Noise Measurements - Stanford Research Systems SR810 Manual

NOISE MEASUREMENTS

Lock-in amplifiers can be used to measure noise.
Noise measurements are generally used to
characterize components and detectors.
The SR810 measures input signal noise AT the
reference frequency. Many noise sources have a
frequency dependence which the lock-in can
measure.
How does a lock-in measure noise?
Remember that the lock-in detects signals close to
the reference frequency. How close? Input signals
within the detection bandwidth set by the low pass
filter time constant and roll-off appear at the output
at a frequency f=f -f
sig
appears as noise at the output with a bandwidth of
DC to the detection bandwidth.
For Gaussian noise,
bandwidth (ENBW) of a low pass filter is the
bandwidth of the perfect rectangular filter which
passes the same amount of noise as the real filter.
The ENBW is determined by the time constant and
slope as shown below. Wait time is the time
required to reach 99 % of its final value.
T= Time Constant
Slope ENBW
6 dB/oct 1/(4T)
12 dB/oct 1/(8T)
18 dB/oct 3/(32T)
24 dB/oct 5/(64T)
Noise estimation
The noise is simply the standard deviation (root of
the mean of the squared deviations)of the
measured X, Y or R .
The above technique, while mathematically sound,
can not provide a real time output or an analog
output proportional to the measured noise. For
these measurements, the SR810 estimates the X
or Y noise directly.
To display the noise of X, for example, simply set
the CH1 display to X noise. The quantity X noise is
. Input noise near fref
ref
the equivalent noise
Wait Time
5T
7T
9T
10T
computed from the measured values of X using
the following algorithm. The moving average of X
is computed. This is the mean value of X over
some past history. The present mean value of X is
subtracted from the present value of X to find the
deviation of X from the mean. Finally, the moving
average of the absolute value of the deviations is
calculated. This calculation is called the mean
average deviation or MAD. This is not the same as
an RMS calculation. However, if the noise is
Gaussian in nature, then the RMS noise and the
MAD noise are related by a constant factor.
The SR810 uses the MAD method to estimate the
RMS noise of X and Y. The advantage of this
technique is its numerical simplicity and speed.
The noise calculations for X and Y occur at
512 Hz. At each sample, the mean and moving
average of the absolute value of the deviations is
calculated. The averaging time (for the mean and
average deviation) depends upon the time
constant. The averaging time is selected by the
SR810 and ranges from 10 to 80 times the time
constant. Shorter averaging times yield a very
poor estimate of the noise (the mean varies
rapidly and the deviations are not averaged well).
Longer averaging times, while yielding better
results, take a long time to settle to a steady
answer.
To change the settling time, change the time
constant. Remember, shorter settling times use
smaller time constants (higher noise bandwidths)
and yield noisier noise estimates.
X and Y noise are displayed in units of
Volts/√Hz. The ENBW of the time constant is
already factored into the calculation. Thus, the
mean displayed value of the noise should not
depend upon the time constant.
The SR810 performs the noise calculations all of
the time, whether or not X or Y noise are being
displayed. Thus, as soon as X noise is displayed,
the value shown is up to date and no settling time
is required. If the sensitivity is changed, then the
noise estimate will need to settle to the correct
value.
3-23
SR810 Basics