Stanford Research Systems SR810 Manual page 27

SR810 Basics
bandwidth 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,
- θ
otherwise cos(θ ) will change and V
sig ref
be a DC signal. In other words, the lock-in
reference 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
reference 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
with a fixed phase shift of θ
sine wave at w
r
Since 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
excitation source (the function generator). This is
called an external reference source. In many
situations, the SR810's internal oscillator may be
used instead. The internal oscillator is just like a
function generator (with variable sine output and a
TTL sync) which is always phase-locked to the
reference 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
reference oscillator. By adjusting θ
= ω
. Not only do
r L
will not
psd
ref
- θ ). θ is the phase
sig ref
we can make
ref
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
multiplies the signal with the reference oscillator
shifted by 90°, i.e. V
pass filtered output will be
V = ½ V
psd2 sig
V ~ V sinθ
psd2 sig
Now we have two outputs, one proportional to
cosq and the other proportional to sinθ. If we call
the first output X and the second Y,
X = V cosθ
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 ½
R = (X + Y ) = Vsig
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 SR810, has two
PSD's, with reference oscillators 90° apart, and
can measure X, Y and R directly. In addition, the
phase q between the signal and lock-in reference,
can be measured according to
θ = tan
-1
(Y/X)
3-2
sig
t + θ
sin(w + 90°), its low
L L ref
- θ
V sin(θ )
L sig ref
Y = V sinθ
sig
sig
cosθ.