THE CARBON MICROPHONE 173 



Recent Theories 



The first attempt at a quantitative theory of microphonic action 

 was made by Professor P. O. Pedersen in 1916.^ He assumed that 

 microphonic action is due to the variation of the contact area arising 

 from the elastic deformation of the contact material by pressure. 

 Considering the case of two elastic conducting spheres brought into 

 contact, Pedersen assumed that the resistance is made up of two 

 parts; viz., (1) the resistance of a conducting film having a specific 

 resistivity differing from bulk carbon and independent of pressure, 

 and (2) the so-called "spreading resistance" or that which is caused 

 by the concentration of the current flow within the region of the 

 contact area and which would exist independently of any film. 



This theory results in a quantitative expression ^ for the dependence 

 of the contact resistance on the force holding the contacts together. 

 Pedersen tested it by experiments on carbon spheres and found 

 reasonable agreement over a wide range of force. However a very 

 similar expression can be obtained without postulating the existence 

 of the high resistance film. We have merely to suppose that contact 

 does not take place over the whole contact area owing to surface 

 roughness (the existence of which can be observed under a microscope, 

 especially in the case of carbon). 



Dr. F. Gray of Bell Telephone Laboratories worked out an ex- 

 pression ^ based on this assumption which was so nearly like Pedersen's 

 that it was difficult to discriminate between them experimentally. 

 He assumed both that the number of microscopic hills in electrical 

 contact increases as the contact force is increased and that the re- 

 sistance per hill varies in accordance with the theory of spreading 

 resistance as assumed by Pedersen. His equation was found to fit 

 experimental curves remarkably well for contact forces which are 

 relatively larger than those holding the granules together in a micro- 

 phone. In the range of smaller forces, however, marked departures 

 from theory were found, the measured value of resistance decreasing 

 too rapidly with an increase of force. Although these departures 

 were believed to be due at least in part to a plastic deformation of 

 the contact material, it appeared possible that other factors come into 

 play and may even be dominant in this region of small contact forces. 



For instance, it had been demonstrated that adsorbed films of air 

 are capable of producing a marked increase in the resistance of granular 

 carbon contacts. This revived the air film theory as a possibility 

 under the condition of small contact forces. 



2 The Electrician, Jan. 28-Feb. 4, 1916. 



37? = AF-^'^ + BF-^i\ 



*R = AF-^l^ + 5/^1/3 {Phys. Rev., 36, 375, 1930). 



