The most common beam shapes found in radar antennae are the fan beam and the pencil beam. Radar warning receivers and intercept equipment used in electronic combat employ sector beams. The latter are essentially fan beams that have been extended to simultaneously cover some dozen degrees of azimuth and elevation.

A special case of the fan beam is the cosecant beam (or cosecant-squared beam). The name is derived from the mathematical function which forms the basis for the calculations. An air surveillance radar doesn't need to cover more than around 10,000 metres of height because aircraft don't fly much higher. Using a fan beam for a radar with 200km range would imply a significant waste of energy because the radar would be looking for non-existing aircraft in space too. A cosecant beam has the significant feature that it has a linear upper boundary. The same beam is used (in an upside-down geometry) in some airborne ground-mapping radars.

30° ::::::::: 20° :::::::::::: ::::::::::::::: ::: fan beam :::: 10° ::::::::::::::::::: ::::::::::::::::::::: ::::::::::::::::::::::: 5° 10km xxxxxxxxxxxxxxxxxxxxxxxxx aircraft xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxx cosecant beam xxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx O xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx ================================|============================ 50 km

There is no such thing as the ideal beam shape, as the choice heavily depends on the application in question. An example is discussed below.

### Selecting a Beam Shape - An Example

It has been pointed out that there is a fixed relation between an antenna's aperture and the width of the beam. Air surveillance radars are usually built with beamwidths of around 1°, and less beamwidth isn't desirable because scanning a given area requires much more time when a narrow beam is used. This is easy to explain with a (somewhat constructed) example:

Assume an Air Traffic Control (ATC) radar with a phased array antenna and a 1° x 1° pencil beam. It takes 360 horizontal beam positions to scan a full circle at a certain elevation angle, and there are, say, 45° of elevation to be examined1. This yields 360 x 45 = 16200 positions for hemispherical coverage. With a design range of 150km, the pulse repetition time becomes 1ms.

Let's assume that a single pulse does the job of finding all the targets in a given direction, hence the time for a full scan is 16200 x 1ms = 16.2 seconds. That is, a space position will be revisited roughly four times a minute. If the beamwidth were only 0.5° x 0.5° then there were twice as many azimuth and elevation positions, and the time for one scan would be more than one minute. One minute is a long time, and no air traffic controller can live with an air picture that is that old.

Now, assume a conventional reflector antenna with a cosecant-squared beam of 1° azimuth x 45° elevation: its peculiarity is that it covers all elevations of interest at the same time. Still assuming that a single pulse per beam position is sufficient, this radar has performed a full scan after visiting 360 x 1 (azimuth x elevation) positions, which amounts to 360 x 1ms = 0.36 seconds. Thus, this radar is able to update the whole operator's screen three times a second. Of course, owing to the beam shape this radar cannot distinguish between low-flying and high-flying objects. But, as an ATC radar is considered here, flight level information can be obtained from an aircraft's ATC transponder (see Primary and Secondary Radar).

History: Overview | Isle of Wight Radar During WWII
Technology: Basic Principle | Main Components | Signal Processing | Antennae | Side Lobe Suppression | Phased Array Antennae | Antenna Beam Shapes | Monopulse Antennae | Continuous Wave Radar
Theoretical Basics: The Radar Equation | Ambiguous Measurements | Signals and Range Resolution | Ambiguity and PRFs