Stanford Research Systems SR860, Руководство по эксплуатации

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Dual Reference Detection 175
SR860 DSP Lock-in Amplifier
Appendix E
Dual Reference Detection
In a typical lock-
in experiment the signal of interest is at a known frequency ω
sig
. The
lock-in is set up to detect signals at only this frequency by multiplying the input signal by
sin(ω
sig
t) (using either internal or external reference mode).
If the signal is
) sin(
sig sig
t A
ω
then the result of the lock-in multiplication is
[ ]
) 2 cos( 1
2
) sin( ) sin(
sig
sig
sig sig sig
t
A
t t A
ω ω ω
− = ×
and the time constant low pass filter removes the
2ω
sig
component leaving a dc result
proportional to A
sig
.
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
car
and ω
mod
for carrier and modulation and
assume ω
mod
<< ω
car
.
If the carrier signal is
) sin(
car car
t A
ω
,
then the experiment modulates this by multiplying by the modulation signal resulting in
{ } { }
[ ]
) cos( ) cos(
2
) sin( ) sin(
mod car mod car
mod car
mod mod car car
t t
A A
t A t A
ω ω ω ω ω ω
+ − − = ×
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
car
. The output of this lock-in will contain sum and
difference components from both signal components. One of these will be