472 



BELL SYSTEM TECHNICAL JOURNAL 



on opposite sides of the control grid wires and are assumed to be 

 sufficiently far away from the grid to insure that the potential distribu- 

 tion at these planes is essentially that of a grid-free space. Moreover, 

 if the grid is fine-meshed these planes may be located quite close 

 together so that the distance between them is negligible in comparison 

 with the distances between Gi and plane 2, and between plane 3 and 

 the plate. This insures that the potentials of the two planes are 

 practically equal. Since the grid d draws only displacement current, 

 the conduction currents at the planes 2 and 3 are equal. Since the 

 potentials of the two planes are equal, the electron speeds are also 

 equal. The boundary conditions in the plane of Gi are the same as 

 those used in deriving (1), i.e., constant conduction current and 

 electron-speed. Then, following the method employed by Llewellyn ^ 

 in his treatment of the negative triode, the input impedance may be 

 found. Since the details are uninteresting the result is merely quoted. 

 On the assumption that the plate is short-circuited to the cathode by 

 a large condenser the input impedance between grid and cathode 

 may be written as: 



Z ^ Z,-\- 



AxA, 



eiA^ + A^ + G.B-i + D.Ci)' 



(11) 



where Zg is the impedance (capacitive) between the planes 2 or 3 and 

 Gi and where Ai, A^, Gu B^, Di and d have the values: 



A, = 

 A2 = 



Gy = 



B,= 



C2 = 



In (12): 



1 



(ic 



1 





{io})Hi + -^ (2 - 2e-'»i - idi - id,e-'^0 

 kme 



(iooydi + ^ (2 - 2e-'«2 - i92 - id2e-'^') 

 kme 



1 



(1 _ g-iBi _ ie^e~^^i) 



1 



(*w) 2 



3 la^SG^e-^^^ + g-^«2 - 1) -f Mo2iw(g-''«2 - 1) 



1 - e-'^i - T 



ao2 



(1 -e- 



iBi 



hneiioiY 



t(j^U02 



idie' 



-"o] 



(12) 



M02 is the d-c. speed at planes 2 or 3. 



ao2 and aos are the d-c. accelerations at the planes 2 and 3 

 respectively. 



2 Loc. cit. 



