9

Antennas

Antennas transmit and receive radio waves. They operate as matching devices from a transmission line to the free space and vice versa. An ideal antenna radiates all the power incident from the transmission line feeding the antenna. It radiates to (or receives from) desired directions; in other words, an antenna has a certain radiation pattern.

Antennas are needed in nearly all applications of radio engineering. The congestion of the radio spectrum due to the increasing number of users and applications sets increasingly strict requirements for antennas. A large number of antenna structures have been developed for different frequencies and applications. Antennas can be categorized, for example, into current element antennas, traveling-wave antennas, aperture antennas, and antenna arrays.

In this chapter, the fundamental concepts of antennas, the calculation of radiation pattern and other antenna quantities, different types of antennas, and the link between two antennas are treated. Antennas are the subject of many books [1–8].

9.1 Fundamental Concepts of Antennas

Antennas are reciprocal devices. That means that the properties of an antenna are similar both in the transmitting mode and in the receiving mode. For example, if a transmitting antenna radiates to certain directions, it can also receive from those directions—the same radiation pattern applies for both

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206 Radio Engineering for Wireless Communication and Sensor Applications

cases. The reciprocity does not apply if nonreciprocal components such as ferrite devices or amplifiers are integrated into the antenna. Also, a link between two antennas is reciprocal: The total loss is the same in both directions. However, magnetized plasma, such as in the ionosphere, between the antennas may cause Faraday rotation, making the link nonreciprocal.

The space surrounding an antenna can be divided into three regions according to the properties of the radiated field. Because the field changes smoothly, the boundaries between the regions are more or less arbitrary. The reactive near-field region is closest to the antenna. In this region, the reactive field component is larger than the radiating one. For a short current element, the reactive and radiating components are equal at a distance of l/(2p ) from the element. For other current distributions this distance is shorter. As the distance increases, the reactive field decreases as 1/r 2 or 1/r 3 and becomes negligible compared to the radiating field. In the radiating near-field region or Fresnel region, the shape of the normalized radiation pattern depends on the distance. As the distance of the observation point changes, the difference in distances to different parts of the antenna changes essentially compared to the wavelength. In the far-field region or Fraunhofer region, the normalized radiation pattern is practically independent of the distance and the field decreases as 1/r . The boundary between the near-field and far-field regions is usually chosen to be at the distance of

where D is the largest dimension of the antenna perpendicular to the direction of observation. At the boundary, the edges of a planar antenna are l/16 farther away from the observation point P than the center of the antenna, as illustrated in Figure 9.1. This difference in distance corresponds to a phase

Figure 9.1 At the boundary of near-field and far-field regions.

difference of 22.5°. Because antennas are usually operated at large distances, the far-field pattern is of interest. It should be noted that at lower frequencies in case of small antennas, the outer limit of the reactive near-field region, l/(2p ), is larger than the distance obtained from (9.1).

The coordinate system used for antenna analysis or measurements should be defined clearly. In analysis, the complexity of equations depends on the system. Figure 9.2 shows the spherical coordinate system that is often used. The elevation angle u increases along a great circle from 0° to 180°. The azimuth angle f is obtained from the projection of the directional vector in the xy -plane, and it is between 0° and 360°.

An antenna can be described by several properties, which are related to the field radiated by the antenna, for example, directional pattern, gain, and polarization. Due to the reciprocity, these properties also describe the ability of the antenna to receive waves coming from different directions and having different polarizations. The importance of different radiation properties depends on the application. As a circuit element an antenna also has an impedance, efficiency, and bandwidth. Often mechanical properties such as the size, weight, and wind load are also very important.

Figure 9.2 Spherical coordinate system used for antenna analysis and measurements.

the depths of nulls can be obtained from the directional pattern. The halfpower beamwidth, u 3dB or f3dB , is often used as the measure of the main lobe width.

Figure 9.3 shows different representations of directional patterns. The rectangular representation is suitable for directive antennas having a narrow main beam. The polar representation is natural for an antenna radiating over a wide range of angles. Both rectangular and polar plots are twodimensional cuts of the three-dimensional pattern. The directional patterns are often u-cuts or f -cuts. For a u -cut, for example, the angle u is constant and the angle f is variable. The most important cuts are the cuts in the principal planes. The principal planes are orthogonal planes that intersect at the maximum of the main lobe, that is, at the boresight. For example, for a linearly polarized antenna, the principal planes are the E -plane and H -plane, which are the planes parallel to the electric field vector and magnetic field vector, respectively. The whole pattern can be represented as a threedimensional or contour plot. The scale of different plots may be a linear power, a linear field, or a logarithmic (decibel) scale.

The number of different shapes of directional patterns is countless. A pencil beam antenna has a narrow and symmetrical main lobe. Such highly directional antennas are used, for example, in point-to-point radio links, satellite communication, and radio astronomy. The directional pattern of a terrestrial broadcasting antenna should be constant in the azimuth plane and shaped in the vertical plane to give a field strength that is constant over the service area. The directional pattern of an antenna in a satellite should follow the shape of the geographic service area.

The directivity D of an antenna is obtained by integrating the normalized power pattern Pn (u, f) over the whole solid angle 4p:

Pn (u, f ) d V

4p

where d V is an element of the solid angle. Because Pn (u, f ) = P (u, f )/ Pmax , the directivity is the maximum power density divided by the average power density.

Example 9.1

The beam of an antenna is rotationally symmetric. Within the 1°-wide beam, the pattern level is Pn = 1, and outside the beam the pattern level is

where A phys is the physical area of the aperture.

The phase pattern c(u, f ) is the phase difference of the constant phase front radiated by the antenna and the spherical phase front of an ideal antenna. The position of the reference point where the spherical wave is assumed to emanate must be given. The phase center of an antenna is the reference point that minimizes the phase difference over the main beam. For example, the phase center of the feed antenna and the focal point of the reflector that is illuminated by the feed should coincide.

The polarization of an antenna describes how the orientation of the electric field radiated by the antenna behaves as a function of time. We can imagine that the tip of the electric field vector makes an ellipse during one cycle on a plane that is perpendicular to the direction of propagation (Figure 9.4). The polarization ellipse is defined by its axial ratio Emax /Emin , its tilt angle t , and its sense of rotation. The special cases of the elliptical polarization are the linear polarization and the circular polarization. The polarization of an antenna is also a function of angle (u, f).

The field radiated by the antenna can be divided into two orthogonal components: the copolar and cross-polar field. Often the copolar component is used for the intended operation and the cross-polar component represents an unwanted radiation or an interference. Linear polarizations that are perpendicular to each other, as for example the vertical and horizontal polarizations, are orthogonal. The right-handed and left-handed circular polarization are orthogonal to each other as well.

Figure 9.4 Polarization ellipse.