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,

_

V2 = ∫4kT Re[Z(f)] df = 4kTR ∆ f

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where k=Boltzman's constant, 1.38x10- J/°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,

_

(V2)1/2 = 0.13 ∝ V/√ Hz

To obtain the rms noise voltage that you would see across this 1MΩ resistor, we multiply

0.13∝ V/√ 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

_

(V2)1/2 = 0.13 ∝ V/√ Hz*(106 Hz)1/2 = 130 ∝ V

'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 = A R2 I2 ∆ f/f

where A is a dimensionless constant, 10-11for 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

Vnoise = 3 ∝ Vrms

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.

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