Antennae are devices which determine the shape of a radar's beam. Upon transmission, they direct the transmitter's energy into a selected area of the surrounding space. Upon reception, they collect the signals from out of the air.

### The Basic Principle

In general, a single radiation source distributes power equally and provides an omnidirectional pattern. This can be compared with throwing a stone into a silent pond, which yields waves that propagate evenly in all directions. If a second radiation source is added then the waves emanating from the sources will interact with each other and produce an interference pattern. In some circumstances, then, there are directions where waves add to each other's power, and others where they cancel each other out (comparable with throwing two stones simultaneously). When the sources combine to produce a greater power in a single direction, this is the known as the 'maximum,' or 'main lobe.' Situations where there are as many positive contributions as negative ones are known as 'nulls' in the pattern. Occasions when the intensity of the resultant wave takes on some intermediate value are called 'sidelobes.'

The precise shape of such an interference pattern depends on the number of radiation sources and the spacing between them, and can be calculated using some rather complicated mathematical concepts. But the basic principle is this: the more radiation sources that are added and combined into a linear arrangement, the narrower and stronger the main lobe will get. The sidelobes will not vanish, nor will they become weaker in relation to the main lobe, but there will be more of them and they will be closer to each other. Every lobe is separated from its neighbour by a null. A polar diagram (that is, an antenna pattern viewed from somewhere above) of a typical antenna pattern looks similar to a bundle of baseball clubs of different sizes:

x main lobe xxxxx xxxxxxx xxxxxxx null xxxxxxx xxxxx xxxxx xxxxx sidelobe xx xxxxx xx xxxx xxx xxxx xxxx xxx xxxx xxx xxx xxx null xx xxx xx xx x xx xx x x x xx xxxxxxxx-O-xxxxxxxx sidelobe xx x xx x xxx null xxx x rear lobe

If a narrow beam is desired, then more radiation sources are called for. A higher number of sources directly translates into a bigger antenna. Big antennae have their disadvantages as they are bulky and heavy and they may not fit into a small platform like an aircraft or a satellite, and wind forces can pose a severe problem if they are mounted on ground installations.

Any metallic object and every square centimetre of a metallic structure can act as a source, once it is illuminated by an electromagnetic wave of proper wavelength. Therefore, a dish antenna can be treated like an arrangement of a vast number of radiating sources which are fed not from a wire but from the primary illuminating element. In consequence, it is the active area or aperture of an antenna which determines its beamwidth.

#### Construction

Elements of radar antennae exhibit a huge variety of shapes, for example:

• Monopole and dipole rods (the 'big brothers' of a walkie-talkie's telescopic antenna)
• Yagi elements (like those used for terrestrial TV reception)
• Horns and dishes of all imaginable sizes
• Bars like those to be seen on your sea-going 18m-yacht
• Spirals which could as well have been taken out of an old sofa
and a multitude of other shapes. In fact, almost any structure made from metal can be turned into an antenna. The only precondition is that some feature of it must bear dimensions that are equal to a quarter of the wavelength (or an integer multiple thereof) being used. However, it takes some rather complicated calculations to make a good antenna element. Apart from metal structures, lenses and mirrors can be used like they are used for shaping beams in the optical part of the electromagnetic spectrum.

#### Antenna Types

An important distinction must be made between antennae with a single source of illumination, and arrays. The former consist of the illuminating element and a reflector which is shaped such that the radar beam gets its desired form. Array Antennae are built quite differently.

### Figures of Merit

Antennae are characterised by their beamwidth, angular resolution, sidelobe level, gain and beam shape. These parameters are explained below.

#### Beamwidth

The most prominent property of an antenna is its beamwidth. A narrow beam is desirable in most cases because:

• transmitting through a wide beam distributes the energy over too big an area
• receiving through a wide beam collects more noise which later on competes with target returns
However, narrow antenna beams come at a price because beamwidth is related to antenna size as explained above. As a rule of thumb, the beamwidth can be calculated as
beamwidth (degrees) =
 51 * wavelength (metres) length of structure (metres)

Hence, in order to achieve a beamwidth of 2°, the required length of the antenna structure in the corresponding dimension is somewhere around:
• 0.099 metres (9.9 centimetres) for an Automotive Radar operating at 77GHz
• 0.765 metres for a tracking radar (10GHz)
• 7.65 metres for an air traffic control (ATC) radar (1GHz)
• 51 metres for an air surveillance radar (150MHz)
• 1.53 kilometres for an Over The Horizon radar (5MHz)

If the requirement calls for a pencil beam then the formula above must be applied to the horizontal and vertical antenna dimensions separately.

#### Angular Resolution

Angular resolution is the capability to identify two targets as separate entities and not as a single (and bigger) target. Without some clever techniques such as superresolution, the beamwidth and angular resolution are identical - and so, if the beamwidth is 2° then targets are seen as individuals as soon as their angular separation exceeds this value.

#### Sidelobe Level

The sidelobe level - sometimes called 'peak sidelobe level' - is the difference1 between the power measured in the main lobe and the power measured in the strongest sidelobe of the antenna pattern. An average sidelobe level is sometimes calculated but really isn't an important number. The design goal is to have low sidelobe levels, and a good antenna features some -40dB (decibels) which equates to a factor of 10,000 between the power in the main lobe and the strongest sidelobe.

Low sidelobes are important for two reasons:

• The Signal Processor simply assumes that any return was obtained through the main lobe. If the antenna receives a strong echo through a sidelobe then this echo will be displayed with the correct range value, but at an azimuth which corresponds to the current main lobe direction. This type of misreading can severely impede air traffic safety, even if measures like Side Lobe Suppression are taken.
• 'Injecting' false targets through a radar antenna's sidelobes is one of the various methods of Electronic Combat. Presented with a wealth of 'ghost' targets, an anti-aircraft system would have a hard job sorting the true ones out.

If the radiating elements of an antenna are all transmitting the same power then some mathematical analysis shows that there is only one fixed relation, with no way to improve sidelobe levels. This relation says that the strongest sidelobe is 13.1dB below the mainlobe (that is, the signal power in the sidelobe is roughly 1/20 of that in the mainlobe) and that is it. 13.1dB is nothing that a radar operator would accept.

The way to get around this is to play with the power distribution along the antenna aperture (by having the elements radiate at different power levels, with the most powerful elements located towards the centre of the aperture). Doing this via a systematic approach involves some examination of higher order polynomials, the Fourier transform and other areas of advanced mathematics (which we won't look at here). The outcome is that the sidelobe level can be improved by applying an aperture tapering function, of which several are available. They all have one thing in common: the sidelobes can be reduced by several orders of magnitude, but at the price of a wider main beam. In consequence, the aperture area needs to be further increased in order to compensate for this.

#### Antenna Gain

This number is best defined as the answer to a certain question2: How many times more power would be needed in order to achieve a given amount of power in the main beam direction if a truly omnidirectional antenna was used rather than the antenna in question? If the answer was '42 times more' then the antenna is said to have a gain of 42. Antenna gains on the order of 10,000 are quite common, but low frequency radars may have to cope with 20 or even less.

### Beam Shapes

This subject is discussed in a separate entry, Antenna Beam Shapes.

### Miscellaneous Items

A common misconception is to believe there is a relation between antenna size and transmitter power. Apart from some minimum required size to prevent sparking, there isn't any. If you see a 'big' antenna then the only conclusions possible are that it either

• operates on a low frequency,
• features a very narrow beam,
• or both.

Just to repeat the point: there are two factors which lead to huge antennae - frequency and beamwidth. First, if you're using a low transmitter frequency (with a large wavelength) then a quarter of the wavelength may still amount to some 10m as the size of a single antenna element. Second, if a narrow beam is required then it either takes a 'king-size' dish or hundreds and thousands of array elements to achieve its goal.

1on a logarithmic scale2Noooh, not what you might be thinking now.