Phys 470 Lock-In Amplifier

Lock-in Amplifier Physics 470 Fall 2011

Purpose

Prior to using a lock-in amplifier to detect low-level signals of a known frequency and phase, you should become familiar with the various subcomponents of the lock-in. This lab will investigate the function and operation of an oscillator, noise generator, amplifier, various types of filters, phase shifters, and the lock-in detector itself.

Method

The method of this lab will be to follow a step-by-step tutorial procedure, with a few sections where data should be collected and graphed. Thus, the goal is primarily to learn the operation of various components rather than check some theory. Make notes of the procedures, and take data where requested. The lab report should focus on explaining the data collected for frequency response of the pre-amp and the filter, and in the explanation of the waveforms in the lock-in section’s output.

Procedure (by component)

1. Reference oscillator

Connect the reference oscillator output to Ch. 1 of the digital oscilloscope. Use the “measure” button on the scope to monitor Ch. 1 p-p amplitude and Ch. 1 freq.

Play with the amplitude and frequency knobs to see how they work.

Set the amplitude of the signal at 200 mV and the frequency to 500 Hz.

Check the function of the x1 and the “divide by” 100 switch.

Check the sine-square switch.

Understand how the “freq fine” and the “freq” knobs work.

Question: What is the maximum amplitude of the output at 500 Hz?

Vary the freq range and see how the maximum p-p amplitude varies.

Reset the amplitude to 200 mV.

Connect Ch. 2 of the scope to measure the “output/phase shifter” and measure the p-p amplitude of this output. It will be used as a reference output later in the lab. Noise generator

Use the Reference Oscillator output (set it to 200 mV amplitude and 500 Hz before connecting to other components!) and connect it to the Noise Generator “input signal” jack.

Set “noise amplitude” = OFF and set “signal attenuation” to 1.

Connect the “output signal + noise” to Ch. 2 of the scope.

Question: What is the relative phase of the signals that you now see in Ch. 1 and Ch. 2?

Is there a gain in the amplitude?

Understand the effect of rotating the “signal attenuation” knob.

Now add noise by rotating the “noise” knob and finally leave it set in the 10-1 position.

Use the red “Math” button on the scope to study the frequency spectrum of the two signals seen in Ch. 1 and Ch. 2 of the scope. Press “Math” and then use the top-most soft-key to select the “operation” FFT. You can select FFT “source” as Ch. 1 or Ch. 2 and you will need to use the SEC/DIV know to select 250 Hz/division. There should be a peak at 500 Hz in the Ch.1 spectrum. Now select “source” button - Ch. 2 and you should see broad-band (“white”) noise appear below the peak across the entire screen’s frequency range. Vary the SEC/DIV knob to see how high in frequency it appears to go. Then back in the 250 Hz/division range, you should see the 500 Hz peak. Make this disappear by switching the “divide by” 100 on the reference oscillator. Later, we will try to recover this signal with the lock-in method.

Switch back to x1 on the ref. oscillator and recover the 500 Hz signal on Ch. 1 by pushing the yellow “Ch. 1 Menu” button. Try the signal attenuator to see what happens to the noisy signal. Pre-amplifier

Now use a BNC tee to connect the Reference Oscillator output to Ch. 1 of the scope AND to the pre-amp + input (use the scope to check that the amplitude was 200 mV).

Connect the pre-amp output to Ch. 2 of the scope. Reset the scope to Ch. 1 (yellow button) and push “Measure” to see the amplitude and freq. for both Ch. 1 and Ch. 2.

Understand the gain by switching the gain one range at a time. You will need to adjust the vertical knob for Ch. 2 (VOLTS/DIV) on the scope to keep the signal on the screen.

Question: At what gain does the output signal become flat-topped?

Do not exceed this range or there is a risk of overloading the pre-amp.

What is the p-p maximum amplitude that you see on the flat-topped signal?

Switch to gain = 10

Measure the gain by calculating the ratio of p-p amplitudes for Ch. 1 and Ch. 2 and dividing Ch. 2 p-p by Ch. 1 p-p. It should be close to 10.

Record the p-p amplitudes for Ch. 1 and Ch. 2 for the following frequencies (by changing the frequency from the ref oscillator). You will need to adjust the SEC/DIV knob on both Ch. 1 and Ch. 2 for the scope to properly measure the p-p amplitude, since there have to be several cycles displayed on the screen for the automatic p-p measurement to work correctly.

Frequency: 5, 15, 50, 150, 500, and 1500 Hz

(You will notice that these can be obtained by merely switching the range knob with little or no adjustment of the “freq fine” knob on the ref. oscillator)

In your lab report, you will plot the gain vs. frequency for this data and comment on the low-frequency behavior.

Now return to f = 500 Hz and connect the ref. oscillator output to the – (minus) input of the pre-amp.

Question: What is the relative phase between the input and the output of the pre-amp now? What do the DC, AC, and the GND switches do the to output? Filter

Connect the reference Oscillator output to the Filter input signal and to Ch. 1 on the scope using a tee.

Connect the output “low-pass” to Ch. 2 of the scope. Set the “gain” to 5.

You will now need to vary the “frequency fine” and the “frequency range” knobs.

Question: Is there gain? For which filter frequency is the gain maximum?

Hint: the filter frequency must match the oscillator frequency.

Now we begin a set of measurement procedures: a. Set the filter frequency at 500 Hz. b. Vary the input frequency (the oscillator frequency) by using the reference oscillator controls. Use this set as a suggestion:

Frequency: 5, 15, 50, 150, 500, and 1500 Hz c. Record a table of values of frequency, input p-p amplitude, and output p-p amplitude. d. Plot the data to get the frequency response of the filter. e. Go back to the input frequency range from 150 to 1500 Hz and examine the phase difference between the input and the output from the filter. Record some data and make a plot of phase difference across this range. It might fall in the range from -90o to +90o. Does it cross 0o when the gain is maximum?

Now connect Ch. 2 to the “output high-pass” and repeat steps a. through e.

Repeat this for the “output band-pass”.

Switch “Q” to CHEB and repeat the band-pass measurements.

In your report you will plot gain vs. frequency for these measurements. The frequency scale should be logarithmic. On top of this data, you could plot the phase shift, using a different color. Phase shifter

Disconnect the scope from the lock-in unit.

Now connect the Reference Oscillator “output phase-shifter” to both Ch.1 of the scope AND to the input of the Phase Shifter section. Recall that the Ref Oscillator “output phase-shifter was in-phase with the standard output of the Reference Oscillator, although the amplitude might vary.

Try out the phase and fine phase knobs to see how they function. Notice that the output amplitude might not be constant. Is the phase shift seen on the scope consistent with the markings on the knobs?

Filtering noise

Now leave the tee on the Reference Oscillator “output phase shift” with this output going to Ch. 1 of the scope and to the Phase Shifter input.

Connect the phase shifter output to the Lock-in “input reference”.

The Reference Oscillator output should go through the noise section and you should try a Noise Generator amplitude of 10-3 and attenuation 1.

Look at the output signal + noise with Ch. 2.

Now disconnect Ch. 2 and connect the signal + noise output to the filter input. Connect the filter “output band-pass” to Ch. 2 of the scope. Set Q = 5 and ref osc freq to 500 Hz.

Compare Ch. 1 and Ch. 2 signals. Vary the filter frequency to maximize the signal.

Now move the Ch. 1 cable to the signal + noise output. Look at Ch. 2 and consider the effect of the band-pass filter. What does this do to the noise? Vary the noise amplitude to 10-1 or even 1 and see the effect on the filter output. (You may need to change the scope triggering to Ch. 2 by pushing TRIG MENU and selecting source = CH2.)

Lock-in detection

Now pull Ch. 2 off the filter and put it on the Lock-in output (which has a different type of tee connector, which you can leave on that output permanently).

Connect the filter output to the Lock-in “input signal”.

Play with the phase shifter and look at the lock-in output waveform. Look at the description of the detection process to understand what is going on. Equipment

Teach-Spin Signal Processor/Lock-in Amplifier Tektronix TDS 2012 digital oscilloscope or similar BNC cables (3 ea. 24” and several jumpers, and 3 or more tees)

Supplemental material

Teach-Spin brochure Am. J. Physics 62, 129 Am. J. Physics 71, 1208