Noise Measurements; How Does A Lock-In Measure Noise; Noise Estimation - Stanford Research Systems SR844 User Manual

Noise Measurements

Lock-in amplifiers can be used to measure noise. Noise measurements are usually used to
characterize components and detectors.
The SR844 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 time constant and filter rolloff appear at the
output at a frequency f=f
the output with a bandwidth of DC to the detection bandwidth.
For Gaussian noise, the equivalent noise bandwidth (ENBW) of a low-pass filter is the
bandwidth of a 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.

Noise Estimation

The noise is simply the standard deviation (root of the mean of the squared deviations) of the
measured X or Y. This formula, while mathematically exact, is not suited to providing a real-
time output proportional to the measured noise. Therefore the SR844 uses a simplified
algorithm to estimate the X or Y noise.
The moving average of X is computed over some past history, and subtracted from the
present value X to get the deviation. The Mean Average Deviation (MAD) is computed as a
moving average of the absolute value of the deviations. For Gaussian noise, the MAD is
related to the RMS deviation by a constant factor. The MAD is scaled by this factor and by
the ENBW to obtain noise in units of Volts/
√
Volts/ Hz. The average reading is independent of the time constant and slope but the
variations or noisiness in the reading is not. For more stable readings, use longer time
constants.
In the SR844 the X and Y noise are computed in the host processor; the MAD algorithm is
used because it requires less computation and is a moving average. The X and Y data values
are sampled (from the DSP) at a 512 Hz rate; the moving average and MAD are then
updated. The moving averages have an exponential time constant that varies between 10 to
80 times the filter time constant. Shorter averaging times settle quickly but fluctuate a lot and
yield a poor estimate of the noise, while longer averaging times yield better noise estimates
but take a long time to settle to a steady answer.
The SR844 performs the noise calculations all the time, whether or not X or Y noise is being
displayed. Thus, as soon as X noise is displayed, the value shown is up to date and no extra
–f . Input noise near the reference frequency appears as noise at
SIG REF
Slope [dB/octave]
6
12
18
24
SR844 Basics 2-23
ENBW for Time Constant T
1/(4T)
1/(8T)
3/(32T)
5/(64T)
√
Hz. X and Y noise are displayed in units of
SR844 RF Lock-In Amplifier