THEORY Of THE HOUTJNG TELETHON E 



29 



General Solution of the Howling CiRcurr 



The elements of a telephone s\steni w hich is howling are the trans- 

 mitter, the receixer, the mechanical coupler and the electrical coupler 

 as indicated in Fig. 1. If there is a source of electrical power in the 

 electrical coupler, which is released by nioxements of the transmitter 

 diaphragm in the form of electrical vibrations, and also, if there is a 

 proper relationship between these four elements, then a sustained 



-»-Z. 



MECHAMICM OR 

 ACOUSTIC COUPLER 



.T- 



ELECTRICAL 

 COUPLER 



R-*- 



Fig. 1 



howling will result. In other words, if the gain in the transmitter 

 due to its amplifying action is just equal to the losses in the electrical 

 and mechanical circuits, then a steady oscillatory state will be 

 maintained. The problem is to determine the nature of these 

 relationships. 



Assume that the conditions are such that a stead>' oscillatory 

 state has been set up. Under such conditions let T be the electrical 

 impedance of the transmitter, R the impedance looking away from 

 the transmitter terminals into the electrical coupler, and Zr the 

 impedance of the receiver. It is well known that the impedance Zr 

 is dependent upon the velocity of motion of the recei\er diaphragm. 

 Also, T is dependent upon the amplitude of motion of the transmitter 

 diaphragm as well as upon the direct current supplied to it. Conse- 

 quently, the impedances defined above are not only dependent upon 

 frequency but also upon the mechanical coupling and magnitude of 

 the current supplied to the transmitter. 



If e is the electromotixe force created in the transmitter, and / the 



