Stanford Research Systems SR844, User Manual

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SR844 Basics 2-5
SR844 RF Lock-In Amplifier
Phase is always reported in degrees. Again, the equations are usually written as if
θ
were
in radians.
Volts or dBm ?
The SR844 permits users to display some output quantities in either Vrms or dBm. The
quantities that may be displayed in dBm are R (amplitude of the input signal) and Y-
noise. Note that X and Y may only be displayed in Volts — they are the components of
the input signal in rectangular coordinates and may be both positive and negative. Any
conversion to dBm would be artificial, and possibly misleading. The SR844 assumes
50
Ω
while computing dBm, so that the R[dBm] quantity indicates the power that would
be dissipated if the input voltage were applied to a 50
Ω
load. This is only accurate if the
signal load is actually 50
Ω
. When using the 1 M
Ω
signal input, this is unlikely to be the
true power in the signal.
What About Signals at Other Frequencies ?
In the above calculation we assumed that the input signal was at the reference frequency,
which is
always the case for the signal of interest in a lock-in measurement. However,
there is always noise, and often times spurious signals at other frequencies. It is
instructive to follow such a signal through a mixer.
The signal input is V
X
sin(
ω
X
t+
θ
X
) and the reference input is V
R
sin(
ω
R
t+
θ
R
) as before.
Then the mixer output is
V
MX
=
½ V
X
V
R
cos( (
ω
R
–
ω
X
)t +
θ
R
–
θ
X
)
+ ½ V
I
V
R
sin( (
ω
R
+
ω
X
)t +
θ
R
+
θ
X
)
(2-11)
The second term will always be a high frequency term and will not pass through the low
pass filter. Whether the first term makes it through or not depends upon the filter
bandwidth compared to the frequency difference between the spurious signal and the
reference. For (
ω
R
–
ω
X
) much greater than the filter bandwidth,
V
MX+FILT
≅
0 (2-12)
We see that the output low pass filter directly determines the bandwidth of the lock-in
amplifier. The relationship between the filter time constant and the low-pass filter
bandwidth is
∆
F
LP
=
1 / (2
π τ
)
(2-13)
Here
∆
F
LP
is the bandwidth of the low-pass filter and
τ
is the instrument time constant.
Since frequencies both above and below the reference frequency can mix down into the
low-pass filter bandwidth, the measurement bandwidth at the reference frequency is twice
the low-pass filter bandwidth.
∆
F
INPUT
=
2
∆
F
LP
(2-14)
=
1 / (
π τ
)
(2-15)