A LARGE SIGNAL THEORY OF TRAVELING- WAVE AMPLIFIERS 365 



nent is coupled to the beam and has an amplitude equal to 



Zolo C 

 IC 2(1 + bC) 



VX^'Y + 



K^y / 



\dy) 



which generally grows with the forward wave. It thus has a much larger 

 amplitude at the output end than at the input end. The other component 

 is a wave of constant amplitude, which travels in the direction opposite 

 to the electron flow with a phase velocity equal to that of the cold cir- 

 cuit. At the output end, 2 = Z), both components have the same ampli- 

 tude but are opposite in sign. One thus realizes that there exists a re- 

 flected wave of noticeable amplitude, in the form of (26), even though 

 the output circuit is properly matched by cold measurements. Under 

 j such circumstances, the voltage at the output end is the voltage of the 

 forward wave and the power output is the power carried by the forward 

 wave only. This is computed in (23). 

 Since (26) is a cold circuit wave it may be eliminated by properly ad- 



c[-w], 



■C[w], 



5.0 



4.5 



4.0 



3.5 



5 3.0 



2 



o 



9- 2.5 



1.5 



1.0 



0.5 



0.1 0.2 0.3 0.4 0.5 1.0 



QC 



1.5 2.0 2.5 

 b 



0.05 0.10 0.15 0.20 



Fig. 5 — Cw(y, <po) of the fast and the slowest electrons at the saturation level, 

 (a) versus QC for k = 2.5, C = 0.1 and b for maximum small-signal gain; (b) versus 

 6 for A; = 2.50, C = 0.1 and QC = 0.2; and (c) versus C for A- = 2.50, QC = 0.2 

 and b for maximum small-signal gain. 



