THE IMPEDANCE OF TELEPHONE RECEIVERS AS 



AFFECTED BY THE MOTION OF THEIR 



DIAPHRAGMS. 



By a. E. Kennelly and G. W. Pierce 

 Received July 16, 1912. 



I. Introduction. 



The writers have made a series of measurements of the resistance 

 and inductance of several forms of telephone receivers over a wide 

 range of frequency of current. In the course of the measurements 

 some interesting results have been obtained, which form the subject 

 of this paper. 



As the period of the e. m. f. used in the measurements approaches 

 the natural period of the diaphragm, the note emitted by the telephone 

 receiver increases markedlv in loudness, and the resistance and in- 

 ductance of the receiver undergo wide deviations from values obtained 

 when the diaphragm is prevented from vibrating by being damped. 

 That is to say, the motion of the diaphragm has an effect upon the 

 resistance and inductance of the receiver, and this effect grows rapidly 

 as the electrical period approaches the mechanical period. 



In the tests to be described, the resistance and the inductance of a 

 given receiver were measured, first with the diaphragm free and sound- 

 ing, and, second, with the diaphragm damped, or arrested. The values 

 when the diaphragm is free may be called free values; the values when 

 the diaphragm is damped may be called dami^ed values. The difference 

 obtained by subtracting the damped values from the corresponding 

 free values maybe called the motional values of resistance, inductance, 

 etc. ; since such differences are due to the motion of the diaphragm. 



It is found that when the impressed frequency differs widely from 

 the natural frequency of the diaphragm, the motional resistance and 

 inductance are very small. In the neighborhood of resonance, which 

 is often very sharply- marked, these motional values become relatively 

 large, and one or both pass through a change of sign, in such a manner 

 that, when the motional impedance for different frequencies is drawn 

 vectorially from a fixed point as origin, all the points given by the 

 observations lie upon a circular graph, which may be called the ino- 



