DISCONTINUITIES 



421 



Whence, just beyond the break which makes V = Q,V,v and i are 



F = 



{ju,C/-n)v = Fi/5i + F2/52 + F3/53 

 (-2FoCV/o)/" = Fi/5I + V,/bl + F3/53' 



(9.21) 



Putting these values in (9.4), we can find V\ , the value of the increasing wave 

 to the right of the break. The ratio of the magnitude of the increasing wave 

 to the magnitude it would have if it were not for the break is then | Vi/ Vi \ , 

 and this ratio is plotted vs CN in Fig. 9.6, where N is the number of wave- 

 lengths in the first section. 



0.2 



Fig. 9.6 — Suppose the circuit is severed a distance measured by CN beyond the input, 

 so that the voltage just beyond the break is zero. The ordinate is the ratio of the ampli- 

 tude of the increasing wave beyond the break to that it would have had with an unbroken 

 circuit (6 = QC = 0). 



We see that there will be least loss in severing the helix for CN equal to 

 approximately j. From Fig. 9.1, we see that at CN = j the voltage is just 

 beginning to rise. In a typical 4,000 megacycle traveling-wave tube, CN is 

 approximately unity for a 10 inch helix, so the loss should be put at least 

 2.5" beyond the input. Putting the loss further on changes things little; 

 asymptotically, | Fi/F | approaches f , or 3.52 db loss, for large values of 

 CN (loss for from input). 



It is of some interest to know how the voltage rises to the right of the cut. 

 It was assumed that the cut was far from the point of excitation, so that 

 only increasing wave of magnitude Vi was present just to the left of the cut. 

 The initial amplitudes of the three waves, Fi , F2 , F3 to the right of the 

 cut were computed and the magnitude of their sum plotted vs CN as it 

 varies with distance to the right of the cut. The resulting curve, expressed 

 in db with respect to the magnitude of the increasing wave Vi just to the 

 left of the cut, is shown in Fig. 9.7. Again, we see that at a distance CN = \ 

 to the right of the cut the increasing wave (dashed straight line) 

 predominates. 



