VACUUM TUBE ELECTRONICS 81 



where Vi is the potential at the virtual cathode. 

 This relation is of the form 



V„- V,^-{M+iN) (^'^,) [(l-cosf)-i-(f-sinf)] + /,Z„ (35) 



where Jp is the plate current, and Z^ is the effective impedance: 



In terms of the cold capacity Ci between plate and grid plane this 

 becomes 



Z = -^^ 



PC. f ^ 



\^' -|(1 -cosr) +2sinf 



which is plotted in Fig. 10. 



The form of (35) shows that the equivalent network between the 

 plane of the grid and the plate may be represented by an equivalent 

 generator acting in series with the impedance, Z^. This is evidenced 

 by the fact that the velocity M + iN with which the electrons pass 

 the grid, may be expressed in terms of the grid potential Vg by means 

 of conditions between the grid and cathode. When complete space 

 charge exists near the cathode, these conditions are expressed by (25) 

 and (26). On the other hand, tubes with positive grid are sometimes 

 operated with inappreciable space charge between grid and cathode. 

 In this event, a similar analysis leads to values for the alternating- 

 current velocity and potential at the grid as follows: 



U, = .1/ + iN = - |, I ( '' r '' ) + M ^—i^^ ) , (37) 

 V, = i^A =^, (38) 



p pc 



where 77 is the transit angle in the absence of space charge, and C is 

 the electrostatic capacity between unit area of cathode and of grid 

 plane. The right-hand side of (38) does not contain a minus sign be- 

 cause of the assumed current direction which is away from the cathode, 

 as is also the convention employed in (25) and (26) where the electron 

 charge e is a positive number. 



The relations given by (35) allow the potential difference between 

 grid and plate to be determined in terms of the total current flowing 

 to the plate, and the total current flowing from the cathode, which ap- 



