POWER OUTPUT 



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be the same as its phase velocity in the small-signal region. It is interesting, 

 however, to see what limiting efficiencies this leads to. 

 The initial electron velocity for the increasing wave is approximately 



i>a = VcCi- — yiC) 



(i2.li: 



where Vc is the phase velocity of the wave in the absence of electrons. The 

 quantity yi is negative. According to Slater's reckoning, the final electron 

 velocity cannot be less than 



Vb = Veil + yiC) 



(12.12) 



Fig. 12.5 — The efficiency parameter k calculated as in Fig. 12.3, for zero loss and for an 

 electron velocity which makes the gain of the increasing wave greatest, vs the space- 

 charge parameter QC. 



The limiting efficiency rj accordingly will be, from considerations of kinetic 

 energy 



V = 



2 2 



Va — ^'6 



If yiC <K 1, very nearly 



4yiC 



(\-y,cy 



r? = 4 yiC 



(12.13) 



We see that this also indicates an efficiency proportional to C. In Fig. 

 12.6 4yi is plotted vs. b for QC = d = 0. We see that this quantity ranges 



