Stanford Research Systems SR830 Manual page 29

SR830 Basics
This is a very nice signal - it is a DC signal propor-
tional 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 sig-
nals whose frequencies are very close to the lock-
in reference frequency. Noise signals at frequen-
cies far from the reference are attenuated at the
PSD output by the low pass filter (neither ω
ω nor ω
+ω are close to DC). Noise at fre-
ref noise ref
quencies very close to the reference frequency will
result in very low frequency AC outputs from the
PSD (|ω -ω | is small). Their attenuation
noise ref
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 bandwidth determines the band-
width of detection. Only the signal at the reference
frequency will result in a true DC output and be
unaffected by the low pass filter. This is the signal
we want to measure.
Where does the
lock-in reference come from?
We need to make the lock-in reference the same
as the signal frequency, i.e. ω
the frequencies have to be the same, the phase
between the signals can not change with time, oth-
- θ
erwise cos(θ ) will change and V
sig ref
be a DC signal. In other words, the lock-in refer-
ence needs to be phase-locked to the signal
reference.
Lock-in amplifiers use a phase-locked-loop (PLL)
to generate the reference signal. An external refer-
ence signal (in this case, the reference square
wave) is provided to the lock-in. The PLL in the
lock-in locks the internal reference oscillator to this
external reference, resulting in a reference sine
wave at ω with a fixed phase shift of θ
r
the PLL actively tracks the external reference,
changes in the external reference frequency do
not affect the measurement.
All lock-in measurements
require a reference signal.
In this case, the reference is provided by the exci-
tation source (the function generator). This is
called an external reference source. In many situa-
tions, the SR830's internal oscillator may be used
instead. The internal oscillator is just like a func-
tion generator (with variable sine output and a TTL
-
noise
= ω
. Not only do
r L
will not
psd
. Since
ref
3-2
sync) which is always phase-locked to the refer-
ence oscillator.
Magnitude and phase
Remember that the PSD output is proportional
cosθ where θ = (θ
to V
sig
difference between the signal and the lock-in refer-
ence oscillator. By adjusting θ
equal to zero, in which case we can measure V
(cosθ=1). Conversely, if θ is 90°, there will be no
output at all. A lock-in with a single PSD is called a
single-phase lock-in and its output is V
This phase dependency can be eliminated by
adding a second PSD. If the second PSD multi-
plies the signal with the reference oscillator shifted
t + θ
by 90°, i.e. V sin(ω
L L
tered output will be
V = 1/2 V V sin(θ
psd2 sig L
V ~ V sinθ
psd2 sig
Now we have two outputs, one proportional to
cosθ and the other proportional to sinθ. If we call
the first output X and the second Y,
X = V cosθ Y = V
sig
these two quantities represent the signal as a
vector relative to the lock-in reference oscillator. X
is called the 'in-phase' component and Y the
'quadrature' component. This is because when
θ=0, X measures the signal while Y is zero.
By computing the magnitude (R) of the signal
vector, the phase dependency is removed.
2 2 1/2
R = (X + Y ) = V
sig
R measures the signal amplitude and does not
depend upon the phase between the signal and
lock-in reference.
A dual-phase lock-in, such as the SR830, has two
PSD's, with reference oscillators 90° apart, and
can measure X, Y and R directly. In addition, the
phase θ between the signal and lock-in reference,
can be measured according to
-1
θ = tan
(Y/X)
- θ ). θ is the phase
sig ref
we can make θ
ref
sig
cosθ.
sig
+ 90°), its low pass fil-
ref
- θ
)
sig ref
sinθ
sig