SVR 3
Phase sensitive detection
Lock-In
Amplifier
Leiden 2003
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INTRODUCTION
Lock-In amplifiers are used to detect and measure very small AC signals – all the way down to a few
nanovolts! Accurate measurements may be made even when the small signal is obscured by noise sources
many thousands of times larger. Lock-In amplifiers use a technique known as phase-sensitive detection to
single out the component of the signal at a specific reference frequency and phase. Noise signals at
frequencies other than the reference frequency are rejected and do not affect the measurements.
Why use a LOCK-IN? For example measuring the signal of about 10nV at 10kHz with a very good low
noise amplifier (5nV/Hz of input noise, 100kHz bandwidth, gain is 1000.) we can expect our output to be
about 10V of signal and about 1.6mV of broadband noise. Even if we follow the amplifier with an
excellent band pass filter (Q=100), centered at 10kHz, any signal in a 100Hz (10kHz/Q) bandwidth will be
detected. Finally we have 10V of our signal competing with 50V of noise. Using the amplifier with a
phase-sensitive detector (PSD) we can detect the signal at 10kHz with a bandwidth as narrow as 0.01Hz!
That gives us 10V of signal and only 0.5V of noise (signal to noise ratio is 20!) as an output.
What is a phase-sensitive detection? Lock-In measurements require a frequency reference. Generally, an
experiment is performed at a fixed frequency (from an oscillator or function generator) and the lock-in
detects the response from the experiment at the reference frequency. In the diagram below, the reference
signal is a square wave at frequency R(for instance a sync output from a function generator). If the sin
output from the function generator is used to excite the experiment, the response might be the signal
waveform shown below. The signal is V SIGsin(Rt+SIG). Assume the lock-in reference is VLsin(Lt+REF).
Reference
SIG
Signal
Lock-In Reference
REF
After the amplification the signal is multiplied by the lock-in reference using a PSD or multiplier. The
output of the PSD is simply the product of two sine waves.
VPSD = VSIGVLsin(Rt+SIG)sin(Lt+REF) = 1/2 VSIGVL cos([ R - L]t +SIG - REF) -1/2 VSIGVLcos ([ R + L]t +SIG + REF)
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If the PSD output is passed through a low pass filter, the AC signals are removed. What will be left? In the
general case, nothing. However, if R equals L, the difference frequency component will be a DC signal.
In this case, the filtered PSD output will be
VPSD = 1/2 VSIGVL cos(SIG - REF)
This is a very nice signal – it is a DC signal proportional to the signal amplitude.
Where does the lock-in reference come from? We need to make lock-in reference the same as the signal
frequency, R equals L. Not only do the frequencies have to be the same, the phase between the signals
can not change with time, otherwise cos(SIG - REF) will change and VPSD will not be a DC signal. In other
words, the lock-in reference needs to be phase-locked to the signal reference.
Generally, lock-in amplifiers use a phase-locked-loop (PLL) to generate the reference signal. An external
reference signal (the square wave in the diagram above) is provided to the lock-in. The PLL in the lock-in
locks the internal reference oscillator to the external reference, resulting in a reference sine wave at R with
a fixed phase shift of REF. Since the PLL actively tracks the external reference, changes in the external
reference frequency do not affect the measurement.
In the following experiment you are offered to build a simplified scheme of a phase sensitive detector
consisting of: Signal Source /Strain Gauge, Modulation Generator, Band Pass Amplifier, Phase-Shifter
(reference signal), Demodulator (Sync Detector), Low Pass Filter and Meter (Oscilloscope). The blockscheme of the device is shown in the picture below.
Synchrodetector
Signal/
Strain Gauge
Band Pass
Amplifier
Demodulator
Low Pass
Filter
Modulating
Generator
Phase-Shifter
METER
Oscilloscope
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The Strain Gauge
R4
R2 + ΔR
∾
R3 - ΔR
82 Ω
200 Ω
10 Ω
…To amplifier
Modulation
(sin wave)
82 Ω
R1
The Strain Gauge used for measuring weights is integrated into a Wheatstone Bridge. The electrical
circuit of the device is shown below*. Additional 200 Ohm potentiometer connected parallel to the 10 Ohm
resistor is used for balancing the bridge when no weight is measured. This scheme allows fine tuning the
balancing resistance. The input signal (sin wave modulation) passes a ground isolating transformer, which
has a double function: 1) It allows us to ground both, input and output signals 2) The possible “ground
loop” noise is expluded, which increases the stability of the measurement system.
Transformer
R2 = R3 = 120 Ω, the gauge factor G = (ΔR/R)/(Δ/) ≈ 2.1
In present task students are supposed to build a simplified Lock-In amplifier
integrated into a “jewellery-balance” (The strain Gauge). Each electronic component
of the device has to be implemented and studied independently. In conclusion
students are offered to calibrate the balance and measure several unknown weights,
using phase sensitive detection. The ideal scenario assumes students to perform
exercise N1 during the first session and exercises N2 – 4 during the second session,
so the last session can be used for the balance calibration (exercise N5) and planning
the final report.
• The Authors strongly recommend to make your report as a sequence of sub-reports
about each part of the task.
*As an additional exercise write down the condition for the bridge balance. What are the possible disadvantages of the given device?
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Exercise № 1.
The band pass amplifier.
1. What is a band pass amplifier? Give a quantitative description, general function and
characteristics.
2. Build the scheme shown in the picture 1 using following values of resistors and
capacitors:
Rin= Rf = 12 kΩ, C=20 nF. (R is supposed to be calculated for operating around 1kHz)
3. Calculate the optimal theoretical value of  to have the best Q-factor, i.e. the smallest
amplification bandwidth. Study the frequency characteristic of the amplifier for different
values of  (typically 3) and calculate the Q-quality for each of them. Find the optimal 
and compare it with the theoretical value.
4. Connect the Strain Gauge to the input and the oscilloscope to the output of the
amplifier respectively. Would that be enough to measure the weight of a coin? Why? Try
to get sufficient signal/noise ratio using 2 or 3 coins.
5. Report should include
a). The table with Q-quality and 0 (center frequency) values for different .
b). The drawing of log |H()| versus log() for all .
Rf
C
GENERAL EQUATIONS
+
Rin
(1-)R*
-
H   
R*
Vout

C
R
i 2  i  0   02
Q
R*
Vin
i
1
RF C
Q
Picture 1. The band pass amplifier.
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
1
 4  


0 
1
C
2
RF R
2
R
RF

RF
R
Exercise № 2.
The phase-shifter.
1. What is a phase-shifter? Give a quantitative description, general function and
characteristics. What role does it play for the phase-sensitive synchro-detector?
2. Build the scheme shown in the picture 2 using following values of resistors and
capacitors:
Rin= Rf = 12 kΩ, (Choose values R* and C to have a phase shift range > 45 deg.)
3. What are the theoretical limits one can shift the phase between input and output
signals?
4. Study the frequency characteristic of the phase-shifter.
5. Report should also include
a). The table with the values of the phase shift Δφ between input and output
signals as a function of R* (typically 10 values)
b) The graph of the phase shift Δφ between input and output signals as a function
of log (ω) for one value of R*.
Rf
-
Rin
+
C
Vout
R*
Vin
Picture 2. The phase-shifter.
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Exercise № 3.
The low pass filter.
1. What is a low pass filter? Give a quantitative description, general function and
characteristics. What role does it play for the phase-sensitive synchro-detector?
2. Build the scheme shown in the picture 3 using following values of resistors and
capacitors:
R1= 10 kΩ, R2 = 100 kΩ, C = 1F (What would be RC-time in this case?)
3. Study the frequency characteristic of the low pass filter.
4. Report should also include
a). The graph of the output signal amplitude as a function of frequency.
C
R2
-
R1
+
Vin
Vout
Picture 3. The band pass filter.
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Exercise № 4.
The mixer.
1. What is a mixer? Give a quantitative description, general function and characteristics.
What role does it play for the phase-sensitive synchro-detector?
2. Build the scheme shown in the picture. NOTE! Pins 1,10, 14,12 marked as GND are
independent, therefore each of them requires a connection to your ground line.
3. At what value of the input signal does the mixer begin working properly? Why?
4. Report should also include
a). The graph of the output signal.
GND 1
20
2
19
3
18
AD630
4
5
17
4
16
6
15
7
14 GND
- 15V 8
SIGNAL
INPUT
13 Output
Reference input (phase-shifter) 9
12 GND
GND 10
11 +15V
Picture 4. The Mixer.
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Exercise № 5.
Testing and calibrating the balance.
1. Estimate on the basis of theory and the previous exercises the relation between the
signal and measured weight:
a. At the output of the Weatstone bridge.
b. At the output of the band pass amplifier connected to the input of the
demodulator.
c. At the output of the low pass filter.
2. Measure using an oscilloscope the signal at the output of the band pass amplifier for a
few different weights on the balance. Describe and explain qualitatively and
quantitatively what you observe.
3. Use either a voltmeter or an oscilloscope (preferably in the slow scan storage mode) to
measure the signal at the output of the low pass filter as function of measuring weight on
the Weatstone bridge. Make a plot and calibrate the sensitivity of the balance in units of
mV/mg.
4. Make a realistic estimate of the noise level. What is the accuracy of the weight
measurement?
5. To what extent are you bothered by noise and drift in this experiment? Give a
qualitative explanation.
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