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Doppler Measurement

Chapter 10

Introduction  The apparent difference between the

frequency at which sound or light waves leave a source and at which they reach an observer caused by relative motion of the observer and the wave source

 First described in 1842 by Christian Doppler

 Acoustic examples include the apparent difference in frequency of a motor vehicle approaching and receding from an observer

 EM examples include the red shift of most galaxies due to the expansion of the universe

 The principle is generally used to determine the radial velocity of one object relative to another

Doppler Frequency Shift Movie

www.modellflug.tv

Definition of Directions

RS Vs Vr

Source Receiver

Doppler Frequency Shift  It is shown in the Sensors book that the

relationship between the velocities of the source and receiver and the transmit and receive frequencies is

 The Doppler shift is the difference between the received and transmitted frequency

 For EM radiation where vs << c this reduces to

s s

r r f

vc f

 



s s

sr s

r srd f

vv f

vc fff

 

 

  

 

 

 1

sr s

sr srd

vv f

vv fff

 

 



Higher frequency

Lower frequency

Doppler Effect Animation

http://www.youtube.com/watch?v=ZRGg7e9b5wY&feature=related

Example

 An electromagnetic source operating at 77GHz ( = 3.9mm) and a sound source operating at 90kHz ( = 3.9mm) are each moving at a speed of 30m/s, what is the Doppler shift observed by a stationary observer in each case

 For the EM radiation

 For the sound

kHzf vc

vv f s

sr d 7.71077

103

300 9 8

  

  



kHzf vc

vv f s

sr d 7.81090

30340

300 3   

  



kHz v

f sd 7.7 109.3

30 3 

 

 As an exercise, consider the case when vs = c

An Enigma (so far)

s s

r rs

r r f

vc ff

vc f

 

  

  

  



S R S R S R S R

fd = -2.42kHz fd = -4.57kHz fd = 4.85kHz fd = 2.28kHz

For the following values

c = 340m/s

vr = 30m/s

vs = 10m/s

fs = 40kHz

BBC Christmas Lectures

Activity: Doppler Ultrasound

Doppler Geometry (v<c)  In most Doppler sensors, both the receiver and transmitter are

stationary and they illuminate a moving target

 This is equivalent to the receiver moving away from the transmitter

 For collocated transducers where v is the radial velocity from the target to the sensor

 Equating

r s

c v f f

c v

  



srd fff 

RS Vs Vr

2 s d

vf f

c v  



Doppler Geometry (v<c)

 For separated transducers this is

 And for co-located transducers where r = t =  just replace the two angles with the common offset angle

Transmitter

Receiver Target

t r

cos

cos r

r s t

c v f f

c v

 

  

 srd fff 

Doppler Geometry (v<<c)  For stationary receiver and transmitter illuminating a moving target

 This is equivalent to the receiver moving away from the transmitter at a velocity v.cost + v.cosr if v<<c

 For separated transducers this is

 For co-located transducers r = t = 

Transmitter

Receiver Target

t r

 rtsd c

vf f  coscos 

 

 cos 2

cos 2

s d

vf f 

Doppler Frequency Extraction

Doppler Frequency Extraction  For a transmitter signal of the form

 The corresponding echo received from a moving target will be

where  - phase term dependent on the distance to the target (rad) s = 2fs (rad/s) d = 2fd (rad/s)

 Mixing (multiplying) the two signals

Doppler Component at 2fs

)cos()( ttx sss 

)]cos([)(   ttx dsrr

      





tttxtx

dsd rs

dsssrrs

2coscos 2

)]cos([)cos()()(

Filtering  As we are not interested in the signal at 2 s it is filtered out using a

lowpass filter as shown in the figure

 In Doppler ultrasound applications, there is also a large static return from non moving targets that could be 40 to 50dB larger than the Doppler signal

 This is often filtered out using a high pass filter

)cos( 2

)(  

 ttx d rs

Doppler Direction Discrimination

 The mixing process described in the previous slides can only provide an absolute difference in frequency. It contains no information regarding the direction of motion

 The following are the most common techniques used to preserve the direction information  Sideband filtering

 Offset carrier demodulation

 In phase / Quadrature demodulation

 In the descriptions remember that  d > 0 Target velocity towards the sensor  d < 0 Target velocity away from the sensor

Sideband Filtering

Channel A Channel B

smssm s

in in

sin|

Input

Output

Bandpass Filter

(s,s+m)

Bandpass Filter

(s-m,s)

Reference s Audio

Bandpass Filter

Audio Bandpass

Filter

+ve shifted Doppler

-ve shifted Doppler

Signal in

Offset Carrier Demodulation  Instead of mixing down to baseband, the received, Doppler shifted

signal is mixed with a reference signal s + 1 where 1 < |s+ dmax|  After filtering to remove the signal at 2s , in the absence of a moving

target, the resultant is a signal at a frequency 1 which is removed with a notch filter

 If the target is moving, then the frequency will shift upwards if it is approaching, and downwards if it is receding

1 + d > 1 +ve shift 1 + d < 1 -ve shift

s

b

s1-a|

Input

Output

s1

a

s1-b|

1 Receding Approaching

Reference (s+1)

Bandpass Filter & Notch

Filter

Doppler shifted output signal

Signal in

In Phase and Quadrature Demodulation

Audio Bandpass

Filter

Audio Bandpass

Filter

in phase Doppler

quadrature Doppler

Signal in

Reference s

90

 The output signals are

 If q(t) is retarded by /2 with respect to i(t) the target is approaching

 If q(t) is advanced by /2 with respect to i(t) the target is receding

  )sin()(

cos)(

   

ttq

tti

Lissajous Representation of IQ Signals

1 2

Lagging Leading

i(t)

q(t) q(t)

i(t)

Pulsed Doppler Principles

(a)

(b)

(c)

The number of cycles received during the pulse period at each range depends on the Doppler frequency and the pulsewidth

Combines aspects of TOF range measurement with Doppler velocity measurement

Doppler Outputs for I/Q Detection

Pulsed Doppler Outputs

Approaching Receding

Spectrogram  A spectrogram based on a short time Fourier transform

conveys information about the Doppler spectrum (amplitude and frequency) as a function of time

 This is plotted on frequency-time axes with amplitude (intensity) encoded by colour

 If the complex FFT takes in I and Q inputs then the spectrogram provides both speed and direction

Doppler Sensors

 Many sensors using both ultrasound and electromagnetic waves make use of the Doppler principle to measure target motion effects

 Sensors can either use continuous wave (CW) or pulsed waveforms

 CW sources generally determine velocity only

 Pulsed sources can discriminate range and velocity

Continuous Wave Ultrasound Example

Doppler Flow and Heartbeat MonitorSchematic of Monitor

Continuous Wave Radar Examples

•X-Band (8-12GHz) intruder alarm •Iris coupled Gunn Oscillator Based •Output power 1-10mW •Integral horn antenna

K-band (24.15GHz) sports radar Gunn oscillator Output power 40-100mW Lens antenna Accuracy +/-1km/h (typical)

Fraden J, ”Handbook of Modern Sensors

http://williamson-labs.com/images/gunn.gif

http://www.stalkerradar.com/

Doppler Missile Tracker  A narrow band fixed frequency tracking filter at fo in the IF chain rejects

noise and crosstalk from the transmitter

 The filter is followed by a discriminator that produces a DC voltage proportional to the frequency error

 This drives a voltage controlled oscillator (VCO) that produces a signal fo+fd that is mixed with the transmit signal to produce the local oscillator

 This automatic frequency control ensures that the received signal ft+/-fd is always down converted to a constant frequency fo irrespective of the target speed

Frequency Discriminator

Amp

Mixer

Coupler

Antenna

CirculatorTransmitter

IF Filter

ftx

VCO

ftx+fo+fd

fo+fd

ftx

ftx+fd

ftx

Doppler Target Identification

 Moving targets, or moving components of targets can be used to identify them  In military applications this includes

helicopter blade spectra and tank track signatures

 In security applications, Doppler spectra can discriminate between human and animal intruders

Doppler spectrogram of a large white dog

Doppler spectrogram of a small human target

Helicopter spectrum

Tank tread spectra

Curie N, ”Principles and Applications of Millimeter Wave RadarCourtesy Dropman D

Pulsed Doppler Ultrasound

 Pulsed Doppler ultrasound systems can produce 2D images encoded for movements

 Because the transmit and receive signals are separated in time, a single transducer can be used

 Pulsed Doppler is often incorporated into conventional pulsed echo ultrasound systems (duplex scanning)

 Very short pulses are used, typically only a few cycles long, to obtain the best possible resolution

 Typically a “sampling volume” that is smaller than the whole image is processed for Doppler

Courtesy Philips Research

Pulsed Doppler Ultrasound Image

Sampling volume for Doppler processing

Courtesy Siemens GMBH

Pulsed Doppler Weather Radar

Courtesy National Weather Service NEXRAD

http://www.weatherzone.com.au/radar.jsp

Doppler Targets  For calibration of Doppler sensors, we need a “static” moving target

 Options include the following:  Rotating trihedral (variable velocity)

 Tuning fork (fixed velocity)

 Piezo transducer or loud speaker (variable velocity)

 Echo box

Rotating trihedral

Piezo transducer with spherical target

Radar echo box

Target Signature for Rotating Trihedral

Target Model

Doppler Signature

Case Study: Estimating the Speed of a RC Aircraft using Sound Files

Sound File

Spectral Content

Fundamental at 600Hz

Clusters of Harmonics

Expanded View

Spectrogram

In te

n si

Expected Frequency Shift of a Flypast

222 zyxr 

s s

r f vc

c f

 

The problem is – the true frequency fs is unknown In this example, it is assumed to be 3.4kHz

Spectrogram Expanded

Approaching target asymptote 3.69kHz

Receding target asymptote 3.09kHzSelect any clear pair of asymptotes

Solving for the Target Speed

 The formulae used to determine the asymptotic values for the Doppler frequencies of the approaching and receding targets are

 Taking the ratio of f1/f2 = k = 1.194 results in an equation that does not require the unshifted frequency, fs.

 Solving for the target speed, vs, gives the following

3.69kHz1   s

f vc

c f 3.09kHz2 

 s s

f vc

c f

s vc

c k

 

 

  .

  30.06m/s

1194.1

1194.1340

)1( 

 

  

 k

kc vs