Waves: Part 12 - Elementary Antennas

To be useful for information purposes, electromagnetic radiation needs antennas. It’s a large subject with many specialist areas.

As they are both based on waves, acoustics and electromagnetics have a lot in common. In both, the wavelength varies enormously. The wavelength goes from much smaller than any feasible transducer to much larger. The number of octaves involved in the electromagnetic spectrum is hard to grasp. The visible spectrum forms but a tiny part of the whole thing, but the designer gets a break because practical devices are always limited in bandwidth which eases the design of an antenna. Pity the loudspeaker designer who has to deal with the entire audio spectrum at once.

The other strong parallel with audio is that antennas are often required to display directivity. As with microphones, the directivity of an antenna may be its most important characteristic. In the case of a transmitter, directivity reduces power waste by directing the signal only where it might be needed. In the case of a receiver antenna, directivity reduces the level of signals not emanating from the intended transmitter or versions of the true signal that have been reflected by some nearby object. In analog television, reflections caused ghosting, whereas in digital television they increase the error rate.

The directivity of antennas is traditionally described by their gain, measured in dBi, where i stands for isotropic. An isotropic antenna radiates equally in all directions. There is no power gain in a directional antenna, but instead what happens is that the available power is directed into a smaller solid angle than that of an isotropic antenna so that within that angle the transmitter appears more powerful. Needless to say, outside that solid angle the power is reduced. Very large dish antennas such as radio telescopes may reach 50dBi, but that is uncommon.

The effect is mirrored at a receiving antenna where the energy is taken from a small solid angle. An isotropic antenna would need energy from all directions to match it. As an antenna is often a passive device it is advantageous to use directivity to reduce the power needed at the transmitter and/or to enhance the apparent sensitivity of a receiver.

Terrestrial TV transmitters are typically designed so that most of the energy is radiated horizontally as that is where the receivers will be found.

Transmitters in satellites need to use highly directional antennas for two reasons. The first is that the amount of available power is limited because it usually comes from solar cells. The second is that from space even entire countries or states subtend a very small angle and it is wasteful to radiate beyond the intended footprint.

Directional receiving antennas need to be aligned with the chosen transmitter. That is not especially difficult in a fixed location. If a number of different transmitters need to be received, an antenna rotator will be needed. Problems arise when the receiver is mobile, perhaps portable or installed in a vehicle or a boat. Early AM transistor radios used ferrite rod antennas that were directional, and the user learned to turn the radio for best reception. Later FM radios had telescopic antenna that could be turned for the best reception, at least until they got broken.

In vehicles, the receiving antenna may need to be motorized in two axes to orient towards the transmitter. In the case of communication with satellites, the orientation can be fixed once a geostationary satellite is located, whereas orbiting satellites will need to be tracked.

In the case of some marine antennas, the rolling, pitching and heading changes of the vessel need constantly to be corrected and the antenna can be thought of as a stabilized platform of the type used in early inertial navigators that maintains its orientation despite movement of its supports.

As the cost of computing and GPS receivers has fallen, it becomes feasible to compute the angles at which an antenna should be pointed to receive a given satellite. Using dead reckoning it is possible to get the antenna somewhere near the right direction and from there it carries out a scan in order to find and maximize the signal strength.

Highly directional antennae are frequently used in microwave links. The links are typically line-of-sight between a series of towers. When the transmitted beam is very narrow, the towers may be arranged so they are not in a straight line. As Fig.1 shows, this means that the same frequency can be used for all of the links, because receiver C is not aligned with the beam from transmitter A, whereas receiver B is.

In another parallel with sound, electromagnetic wavelengths that are much shorter than the size of the antenna are easy to direct and hard to make omnidirectional. At the other extreme, wavelengths that are much longer than practical antennas are hard to make directional. Somewhere in between, things get a bit easier.

Microwaves behave much like scaled-up light, and larger versions of optical techniques can usefully be employed. However, in optics, directionality can be obtained with lenses or with mirrors. Lenses are practically unknown in radio systems which rely primarily on reflection from metallic elements. One advantage of staying with reflection is that it has no equivalent of the dispersion that occurs with refractive devices. In comparison with reflectors, lenses are also heavy and place limits on the available size. Large optical telescopes universally use mirrors.

A directional beam of energy must have finite width so that it can contain wave fronts. If those wave fronts are substantially flat, they will propagate forwards. According to Huygens, a wave front can be considered to be an infinite number of point sources working in the same phase. These can only interfere constructively in a new wave front parallel to the earlier one.

Fig.1 - In multi-hop microwave links, the towers are not arranged in a straight line, but may be positioned as shown here. Radiation from A directed at B will not be seen by C. This means that both links can use the same frequency.

Fig.1 - In multi-hop microwave links, the towers are not arranged in a straight line, but may be positioned as shown here. Radiation from A directed at B will not be seen by C. This means that both links can use the same frequency.

This tells us that a directional antenna must be significantly larger than the wavelength so that it can create wavefronts. It must also be designed such that radiation will have the same phase no matter where it appears in the aperture.

The parabolic reflector meets those two requirements because radiation launched by a horn at the focus will reflect as a plane wave, provided the parabola is sufficiently accurate. As wavelength falls, the parabola needs to be more precisely made so that phase errors do not creep in.

The parabola does not need to be axisymmetric. Successful designs have been made where the reflector forms only part of a much larger parabola, with appropriate illumination by the feeder. This asymmetric design allows the feed to be out of the path of radiation to or from the reflector. Most consumer satellite dishes are built that way.

The biggest drawback of the parabolic reflector is windage. The curvature of the surface can create tremendous lift in the worst-case wind direction. The 76-meter Lovell telescope in the UK once did itself some harm in a gale and required strengthening.

Windage and weight can often be reduced because the parabolic surface does not have to be continuous. It can be perforated provided the holes are small compared to the wavelength. This can be seen in the window of any microwave oven, where the glass is backed by a perforated metal sheet that allows vision but reflects the radiation back in.

At some wavelengths, an effective parabolic reflector can be made from chicken wire on light supports. Another approach to windage is to encase the parabolic element in an outer shell, typically of fiberglass, that has better aerodynamic properties.

In vehicle mounted applications, the dish and its feeder are designed to fold down parallel to the roof for travel. Asymmetric dishes are relatively common.

Directional antennas are a good example of transform duality. Spatially speaking, a uniformly illuminated circular parabola considered across any diameter produces a rectangular pulse (in space) with energy inside and no energy outside. The Fourier Transform of that pulse will reveal the spatial frequencies. The Fourier Transform of a rectangle is a sinx/x function, having a central peak, which is the main lobe, and smaller peaks at either side, which are the side lobes.

The analogy with digital FIR filters is quite good here. A larger antenna corresponds to a filter with more points, which can deliver a sharper roll off, corresponding to a narrower main lobe in an antenna. Just as a digital filter can be optimized by modifying the impulse response with a window function, the response of a parabolic antenna can be optimized by tapering the illumination from the horn.

Side lobes may or may not matter according to the application. In a microwave link, the side lobes simply waste a bit of power, whereas in a radar set, side lobes give false returns and need to be suppressed. That explains the large horizontal dimensions of the rotating radars seen at airports. The vertical dimensions are much smaller because these radars do not determine height. The height information comes from a transponder in the airplane driven by the altimeter.

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