Radar Fundamentals

RADAR stands for Radio Detection And Ranging. The name tells you everything: it detects objects and measures how far away they are, using radio waves.

The idea is beautifully simple. You shout into a canyon — and a moment later you hear your echo. The longer the echo takes to come back, the further away the canyon wall is. Radar does exactly the same thing, but with radio waves instead of sound, and electronics instead of your ears.

Radio waves travel at the speed of light — 300,000 km per second. So if the echo takes 1 microsecond (one millionth of a second) to return, the target is at: R = c × t / 2 = 300,000,000 × 0.000001 / 2 = 150 metres away. The factor of 2 is because the pulse has to travel there AND back.

That's it. The entire concept of radar timing in one picture. The radar sends a pulse, waits for the echo, and measures the wait time. Longer wait = further away. A 10 microsecond round-trip means the target is 1.5 km away. A 100 microsecond round-trip means 15 km. It scales perfectly linearly.

The big question in radar design is: "How far away can I detect a target?" The answer involves a chain of gains and losses — just like a link budget. The radar range equation connects all of them.

The most important thing to notice: range appears to the power of 4. This is because the signal spreads out as it travels to the target (inverse square law), AND spreads out again on the way back. So to double the detection range, you need to increase power by 2⁴ = 16 times. This is why radar engineers obsess over every dB of sensitivity — it pays off far more than in a one-way communication link.

RCS (σ, measured in m²) describes how much of your radar signal a target reflects back toward you. It is NOT the physical size of the object — it depends on the shape, material, and the angle you're looking from.

A stealth aircraft has the same physical size as a normal fighter jet but is shaped with angled surfaces that scatter radar signals away rather than reflecting them back. Its RCS is reduced from ~6 m² to ~0.01 m² — a 600× reduction. Using the R⁴ rule, this means a radar can only see the stealth aircraft at (0.01/6)^(1/4) = 0.34× the normal detection range — about a third as far. That's the entire principle of stealth design in one number.

There are three main ways to design a radar, each with different strengths. The choice depends on what you're trying to measure — range, velocity, or both.

Pulse radar sends a short burst of RF energy, then goes completely silent and listens for the echo. It's like shouting "Hey!" into a canyon and then listening carefully. The silence between pulses is where the echoes arrive.

CW radar transmits continuously — no pulses. It cannot measure range (because you can't measure a delay when there's no gap), but it can measure velocity perfectly using the Doppler effect. Your car's speed camera is a CW radar. So is the police speed gun.

Frequency Modulated Continuous Wave (FMCW) is the most popular radar type today. It's in every modern car, many weather radars, and most short-range industrial radars. It solves the problem of CW (can't measure range) by sweeping the frequency up and down — like a siren that goes from low to high pitch. The clever trick is measuring the difference in frequency between what's being transmitted right now and what's coming back as an echo. That frequency difference tells you the range.

The genius of FMCW in plain English: While you're sending a signal at frequency 77.1 GHz, the echo arriving back was sent when you were at 77.0 GHz. The difference is 0.1 GHz — that's the "beat" frequency. Mix the outgoing and incoming signal together, and you get a pure tone at the beat frequency. That tone frequency tells you exactly how far away the target is. A fast chirp, far target = high beat frequency. Close target = low beat frequency. Then do a Fourier transform and all the targets at different ranges show up as separate peaks.

Range resolution is how close together two targets can be before the radar can no longer tell them apart as separate objects. Think of it like camera resolution — a blurry photo can't distinguish two people standing close together.

You've heard the Doppler effect with sound — a police siren sounds higher pitched as it drives toward you, and lower pitched as it drives away. The same thing happens with radio waves. A target moving toward the radar compresses the returning waves, making them appear slightly higher in frequency. A target moving away stretches the waves, making them appear lower in frequency.

There's a fundamental tension in pulse radar: you want a long pulse to carry a lot of energy (better SNR, longer range), but you also want a short pulse for fine range resolution. You can't have both… unless you're clever.

Pulse compression is the solution. Instead of a plain pulse at a single frequency, you transmit a long pulse whose frequency is swept — a chirp (just like FMCW). Then at the receiver, you pass the echo through a matched filter that effectively "compresses" the long chirp into a short spike. You get the energy of a long pulse with the resolution of a short pulse.

Pulse compression is why modern radar is so powerful. A radar with B=100 MHz bandwidth and T=100 μs chirp gets 40 dB of processing gain — equivalent to having 10,000× more transmit power, at zero extra cost. It's purely signal processing. This is used in weather radar, military radar, SAR imaging satellites, and all automotive FMCW radars.

Radar has a fundamental tradeoff called the ambiguity function. It says: you cannot have fine range resolution AND fine velocity resolution simultaneously with unlimited unambiguous range.

Adjust the parameters and instantly see what your radar can detect, how far it can see, and the range resolution it achieves.