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Appendix A:
Noise Sources and Cures
Noise, random and uncorrelated fluctuations of
electronic signals, finds its way into experiments
in a variety of ways. Good laboratory practice
can reduce noise sources to a manageable
level, and the lock-in technique can be used to
recover signals which may still be buried in
noise.
Intrinsic Noise Sources
Johnson Noise. Arising from fluctuations of
electron density in a resistor at finite
temperature, these fluctuations give rise to a
mean square noise voltage,
_
V
2
= ∫4kT Re[Z(f)] df = 4kTR ∆f
where k=Boltzman's constant, 1.38x10-23J/°K; T
is the absolute temperature in Kelvin; the real
part of the impedance, Re[z(f)] is the resistance
R; and we are looking at the noise source with a
detector, or ac voltmeter, with a bandwidth of ∆f
in Hz. For a 1MΩ resistor,
_
(V
2
)
1/2
= 0.13 µV/√Hz
To obtain the rms noise voltage that you would
see across this 1M½ resistor, we multiply
0.13µV/√Hz by the square root of the detector
bandwidth. If, for example, we were looking at
all frequencies between dc and 1 MHz, we
would expect to see an rms Johnson noise of
_
(V
2
)
1/2
= 0.13 µV/√Hz*(10
6
Hz)
1/2
= 130 µV
'1/f Noise'. Arising from resistance fluctuations
in a current carrying resistor, the mean squared
noise voltage due to '1/f' noise is given by
_
V
2
= A R
2
I
2
∆f/f
where A is a dimensionless constant, 10
-11
for
carbon, R is the resistance, I the current, ∆f the
bandwidth of our detector, and f is the frequency
to which the detector is tuned. For a carbon
resistor carrying 10 mA with R = 1k, ∆f = f = 1Hz,
we have
V
noise
= 3 µVrms
And Others. Other noise sources include flicker
noise found in vacuum tubes, and generation and
recombination noise found in semiconductors.
All of these noise sources are incoherent. Thus, the
total noise is the square root of the sum of the
squares of all the incoherent noise sources.
Non-Essential Noise Sources
In addition to the "intrinsic" noise sources listed
above there are a variety of "non-essential" noise
sources, i.e. those noise sources which can be
minimized with good laboratory practice. It is
worthwhile to look at what might be a typical noise
spectrum encountered in the laboratory
environment:
Noise Spectrum
Some of the non-essential noise sources appear in
this spectrum as spikes on the intrinsic background.
There are several ways which these noise sources
work their way into an experiment.