Stanford Research Systems SR865A, Operation Manual

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176 Dual Reference Detection Appendix E
SR865A DSP Lock-in Amplifier
^ ` > @
) sin(
2
) sin( 2
4
mod
mod car
car mod car
mod car
t
A A
t
A A
Z Z Z Z
The time constant is adjusted to remove the high frequency
sum components at 2ω
car
and
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
mod
. The output of this second lock-in is
> @
) 2 cos( 1
4
) sin( ) sin(
2
mod
mod car
mod mod
mod car
t
A A
t t
A A
Z Z Z
u
The second lock- in time constant is adjusted to remove the 2ω
mod
component leaving a dc
signal proportional to A
car
A
mod
as desired.
SR865A Dual Reference Mode
The SR865A 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 SR865A
detects at |ω
ext
− ω
int
|, i.e. the difference frequency. It
doesn’t 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
^ ` ^ `
> @
) cos( ) cos(
2
mod car mod car
mod car
t t
A A
Z Z Z Z
In Dual Reference mode, the SR865A multiplies by cos({ ω
car
− ω
mod
}t) in a single step
resulting in the output
^ `
> @
) 2 cos( ) 2 cos( ) 2 cos( 1
4
mod car mod car
mod car
t t t
A A
Z Z Z Z
The SR865A time constant is adjusted to remove all components at 2|
ω
car
− ω
mod
|
, 2ω
car
and 2ω
mod
leaving a dc signal proportional to A
car
A
mod
as desired. It should be noted the
lock-in reports the measured amplitude
at (ω
car
− ω
mod
), which is (A
car
A
mod
)/2. Correcting
for rms, the displayed result will be (A
car
A
mod
)/(2√2).
The Dual Reference mode in the SR865A does not care about the “ order ” of ω
ext
and ω
int
.
The expermental signal could be a fast modulation of a slow carrier or vice versa. The
SR865A 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 SR865A 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 4 MHz.