MODULATION IN VACUUM TUBES 



443 



of quality in speech amplifiers, and crosstalk in the multi-channel 

 amplifiers of carrier telephony, to take but two examples. The modu- 

 lation level in the last case is restricted to much smaller values than 

 are tolerated in the first; it is commonly required to reduce modulation 

 products to the thousandth part, or even less, of the fundamentals 

 which produce them. This last case is the one in which we are 

 primarily interested; other cases of greater distortion referred to 

 above may be treated by an extension of the methods used below in 

 the case of grid current flow, and by Fourier series or e^^pansions in 

 terms of Bessel functions when the negative end of the tube charac- 

 teristic is exceeded. 



A thoroughgoing study of the amplifier problem would relate the 

 static characteristics of a tube and the parameters of the circuit in 

 which it works to its operating characteristics, and then would relate 

 its static characteristics to the internal structure of the tube; it 

 would in brief enable us to link the details of tube structure to the 

 fundamental and modulation currents produced in the output wave 

 of the amplifier. In the following, however, we shall treat only that 

 part of the general problem which relates the operating characteristics 

 and circuit parameters to the static characteristics. 



A consideration of the usual plate current characteristics of a three 

 electrode vacuum tube, as shown in Fig. 1, demonstrates the well- 



Fig. 1- 



V0LT5 GRID POTENTIAL 



-Plate current as a function of grid potential with plate potential as a 

 parameter. EL tube No. 109,150. // = 1.1 amperes 



known dependence of the plate current upon the two variables, the 

 grid and plate potentials. That is to say, the plate current varies 

 with the grid potential when the plate potential is fixed, and it varies 

 with the plate potential when the grid potential is fixed. It has 

 been found of great convenience in the past to utilize an approximate 

 relation between the grid and plate potentials as expressed in what is 



