Radar (Radio Detection And Ranging) uses reflected electromagnetic waves to detect objects and measure their range, velocity, and angular position. The radar equation relates transmitted power to received echo power.

Radar Equation

where \(\sigma\) is the target radar cross section (RCS) in m², and \(R\) is range. Note the \(R^4\) dependence — radar range halves when range doubles require 16× more transmit power.

Range Resolution

The ability to distinguish two closely spaced targets in range depends on pulse width \(\tau\): \(\Delta R = c\tau/2\). Shorter pulses → better resolution. Pulse compression (chirp or phase coding) allows high range resolution while maintaining high average power.

Doppler Effect

A target moving with radial velocity \(v_r\) shifts the echo frequency by the Doppler shift: \(f_d = 2v_r/\lambda\). At 10 GHz, a 100 km/h target produces \(f_d \approx 1.85\) kHz. Moving target indicator (MTI) and pulse-Doppler processing use this to separate moving targets from stationary clutter.

Radar Cross Section (RCS)

RCS (\(\sigma\)) characterises how effectively a target reflects radar energy back toward the receiver. It depends on target size, shape, material, and radar frequency. Stealth aircraft are designed to minimise RCS through shape (angled surfaces scatter energy away from radar) and radar-absorbing materials.