Measuring of small AC signals

using lock-in amplifiers.

Narrow band selective amplifiers + amplitude detector.

Lock-in amplifiers

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Lock-in amplifier technique

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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Lock-in amplifier technique 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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Lock-in amplifier technique 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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Lock-in amplifier technique. Simple math.

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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Lock-in amplifier technique 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

x j

y

Ey

Ex

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Lock-in amplifier technique Analog and digital lock-ins

Block-diagram of analog lock-in

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Lock-in amplifier technique 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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Lock-in amplifier technique Analog and digital lock-ins

Block-diagram of digital lock-in

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Lock-in amplifier technique SR830 digital lock-ins

Block-diagram of digital lock-in

Input amplifier

+ filters

Vin Main

ADC DSP

Output

filters

Output

filters

Function

generator

Ref. out

GPIB

ADC1 ADC2

ADC3 ADC4

clock DAC1

DAC1

DAC1

DAC1

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Lock-in amplifier technique Analog and 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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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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Lock-in amplifier technique: some applications

(ii) Modulating of the studied signal by the signal locked to

the reference signal

Examples: fluorescence experiment

Function

generator

LED

Power

supply

modulation Green

LED

Detector

SR830 lock-in

Fluorescence

response

Crystal under study

signal

input

reference

input

sync

output

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Lock-in amplifier technique Examples of application

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 Examples of application.

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 Examples of application.

Optical pumping

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Rb

cell

Function

generator

DMM

5.1kW

Sweep

coil

B0- main field

SR830 lock-in

reference

From

TeachSpin

detector

Examples of application.

Optical pumping

B0+B1sin(wt)

Examples of application.

Optical pumping

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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

Lock-in amplifier technique Examples of application.

Optical pumping

Analog detector record (I(f))

Lock-in detector record 𝝏𝑰

𝝏𝑯(𝒇)

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Lock-in amplifier technique: demo

Function

generator

Noise

S Lock-in amplifier

demo lock-in

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