Which expression gives the velocity unambiguous limit for a given PRF and wavelength?

Which expression gives the velocity unambiguous limit for a given PRF and wavelength?

• A. v_max = c / (2 PRF)
• B. v_max = PRF λ / 4
• C. v_max = c / (PRF)
• D. v_max = 4 /(PRF λ)

Answer: (B)

The unambiguous velocity limit in pulsed-Doppler radar comes from combining how Doppler shift relates to speed with how often you sample the signal. A target moving with radial speed v produces a Doppler frequency shift Δf = 2v/λ (round-trip). Because the radar samples at a rate PRF, the largest Doppler frequency you can measure without aliasing is ±PRF/2 (Nyquist limit). Set Δf_max = PRF/2 and solve for v: v_max = Δf_max · (λ/2) = (PRF/2) · (λ/2) = PRF λ / 4. So the speed limit scales with both the PRF and the wavelength.

The unambiguous velocity limit in pulsed-Doppler radar comes from combining how Doppler shift relates to speed with how often you sample the signal. A target moving with radial speed v produces a Doppler frequency shift Δf = 2v/λ (round-trip). Because the radar samples at a rate PRF, the largest Doppler frequency you can measure without aliasing is ±PRF/2 (Nyquist limit). Set Δf_max = PRF/2 and solve for v: v_max = Δf_max · (λ/2) = (PRF/2) · (λ/2) = PRF λ / 4. So the speed limit scales with both the PRF and the wavelength.