APPENDIX B
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
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,
_
V2 = ∫4kT Re [Z(f)]df = 4 kTR∆f
where k = Boltzmann’s constant,
1.38x
_
(V2) 1/2 = 0.13µV/√Hz
To obtain the rms noise voltage that you would see across this 1MΩ resistor, we multiply 0.3 µV/√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 a rms Johnson noise of:
_
(V2) 1/2 = 0.13µV/√Hz * (106 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,
_
V2 = AR2I2 ∆f/f
where A is a dimensionless constant,
for carbon, R is the resistance, I the current, 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 = 1 k, ∆f = f = 1 Hz, we have:
Vnoise= 3µVrms
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
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