Radar does one simple thing extremely fast. It shouts into the dark, listens for an echo, and times how long the echo took to come back. Everything else is refinement.
The shout is a pulse of radio energy. The echo is a vanishingly small fraction of that pulse scattered back off whatever it hit. The timing is the measurement, because radio waves travel at the speed of light and that speed is known to nine significant figures.
From that one measurement, plus where the antenna was pointing and how the echo’s frequency changed, a radar builds range, bearing and closing speed. Here is how each of those falls out.
Quick Facts
What radar measures directly: The time between transmitting a pulse and receiving its echo
Range formula: Range = (speed of light × echo time) ÷ 2, halved because the pulse makes a round trip
Speed of light: 299,792,458 metres per second, so a target at 150 km returns its echo in about one millisecond
Bearing: Comes from where the antenna beam was pointing when the echo arrived
Speed: Comes from the Doppler shift in the returned frequency
The harsh bit: Received power falls off as the fourth power of range
Maximum unambiguous range: Set by the pulse repetition frequency, the distance a pulse can travel out and back before the next one is sent
Main enemy: Clutter, meaning echoes from ground, sea, rain, birds and anything else you did not want to see
Range: a stopwatch, nothing more
The transmitter emits a short burst. A duplexer then switches the antenna over to the receiver, because the same aerial does both jobs and the transmit pulse would destroy a receiver listening at the same moment. The receiver waits.
When an echo arrives, the elapsed time gives the distance. Light covers 300,000 kilometres per second, so the round trip to a target 150 kilometres away takes about one millisecond. At 1.5 kilometres it is ten microseconds. Radar is a stopwatch operating on timescales where a microsecond is 150 metres of error.
Bearing: you know it because you pointed it there
The echo itself carries no direction information. Bearing comes from the antenna. A dish or planar array concentrates energy into a narrow beam, and if an echo comes back while the beam is pointing at 043 degrees, the target is at 043 degrees, to within the width of the beam.
That is why angular accuracy depends on beam width, and beam width depends on antenna size relative to wavelength. A bigger antenna at a shorter wavelength gives a tighter beam and a sharper picture. It is also why a rotating surveillance radar only updates a given bearing once per sweep, typically every four to twelve seconds.
Speed: the Doppler shift
A target moving towards the radar compresses the returning wave and a target moving away stretches it. The frequency of the echo is therefore slightly different from the frequency transmitted, and the size of that difference gives the component of the target’s velocity along the radar line of sight.
This is far more than a bonus number. Pulse-Doppler processing is the single most effective way to separate real targets from clutter, because the ground does not move and an aircraft does. Filter out everything with zero Doppler shift and most of the ground returns disappear with it. It is what lets a fighter radar look down at a low-flying target without drowning in returns from the terrain behind it.
Why detection range is so hard to buy
The radar equation contains a brutal term: the power that comes back falls off as the fourth power of range. The pulse spreads on the way out and the scattered echo spreads on the way back, and the two inverse-square losses multiply.
In practice that means doubling your detection range needs sixteen times the transmitted power, all else being equal. This is why radar development has focused relentlessly on receiver sensitivity, signal processing and pulse integration rather than simply shouting louder, and why halving a target’s radar cross section only cuts detection range by about sixteen per cent.
Pulses, gaps and the range you cannot see
A radar cannot transmit and listen at the same instant, so it alternates. The rate at which it sends pulses is the pulse repetition frequency, and it forces a trade-off that runs through every radar design.
A high PRF gives excellent Doppler resolution and good performance against fast targets, but the next pulse goes out before distant echoes have returned, so range becomes ambiguous. A low PRF measures long ranges unambiguously but handles Doppler badly. Modern radars solve this by switching PRF constantly and resolving the ambiguities in software.
Moving the beam without moving the antenna
A mechanically scanned radar physically swings its dish. An active electronically scanned array does not move at all. Its face carries hundreds or thousands of individual transmit and receive modules, and the beam is steered by adjusting the phase of each one so the wavefronts add up in the desired direction.
Because the beam has no inertia, it can jump across the sky in microseconds, track many targets at once, and split into several beams doing different jobs. It also degrades gracefully: lose a few modules and you lose a little performance, rather than the whole radar.
Radar is eighty years old and still the only sensor that gives range, bearing and velocity through cloud, darkness and weather, in one box. Nothing else comes close, which is why every serious attempt to hide from it has gone after the echo rather than the physics.
Sources: standard radar theory as set out in Wikipedia’s “Radar”, “Radar equation”, “Pulse-Doppler radar” and “Pulse repetition frequency” articles; IEEE radar band designations; speed of light per the SI definition.
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