lab 6 — lock-in amplifier

8/4/2019 Lab 6 Lock-In Amplifier

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Physics 404 Lock-In Amplifier Lab Physics Department, UIUCPage 1/5

Lab 6 Lock-In Amplifier

A lock-in amplifier is able to measure a small signal even in the presence of a lotof noise. It does this with the help of some signal processing. If the signal weare looking at is

` ( )v V tin = 0 sin

and we multiply it by a square wave which has a Fourier series of

( ) ( ) ( )4 1 1

sin sin 3 sin 53 5

sqv t t t

= + +

+

we get

( ) ( ) ( )

= ttt

Vvout

6cos35

24cos

15

22cos

3

21

2 0

Notice that output has a DC level proportional to the input voltage.

To perform this operation we can use a switch which gates through vin when vsq ishigh and gates through - vin when vsq is low. This is shown below.

vsq is derived from a reference signal. This signal needs to be converted to asquare wave. This is done with a comparator. In this lab we will use the LM339comparator.

1) Determine how to implement the CMOS switch using the 4066 (replacementfor obsolete 4016) switch and the LM339 comparator.

2) Construct the circuit. Note, for a bipolar input signal, both the CMOS 4066switch and the LM339 comparator should be powered from the 5V powersupplies. Note also that the LM339 outputs are open-collector outputs, thus a10K pullup resistor, connecting LM339 output to +5V is needed.

3) Test the circuit using vin = vref= 1VAC4) Use the DMM to measure the DC component of the output.

Revised 4/2003.

Copyright 1999. The Board of Trustees of the University of Illinois. All rights reserved.


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Is it what you expect?Does the output DC level vary with frequency and should it vary with

frequency ?

In the first section you built a phase sensitive rectifier which is the signalprocessing element of a lock-in amplifier. Your design should have been similarto the one below where the switches are the analog switches in the 4066. If your

design was different, reconstruct it to match the circuit shown. Again, note for abipolar input signal, both the CMOS 4066 switch and the LM339 comparatorshould be powered from the 5V power supplies. Note also that the LM339outputs are open-collector outputs, thus a 10K pullup resistor, connectingLM339 output to +5V is needed.

This is called a phase sensitive rectifier because the circuit rectifies vin in phasewith vref (or vsq). If there is a phase shift between vin and vref the DC level is theprojection of vinon vref (vsq) or if

( )v V tin = +0 sin then the DC component of the output is

( )VV

ou t =2 0

cos .

A better way to visualize phase is to think of v in as a complex voltage. Using thisidea the DC output is the real part (i.e. in-phase) of the vin. Using a schemeshown below it is possible to measure the imaginary part (i.e. 90 out of phase) ofvin.

Revised 4/2003.



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If we add a phase shifter () then vsq is no longer in phase with vref. The outputlevel is then the projection of vin on vsq as shown in a) in the diagram below. In atypical application vin will have a phase shift relative to vref. To measure a

maximum output level, is adjusted until vsq is in phase with vin.

Therefore, if we set = 90, then the projection of vin on vsq is the imaginary partof vin. We then measure a complex voltage by measuring the output voltage with

= 0 to get the real part and then again measure the output voltage with =90 to get the imaginary part.

Phase Shifters

There are two circuit which we have see that will give us a phase shift. Thesimplest is a 180 phase shifter which is simply an inverter. The next circuit wehave used is an integrator which gives a phase shift of 90.

The most useful circuit is a 0-180 phase shifter.

Determine the phase shift for this circuit in terms of R, C, and R1. Note thatR is a variable resistor and C and R1 have fixed values.

In general the 0-180 and 180 phase shifters work the best. The fixed 90 phaseshifter has a problem of developing a DC offset and it is possible that the signalnever crosses ground resulting in a bad output.

Revised 4/2003.



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Complex Voltage Measurement

We are now going to use our lock-in amplifier to measure the complex voltage atnode v2. Use the procedure below to measure this voltage.

1) Design a 0-180 phase shifter with the operating point around 10 KHz. Whenyou choose your components, remember that when you use a potentiometer,you are limited to a certain range of R. Therefore think about what values ofR and C corresponds to a 90 shift at 10 KHz.

2) Set v1 to 1V at 10KHz.

3) Apply this signal to vin and to vref.4) Adjust the phase shifter so that the DC output is 0 (on the DMM). Youshould also look at the output on the scope. When the DC output is 0, vsq hasa 90 shift. Why?

5) Now construct the test circuit above and attach v2 to vin.6) Measure the real part of v2 by connecting vrefto the comparators (no phase

shift)7) Measure the imaginary part of v2 by including the 90 phase shifter.8) Using the value of v2 you measured, calculate the impedance between v1 and

v2. Does this impedance match the values you used ?

Rejection of NoiseThe test of a lock-in is its ability to filter out all signals except those within a

bandwidth roughly 1 RC time constant of the reference frequency. We will use thephoto-detector circuit to test the noise rejection of your lock-in. The signal ofinterest will be a train of light pulses from an LED while the noise will be 60 Hzpickup from the overhead fluorescent lights. We want the lock-in to detect the RMSvoltage from the photo-detector that is due to the LED and to reject everything else.

A test circuit for noise rejection of lock-in is shown below.

Revised 4/2003.



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+

+

741

LM339LED

1M

1M

3K

+15 V

+15 V

Lock-in

REF

IN

As in all lock-in measurements, you need to make your desired signal vary atthe reference frequency. Use a comparator (LM339- the specs are on your bench-book) to turn the LED on and off synchronously with the lock-in reference. At a lowenough frequency you can see the LED blink on and off. Next, wire up the photo-detector with an MRD500 or VTP1188S photodiode and a current amplifier. Attacha couple of long leads to the LED so that you can move it around relative to thephoto-detector. Watch the current amp output on the scope and look for the signalfrom the LED as you bring it close to the photodiode. You should be able to see theLED signal when it is within a few inches of the photodiode. (The diode is more

sensitive to red than green.)

Now, as you monitor with the scope, send the current amp output to yourlock-in and try to detect the RMS level due to the LED. Choose an operatingfrequency far from 60Hz (maybe 500 Hz). Vary the phase shifter setting tomaximize the signal. Move the LED farther and farther away to test how small asignal the lock-in can detect in the presence of noise. (You can block the LED withyour hand to see if the lock-in output is coming from it and not some other source.)Obtain a rough measure of the minimum signal to noise ratio that the lock-in candetect at its input with a 1 second time constant. Vary the frequency of the signal tosee how close to 60 Hz you can get and still distinguish signal from noise. Brieflydescribe your test with your data.

Revised 4/2003.


lab 6 — lock-in amplifier

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