spontaneous Resistance Fluctuations in Carbon 

 Microphones and Other Granular Resistances 



By C. J. CHRISTENSEN and G. L. PEARSON 



Voltage fluctuations which occur in resistance elements of the granular 

 type when a direct current is flowing have been measured in the granular 

 carbon microphone, commercial grid leaks, and sputtered or evaporated metal 

 films. The results can be experessed by the formula 



V) = KVR^ log {F2/F1), 



where Vc^ is the mean square fluctuation voltage, V is the d.-c. voltage across 

 the resistance R, a and are constants having values of about 1.85 and 1.25, 

 respectively, and F2 and Fi are the limits of the frequency range over which 

 the fluctuation voltage is measured. The constant K depends, among other 

 things on the temperature, the surrounding medium, and the dimensions 

 and material of the resistance element; for a commonly used carbon trans- 

 mitter at ordinary operating conditions its value is about 1.3 X 10~i'. 



The spontaneous voltage fluctuations and the signal due to acoustic modu- 

 lation are affected in almost an equivalent manner by the applied d.-c. voltage 

 which suggests that the two effects arise from the same type of mechanism, 

 namely a fluctuating resistance at the points of contact between granules. 

 Experiment shows that although the acoustic signal produces a resistance 

 modulation which is in phase at all contacts the spontaneous resistance 

 fluctuations are completely random. 



On the assumption that a region of secondary conduction, wherein the re- 

 sistance fluctuation lies, surrounds each area of primary conduction as postu- 

 lated in recent contact theory a value of /3 consistent with experiment has been 

 deduced. On the further assumptions that thermal energy produces the 

 mechanical fluctuations and that the equipartition law governs the distri- 

 bution of energy between oscillators the observed frequency distribution 

 follows. 



Introduction 



AX /"HEN a direct current is passed through certain types of re- 

 * ^ sistance elements a small potential fluctuation between the 

 terminals of the resistance can be observed in addition to that caused 

 by the thermal agitation of electric charge. The resistances in which 

 this effect is particularly noted are granular carbon microphones and 

 commercial grid leaks which are granular in nature, such as sputtered 

 or evaporated metal films, and any of a number of composite materials 

 containing carbon in a finely divided state. If such a resistance ele- 

 ment is in a current-carrying circuit associated with a telephone re- 

 ceiver or loud speaker, particularly when amplification is present, a 

 steady hissing noise which sounds like that due to shot effect or thermal 

 agitation of electric charge is heard. It is this noise which sets a 

 practical limit to the use of the carbon microphone in sound fields of 

 low intensity, and of commercial grid leaks in circuits carrying direct 

 current and working at low signal levels. 



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