SRS Labs manual SR850 Basics What is a LOCK-IN AMPLIFIER?, Why use a lock-in?

SR850 BASICS

WHAT IS A LOCK-IN AMPLIFIER?

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 compo- nent 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 measurement.

Why use a lock-in?

Let's consider an example. Suppose the signal is a 10 nV sine wave at 10 kHz. Clearly some amplifi- cation is required. A good low noise amplifier will have about 5 nV/√Hz of input noise. If the amplifier bandwidth is 100 kHz and the gain is 1000, then we can expect our output to be 10 µV of signal (10 nV x 1000) and 1.6 mV of broadband noise (5 nV/√Hz x √100 kHz x 1000). We won't have much luck measuring the output signal unless we single out the frequency of interest.

If we follow the amplifier with a band pass filter with a Q=100 (a VERY good filter) centered at 10 kHz, any signal in a 100 Hz bandwidth will be detected (10 kHz/Q). The noise in the filter pass band will be 50 µV (5 nV/√Hz x √100 Hz x 1000) and the signal will still be 10 µV. The output noise is much greater than the signal and an accurate measurement can not be made. Further gain will not help the signal to noise problem.

Now try following the amplifier with a phase- sensitive detector (PSD). The PSD can detect the signal at 10 kHz with a bandwidth as narrow as

0.01Hz! In this case, the noise in the detection bandwidth will be only 0.5 µV (5 nV/√Hz x √.01 Hz x 1000) while the signal is still 10 µV. The signal to noise ratio is now 20 and an accurate measure- ment of the signal is possible.

What is phase-sensitive detection?

Lock-in measurements require a frequency refer- ence. Typically an experiment is excited 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 dia- gram below, the reference signal is a square wave at frequency ωr. This might be the sync output from a function generator. If the sine output from the function generator is used to excite the experi- ment, the response might be the signal waveform

shown below. The signal is Vsigsin(ωrt + θsig) where Vsig is the signal amplitude.

The SR850 generates its own sine wave, shown as the lock-in reference below. The lock-in refer- ence is VLsin(ωLt + θref).

Reference

θ sig

Signal

θ ref

Lock-in Reference

The SR850 amplifies the signal and then multiplies it by the lock-in reference using a phase-sensitive detector or multiplier. The output of the PSD is simply the product of two sine waves.

Vpsd = VsigVLsin(ωrt + θsig)sin(ωLt + θref)

=1/2 VsigVLcos([ωr - ωL]t + θsig - θref) - 1/2 VsigVLcos([ωr + ωL]t + θsig + θref)

The PSD output is two AC signals, one at the dif- ference frequency (ωr - ωL) and the other at the sum frequency (ωr + ωL).

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 ωr equals ωL, the difference frequency component will be a DC signal. In this case, the filtered PSD output will be

Vpsd = 1/2 VsigVLcos(θsig - θref)

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