Signal Input Amplifier And Filters - Stanford Research Systems SR810 Manual

SR810 Basics

SIGNAL INPUT AMPLIFIER and FILTERS

A lock-in can measure signals as small as a few
nanovolts. A low noise signal amplifier is required
to boost the signal to a level where the A/D
converter can digitize the signal without degrading
the signal to noise. The analog gain in the SR810
ranges from roughly 7 to 1000. As discussed
previously, higher gains do not improve signal to
noise and are not necessary.
The overall gain (AC plus DC) is determined by
the sensitivity. The distribution of the gain (AC
versus DC) is set by the dynamic reserve.
Input noise
The input noise of the SR810 signal amplifier is
about 5 nVrms/√Hz. What does this noise figure
mean? Let's set up an experiment. If an amplifier
has 5 nVrms/√Hz of input noise and a gain of
1000, then the output will have 5 µVrms/√Hz of
noise. Suppose the amplifier output is low pass
filtered with a single RC filter (6 dB/oct roll off) with
a time constant of 100 ms. What will be the noise
at the filter output?
Amplifier input noise and Johnson noise of
resistors are Gaussian in nature. That is, the
amount of noise is proportional to the square root
of the bandwidth in which the noise is measured.
A single stage RC filter has an equivalent noise
bandwidth (ENBW) of 1/4T where T is the time
constant (RxC). This means that Gaussian noise
at the filter input is filtered with an effective
bandwidth equal to the ENBW. In this example,
the filter sees 5 µVrms/√Hz of noise at its input. It
has an ENBW of 1/(4x100ms) or 2.5 Hz. The
voltage noise at the
5 µVrms/√Hz x √2.5Hz
Gaussian noise, the peak to peak noise is about 5
times the rms noise. Thus, the output will have
about 40 µV pk-pk of noise.
Input noise for a lock-in works the same way. For
sensitivities below about 5 µV full scale, the input
noise will determine the output noise (at minimum
reserve). The amount of noise at the output is
determined by the ENBW of the low pass filter.
See the discussion of noise later in this section for
more information on ENBW. The ENBW depends
upon the time constant and filter roll off. For
example, suppose the SR810 is set to 5 µV full
scale with a 100 ms time constant and 6 dB/oct of
filter roll off. The ENBW of a 100 ms, 6 dB/oct filter
filter output will be
or 7.9 µVrms. For
is 2.5 Hz. The lock-in will measure the input noise
with an ENBW of 2.5 Hz. This translates to
7.9 nVrms at the input. At the output, this
represents about 0.16 % of full scale (7.9 nV/5
µV). The peak to peak noise will be about 0.8 % of
full scale.
All of this assumes that the signal input is being
driven from a low impedance source. Remember
resistors have
0.13x√R nVrms/√Hz. Even a 50Ω resistor has
almost 1 nVrms/√Hz of noise! A signal source
impedance of 2 kΩ will have a Johnson noise
greater than the SR810's input noise. To
determine the overall noise of multiple noise
sources, take the square root of the sum of the
squares of the individual noise figures. For
example, if a 2 kΩ source impedance is used, the
Johnson noise will be 5.8 nVrms/√Hz. The overall
noise at the SR810 input will be [52 + 5.82]
7.7 nVrms/√Hz.
We'll talk more about noise sources later in this
section.
At lower gains (sensitivities above 50 µV), there is
not enough gain at high reserve to amplify the
input noise to a level greater than the noise of the
A/D converter. In these cases, the output noise is
determined by the A/D noise. Fortunately, at these
sensitivities, the DC gain is low and the noise at
the output is negligible.
Notch filters
The SR810 has two notch filters in the signal
amplifier chain. These are pre-tuned to the line
frequency (50 or 60 Hz) and twice the line
frequency (100 or 120 Hz). In circumstances
where the largest noise signals are at the power
line frequencies, these filters can be engaged to
remove noise signals at these frequencies.
Removing the largest noise signals before the final
gain stage can reduce the amount of dynamic
reserve required to perform a measurement. To
the extent that these filters reduce the required
reserve to either 60 dB or the minimum reserve
(whichever is higher), then some improvement
might be gained. If the required reserve without
these notch filters is below 60 dB or if the
minimum reserve is sufficient, then these filters do
not significantly improve the measurement.
3-14
Johnson noise equal to
½
or