ULTRA-HIGH-FREQUENCY VACUUM TUBES 663 



so that 



1 (coC)" r^ \f^A - yB + C 



^2 rp \ y-A - y 

 5 MO [ {y - 



Ra 45 MO L {y - h'Y 



X 



Mo 



MO +|(1 +3')(1 +h) -1(1 -^hy 



(100a) 



Comparison of (100) and (100a) shows that the transconductance 

 Ho/fp appears in the numerator of the former, but in the denominator 

 of the latter, and illustrates the care that must be taken in deriving 

 sweeping conclusions concerning the effect of various tube parameters 

 without taking all of the contributing factors into consideration. In 

 the case of (100) the conclusion is that the loss may be reduced by 

 decreasing the transconductance, but only if the transit angle 6c is 

 unchanged. On the other hand, (100a) says that the loss may be 

 reduced by increasing the transconductance, but only if this is accom- 

 plished without change in the cathode-grid spacing, and without 

 altering h by an amount large enough to affect materially the factors 

 in square brackets. 



Experimentally, it is found in many tubes that the loss increases 

 when the transconductance is increased by changing the voltages 

 applied to a given tube. This would seem to be at variance with 

 (100a), for the cathode-grid spacing, and hence Cc, has not been 

 altered by the voltage change. The explanation of the difficulty 

 apparently lies in the departure of the static characteristics of many 

 tubes from the 3/2 power law, which again may be explained in part 

 by the presence of initial velocities and the large size of the potential 

 pockets surrounding the grid wires. In a rough way the action of 

 the latter is to vary the effective cathode area when the voltages are 

 changed, producing an increased area with increase of current, and 

 hence producing a current variation greater than the 3/2 power law. 



In a recent paper, D. O. North " derives a formula for the active 

 grid loss by neglecting space charge between grid and plate. His 

 result is similar in many respects to (100) and both contain the factors 

 Oc^ixo/rp. In an experimental check, W. R. Ferris i" secures excellent 

 results by obtaining the transconductance from the static character- 

 istics of the tubes used, but computing dc by a formula which differs 

 only slightly from (94). It can be shown that such a procedure would 

 give a computed loss which increases with transconductance when the 

 static characteristic is of the form / = K{Vpo -\- MoFpo)" and when n 

 is greater than 2. The static characteristics are not given in Mr. 



