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176
Dual Reference Detection
The time constant is adjusted to remove the high frequency sum components at 2ω
the analog output of this first lock-in is the signal input to the second lock-in. The second
lock-in is set to detect at ω
The second lock-in time constant is adjusted to remove the 2ω
signal proportional to A
SR865 Dual Reference Mode
The SR865 Dual Reference mode makes this measurement in a single lock-in. One of the
frequencies is the external reference and the other is the internal reference. In Dual
Reference mode, the SR865 detects at |ω
matter which is the carrier and which is the modulation. It also doesn't matter which
frequency is greater or by how much. The detection frequency is the difference between
the two frequencies and will always be lower than the greater frequency.
The original experimental signal contains components at the sum and difference
frequencies
In Dual Reference mode, the SR865 multiplies by cos({ω
resulting in the output
The SR865 time constant is adjusted to remove all components at 2|ω
2ω
leaving a dc signal proportional to A
mod
in reports the measured amplitude at (ω
rms, the displayed result will be (A
The Dual Reference mode in the SR865 does not care about the "order" of ω
The expermental signal could be a fast modulation of a slow carrier or vice versa. The
SR865 does not require that one of the frequencies be much greater than the other. The
two frequencies can be very close together. The only requirement is that the time constant
remove all output components other than dc.
The SR865 does require that one of the frequencies be the internal reference and the other
the external reference and the difference between them must be less than 2.5 MHz.
SR865 DSP Lock-in Amplifier
[
A
A
{
ω
+
car
mod
2
sin(
car
4
. The output of this second lock-in is
mod
A
A
ω
×
car
mod
sin(
t
)
sin(
mod
2
A
as desired.
car
mod
A
A
[
{
ω
car
mod
cos(
car
2
A
A
[
{
ω
+
car
mod
1
cos(
2
car
4
car
]
}
A
A
ω
ω
−
=
car
t
)
mod
car
2
[
A
A
ω
=
car
mod
t
)
1
mod
4
− ω
|, i.e. the difference frequency. It doesn't
ext
int
}
{
ω
ω
−
−
+
t
)
cos(
mod
car
− ω
car
}
ω
ω
−
−
t
)
cos(
2
t
)
mod
car
A
as desired. It should be noted the lock-
car
mod
− ω
), which is (A
car
mod
A
)/(2√2).
mod
Appendix E
ω
mod
sin(
t
)
mod
and
car
]
ω
−
cos(
2
t
)
mod
component leaving a dc
mod
]
}
ω
t
)
mod
}t) in a single step
mod
]
ω
−
cos(
2
t
)
mod
− ω
|, 2ω
car
mod
car
A
)/2. Correcting for
car
mod
and ω
ext
int
and
.
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