The Radio Link--A tutorial--Part II

Antenna Radiation Patterns

A rock dropped into a still pond will create ripples that appear as concentric circles propagating radially outward from the point where the rock strikes the water. Well-formed ripples appear at some distance from the point of impact; however, the motion of the water is not so well defined at the point of impact or its immediately surrounding area.

A physically realizable antenna launches both electric and magnetic fields. At a distance sufficiently far from the antenna we can observe these fields propagating in a radial direction from the antenna in much the same fashion as the ripples on the surface of the pond. The region of well-defined radially propagating "ripples" is known as the far-field radiation region, or the Fraunhofer region. It is the region of interest for most (if not all) communication applications.

Much nearer to the antenna there are capacitive and inductive "near" fields that vary greatly from point to point and rapidly become negligible with distance from the antenna. A good approximation is that the far field begins at a distance from the antenna of

where l  is the antenna's largest physical dimension.¹  Often in communication applications, the antenna╒s physical dimensions, though greater than λ/10 , are less than a wavelength, so that the far field begins at a distance less than twice the largest dimension of the antenna. For cellular telephone applications, the far field begins a few centimeters away from the handset.

A polar plot of the far-field power density as a function of angle referenced to some axis of the antenna structure is known as a power pattern. The peak or lobe in the desired direction is called the main lobe or main beam. The remainder of the power (i.e., the power outside the main beam) is radiated in lobes called side lobes. "Directive" antennas can be designed that radiate most of the antenna input power in a given direction.

Figure 2.3 illustrates the beam pattern of a directive antenna with a conical beam. The antenna is located at the left of the figure from which the several lobes of the pattern emanate.

The plot represents the far-field power density measured at an arbitrary constant distance d  from the antenna, where d  > d_{far field}. The shape of the beam represents the power density as a function of angle, usually referenced to the peak of the main beam or lobe. For the antenna represented in the figure, most of the power is radiated within a small solid angle directed to the right in the plot. In general, a convenient coordinate system is chosen in which to describe the power pattern. For example, one might plot the power density versus the spherical coordinates θ  and φ  for an antenna oriented along one of the coordinate axes as shown in Figure 2.4. For each angular position (θ, φ), the radius of the plot represents the value of power density measured at distance d. Since d is arbitrary, the graph is usually normalized by expressing the power density as a ratio in decibels relative to the power density value at the peak of the pattern. Alternatively, the normalization factor can be the power density produced at distance d  by an isotropic antenna, see Equation (2.2). When an isotropic antenna is used to provide the reference power density, the units of power density are dBi, where the i stands for "isotropic reference." Figure 2.5 shows an antenna power pattern plotted versus one coordinate angle θ with the other coordinate angle φ held constant. This kind of plot is easier to draw than the full three-dimensional power pattern and is often adequate to characterize an antenna.

Example

A  "half-wave dipole" or just "dipole" is a very simple but practical antenna. It is made from a length of wire a half-wavelength long, fed in the center by a source. Figure 2.6 shows a schematic representation of a dipole antenna. A slice through the power pattern is shown in Figure 2.7. The dipole does not radiate in the directions of the ends of the wire, so the power pattern is doughnut shaped. If the wire were oriented vertically, the dipole would radiate uniformly in all horizontal directions, but not up or down. In this orientation the dipole is sometimes described as having an "omnidirectional"  pattern. The peak power density, in any direction perpendicular to the wire, is 2.15 dB greater than the power density obtained from an isotropic antenna (with all measurements made at the same distance from the antenna). Dipole antennas are often used for making radiation measurements. Because a dipole is a practical antenna, whereas an isotropic antenna is only a hypothetical construct, power patterns of other antennas are often normalized with respect to the maximum power density obtained from a dipole. In this case the power pattern will be labeled in dBd. Measurements expressed in dBd can easily be converted to dBi by adding 2.15 dB.

The antenna beamwidth  along the main lobe axis in a specified plane is defined as the angle between points where the power density is one-half the power density at the peak, or 3 dB down from the peak. This is known as the "3 dB beamwidth" or the "half-power beamwidth" as shown in Figure 2.8. This terminology is analogous to that used in describing the 3 dB bandwidth of a filter.

The "first null-to-null beamwidth," as shown in the figure, is often another parameter of interest. Since a power pattern is a three-dimensional plot, beamwidths can be defined in various planes. Typically the beamwidths in two orthogonal planes are specified. Often the two planes of interest are the azimuth and elevation planes. In cellular telephone systems, where all of the transmitters and receivers are located near the surface of the Earth, the beamwidth in the azimuth plane is of primary interest. The azimuth-plane beamwidth is shown in Figure 2.8.

The physics governing radiation from an antenna indicates that the narrower the beamwidth of an antenna, the larger must be its physical extent. An approximate relationship exists between the beamwidth of an antenna in any given plane and its physical dimensions in that same plane. Typically beamwidth in any given plane is expressed by

where L is the length of the antenna in the given plane, λ  is the wavelength, and k  is a proportionality constant called the "beamwidth factor" that depends on the antenna type. A transmitting antenna with a narrow "pencil" beam will have large physical dimensions. This implies that if the same antenna were used for receiving, it would have a large effective aperture A_e.

Example

The relation between beamwidth and effective aperture is easiest to visualize for parabolic antennas such as the "dish" antennas that are used to receive television signals from satellites. For a parabolic dish antenna, the term large aperture means that the dish is large, or, more precisely, that it has a large cross-sectional area. It is easy to see that when used for receiving, a large parabolic antenna will capture more power than a small one will. On the other hand, should the dish be used for transmitting, a large parabola will focus the transmitted power into a narrower beam than a small one.

Beamwidth is one parameter that engineers use to describe the ability of an antenna to focus power density in a particular direction. Another parameter used for this same purpose is antenna gain. The gain of an antenna measures the antenna╒s ability to focus its input power in a given direction but also includes the antenna's physical losses. The gain G is defined as the ratio of the peak power density actually produced (after losses) in the direction of the main lobe to the power density produced by a reference antenna. Both antennas are assumed to be supplied with the same power, and both power densities are measured at the same distance in the far field. A lossless isotropic antenna is a common choice for the reference antenna. To visualize the relationship between gain and beamwidth, consider the total power radiated as being analogous to a certain volume of water enclosed within a flexible balloon. Normally, the balloon is spherical in shape, corresponding to an antenna that radiates isotropically in all directions. When pressure is applied to the balloon, the regions of greater pressure are compressed, while the regions of lesser pressure expand; but the total volume remains unaltered. Similarly, proper antenna design alters the antenna power pattern by increasing the power density in certain directions with an accompanying decrease in the power density in other directions. Because the total power radiated remains unaltered, a high power density in a particular direction can be achieved only if the width of the high-power-density beam is small.

Beamwidth, antenna gain, and effective aperture are all different ways of describing the same phenomenon. (Technically, gain also takes into account ohmic losses in the antenna.) It can be shown that the gain is related to the effective antenna aperture A_e  in the relationship^2.

where the losses are represented by the parameter ? . For most telecommunications antennas the losses are small, and in the following development we will usually assume η =  1. The gain given by Equation (2.6) is referenced to an isotropic radiator.

Example

Suppose an isotropic radiator is emitting a total radiated power of 1 W. The receiving antenna has a gain described by Equation (2.6) with η = 1. Compute the required effective aperture of a receiving antenna at 10 km that will produce the same power Pr at the receiver input as would be produced by a receiving antenna with an effective aperture of A_er1 = 1 cm² at a distance of 1 km.

Solution

The power density of the transmitted wave is given by Equation (2.2). As we showed in a previous example, p₁ = 80 x 10^-9 W/m² at d = 1 km and p₂ = 800 z 10^-12 W/m² at d = 10km. According to Equation (2.3), the total power produced at the receiver input is the power density multiplied by the effective receiving antenna aperture. Thus, for the antenna at 1 km,

Solving gives A_er2 = 0.01 m². This equals an area of 100 cm², a much larger antenna. Since gain is proportional to effective area, the second antenna requires 100 times the gain of the first in this scenario, or an additional 20 dB. Note that we could have predicted these results simply by realizing that the power density falls off as the square of the range.

Example

Continuing the previous example, suppose the communication link operates at a frequency of 10 GHz. Find the gains of the two receiving antennas.

It is very important to keep in mind that although an antenna has "gain," the antenna does not raise the power level of a signal passing through it. An antenna is a passive device, and when transmitting, its total radiated power must be less than or equal to its input power. The gain of an antenna represents the antenna's ability to focus power in a preferred direction. This is always accompanied by a reduction in the power radiated in other directions. To a receiver whose antenna lies in the direction of the transmitter's main beam, increasing the transmitting antenna's gain is equivalent to increasing its power. This is a consequence of improved focusing, however, and not a consequence of amplification. Increasing the receiving antenna's gain will also increase the received power. This is because antenna gain is obtained by increasing the antenna's effective aperture, thereby allowing the antenna to capture more of the power that has already been radiated by the transmitter antenna.

It should be apparent from our discussion to this point that both transmitting and receiving antennas have gain, and both receiving and transmitting antennas have effective apertures. In fact, there is no difference between a transmitting and a receiving antenna; the same antenna can be used for either purpose. An important theorem from electromagnetics shows that antennas obey the property called reciprocity. This means that an antenna has the same gain when used for either transmitting or receiving, and consequently, by Equation (2.6), it has the same effective aperture when used for either transmitting or receiving as well.

Next: The Range Equation

Introduction to Wireless Systems By Bruce A. Black, Philip S. DiPiazza, Bruce A. Ferguson, David R. Voltmer, Frederick C. Berry, Published Jun 7, 2011 by Prentice Hall, is reprinted with permission by Pearson Publishing.