VACUUM TUBE ELECTRONICS 



73 



In any event, this relation may be justified if the factor of proportion- 

 aHty, k, be allowed to assume complex values, and ^i is not taken too 

 near the origin. Actually, the electron-free space surrounding the grid 

 wires, and the fact that the electric intensity at a point midway be- 

 tween any two of the wires is directed perpendicularly to the plane of 

 the grid, gives us more confidence in extending the approximation, so 

 that k will be regarded as real, and ^i will be taken very small. 



1.0 

 0.9 

 Q8 

 0.7 

 0.6 

 0.5 

 0.4 

 0.3 

 0.2 

 0.1 

 



6 7 



10 11 12 13 



-2 

 -3 

 -4 

 -5 

 -6 

 -7 



I 



Fig. 4 — Magnitude and phase angle of electron velocity fluctuation 

 in diodes versus transit angle. 



Equation (24) may, therefore, be applied under the conditions that 

 ^1 -^ 0, and gives the following for the potential diliference between 

 plate and cathode: 



l lrpA 



(^ sin ^+2 cos ^-2)+f(^ + i^3_2 sin ^-f^cos ^ 



- (M+iW) ^ [(t sin ^+cos ^-\)-i{sm ^-^cos^)] 



(31) 



