IMPEDANCE PROPERTIES OF ELECTRON STREAMS 



475 



T 3 



^0 T^-r 



/o 



[Va/2 _ 1 4. V(^^)l/2 - 1]3 



ddi (^1/2 _|_ 2)V?^'" - 1 



2n< 



ikfY" 



Type 



(23) 



"P \ ^if ^ 



The parameter ^ is without physical significance for the D solutions 

 but serves merely as a convenient constant of integration. For the 

 solutions of C type, however, ^ is of direct physical significance. For 



here ^ represents the ratio -^7— . In the language used in the previous 



Va 



1 . 



qualitative discussion of space charge it is clear that ^ = — is the point 



where a potential minimum sets in and ^ = ( 1 H — p I is the Kipp 



point. Calculations for C2 solutions are not included. 



The result of the calculations of capacitance and conductance are 

 shown on Figs. 4 to 8. Figure 8 is an enlargement of Fig. 7 for small 



1.3 1.4 1.5 1.6 1.7 1.8 1.9 



INTEGRATION CONSTANT /^ 



2.0 2.1 



2.2 



Fig. 4 — Relative input capacitance of an idealized space charge grid tube for different 

 space charge conditions (voltage ratio tp = 1.0). 



values of F. Three values of the parameter <p were selected, i.e., 0.04, 

 0.25 and 1. The curves demonstrate regions of negative capacitance 

 as well as of negative conductance. Note that as the parameter (p is 

 made smaller both the capacitance and conductance pass through 



