POWER OUTPUT 



609 



are acted on equally favorably. Third, most tubes have a central lossy sec- 

 tion followed by a relatively short output section. Such tubes may overload 

 so severely in the lossy section that a high level in the output section is 

 never attained. There is not enough length of loss-free circuit to provide 

 sufficient gain in the output circuit so that the signal can build up to maxi- 

 mum amplitude from a low level increasing wave. Other tubes with dis- 

 tributed loss suffer because the loss cuts down the efficiency. 



Some power-series non-linear calculations made by L. R. Walker show that 

 for fast velocities of injection the first non-linear effect should be an expan- 

 sion, not a compression. Nordsieck's numerical solutions agree with this. 

 A power series approach is inadequate in dealing with truly large-signal be- 



7 

 6 

 5 

 4 

 3 

 2 



Fig. 12.1 — The calculated efficiency is expressed as kC, where fe is a function of the 

 velocity parameter b. This curve shows k as given by Nordsieck's high-level calculations. 



havior. In fact, Nordsieck's work shows that the power-series attack, if 

 based on an assumption that there is no overtaking of electrons by electrons 

 emitted later, must fail at levels much below the maximum output. 



Further work by Nordsieck indicates that the output may be appreciably 

 reduced by variation of the a-c field across the beam. 



It is unfortunate that Nordsieck's calculations do not cover a wider range 

 of conditions. Fortunately, unlikely as it might seem, the linear theory can 

 tell us a little about what limitation of power we might expect. For instance, 

 from (7.15) we have 



V . r}V 



Mo UqoL 



Uo 



= -J 



2Fo 



(12.2) 



