Johnson and 1/f noise

While trying to perfect the design and manufacture of the vacuum valve, the pioneers of electronic engineering uncovered a fundamental problem — noise. Walter Schottky first postulated the existence of thermal noise and shot noise in 1918. In a letter to Nature in 1927, J. B. Johnson commented on voltage fluctuations that appear "to be the result of thermal agitation of the electric charges in the material of the conductor". Johnson would later become associated with thermal noise — now also known as Johnson noise — after he published a definitive experiment on noise in 1928, alongside Harry Nyquist's theoretical explanation*. But his letter of 1927 was intended to bring "a similar phenomenon" to the attention of Nature readers. In this case the fluctuations depend not on temperature but inversely on frequency — Johnson had discovered '1/f noise'.
Nature 119, 50–51 (1927)
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* Johnson, J. B. Phys. Rev. 32, 97–109 (1928); Nyquist, H. Phys. Rev. 32, 110–113 (1928).

Thermal Agitation of Electricity in Conductors

Ordinary electric conductors are sources of spontaneous fluctuations of voltage which can be measured with sufficiently sensitive instruments. This property of conductors appears to be the result of thermal agitation of the electric charges in the material of the conductor.

The effect has been observed and measured for various conductors, in the form of resistance units, by means of a vacuum tube amplifier terminated in a thermocouple. It manifests itself as a part of the phenomenon which is commonly called 'tube noise.' The part of the effect originating in the resistance gives rise to a mean square voltage fluctuation V² which is proportional to the value R of that resistance. The ratio V²/R is independent of the nature or shape of the conductor, being the same for resistances of metal wire, graphite, thin metallic films, films of drawing ink, and strong or weak electrolytes. It does, however, depend on temperature and is proportional to the absolute temperature of the resistance. This dependence on temperature demonstrates that the component of the noise which is proportional to R comes from the conductor and not from the vacuum tube.

A similar phenomenon appears to have been observed and correctly interpreted in connexion with a current sensitive instrument, the string galvanometer (W. Einthoven, W. F. Einthoven, W. van der Horst, and H. Hirschfeld, Physica, 5, 358–360, No. 11/12, 1925). What is being measured in these cases is the effect upon the measuring device of continual shock excitation resulting from the random interchange of thermal energy and energy of electric potential or current in the conductor. Since the effect is the same for different conductors, it is evidently not dependent on the specific mechanism of conduction.

The amount and character of the observed noise depend upon the frequency-characteristic of the amplifier, as would be expected from experience with the small-shot effect. The apparent input power originating in the resistance is of the order 10^–18 watt at room temperature. The corresponding output power is proportional to the area under the graph of power amplification-frequency, at least in the range of audio frequencies. The magnitude of the 'initial noise,' when the quietest tubes are used without input resistance, is about the same as that produced by a resistance of 5000 ohms at room temperature in the input circuit. For the technique of amplification, therefore, the effect means that the limit to the smallness of voltage which can be usefully amplified is often set, not by the vacuum tube, but by the very matter of which electrical circuits are built.

J. B. JOHNSON.

Bell Telephone Laboratories, Inc.,
New York, N.Y., Nov. 17.

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