580 BELL SYSTEM TECHNICAL JOURNAL 



condenser between cathode and plate and measuring the input im- 

 pedance. The result of computing the impedance from Fig. 7 agrees 

 with that formerly presented ^ as, of course, it should, since both 

 results were derived from the same fundamental analysis. This 

 agreement, however, is mentioned by way of giving an example which 

 checks the algebraic manipulations which were employed in arriving 

 at Fig. 7. 



Finally the values of the various elements in Fig. 7 are summarized 

 in Table I. The formulas naturally are very long and their greatest 



TABLE I 

 Referring to Fig. 7 

 Let CcJ, Cy,/, Ccp be capacitances of cold tube, 



y = -- be ratio oi g — p to c — g spacing, 



Xc 



T 

 h = -^ be ratio oi g — p X.Q c — g transit time, 



•l c 



N = iy - h'){9 + Uh + iSh'-) - 5W - W5¥ - 27h' + 21 h\ 

 Cep - 3 Ccp |_ J ^ ^ _^ ^^ J 1. ' ^ ^' 2 y - h'i 



Tp = same as at low frequencies. 



Ceo = C, 



L 1 + iW + MO J y ' 



" ^"^ L 1 +iW- + Mo J 



r rp(y - ¥) -] r 45MoAn 



L45mo(1 + ^/ + Mo)J L y-h'\' 



use probably is in describing the simple circuit of Fig. 7 where the 

 values of the various elements can actually be measured or computed 

 as convenient. 



The easiest way to visualize the equations is to apply them to a 

 special case which can be approached experimentally; namely the 

 condition that the time required by electrons in moving from grid to 

 plate is much shorter than the cathode-grid time. When this is the 

 case, the formulas reduce to those shown in Table II. These show 



