1 



362 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 195G 



4.5 



0.5 



Fig. 1 — The saturation eff./C versus QC, for k = 2.5, h for maximum small- 

 signal gain and C = small, 0.1, 0.15 and 0.2. 



ixx = Ml (max), 0.94 jui(max), 0.67 iui(max) and 0.3 /ii(niax), respectively. 

 It is seen that Eff./C decreases as C increases particularly when h is 

 large. It is almost constant between k = 1.25 and 2.50 and decreases 

 slowly for large values of C when QC increases. 



The (Eff./C) at saturation is also plotted versus QC in Fig. 4(a) for 

 small C, and in Fig. 4(b) for C = 0.1. It should be noted that for C = 0.1 

 the values of Eff./C fall inside a very narrow region say between 2.5 to 

 3.5, whereas for small C they vary widely. 



8, VELOCITY SPREAD 



In a traveling-wave amplifier, when electrons are decelerated by the 

 circuit field, they contribute power to the circuit, and when electrons 

 are accelerated, they gain kinetic energy at the expense of the circuit 

 power. It is therefore of interest to plot the actual velocities of the fastest 

 and the slowest electrons at the saturation level and find how they vary 

 with the parameters QC, C, b and k. This is done in Fig. 5. These veloci- 

 ties are also plotted versus y for Case 10 in Fig. 6, in which, the A(y) 

 curve is added for reference. 



9. THE BACKWARD WAVE AND THE FUNDAMENTAL COMPONENT OF THE 

 ELECTRON CHARGE DENSITY 



Our calculation of efficiency has been based on the power carried by 

 the forward wave only. One may, however, ask about the actual power 



