Radar

Radar detects and measures objects using radio echoes. Learn pulse radar ranging, range resolution, PRF and maximum unambiguous range, the radar equation, radar cross-section, Doppler velocity, FMCW radar (automotive), pulse compression, clutter and MTI, and modern phased-array and imaging radars.

From air-traffic control to weather forecasting and car ADAS, radar measures distance, speed and angle through darkness, fog and rain. Automotive 77 GHz radars now ship in millions of cars each year.

An analogy

Radar is like shouting in a canyon and timing the echo: the delay gives distance, and a change in pitch (Doppler) tells you if the wall is moving.

Pulse radar

Transmit a short pulse, listen for echoes; time delay gives range. Antenna direction gives angle. PRF sets how often pulses are sent — high PRF limits maximum unambiguous range.

Radar equation

Received echo power falls with R⁴ (two-way spreading), so doubling range needs 16× power. Radar cross-section depends on target size, shape and material (stealth reduces σ).

Doppler and FMCW

Moving targets shift the echo frequency by 2v/λ. FMCW radars sweep frequency (chirps); the beat frequency gives range and phase change between chirps gives velocity — the basis of 77 GHz automotive radar.

Advanced radar

Pulse compression (long coded pulses with fine resolution), MTI and Doppler filtering to reject clutter, CFAR detection, phased-array beam steering, MIMO virtual arrays for angle resolution, SAR imaging from aircraft and satellites.

Formulas

• Range: R = c t / 2
• Range resolution: ΔR = c τ / 2 = c / (2B)
• Max unambiguous range: R_max = c / (2 PRF)
• Doppler: f_d = 2 v / λ
• Radar equation: R_max = [P_t G² λ² σ / ((4π)³ S_min)]^(1/4)

Worked example: Range and resolution

Given: Echo delay 100 µs; Pulse width 1 µs

Find: Range and resolution.

• R = 3 × 10⁸ × 10⁻⁴/2 = 15 km
• ΔR = 3 × 10⁸ × 10⁻⁶/2 = 150 m

Answer: 15 km, 150 m resolution

Worked example: Radar equation

Given: P_t 1 kW, G 30 dB, λ 3 cm, σ 1 m², S_min −100 dBm

Find: Max range.

• R⁴ = 10³ × 10⁶ × 9 × 10⁻⁴ × 1/(1984 × 10⁻¹³)
• R ≈ 8.2 km

Answer: ≈ 8.2 km

Common mistakes

• Wrong: Assuming range scales with power linearly. — Right: Range ∝ P^(1/4).
• Wrong: Choosing PRF without checking ambiguity. — Right: R_max = c/(2 PRF).

Applications

• Automotive ADAS: 77 GHz FMCW for ACC and AEB.
• Weather: Doppler weather radars.
• Air traffic & defence: Surveillance and tracking radars.

Key takeaways

• R = ct/2; ΔR = c/2B.
• R_max,unamb = c/2PRF.
• f_d = 2v/λ.
• R ∝ (P G² λ² σ)^(1/4).

Going further

• CFAR: Adaptive detection thresholds.
• SAR: Synthetic aperture imaging.
• MIMO radar: Virtual arrays for angle resolution.