Radar Principles — Page 192, Lesson 183

Let’s start with the pulse width question, because it sets up everything else. The note says medium range radars use 1 or 2 microseconds, and long range radars use about 5 microseconds. Now, a surface movement radar must measure down to 500 metres. The answer is 3.3 microseconds. Here’s the reasoning: the pulse width in time must be short enough that the radar can distinguish a target at that minimum range. The rule is that the pulse width, in microseconds, is roughly twice the minimum range in kilometres divided by the speed of light factor — but let me give you the exact calculation. The distance an electromagnetic wave travels in 1 microsecond is about 300 metres. For a round trip, the pulse must be short enough that the leading edge of the pulse returns before the trailing edge is sent, so the maximum pulse width is 2 times the minimum range divided by 300 metres per microsecond. For 500 metres, that’s 2 times 500 divided by 300, which gives 3.33, so 3.3 microseconds. That’s the maximum pulse width you can use for that radar. Now, radar measurements. Bearing is obtained using the searchlight principle. Radio pulses are concentrated into very narrow beams, produced by shortening the wavelength or increasing the aerial size, and in advanced systems this is done electronically. The beam rotates at a constant speed. The PPI display — that’s the Plan Position Indicator, the circular screen — is synchronized with the antenna rotation. So the direction of an object is simply the direction of the beam, measured from a fixed datum, at the moment the echo is received. Range is calculated from the time interval between transmission and reception of the pulse. Harmonization is the key word here. To get both bearing and range from the system, you must harmonize four things: the rotary speed of the antenna, the pulse duration or width, the pulse repetition frequency, the focusing, and the transmission power. That’s five items actually — rotary speed, pulse width, PRF, focusing, and power. They all have to work together. Now radar resolution. When a point target is painted on a PPI, it doesn’t appear as a single dot. It appears as a rectangle, called the radar resolution rectangle. The target looks stretched both radially — that’s in range — and in azimuth — that’s in bearing. The rectangle’s dimensions depend on three things: the pulse length, the beamwidth, and the spot size. Radial resolution depends on half the pulse length. For example, a 1 microsecond pulse stretches the target by 150 metres, because that’s the distance an electromagnetic wave travels in 0.5 microseconds. If two targets are within half a pulse width of each other, they get illuminated simultaneously by the pulse and return only a single echo to the receiver — so you can’t separate them. Azimuth resolution depends on the full beamwidth. So a 3-degree beamwidth at a range of 120 kilometres stretches the target in azimuth by 6 kilometres, using the 1 in 60 rule — that’s the rule that at 60 units of range, 1 degree subtends 1 unit of arc. So 3 degrees at 120 km gives 6 km. So to resolve adjacent targets, you want short pulse lengths and narrow beamwidths. But there’s a trade-off: shortening the pulse length reduces the time the target is illuminated, which reduces the chance of a good return. And beamwidths can only be narrowed by increasing the antenna size. Also, the spot size and the target size itself increase the size of the echo on the PPI. Finally, Moving Target Indication, or MTI. Surveillance radar has circuitry designed to eliminate returns from stationary objects like hills or buildings. Those permanent echoes would mask the smaller returns from aircraft. By erasing those permanent echoes, the radar displays only moving targets like aircraft. Let me show you the pulse technique and the range timing on the figures. So to recap: pulse width limits minimum range, bearing comes from beam direction, range from timing, and resolution is governed by pulse length and beamwidth. That’s the core of radar principles.