Stanford Research Systems SR844, User Manual

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2-6 SR844 Basics
SR844 RF Lock-In Amplifier
Signals closer than
∆
F
LP
to the reference frequency will appear at the output and obscure
the output from the actual signal. For
ω
X
very close to the reference frequency, the
filtered output is
V
MX+FILT
=
½ V
X
V
R
cos( (
ω
R
–
ω
X
)t +
θ
R
–
θ
X
)
(2-16)
The filtered output of the second mixer is
V
M2X+FILT
= ½ V
X
V
R
sin( (
ω
R
–
ω
X
)t +
θ
R
–
θ
X
) (2-17)
Spurious signals very close to the reference frequency are detected by a lock-in amplifier;
the phase appears to rotate slowly at the difference frequency.
What About DC Offset and Drift ?
The classic lock-in described above suffers from a serious drawback, namely DC drift.
For weak input signals, typical of many lock-in measurements, the DC output of the
mixers may be very small. This voltage can be less than the input offset of even a very
good DC amplifier. Furthermore, there is the DC output offset of the mixer itself. While it
is possible to null these offsets once, or even periodically, these offsets drift over time
and temperature making it very difficult to make measurements with the sensitivity and
accuracy demanded of lock-in amplifiers.
The solution used in the SR844 is to chop the mixer reference signals. This means that the
mixer reference signals reverse their polarity at the chop frequency. A signal at the
reference frequency generates a mixer output that also changes sign at the chop frequency.
Thus, the mixer output is at the chop frequency and not at DC. While its amplitude may
still be small, the post-mixer amplifier can now be AC coupled, eliminating problems of
DC offset and drift completely. The chop frequency in the SR844 is derived from the
reference frequency, and is in the range of 2 – 12 kHz. This is fast enough to permit
measurement time constants of 1 ms or even 100
µ
s, yet is always slow compared to the
signal frequency.
The recovery of the signal amplitude and phase from the chopped signals is a little more
complicated than equations (2-7) and (2-8) above. In effect, chopping the reference puts
the mixer outputs at an IF (intermediate frequency) equal to the chop frequency. The
mixer is followed by an IF filter (the relevant mixer outputs are between 2 and 12 kHz)
and IF amplifier. The demodulation of the low frequency IF signal is easily handled by the
digital signal processor.
Where Does the Reference Come From ?
The lock-in reference frequency must be the same as the signal frequency, i.e.
ω
R
=
ω
I
. Not
only do the frequencies have to be the same, but the phase between the signals cannot
change with time, otherwise cos(
θ
R
–
θ
I
) will change and the detector outputs will not be
stable. In other words, the lock-in reference needs to be phase-locked to the signal one is
trying to detect.
It is common to provide the lock-in amplifier with a reference signal taken from the
experiment. This external reference signal is connected to the front panel reference input
labeled REF IN. In this case the user is responsible for the external reference being phase-
locked to the signal of interest.