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Appendix E
Dual Reference Detection
In a typical lock-in experiment the signal of interest is at a known frequency ω
lock-in is set up to detect signals at only this frequency by multiplying the input signal by
sin(ω
t) (using either internal or external reference mode).
sig
If the signal is
then the result of the lock-in multiplication is
and the time constant low pass filter removes the 2ω
proportional to A
In some experiments there is an additional modulation of the signal. This results from the
mixing of 2 frequencies in the experiment. Often one of the frequencies is much lower
than the other. Let's call these frequencies ω
assume ω
If the carrier signal is
then the experiment modulates this by multiplying by the modulation signal resulting in
A
sin(
car
The experimental signal consists of equal amplitude components at the sum and
difference frequencies.
Two Lock-in Detection
This signal can be measured using 2 lock-in amplifiers. The signal is input to the first
lock-in which is set to detect at ω
difference components from both signal components. One of these will be
ω
A
sin(
t
)
sig
sig
ω
×
A
sin(
t
)
sig
sig
.
sig
<< ω
.
mod
car
ω
,
A
sin(
t
)
car
car
ω
ω
×
t
)
A
sin(
t
)
car
mod
mod
Dual Reference Detection
[
A
ω
=
−
sig
sin(
t
)
1
cos(
sig
2
component leaving a dc result
sig
and ω
for carrier and modulation and
car
mod
[
A
A
{
ω
=
−
car
mod
cos(
car
2
. The output of this lock-in will contain sum and
car
SR865 DSP Lock-in Amplifier
. The
sig
]
ω
2
t
)
sig
}
{
ω
ω
ω
−
+
t
)
cos(
mod
car
175
]
}
t
)
mod
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