Stanford Research Systems SR865A, Operation Manual

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Basics 37
SR865A DSP Lock-in Amplifier
Chapter 2
Lock-in Amplifier 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
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
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 amplification is required. A good low noise amplifier may
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
μ
V of signal (10 nV × 1000) and 1.6 mV of broadband noise
(5 nV/√Hz × √100 kHz × 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
μ V (5 nV/√Hz × √100 Hz × 1000) and the signal
will still be 10 μ V. The output noise is still much greater than the signal and an accurate
measurement cannot 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 0.01 Hz! In this case, the noise
in the detection bandwidth will be only 0.5
μ V (5 nV/√Hz × √.01 Hz × 1000) while the
signal is still 10 µV. The signal to noise ratio is now 20 and an accurate measurement of
the signal is possible.
What is phase-sensitive detection?
Lock-in measurements require a frequency reference. 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 diagram below, the
reference signal is a square wave at frequency f
ref
. This might be the sync output from a
function generator. If the sine output from the function generator is used to excite the
experiment, the response might be the signal waveform shown below. The signal is
V
sig
sin(ω
ref
t
+ θ
sig
) where
ω
ref
=
2πf
ref
and V
sig
is the signal amplitude.