward the edge leads to a lower aperture efficiency and gain but improves the pattern by lowering the sidelobes. Typically, the field at the edge is 10 dB to 12 dB lower than that at the center, and the aperture efficiency is about 0.6.
Many factors have an effect on the pattern of a reflector antenna: amplitude and phase pattern of the feed; positioning of the feed; aperture blockage due to the struts, feed, and subreflector; multiple reflections between the feed and reflector; and errors in the shape of the reflector and subreflector. Small random errors in the surface of the reflector reduce the gain and move energy from the main beam to the sidelobes. If the rms value of the surface errors is e , the aperture efficiency is
hap = h 0 exp [−(4pe /l)2 ] |
(9.53) |
where h0 is the aperture efficiency for an ideal surface. The surface error e should not exceed l/16.
The struts and the feed or the subreflector block a part of the aperture, which reduces hap and changes the level of sidelobes. They also scatter and diffract energy over a large solid angle. Also the edge of the reflector diffracts, which often produces a back lobe opposite to the main lobe.
The aperture blockage can be avoided by using offset geometry. Figure 9.27 shows offset-fed reflector antennas. The single-offset antenna has a simpler structure but the offset geometry inherently produces cross polarization. The dual-offset antenna has two distinct advantages compared to the single-offset antenna: The cross-polar field can be compensated and the aperture field distribution can be adjusted by shaping the reflectors. Dualoffset reflectors may have excellent sidelobe properties.
9.9 Other Antennas
In addition to the antennas discussed already, there are a large number of other antenna types. Some of them are briefly described here.
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Figure 9.27 Offset-fed reflector antennas: (a) single-offset; and (b) dual-offset.
Microstrip antennas are small, light, and suitable for integration and mass-production [6, 7]. Figure 9.28(a) shows the basic microstrip antenna: a rectangular, half-wave-long patch. It is made on a substrate having a ground plane on the other side. The patch is fed with a microstrip line from the edge and it radiates from both open-ended edges. The linearly polarized main beam is perpendicular to the surface. Because the antenna radiates effectively only at the resonance frequency, it has a narrow bandwidth. Fairly high loss is another disadvantage of microstrip antennas.
Figure 9.28 (a) Microstrip antenna; (b) slot antenna; (c) bow-tie antenna; (d) dielectric rod antenna; and (e) lens antenna.
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There are many variations on the basic microstrip antenna: different shapes of the patch, ways to feed the patch, and possibilities to combine elements to an array. A circularly polarized wave can be produced with a
square patch, which is fed from the adjacent sides so that the phase difference of the feeds is 90°. A patch can also be fed with a coaxial cable through the
substrate, in which case the input impedance depends on the position of the feed point. Feeding through a slot in the ground plane allows the radiating patches to be separated from the feed lines and other circuits. The directivity of a single element is low. A higher directivity is obtained by combining a large number of elements (see Section 9.10).
A slot antenna is a radiating slot in a metal plane, as shown in Figure 9.28(b). It is dual with a dipole antenna; that is, the radiation pattern is that of a dipole except that the electric and magnetic fields are interchanged. A slot antenna can be fed from a parallel-wire line, coaxial line, microstrip line, or waveguide. A waveguide having an array of slots is a common antenna. A slot in a waveguide wall radiates if it disturbs surface currents; a narrow slot, which is along the current flow, does not radiate.
The bow-tie antenna shown in Figure 9.28(c) is an example of a broadband antenna. The feed point is in the center of two planar conductors. The input impedance and directional pattern may be frequency-independent over a frequency range of one decade or more. In an ideal case, the bowtie antenna has no dimensions, which can be expressed in wavelengths; the opening angle of the conductors is the only dimension. In practice, the structure of the feed point and the finite length of the conductors set limits for the frequency range. Often bow-tie antennas are placed on a dielectric substrate. Then the main lobe is on the dielectric side. Other frequencyindependent shapes used in broadband antennas are spirals and cones.
Antennas made of dielectric materials have some mechanical and electrical advantages [8]. Figure 9.28(d) shows a dielectric rod antenna, which is placed at the open end of a circular waveguide. This kind of an antenna works well as a feed antenna.
Like a parabolic reflector, a lens antenna operates as a phase modifier, which changes a spherical phase front to a planar one. The paths of the rays from the focal point of the lens to a plane in front of the lens have equal electrical lengths. Lenses are usually made of low-loss dielectric materials. The phase velocity of the wave is c /√er in the dielectric material. Figure 9.28(e) shows a simple plano-convex lens. The reflections in the air-dielectric interfaces can be eliminated with quarter-wave matching layers. Lenses are often used to correct the phase error at the aperture of a horn antenna.
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9.10 Antenna Arrays
An antenna array is an entity consisting of two or more element antennas. Antenna arrays may have many good properties, which cannot be achieved with a single element, such as high gain, narrow beam, shaped beam, scanning beam, or adaptive beam.
Figure 9.29 shows an array that consists of two elements having a separation of d . Let us assume that the far-field patterns of the antennas are E1 (f) and E2 (f ) and that the phase difference of the feed currents is d (in this case the lengths of the feed lines are different). The total field produced by the array is
E (f ) = E1 (f) e −j (kd cos f + d ) + E2 (f) |
(9.54) |
The path length difference of d cos f in free space produces the phase difference of kd cos f. The fields of the elements are in the same phase in directions fmax that meet the condition of
kd cos f max + d = n 2p |
(9.55) |
where n is an integer. The fields have opposite phases in directions fmin which meet the condition of
kd cos f min + d = n 2p + p |
(9.56) |
Figure 9.29 An array of two elements.
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If the elements of Figure 9.29 are similar, E1 (f ) = E2 (f), and they are fed in phase, d = 0, (9.54) can be written as
E (f) = E1 (f ) (1 + e −jkd cos f ) |
(9.57) |
The array pattern is the product of the element pattern and the array factor. If the element pattern maximum and the array factor maximum coincide in the same direction, the maximum field is twice that produced by a single element, E = 2E1 (f max ). However, even if the power density is now four times that produced by a single element, the gain of the array is only twice the gain of an element. The power density produced by an element would be doubled if all the input power of the array were fed to that element alone. The normalized pattern may look like that shown in Figure 9.30. The envelope follows the element pattern, and at minima the fields of the elements cancel each other out. As the separation d increases, the number of maxima and minima in the pattern increases.
Many kinds of directional patterns can be realized by changing the distance (or frequency) and phase difference of the elements. Figure 9.31 shows some patterns when the elements radiate isotropically in the f-plane (for example dipoles which are perpendicular to the f-plane).
Also, the pattern of an array consisting of more than two elements can be expressed as the product of the element pattern and the array factor. The array factor depends on the positions, amplitudes, and phases of the elements. The array may be linear, planar, or conformal (shaped according to the surface). The elements of a linear array are on a line. Figure 9.32 shows a
Figure 9.30 Pattern of a two-element array (solid line) equals the element pattern multiplied by the array factor.
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Figure 9.31 Directional patterns of two-element arrays in polar form. The elements are isotropic in the f -plane. Ea /Ee = field of array divided by the field of the element.
Figure 9.32 Microstrip antenna array (F = feed point).