[Go
to TOC]
Doppler Shift
Doppler is the apparent change in wavelength (or frequency) of an electromagnetic
or acoustic wave when there is relative movement between the transmitter (or frequency
source) and the receiver.
Summary RF Equation for the TwoWay (radar) case
Summary RF Equation for the OneWay (ESM) case

Rules of Thumb for twoway signal travel (divide
in half for oneway ESM signal measurements) At 10 GHz, f_{D} ≈ 35 Hz per Knot
19 Hz per km/Hr 67 Hz per m/sec 61 Hz per yd/sec 20 Hz per ft/sec

To estimate f_{D} at other frequencies, multiply these by:
The Doppler effect is shown in Figure 1. In
everyday life this effect is commonly noticeable when a whistling train or police
siren passes you. Audio Doppler is depicted, however Doppler can also affect the
frequency of a radar carrier wave, the PRF of a pulse radar signal, or even light
waves causing a shift of color to the observer.
How do we know the universe is expanding?
Answer: The color of light from distant stars is shifted to red (see Section
71: higher 8 or lower frequency means Doppler shift is stretched, i.e. expanding).
A memory aid might be that the lights from a car (going away) at night are red
(tail lights)!
Doppler
frequency shift is directly proportional to velocity and a radar system can therefore
be calibrated to measure velocity instead of (or along with) range. This is done
by measuring the shift in frequency of a wave caused by an object in motion (Figure
2).
* Transmitter in motion
* Reflector in motion
* Receiver in motion
* All three
For a closing relative velocity:* Wave is compressed
* Frequency is increased
For an opening relative velocity:* Wave is stretched
* Frequency is decreased
To compute Doppler frequency we note that velocity is range rate; V = dr/dt
For
the reflector in motion case, You can see the wave compression effect in Figure
3 when the transmitted wave peaks are one wavelength apart. When the first peak
reaches the target, they are still one wavelength apart (point a).
When the 2nd peak reaches the target, the target has advanced according to its
velocity (vt) (point b), and the first reflected peak has traveled toward the radar
by an amount that is less than the original wavelength by the same amount (vt) (point
c).
As the 2nd peak is reflected, the wavelength of the reflected wave is 2(vt) less
than the original wavelength (point d).
The distance the wave travels is twice the target range. The reflected phase
lags transmitted phase by 2x the round trip time.
For a fixed target the received phase will differ from the transmitted phase
by a constant phase shift. For a moving target the received phase will differ by
a changing phase shift.
For the closing target shown in Figure 3, the received phase is advancing with
respect to the transmitted phase and appears as a higher frequency.
Doppler is dependent upon
closing velocity, not actual radar or target velocity as shown in Figure 4.
For the following equations (except radar mapping), we assume the radar and target
are moving directly toward one another in order to simplify calculations (if this
is not the case, use the velocity component of one in the direction of the other
in the formulas).
For the case of a moving reflector, Doppler frequency is proportional to 2x the
transmitted frequency:
Higher rf = higher Doppler shift
f_{D} = (2 x V_{Target})(f/c)
Likewise, it can be shown that for other cases, the following relationships hold:
For an airplane radar
with an airplane target (The "all three moving" case)
f_{D} = 2(V_{Radar} + V_{Target})(f/c)
For the case of a semiactive missile receiving signals (Also "all three moving")
f_{D} = (V_{Radar} + 2V_{Target} +V_{Missile})(f/c)
For the airplane radar with a ground target (radar mapping) or vice versa.
f_{D} = 2(V_{Radar} Cosθ Cosф)(f/c), Where 2 and N are the radar
scan azimuth and depression angles.
For a ground based radar with airborne target  same as previous using target
track crossing angle and ground radar elevation angle.
For the ES/ESM/RWR case where only the target or receiver is moving (Oneway
Doppler measurements)
f_{D} = V_{Receiver or Target} (f/c)
Note: See Figure 4 if radar and target are not moving directly towards or away
from one another.
Figure 5 depicts the results of a plot
of the above equation for a moving reflector such as might be measured with a ground
radar station illuminating a moving aircraft. It can be used for the aircrafttoaircraft
case, if the total net closing rate of the two aircraft is used for the speed entry
in the figure. It can also be used for the ES/ESM case (oneway Doppler measurements)
if the speed of the aircraft is used and the results are divided by two.
Sample Problems:
(1) If a ground radar operating at 10 GHz is tracking an airplane flying at a
speed of 500 km/hr tangential to it (crossing pattern) at a distance of 10 km, what
is the Doppler shift of the returning signal?
Answer: Since the closing velocity is zero, the Doppler is also zero.
(2) If the same aircraft turns directly toward the ground radar, what is the
Doppler shift of the returning signal?
Answer: 500 km/hr = 270 kts from Section 21. From Figure 4
we see that the Doppler frequency is about 9.2 kHz.
(3) Given that a ground radar operating at 7 GHz is Doppler tracking an aircraft
20 km away (slant range) which is flying directly toward it at an altitude of 20,000
ft and a speed of 800 ft/sec, what amount of VGPO switch would be required of the
aircraft jammer to deceive (pull) the radar to a zero Doppler return?
Answer: We use the second equation from the bottom of page 26.3
which is essentially the same for this application except a ground based radar is
tracking an airplane target (versus an airplane during ground mapping), so for our
application we use a positive elevation angle instead of a negative (depression)
angle.
f_{D} = 2(V_{r} Cos θ Cos ф)(f/c), where θ is the aircraft track
crossing angle and ф is the radar elevation angle.
Since the aircraft is flying directly at the radar, 2 = θ°; the aircraft altitude
= 20,000 ft = 6,096 meters.
Using the angle equation in Section 21, sin ф = x/r = altitude / slant range,
so:
ф = sin^{1} (altitude/slant range) = sin^{1} (6,096 m / 20,000
m) = 17.7°
F_{D} = 2(800 ft/sec Cos θ° Cos 17.7°)(7x10 Hz^{9} / 9.8357 x
10^{9} ft/sec) = 10,845 Hz
Table of Contents for Electronics Warfare and Radar Engineering Handbook
Introduction 
Abbreviations  Decibel  Duty
Cycle  Doppler Shift  Radar Horizon / Line
of Sight  Propagation Time / Resolution  Modulation
 Transforms / Wavelets  Antenna Introduction
/ Basics  Polarization  Radiation Patterns 
Frequency / Phase Effects of Antennas 
Antenna Near Field  Radiation Hazards 
Power Density  OneWay Radar Equation / RF Propagation
 TwoWay Radar Equation (Monostatic) 
Alternate TwoWay Radar Equation 
TwoWay Radar Equation (Bistatic) 
Jamming to Signal (J/S) Ratio  Constant Power [Saturated] Jamming
 Support Jamming  Radar Cross Section (RCS) 
Emission Control (EMCON)  RF Atmospheric
Absorption / Ducting  Receiver Sensitivity / Noise 
Receiver Types and Characteristics 
General Radar Display Types 
IFF  Identification  Friend or Foe  Receiver
Tests  Signal Sorting Methods and Direction Finding 
Voltage Standing Wave Ratio (VSWR) / Reflection Coefficient / Return
Loss / Mismatch Loss  Microwave Coaxial Connectors 
Power Dividers/Combiner and Directional Couplers 
Attenuators / Filters / DC Blocks 
Terminations / Dummy Loads  Circulators
and Diplexers  Mixers and Frequency Discriminators 
Detectors  Microwave Measurements 
Microwave Waveguides and Coaxial Cable 
ElectroOptics  Laser Safety 
Mach Number and Airspeed vs. Altitude Mach Number 
EMP/ Aircraft Dimensions  Data Busses  RS232 Interface
 RS422 Balanced Voltage Interface  RS485 Interface 
IEEE488 Interface Bus (HPIB/GPIB)  MILSTD1553 &
1773 Data Bus  This HTML version may be printed but not reproduced on websites.
Related Pages on RF Cafe  Radar Equation, 2Way
(another) 
Radar Equation, 1Way 
Radar Equation, Bistatic
 Radar Techniques  Primer (1945
QST)  Radar Postage Stamps 
RF Cafe Quiz #7  Radar Principles 
AN/MPN14 USAF Radar Shop 
AN/TPN19 USAF Radar Shop 
EW/Radar Handbook  Doppler Shift 
Doppler Shift Calculator 
Identification Friend or Foe
(IFF)  Radar Horizon / Line
of Sight  Radar Systems Vendors 
NEETS Radar Principles 
Radar System Vendors
 Who Invented Radar? 
Simple Modification Increases ATC Reliability
