Sr810 Basics; What Is A Lock-In Amplifier - Stanford Research Systems SR810 Manual

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.
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 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
0.01 Hz! 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
measurement of the signal is possible.
What is phase-sensitive detection?
Lock-in measurements
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 ω
Noise signals at
20 and an accurate
require a frequency
. This might be the
r
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
t + θ
V sin(ω ) where V
sig r sig
The SR810 generates its own sine wave, shown
as the lock-in reference below. The lock-in
reference is V sin(ω
L
The SR810 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.
V = V V sin(ω
psd sig L
= 1/2 V V cos([ω
sig L
1/2 V V cos([ω
sig L
The PSD output is two AC signals, one at the
difference frequency (ω
sum frequency (ω
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 wr
equals ω
, the difference frequency component will
L
be a DC signal. In this case, the filtered PSD
output will be
V = ½ V V cos(θ
psd sig L
This is a very nice signal - it is a DC signal
proportional to the signal amplitude.
Narrow band detection
Now suppose the input is made up of signal plus
noise. The PSD and low pass filter only detect
signals whose frequencies are very close to the
lock-in reference frequency. Noise signals at
frequencies far from the reference are attenuated
at the PSD output by the low pass filter (neither
ω nor ω
-ω
noise ref noise
frequencies very close to the reference frequency
will result in very low frequency AC outputs from
the PSD (|ω -ω
noise
depends upon the low pass filter bandwidth and
roll-off. A narrower bandwidth will remove noise
sources very close to the reference frequency, a
wider bandwidth allows these signals to pass. The
low pass filter
3-1

SR810 Basics

is the signal amplitude.
sig
t + θ
).
L ref
t + θ t + θ
)sin(ω )
r sig L ref
- ω ]t + θ - θ
) -
r L sig ref
+ ω ]t + θ + θ
)
r L sig ref
- ω
) and the other at the
r L
+ ω
).
r L
- θ
)
sig ref
+ω are close to DC). Noise at
ref
| is small). Their attenuation
ref
bandwidth determines the