80 BELL SYSTEM TECHNICAL JOURNAL 



curve of the potential suddenly changes its shape with a resulting 

 change in plate current. Again, the plate may be operated at a 

 negative potential. In this case, none of the electrons will reach it 

 and the potential distribution curves have the character illustrated 

 at [c) and (d) in Fig. 9. 



In attempting to apply the fundamental relations to this grid-plate 

 region, we must choose our origin at a point where the potential dis- 

 tribution curve touches the zero axis and is tangent to it. Whenever 

 such a point exists, the relations may be applied as described below. 

 Even when this condition does not exist inside the vacuum tube, there 

 may be a virtual cathode existing outside of the plate. 



Whenever all of the electrons passing the grid reach the plate the 

 general equations may be applied in a straightforward manner with 

 the origin taken at the virtual cathode. Whenever some of the elec- 

 trons are turned back toward the grid, slightly different equations are 

 required, although they may be applied in the same manner. These 

 modified equations will be derived and discussed after the application 

 of the equations already derived has been made to the case where all 

 of the electrons reach the plate. 



Choosing the origin for this latter case at the point of zero potential 

 or virtual cathode, we can compute the impedance between the grid- 

 plane and the virtual cathode when we know the alternating-current 

 velocities with which the electrons pass through the grid-plane. This 

 has been found for the condition of complete space charge between 

 cathode and grid and was given by (25). Likewise, it can be found on 

 the supposition that no space charge exists in the cathode-grid region 

 and the result will be calculated later. Thus, two limiting cases are 

 available for numerical application. 



In order to prevent confusion for the grid — virtual-cathode region 

 where the electron fiow is toward the origin rather than away from it, 

 as was assumed in the derivation of the fundamental relations, it will 

 be convenient to change the symbol for transit angle from ^ to — f. 

 This will automatically take care of all algebraic signs, currents and 

 velocities now being considered positive when directed towards the 

 origin. 



Since we are computing the impedance between an origin at the 

 virtual cathode and the grid plane we may apply (24) to find the po- 

 tential difference, getting 



V, 





