Doppler Shift
Relative motion between a transmitter and receiver shifts the observed frequency. For a one-way link the shift is set by the radial velocity; for radar the signal makes a round trip, so the echo is shifted twice as much. Enter the carrier frequency, the relative speed and the angle between the velocity and the line of sight.
Equations & Parameters ▸
one-way: \(f_d = \dfrac{v\cos\theta}{c}\,f = \dfrac{v_r}{\lambda}\)
two-way (radar): \(f_d = \dfrac{2\,v\cos\theta}{c}\,f = \dfrac{2 v_r}{\lambda}\)
two-way (radar): \(f_d = \dfrac{2\,v\cos\theta}{c}\,f = \dfrac{2 v_r}{\lambda}\)
| f | Carrier frequency (GHz). |
| v | Relative speed (m/s). Positive = closing. |
| θ | Angle between the velocity vector and the line of sight (degrees). 0° = directly toward. |
| vr | Radial (line-of-sight) velocity = v·cosθ. |
| mode | One-way (comms) or two-way (radar round trip). |
References: M. I. Skolnik, Introduction to Radar Systems, 3rd ed., McGraw-Hill, 2001. · M. A. Richards, Fundamentals of Radar Signal Processing, 2nd ed., McGraw-Hill, 2014.
Inputs
GHz
Carrierm/s
Relative speeddeg
0 = head-onRound trip?
Results
Doppler
Doppler shift—
Fractional shift—
Geometry
Radial velocity—
Wavelength—
Diagram