Stanford Research Systems SR865 Operation Manual page 57

Chapter 2
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
only do the frequencies have to be the same, the phase between the signals cannot change
with time, otherwise cos(θ
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 sine wave at ω
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 lock-in'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 to V
phase difference between the signal and the lock-in reference oscillator. By adjusting θ
we can make θ equal to zero, in which case we can measure V
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. sin(ω
its low pass filtered output will be
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,
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.
− θ
sig ref
sig
sin(θ
V = 1/2 V
psd2 sig sig
sinθ
V ~ V
psd2 sig
cosθ
X = V Y = V
sig
2 2 1/2
R = (X + Y ) = V
sig
) will change and V will not be a dc signal. In other
psd
with a fixed phase shift of θ
r
cosθ where θ = (θ
sig
cosθ.
− θ
)
ref
sinθ
sig
SR865 DSP Lock-in Amplifier
Basics
= ω
. Not
r L
. Since
ref
− θ ). θ is the
sig ref
(cosθ = 1). Conversely,
sig
t + θ
+ 90°),
L ref
39
ref