Stanford Research Systems SR844, User Manual

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SR844 Basics 2-3
SR844 RF Lock-In Amplifier
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 Amplifier ?
Let’s consider an example. Suppose the signal is a 1
µ
V sinewave at 10 MHz. Clearly
some amplification is required. A good low noise amplifier will have about 3 nV/
√
Hz of
input noise. If the amplifier bandwidth is 200 MHz and the gain is 1000, then we can
expect our output to be 1 mV of signal and 43 mV of broadband noise ( 3 nV/
√
Hz
×
√
200 MHz
×
1000 ). We won’t have much luck measuring the output signal unless we
single out the frequency of interest.
Now try following the amplifier with a phase sensitive detector (PSD). The PSD can
detect the signal at 10 MHz with a bandwidth as narrow as 0.01 Hz (or even narrower if
you have the patience to wait for several time constants). Using a 1 Hz detection
bandwidth, the output noise will be only 3
µ
V ( 3 nV/
√
Hz
× √
1 Hz
×
1000 ) which is
considerable less than the amplified signal of 1 mV. The signal to noise ratio is now
300 and accurate measurement 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 amplifier
detects the response from the experiment at the reference frequency. Suppose the
reference signal is a square wave at frequency
ω
R
. 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 V
I
sin(
ω
R
t+
θ
I
) where V
I
is the signal amplitude.
The lock-in amplifier multiplies the signal by the reference V
R
sin(
ω
R
t+
θ
R
) using a mixer.
( Note: The SR844 uses a more complicated reference signal for reasons discussed below,
but the principle is the same.) The mixer generates the product of its two inputs as its
output V
M1
.
V
M1
=
V
I
V
R
sin(
ω
R
t+
θ
I
)sin(
ω
R
t+
θ
R
)
(2–1)
=
½ V
I
V
R
cos(
θ
R
–
θ
I
) + ½ V
I
V
R
sin(2
ω
R
t+
θ
R
+
θ
I
)
(2–2)
Since the two inputs to the mixer are at exactly the same frequency, the first term in the
mixer output is at DC. The second term is at a frequency 2
ω
R
, which is at a high
frequency and can be readily removed using a low pass filter. After filtering
V
M1+FILT
=
½ V
I
V
R
cos(
θ
R
–
θ
I
)
(2-3)