Radar Principles — Page 192, Lesson 183

Let's start with a quick calculation that sets the tone for the whole subject. The note at the top tells us that medium range radars use a pulse width of 1 or 2 microseconds, and long range radars use about 5 microseconds. A microsecond is one millionth of a second — that's the unit we're working in throughout radar. Now, the worked example: a surface movement radar must measure down to 500 metres. We need the maximum pulse width in microseconds. The answer is 3.3 microseconds. Let me show you why, because this is the heart of radar range measurement. The radar sends out a pulse of energy. That pulse travels out to the target and back. The distance to the target is found by timing the interval between transmission and reception. But here's the catch: the pulse itself has a physical length in space. A pulse of 1 microsecond duration is, in space, about 300 metres long, because electromagnetic waves travel at roughly 300,000 kilometres per second. So a 1 microsecond pulse occupies 300 metres of space. Now, to resolve two targets that are close together, the pulse must be short enough that it doesn't illuminate both at once. The rule is that the pulse width in time, multiplied by the speed of light, gives the distance the pulse occupies. For a 500 metre minimum range, the pulse must be no longer than the time it takes light to travel 500 metres. Light travels 500 metres in about 1.67 microseconds. But wait — the pulse goes out and comes back, so the round trip is double. Actually, let me be careful here. The limiting factor is that the pulse must be short enough that the echo from a target at 500 metres doesn't overlap with the transmitted pulse. The pulse width in time must be less than the round-trip time to 500 metres. Round trip to 500 metres is 1000 metres of travel, which takes about 3.3 microseconds. That's exactly the answer: 3.3 microseconds. So the maximum pulse width is 3.3 microseconds — any longer and the echo from a target at 500 metres would arrive while the transmitter is still sending, and you couldn't separate them. Now let's move to the measurements themselves. Bearing measurement uses what's called the searchlight principle. Radio pulses are concentrated into very narrow beams. You get a narrow beam by shortening the wavelength or increasing the aerial size, and in advanced systems this is done electronically. The beam is rotated at a constant speed. The PPI display — that's the Plan Position Indicator, the circular radar screen — is synchronized with the antenna rotation. So the direction of an object is simply the direction the beam is pointing, measured from a fixed datum, at the moment the echo comes back. That's how you get bearing. Range, as I said, is calculated from the time interval between transmission and reception of the pulse. Now, harmonization. For the system to give you both bearing and range, you have to harmonize several things: the rotary speed of the antenna, the pulse duration or width, the pulse repetition frequency — that's how often pulses are sent — plus focusing and transmission power. All of these have to work together. Let's look at the figures here. shows the pulse technique, and shows how distance is found by timing the interval. shows a PPI display of primary raw radar, and shows typical radar antennae. Now, radar resolution. This is crucial. When a point target is painted on a PPI display, it doesn't appear as a single point. It appears as a rectangle — the radar resolution rectangle. The target looks stretched both radially, that's in range, and in azimuth, that's in bearing. The dimensions of that rectangle depend on three things: the pulse length, the beamwidth, and the spot size. Radial resolution depends on half the pulse length. Here's the example: a pulse length of 1 microsecond would stretch the target by 150 metres. Why 150? Because that's the distance an electromagnetic wave travels in 0.5 microseconds. Half of 1 microsecond is 0.5 microseconds, and light travels 150 metres in that time. So the target appears stretched by 150 metres in range. And here's the key consequence: if two targets happen to be within half a pulse width of each other, they'll be illuminated simultaneously by the pulse and return only a single echo to the receiver. You can't separate them — they merge into one return. Azimuth resolution depends on the full beamwidth. The example: a 3 degree beamwidth at a range of 120 kilometres would stretch the target in azimuth by 6 kilometres, using the 1 in 60 rule. The 1 in 60 rule says that at 60 units of range, 1 degree subtends 1 unit of arc. So at 120 kilometres, 1 degree subtends 2 kilometres, and 3 degrees subtends 6 kilometres. That's your azimuth stretch. So to resolve adjacent targets, the radar should have short pulse lengths and narrow beamwidths. But there's a trade-off. Shortening the pulse length reduces the time the target is illuminated by the pulse, and that reduces the chance of getting a good return. And beamwidths can only be narrowed by increasing the size of the antenna. So you can't just shrink everything — there are physical limits. Also, the spot size and the target size itself both increase the size of the echo displayed on the PPI screen. So the displayed echo is bigger than the true target. Finally, Moving Target Indication, or MTI. Surveillance radar incorporates circuitry designed to eliminate returns from stationary objects — hills, buildings, things like that. These fixed objects would give returns that mask the smaller returns from aircraft. By erasing these permanent echoes, the radar can display only the moving targets, like aircraft. That's the whole point of MTI — it cleans up the picture so you can see the aircraft against the ground clutter. So to tie it all together: bearing comes from the beam direction, range comes from the timing, resolution is limited by pulse length and beamwidth, and MTI filters out the stationary stuff. That's the foundation of radar principles.