APPENDIX VII 



HOW TO CALCULATE THE GAIN OF A 

 TRAVELING-WAVE TUBE 



The gain calculation presented here neglects the effect at the output of 

 all waves except the increasing wave. Thus, it can be expected to be ac- 

 curate only for tubes with a considerable net gain. The gain is expressed 

 in db as 



G = A + BCN (1) 



Here A represents an initial loss in setting up the increasing wave and BCN 

 represents the gain of the increasing wave. 



We will modify (1) to take into account approximately the effect of the 

 cold loss of L db in reducing the gain of the increasing wave by writing 



G = A-\- [BCN - aL] (2) 



Here a is the fraction of the cold loss which should be subtracted from the 

 gain of the increasing wave. This expression should hold even for moderately 

 non-uniform loss (see Fig. 9.5). 

 Thus, what we need to know to calculate the gain are the quantities 



A, B, C, N, a, L 



A7.1 Cold Loss L db 



The best way to get the cold loss L is to measure it. One must be sure that 

 the loss measured is the loss of a wave traveling in the circuit and not loss 

 at the input and output couplings. 



A7.2 Length of Circuit in Wavelengths, N 



We can arrive at this in several ways. The ratio of the speed of light c to 

 the speed of an electron Uq is 



c_ _ 505 

 uo ^ VVo ^^^ 



where Vo is the accelerating voltage. Thus, if ^ is the length of the circuit and 

 X is the free-space wavelength and X^, is the wavelength along the axis of 



457 



