^2 BELL SYSTEM TECHNICAL JOURNAL 



Tlie imi)cclaiice Zr of the receiver varies with freciuency and de- 

 pends upon the load on the diaphragm. If S is the loaded stiffness 

 of the diaphragm, that is, its resistance to force under actual working 

 conditions, and Z,/ is the impedance of the receiver when the diaphragm 

 is prex'ented from moving, then it is well-known that 



Zk = Zj + /J- (8) 



It was found that Zj expressed in ohms could be represented in the 

 frequency region near resonance by the formula 



Zrf = 93 + .06/+i(43 + .15/) (9) 



where/ denotes the frequency in cycles per second. 



The electromotive force e created in the transmitter, the direct 

 current / flowing through it, and the displacement of the diaphragm 

 are related in a rather complicated way. For describing this rela- 

 tionship it is convenient to define a modulation factor h by the 

 equation 



e^Ihz (10) 



Combining this equation with (2) it is seen that 



M = Ihi (11) 



t 



which shows that the modulation factor is also an important one in 

 determining the unilateral mutual impedance. For a sustained 

 oscillation the factor III does not enter into the periodic variation 

 and may be thought of as an electro-mechanical impedance between 

 the electromotive force created in the button and the displacement 

 of the diaphragm of the transmitter. However, for a different condi- 

 tion of sustained oscillation which results in giving s a different mag- 

 nitude the value of h changes. In other words h is dependent upon 

 the agitation of the carbon as represented by z, and also upon the 

 direct current supplied to the transmitter. It is mainly this variable 

 character of h that makes it possible to fulfill the conditions for sus- 

 tained howling. 



Simultaneous measurements of e, I and z were made upon several 

 transmitters of the type used in this investigation. From the results 

 obtained and from the defining equation (10) for //, it was found that 



