WAVES IN ELECTRON STREAMS AND CIRCUITS 



643 



Under these circumstances the gain G in db will be very nearly 



20.0 



17.5 



15.0 

 I 

 [12.5 



? 7.5 



5.0 



2.5 



G = 20 logi 



Eo 



20 logio ie^'^'^^ db 



G = -9.54 + g ^ {^'^IceaKY'^t 



0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 



CN 

 Fig. 3.1 — Signal level along the helix of a traveling- wave tube. 



lo^ -^ -^ ^ ^ ^ 



o— 



z=o 



Ejl 



.Jf- 



z=l 



Fig. 4.1 — A high-pass structure in which the phase velocity is in a direction opposite 

 to that of power flow. 



IV. Backward Waves and Other Peculiar Waves 



It is important to notice that, for the usual travelmg-waVe tube, it is 

 possible to express the overall gain in terms of the increasing wave alone 

 only because of the relative ampHtudes of the three waves which make up 

 the solution of the particular problem considered. That this is by no means 

 a trivial point can be demonstrated by considering a case in which the 

 circuit is a high-pass filter, as shown in Fig. 4.1. For such a circuit, the 

 phase constant /3i is negative for a wave excited at the left end of the line 

 which carries energy to the right. Such a wave will not interact with elec- 



