The Linear Theory of Fluctuations Arising from Diffusional 

 Mechanisms — An Attempt at a Theory of Contact Noise 



By J. M. RICHARDSON 



The spectral density is calculated for the electrical resistance when it is linearly 

 coupled to a diffusing medium (particles or heat) undergoing thermally excited 

 fluctuations. Specific forms of the spectral density are given for several types of 

 coupling which are simple and physically reasonable. The principal objective is 

 the understanding of the frequency dependence of the resistance fluctuations in 

 contacts, rectifying crystals, thin films, etc. 



1. Introduction 



WHEN a direct current is passed through a granular resistance such as 

 a carbon microphone or a metallic-film grid leak, or through a single 

 contact, there is produced a voltage fluctuation possessing a component 

 called contact noise which is differentiated from the familiar thermal noise 

 component by the fact that its r.m.s. value in any frequency band is roughly 

 proportional to the magnitude of the average applied voltage, and is differ- 

 entiated from shot noise by the strong frequency dependence of its spectral 

 density. One may regard this component of the voltage fluctuation as aris- 

 ing from the spontaneous resistance fluctuations of the element in question 

 if one is wiUing to allow the resistance to have a slight voltage dependence. 

 This effect has been the subject of numerous experimental investigations, ~ 

 among which we mention in particular that of Christensen and Pearson 

 on granular resistance elements. These authors (henceforth abbreviated 

 as CP) arrived at an empirical formula, to be discussed presently, connect- 

 ing the contact noise power per unit frequency band with the applied volt- 

 : age, the resistance, and the frequency for several types of granular resistance. 

 Their measurements covered a range of frequency from 69 to 10,000 cps, 

 ; and involved the variation of several other parameters, i.e., pressure. More 

 I recently, Wegel and Montgomery^'' have measured the noise power arising 



' H. A. Frederick, Bell Telephone Quarterly 10, 164 (1931). 

 2 A. W. Hull and N. H. Williams, Phys. Rev. 25, 173 (1925). 

 ^ R. Otto, Hoc'/freqiienzleclinlkund Elektroakuslik 45, 187 (1935). 

 ^G. W. Barnes. Jour. Franklin Inst. 219, 100 (1935). 

 ' Erwin Mever and Heinz Thiede, E. N. T. 12, 237 (1935). 



8 F. S. Gjucher, Jour. Franklin Inst. 217, 407 (1934). Bell Sys. Tech. Jour. 13, 163 

 (1934). 



^J. Bernamont, Annales de P'lys., 1937, 71-140. 



8 M. Surdin, R. G. E., 47, 97-101 (1940). 



' C. J. Christensen and G. L. Pearson, Bell Sys. Tech. Jour. 15, 197-223 (1936). 



•0 Private communication. 



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