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Physics 431 Home

Phase-sensitive detection and Lock-in amplifiers

In this exercise, students are introduced to the so called "lock-in" detector, one of the experimentalist's most useful and powerful tools for recovering signals otherwise hopelessly buried in noise. The "signal" of interest is generated by a light emitting diode (LED) driven at the lock-in reference frequency, and the noise signal is generated by a second LED driven by a random noise generator. Light from both LED's is detected by a photodiode and in this process the signal and noise are mixed. Students observe that the light from the signal diode can easily be distinguished from the noise, even when the noise power exceeds the signal power by a factor of several hundred or more. The inevitable trade-off between lock-in response time and output stability is explored, showing that even with this remarkable instrument there is no free lunch when noise is at the table.

Experiment Information

• Write-up
• Keithley 2000 buffer operations
• Ithaco Application Note IAN-35, The evolution of the modern lock-in amplifier, by Edwin H. Fisher.
• Ithaco Application Note IAN-47, Introduction to lock-in amplifiers, by J. L. Scott.
• Ithaco Application Note IAN-49, Speed/accuracy tradeoff when using a lock-in amplifier to measure signals in the presence of random noise, by J. L. Scott.
• Signal Recovery Technical Note TN-1000, What is a lock-in amplifier?

Discussion Questions

1. In Exercise 2 you measured the gain of the Keithley 822 PSD. You should have found that the gain is a little more than 10. Why would the designer of the amplifier choose a gain of this value? Why not use a gain of exactly 10?


2. In the introduction, the Q of a filter is defined as the ratio of the center frequency f to the range of frequencies Δf between the points where the filter response falls by one-half, that is, it's the inverse of the full-width at half maximum of the filter's pass-band expressed in units of the center frequency. Discuss, and show a calculation, of how you would determine the Q of this lock-in when the reference frequency is 1000 and the time constant is 1 second.


3. The digital noise generator needs a clock input (the "noise generator input") supplied by the "aux out" from the function generator. If the signal generator is set to 1 kHz, what would be the highest square-wave frequency that you could see from the noise generator? (It is not 1000 Hz.) Discuss.


4. Why, in Exercise 10, do we use the features of the Kiethley 2000 meter to find the RMS voltage fluctuations? What would happen if we just used the ACV button to make these measurements?


5. In the discussion of Section 5 of the write-up, the claim is made that the phase-sensitive detector's switch effectively multiplies the signal by a square wave, and thus produces output at the reference frequency's odd harmonics as well as the fundamental. Show, by discussion and calculation, that multiplication by a pure sine wave only gives output at the reference's fundamental frequency.