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BELL SYSTEM TECHNICAL JOURNAL 



and hence cannot act on the circuit until it becomes bunched. Finally, of 

 course, the increasing wave must predominate over the other two, and the 

 slope of the line must be 



B = 47.3/CN 



(9.11) 



The dashed line represents the increasing wave, which starts at V^/V = 

 I (—9.54 db) and has the slope specified by (9.11). Thus, if we write for the 

 increasing wave that gain G is 



G = A-{- BCN db 



(9.12) 



0.1 0.2 0.3 0.4 0.5 0.6 



CN 

 Fig. 9.1 — How the signal level varies along a traveling-wave tube for the special case 

 of zero loss and space charge and an electron velocity equal to the circuit phase velocity 

 (solid curve). The dashed curve is the level of the increasing wave alone, which starts 

 off with \ of the applied voltage, or at —9.54 dh. 



This is an asymptotic expression for the total voltage at large values of e, 

 where | F, | » | Fo |, | F., |, and for ^» = J = () = 



(9.13) 



A= - 9.54 db 

 B = 47.3 

 We see that (9.11) is pretty good for C.V > .4, and not too bad for C'.V > .2. 



9.3 Loss IN Helix 



In Chapter VIII, curves were given for 5i , 62 , b^ vs. b for QC = and for 

 </, the loss parameter, equal to 0, 0.5 and 1. From the data from which these 

 curves were derived one can calculate the initial loss parameter by means 

 of (9.6) 



A = 2()log,n| V^/V 



(9.14) 



