Stanford Research Systems SR810 Manual page 34

In the SR810, synchronous filters are available at
detection frequencies below 200 Hz. At higher
frequencies, the filters are not required (2F is
easily removed without using long time constants).
Below 200 Hz, the synchronous filter follows either
one or two stages of normal filters. The output of
the synchronous filter is followed by two more
stages of normal filters. This combination of filters
notches all multiples of the reference frequency
and provides overall noise attenuation as well.
Long Time Constants
Time constants above 100 seconds are difficult to
accomplish using analog filters. This is simply
because the capacitor required for the RC filter is
prohibitively large (in value and in size!). Why
would you use such a long time constant?
Sometimes you have no choice. If the reference is
well below 1 Hz and there is a lot of low frequency
noise, then the PSD output contains many very
low frequency components. The synchronous filter
only notches multiples of the reference frequency,
the noise is filtered by the normal filters.
The SR810 can provide time constants as long as
30000 seconds at reference frequencies below
200 Hz. Obviously you don't use long time
constants unless absolutely necessary, but they're
available.
DC Output Gain
How big is the DC output from the PSD? It
depends on the dynamic reserve. With 60 dB of
dynamic reserve, a noise signal can be 1000
times (60 dB) greater than a full scale signal. At
the PSD, the noise can not exceed the PSD's
input range. In an analog lock-in, the PSD input
range might be 5V. With 60 dB of dynamic
reserve, the signal will be only 5 mV at the PSD
input. The PSD typically has no gain so the DC
output from the PSD will only be a few millivolts!
Even if the PSD had no DC output errors,
amplifying this millivolt signal up to 10 V is error
prone. The DC output gain needs to be about the
same as the dynamic reserve (1000 in this case)
to provide a 10 V output for a full scale input
signal. An offset as small as 1 mV will appear as
1 V at the output! In fact, the PSD output offset
plus the input offset of the DC amplifier needs to
be on the order of 10 µV in order to not affect the
measurement. If the dynamic reserve is increased
to 80dB, then this offset needs to be 10 times
smaller still. This is one of the reasons why analog
lock-ins do not perform well at very high dynamic
reserve.
The digital lock-in does not have an analog DC
amplifier. The output gain is yet another function
handled by the digital signal processor. We
already know that the digital PSD has no DC
output offset. Likewise, the digital DC amplifier has
no input offset. Amplification is simply taking input
numbers and multiplying by the gain. This allows
the SR810 to operate with 100 dB of dynamic
reserve without any output offset or zero drift.
What about resolution?
Just like the analog lock-in where the noise can
not exceed the input range of the PSD, in the
digital lock-in, the noise can not exceed the input
range of the A/D converter. With a 16 bit A/D
converter, a dynamic reserve of 60 dB means that
while the noise has a range of the full 16 bits, the
full scale signal only uses 6 bits. With a dynamic
reserve of 80 dB, the full scale signal uses only
2.5 bits. And with 100 dB dynamic reserve, the
signal is below a single bit! Clearly multiplying
these numbers by a large gain is not going to
result in a sensible output. Where does the output
resolution come from?
The answer is filtering. The low pass filters
effectively combine many data samples together.
For example, at a 1 second time constant, the
output is the result of averaging data over the
previous 4 or 5 seconds. At a sample rate of
256 kHz, this means each output point is the
exponential average of over a million data points.
(A new output point is computed every 4 µs and is
a moving exponential average). What happens
when you average a million points? To first order,
the resulting average has more resolution than the
incoming data points by a factor of million . This
represents a gain of 20 bits in resolution over the
raw data. A 1 bit input data stream is converted to
20 bits of output resolution.
The compromise here is that with high dynamic
reserve (large DC gains), some filtering is
required. The shortest time constants are not
available when the dynamic reserve is very high.
This is not really a limitation since presumably
there is noise which is requiring the high dynamic
reserve and thus substantial output filtering will
also be required.
3-9
SR810 Basics