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

Block-diagram of analog lock-in

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SR530

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 MainADC

DSPOutputfiltersOutputfilters

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

Functiongenerator

LEDPowersupply

modulationGreenLED

Detector

SR830 lock-in

Fluorescence response

Crystal under study

signalinput

referenceinput

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

Optical pumping

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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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