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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
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
t) (using either internal or external reference mode).
Z
A
t
sin(
sig
sig
Z
A
sin(
t
sig
sig
.
sig
<< ω
.
mod
car
Z
A
sin(
t
car
car
Z
Z
u
t
)
A
sin(
car
mod
mod
Dual Reference Detection
)
>
A
Z
u
sig
)
sin(
t
)
1
sig
2
and ω
car
)
,
A
A
>
^
Z
car
mod
t
)
cos(
2
. The output of this lock-in will contain sum and
car
@
Z
cos(
2
t
)
sig
component leaving a dc result
sig
for carrier and modulation and
mod
`
^
Z
Z
t
)
cos(
car
mod
SR865A DSP Lock-in Amplifier
175
. The
sig
@
`
Z
t
)
car
mod
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