ULTRA-HIGH-FREQUENCY VACUUM TUBES 



661 



directly for the impedance Za presented to an input applied between 

 grid and cathode and gives 



^a — ^g I" 



Z2 + Z3 + z. 



(96) 



The impedance Zg is a pure capacitance, but the second term on 

 the right of (96) contains both reactive and resistive components which 

 latter account for the active grid loss which has been the subject of 

 several investigations both of a theoretical and experimental 

 nature.^' ''• ^ At very low frequencies the capacitance represented by 

 Z\ predominates and the resistive component vanishes leaving for the 

 input impedance Za merely the following 



Za ^ Zg -\- Z\ 



Z2-\- Z^ + z 

 {y - ¥) 



iufJLoCc 



Tplr, 



4(1 +y)(l+/,) _ l(i+/,)4 



(97) 



This expression may be written in several different forms but in 

 none of them does a simplification occur in the way in which the 

 transit time ratio h enters the equation. Perhaps the best mode of 

 expression is a comparison of the " hot " capacitance Ca given by 

 (97) where Za — l/ioiCa with the capacitance Co of a cold tube with 

 plate and cathode tied together. This latter may be written 



Co = 



no'Cpjl + y) 

 1 + .V + mo' 



(98) 



where mo' is the " cold " amplification factor, (91), and is related to ^o 

 as shown by (90) so that mo = Mo'(l — h^/y). The ratio Ca/Co is the 

 " dielectric constant " of the hot tube and is 



Ca 



Co 



/ 1 + y + mo' 



V 1 ^y 



|(1 +3.)(1 +/0 -^(1+/;.)^ 



Mo+|(l+3')(l +h) 



1 



(1 + h') 



(99) 



For illustration suppose that a certain tube has the following values : 

 y = l^ lj,Q = 10, h = 1/5. Then from (99) the dielectric constant of 

 the hot tube would be 1.19. This is somewhat less than the value of 



