Traveling-Wave Tubes 



By J. R. PIERCE 



Copyright, 1950, D. Van Nostrand Company, Inc. 



FOURTH INSTALLMENT 



CHAPTER XII 

 POWER OUTPUT 



A THEORETICAL EVALUATION of the power output of a traveling- 

 wave tube requires a theory of the non-hnear behavior of the tube. 

 In this book we have dealt with a linearized theory only. No attempt will 

 be made to develop a non-linear theory. Some results of non-linear theory will 

 be quoted, and some conclusions drawn from experimental work will be 

 presented. 



One thing appears clear both from theory and from experiment: the gain 

 parameter C is very important in determining efficiency. This is perhaps 

 demonstrated most clearly in some unpublished work of A. T. Nordsieck. 



Nordsieck assumed: 



(1) The same a-c field acts on all electrons. 



(2) The only fields present are those associated with the circuit ("neglect 

 of space charge"). 



(3) Field components of harmonic frequency are neglected, 



(4) Backward-traveling energy in the circuit is neglected. 



(5) A lossless circuit is assumed. 



(6) C is small (it always is). 



Nordsieck obtained numerical solutions for such cases for several electron 

 velocities. He found the maximum efficiency to be proportonal to C by a 

 factor we may call k. Thus, the power output P is 



P = kCIoVo (12.1) 



In Fig. 12.1, the factor k is plotted vs. the velocity parameter b. For an 

 electron velocity equal to that of the unperturbed wave the fractional 

 efficiency obtained is 3C; for a faster electron velocity the efficiency rises to 

 7C. For instance, if C = .025, 3C is 7.5% and 7C is 15%. For 1,600 volts 

 15 ma this means 1.8 or 3.6 watts. If, however, C = 0.1, which is attainable, 

 the indicated efficiency is 30% to 70%. 



Experimental efficiencies often fall very far below such figures, although 

 some efficiencies which have been attained lie in this range. There are three 

 apparent reasons for these lower efficiencies. First, small non-uniformities 

 in wave propagation set up new wave components which abstract energy 

 from the increasing wave, and which may subtract from the normal output. 

 Second, when the a-c field varies across the electron flow, not all electrons 



608 



