50 BELL SYSTEM TECHNICAL JOURNAL 



making possible a given voltage amplification with smaller plate 

 battery than could be obtained if the output circuit contained an ap- 

 preciable resistance. 



15. Power Amplification. From Equation 6, which neglects 

 harmonic terms, it is readily seen that the power output is 



fi 2 e 2 r 



{r + r p ) 2 + x v 



where r-\-j x has been substituted for Z. This output is a maximum 

 when r 2 = r P 2 -\-x 2 . The case in which x = is particularly important; 

 evidently for maximum power output, a tube should work into a re- 

 sistance equal to its internal resistance. 



As pointed out in Sec. 13 the input impedance of a tube is not 

 always readily determinable; however, calling the input resistance 30 

 r g , the power amplification produced by a tube is given by the ex- 

 pression, 



H 2 rr g 



{r + r p ) 2 +x 2 



(7) 



This expression has been obtained on the assumption that the grid 

 draws no electron current from the space charge, which in turn requires 

 that the grid remain at a negative potential at all times. Since the 

 power amplification falls rapidly as the grid becomes positive, it is 

 customary in most amplifier circuits to supply means of maintaining 

 the grid at a negative potential. 



Expressions 6 and 7 are of fundamental importance in the design of 

 amplifier circuits. 



16. Selection of Tubes. When selecting tubes for an amplifier, 

 curves such as those shown in Fig. 14 are very useful. By their 

 means it is readily possible to select the tube, the plate potential 

 and the average grid potential which will give satisfactory results 

 for any pre-assigned value of the input voltage. In order to obtain 

 amplification as free from distortion as possible, it is necessary that 

 the grid potential in its excursions neither become positive nor strike 

 the lower end of the characteristic. To a sufficient approximation 

 it is evident that when the variable grid or input voltage e is given, 

 we should choose E g and E p such that 



e 0> -E g >§*. 



30 Where many tubes of the same design are to be interchanged in a given circuit, 

 and where the conditions of manufacture are such that the insulation resistance 

 between filament and grid is not always of the best, it may be found desirable to 

 shunt the input with a fixed resistance, e.g., \ megohm. 



