Measuring of small AC signals
using lock-in amplifiers.
✓Narrow band selective amplifiers + amplitude detector.
✓Lock-in amplifiers
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PSD*
Signal
amplifier
VCO**
Signal
in
Reference
in
Signal
monitor
Reference
out
Low-pass
filter
DC
amplifier
output
*PSD - phase sensitive detector;**VCO - voltage controlled oscillator
Simplified block diagram
of a lock-in amplifier
John H. Scofield, American Journal of
Physics 62 (2) 129-133 (Feb. 1994).
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Phase shift
x
y
reference
V0sin(wt+j) j
j=p/4, Vout=0.72Vin
0 100 200 300 400 500 600 700
-0.6
0.0
0.6
-0.6
0.0
0.6
-0.6
0.0
0.6
time (msec)
Vin=sin(wt+p/4)
reference
output
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Phase shift
x
y
reference
V0sin(wt+j) j
j=0, Ex=Ein
j=p/4, Ex=0.72Ein
j=p/2, Ex=0
j=p, Ex=-Ein
j=3p/2, Ex=0
The dependence of pattern
of the output signal after
demodulator on phase shift
between input and reference
signals
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0 1 1sin( )x xU U tw = + - input signal
2 2sin( )rU tw = + - reference signal
mod 0 1 1 2 2
01 2 1 2 1 2 1 2
sin( ) sin( )
cos( ( ) ) cos( ( ) )2
de x r x
x
U U U U t t
Ut t
w w
w w w w
= • = + • + =
+ + + + − + −
0
2xU
ω1-ω2 ω1+ω2
0
2xU
2ω
ω1≠ω2 ω1=ω2=ω
0mod 1 2 1 2cos( 2 ) cos( )
2x
de
UU tw = + + + −
and after low-pass filtering 0mod 1 2cos( )
2x
de
UU = −
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Two channels demodulation
In many technical applications we need to measure both
components (Ex, Ey) of the input signal. To do this most of the
modern lock-in amplifiers are equipped by two demodulators.
Ein=Eosin(wt+j)
sin(wt)
cos(wt)
to Ex channel
to Ey channel
xj
y
Ey
Ex
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Robert Henry Dicke
1916-1997
In 1961, Princeton Applied Research was founded by a group
of scientists from Princeton University and the Plasma
Physics Laboratory. With a desire to establish significant
improvements to research instrumentation the team
developed the first commercial lock-in amplifier in 1962.
Model HR-8 f range: = 5Hz÷150kHJz
Analog and digital lock-ins
•0.5 Hz to 100 kHz frequency range
•Current and voltage inputs
•Up to 80 dB dynamic reserve
•Tracking band-pass and line filters
•Internal reference oscillator
•Four ADC inputs, two DAC outputs
•GPIB and RS-232 interfaces
SR510 & SR530
Lock-In Amplifiers
Analog lock-ins from Stanford Research Systems
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Analog lock-ins
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SR124
Low noise, all analog design
No digital interference
0.2 Hz to 200 kHz measurement range
Low noise current and voltage inputs
Harmonic detection (f, 2f, or 3f)
Selectable input filtering
Digital lock-ins
Two DSP lock-in
amplifiers: SR830 from
Stanford Research
Systems and 7265 from
Signal Recovery.
The main advantages of digital
lock-ins:
* high phase stability;
* broad frequency range;
* ideal for low and ultra low
frequencies (up to 0.001Hz)
* harmonics up to 65,536 (7265),
19,999 (SR830).
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Analog and digital lock-ins
Block-diagram of digital lock-in
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SR830
SR830 digital lock-ins
Block-diagram of digital lock-in
Input amplifier
+ filters
Vin Main
ADCDSP
Output
filters
Output
filters
Function
generator
Ref. out
GPIB
ADC1 ADC2
ADC3 ADC4
clockDAC1
DAC1
DAC1
DAC1
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Lock-in amplifier technique: some applications
Tested system
Asinwt
(i) Applying a small test signal (locked to the reference signal)
to the studied object
Lock-in
reference
Examples: frequency domain spectroscopy (second sound),tunneling spectroscopy (analysis of the I-V curves), dielectric spectroscopy etc.
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(ii) Modulating of the studied signal by the signal locked to
the reference signal
Examples: fluorescence experiment
Function
generator
LED
Power
supply
modulationGreen
LED
Detector
SR830 lock-in
Fluorescence
response
Crystal under study
signal
input
reference
input
sync
output
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Lock-in amplifier technique: some applications
Preamplifier
I/V
Lock-in
SR830
V input
Asin(wt) AC output
TSample
DT470
Heater
Lakeshore Temperature controller
PC computer
(HP VEE)
GPIB
Experimental setup for measurement of the dielectric susceptibility
(electrical conductivity) in the temperature range 15-450K
Transfer line
Janis
gas flow
cryostat
1
2
3
4 5
6
7
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Lock-in amplifier technique: some applications
Second sound experiment
He4
AC drive signal
Transmitter (heater)
Receiver
Scanning of the frequency of
the AC signal applied to
transmitter we can find the
frequencies of the acoustical
resonance.
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Lock-in amplifier technique: some applications
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Rb
cell
Function
generator
DMM
5.1kW
Sweep
coil
B0- main field
SR830 lock-in
reference
From
TeachSpin
detector
B0+B1sin(wt)
Optical pumping
Lock-in amplifier technique: some applications
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The choice of
amplitude modulation
1
5.1
FG
sweep
sweep sweep
VI
k
B k I
=W
= •
Ksweep 0.6G/A
If VFG = 1V
B1 ~ 0.12mG
Optical pumping
Lock-in amplifier technique: some applications
Analog detector record (I(f))
Lock-in detector record 𝝏𝑰
𝝏𝑯(𝒇)
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Optical pumping
Lock-in amplifier technique: some applications
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eVAC
eVDC
eVDC+eVAC
Lock-in amplifier technique: some applications
Tunneling spectroscopy
Tunneling spectroscopy
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eVDC only
Courtesy of Anna Miller and Everett Vacek
Lock-in amplifier technique: some applications
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eVDC+eVAC
Courtesy of Anna Miller and Everett Vacek
Tunneling spectroscopy
Lock-in amplifier technique: some applications
Lock-in amplifier technique: demo
Function
generator
Noise
S Lock-in amplifier
demo lock-in
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