Radar Fundamentals: Propagation, Pulse Characteristics, Range Resolution and Accuracy
Pulse timing drives nearly every number
- Range from echo delay: R = c·t/2, with c ≈ 300 m/µs, so each microsecond of round-trip delay equals 150 m of range (about 12.35 µs per nautical mile round trip).
- Range resolution: ΔR = cτ/2 ≈ 150 m × pulse length in µs. A 0.1 µs pulse resolves about 15 m; a 1 µs pulse about 150 m.
- Minimum range: roughly ΔR plus duplexer/TR-cell recovery and display blanking; during the pulse the receiver is effectively blind.
- Maximum unambiguous range: R = c/(2·PRF). At 1000 Hz this is 150 km (81 nm); at 2000 Hz, 75 km (40.5 nm). Echoes from beyond reappear as second-trace echoes at a fraction of true range.
- Duty cycle = τ × PRF; average power = peak power × duty cycle. Higher PRF means more hits per scan but less unambiguous range.
- Beamwidth θ ≈ 70λ/D degrees. X-band (≈3 cm) and S-band (≈10 cm) differ mainly in resolution, rain performance and antenna size; a narrow beam sharpens bearing accuracy, not range resolution.
Propagation
With standard 4/3-earth refraction, the radar horizon is d(km) ≈ 4.12(√h₁ + √h₂), heights in metres. Ducting (trapping) extends detection well beyond the geometric horizon and produces long-range false echoes; subrefraction shortens range. X-band suffers markedly more rain attenuation than S-band, which is why S-band is preferred in tropical precipitation.
Accuracy benchmarks
IMO performance standards (MSC.192(79)) call for range accuracy within 1 percent of the range scale in use or 30 m, whichever is greater; bearing accuracy 1°; range discrimination about 40 m; azimuth discrimination 2.5°.
Worked example
A set transmits 0.25 µs pulses at 1200 Hz. Resolution = 150 m × 0.25 = 37.5 m. Unambiguous range = c/(2 × 1200) = 125 km ≈ 67.5 nm. On the 96 nm scale, targets beyond 67.5 nm can be painted closer than they are. Dropping PRF to 600 Hz moves the unambiguous range to 135 nm and removes the ambiguity, at the cost of fewer pulses per scan and weaker echoes at long range.
Traps
- Using c instead of c/2 in range calculations.
- Thinking a narrower beam improves range resolution.
- Believing a higher PRF increases maximum range, when it reduces it.
- Mixing µs and ms for pulse length.