Radar Principles — Page 192, Lesson 176

Let’s start with the heart of radar: the echo principle. A radar transmits a short burst of energy — a pulse — and that pulse travels out to a target, bounces off it, and returns as an echo. The distance to that object is found by timing the interval between the instant of the pulse’s transmission and its return as an echo. That’s the whole idea, and it’s shown in Figure 11.3. So the key measurement is the time between sending the pulse and receiving the echo. Let’s work a concrete example. Suppose the echo time — the time between transmission and reception — is 500 microseconds. A microsecond, µs, is one millionth of a second. The speed of light, c, is 300 000 000 metres per second, or equivalently 162 000 nautical miles per second. Now, here’s the subtle part: that 500 µs is the time for the pulse to go out AND come back. So the distance is half of the total path. Let’s do it in metres first. Distance equals speed times time, divided by 2 because it’s a round trip. So we have 300 000 000 times 500, divided by 1 000 000 (to convert microseconds to seconds), and then divided by 2. That gives 75 000 metres, which is 75 kilometres. Now let’s do the same in nautical miles. Using 162 000 NM per second: 162 000 times 500, divided by 1 000 000, divided by 2, gives 40.5 nautical miles. There’s a quicker way to do this. Since the speed of light is 300 000 000 m/s, and we’re working in microseconds and kilometres, we can use a simplified formula: Range equals 500 times 300, divided by 2. That gives 75 km. The 300 here is the speed of light in kilometres per microsecond — 300 000 000 m/s is 300 km per millisecond, but in microseconds it’s 0.3 km per µs. So 500 µs times 0.3 km/µs gives 150 km for the round trip, and dividing by 2 gives 75 km one-way. That’s the shortcut. For nautical miles, we can convert: Range equals 500 times 300, divided by 2 times 1852. The 1852 is the number of metres in a nautical mile. That gives 40.5 NM. And there’s one more handy method: the radar mile. A radar mile is defined as one nautical mile out and back, and it equals 12.36 microseconds. So if the echo time is 500 µs, the range in NM is simply 500 divided by 12.36, which gives 40.5 NM. That’s a very practical conversion to remember — 12.36 µs per radar mile. Now let’s move to the theoretical maximum range, and how it relates to the PRF — the pulse repetition frequency. PRF is the number of pulses transmitted in one second, measured in pulses per second, or pps. The key idea is this: each pulse must be allowed to travel to the most distant object planned before the next pulse is transmitted. If you transmit the next pulse too soon, you can’t tell whether an echo belongs to the first pulse or the second — you can’t relate a particular echo to a particular pulse. So the maximum range is directly related to the PRF: the greater the range required, the lower the PRF must be. Let’s work through the examples. First: we want a radar to measure a range of up to 187 km. What should the PRF be? The pulse must travel 374 km — that’s 2 times 187 — before the next pulse is transmitted. The time for that journey, T, equals distance divided by speed: 374 000 metres divided by 300 000 000 metres per second. That gives 0.0012466 seconds, which is 1246 microseconds. That time is the PRI — the pulse repetition interval, the time between pulses. So the PRI is 1246 µs, and the PRF is the reciprocal of that. Now, the other examples follow the same logic. For a maximum range of 200 NM, you’d find the round-trip time using the speed in NM per second, and take the reciprocal to get the maximum PRR — pulse repetition rate, another name for PRF. For 170 km, same approach. And for the last one, an AWR — that’s an Airborne Weather Radar — with a PRR of 400 pps, you calculate the maximum range in nautical miles by taking the reciprocal of the PRR to get the PRI, then converting that time to distance using the radar mile or the speed of light. So the whole principle boils down to this: the pulse repetition frequency sets the maximum unambiguous range. Lower PRF means longer range, because each pulse gets more time to travel out and back before the next one is sent. That’s the fundamental trade-off in radar design.