Radar Doppler Shift
Frequency shift of an echo from a moving target; the factor of two accounts for the round trip to the target and back.
Formula
Variables
Example
Target closing at 150 m/s, λ 0.03 m: f_d = 2×150 ÷ 0.03 = 10 kHz
How it works
A radar set sends out a wave of wavelength λ and measures how much the returned echo is shifted in frequency when the target is moving toward or away from it. The shift depends only on the target’s speed along the line of sight, so sideways motion does not contribute. The factor of 2 appears because the wave is shifted once on the way to the target and again on the way back after reflection.
When to use it
Use this when you need to estimate the Doppler shift in pulsed or continuous-wave radar from an aircraft, vehicle, storm, or other moving target. It is especially useful for velocity measurement, target tracking, and separating moving objects from stationary clutter.
Worked example, step by step
Given: radial velocity v_r = 75 m/s, wavelength λ = 0.05 m Step 1: Substitute into the formula f_d = 2v_r / λ Step 2: f_d = 2 × 75 / 0.05 Step 3: f_d = 150 / 0.05 Step 4: f_d = 3000 Hz Final answer: the Doppler shift is 3.0 kHz
Common mistakes to avoid
- Using the full target speed instead of only the radial component toward or away from the radar
- Forgetting the factor of 2 for the two-way path of the radar signal
- Mixing up units, such as using wavelength in cm while velocity is in m/s without converting to meters
Did You Know?
Doppler processing lets a radar separate a fast-moving aircraft from stationary ground clutter — the basis of moving-target indication and airborne weather radar.
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