THE MECHANICS OF TELEPHONE-RECEIVER DIA- 

 PHRAGMS, AS DERIVED FROM THEIR MOTIONAL- 

 IMPEDANCE CIRCLES. 



By a. E. KJENNELLY AND H. A. Affel. 



Received June 11, 1915. 



The following research was carried on, at the Massachusetts Insti- 

 tute of Technology, under an appropriation from the American Tele- 

 graph and Telephone Co. during the year 1914-1915. The experi- 

 mental work was carried out at Pierce Hall, Harvard University. 



This research constitutes a continuation and extension of that 

 reported to the Academy in September 1912, under the title of "The 

 Impedance of Telephone Receivers, as affected by the Motion of their 

 Diaphragms," ^ by A. E. Kennelly and G. W. Pierce. In that paper 

 of 1912, it was shown that the impedance of a telephone receiver is 

 different, when the diaphragm is free to vibrate, from that which it 

 offers when the diaphragm's motion is damped or prevented. The 

 difference between the "free" impedance as the frequency is varied, 

 and the "damped" impedance, is called the "motional impedance," 

 and measures the velocity of the diaphragm's vibration. When 

 plotted vectorially, this "motional impedance" is found to be a 

 circle passing through the origin of coordinates, and with its diameter 

 depressed through a certain angle. Every telephone receiver and 

 diaphragm possesses its own characteristic motional-impedance circle. 

 The characteristics of this circle, in regard to diameter, depression 

 angle, and distribution of frequency positions, determine certain 

 electrical and mechanical properties of the instrument. Examples 

 of such circle diagrams appear in this paper in Figures 4 and 14. 



It was shown in the 1912 paper above referred to, that there are four 

 constants of an ordinary telephone receiver which determine the essen- 

 tials of its behavior, both electrically and mechanically, throughout 

 the range of ordinary telephonic frequencies (100 to 2500 i^ ). 



If we consider the impedance of a telephone receiver with the 

 diaphragm prevented from vibrating, and thus incapable of reacting 

 electromagnetically on the coils, when the latter are excited by alter- 

 nating current, we find that, as might be expected, the impedance of 



1 See Bibliography, No. 11. 



