HIGH-FREQUENCY AMPLIFIER 



49 



In view of the definitions in equations (A-13) and (A-14), both Bi and B2 

 are uniquely defined by a single parameter, namely, the fractional velocity 

 separation, b. That is 



and 



b = 2(wi - U2)/{ux + Wo) = 2(/32 - ^i)/(/32 + iSi) 



= B2- Bi 



B,= 1- ib/2) 

 ^2 = 1 + {b/2) 



(A-38) 



(A-39) 



500 



^ 



0.75 0.80 



1.00 



z 



Fig. 7 — A curve illustrating conditions giving rise to various types of roots. 



A complete plot of F2 , for any value of the parameters W and (a/Xj), 

 would show that equation (A-37) has an infinite number of real solutions. 

 A real solution of equation (A-37) means an unattenuated wave. Thus 

 there are an infinite number of unattenuated waves possible. The waves 

 which will actually be excited in any given case, however, depend upon the 

 boundary conditions at the input and output of the tube. Ordinarily only 

 those waves will be excited which do not have a reversal in phase of the 

 longitudinal E vector, say, as r varies from to a. Attention, therefore, 



