DISCONTINUITIES 413 



For large values of CN corresponding to large gains, the increasing wave 

 predominates and we can neglect the effect of the other waves. This leads 

 to the gain expression 



G = A^- BCN db 



Here BCN is the gain in db of the increasing wave and A measures its ini- 

 tial level with respect to the applied voltage. 



In Fig. 9.2, A is plotted vs. b for several values of the loss parameter d. 

 The fact that A goes to oo for c? = as 6 approaches (3/2) (2) does not 

 imply an infinite gain for, at this value of 6, the gain of the increasing wave 

 approaches zero and the voltage of the decreasing wave approaches the 

 negative of that for the increasing wave. 



Figure 9.3 shows how A varies with d for b = 0. Figure 9.4 shows how A 

 varies with QC ior d = and for b chosen to give a maximum value of B 

 (the greatest gain of the increasing wave). 



Suppose that for b = QC = the loss parameter is suddenly changed from 

 zero to some finite value d. Suppose also that the increasing wave is very 

 large compared with the other waves reaching the discontinuity. We can 

 then calculate the ratio of the increasing wave just beyond the discon- 

 tinuity to the increasing wave reaching the discontinuity. The solid line of 

 Fig. 9.5 shows this ratio expressed in decibels. We see that the voltage of 

 the increasing wave excited in the lossy section is less than the voltage of 

 the incident increasing wave. 



Now, suppose the waves travel on in the lossy section until the increasing 

 wave again predominates. If the circuit is then made suddenly lossless, we 

 find that the increasing wave excited in this lossless section will have a 

 greater voltage than the increasing wave incident from the lossy section, 

 as shown by the dashed curve of Fig. 9.5. This increase is almost as great as 

 the loss in entering the lossy section. Imagine a tube with a long lossless 

 section, a long lossy section and another long lossless section. We see that 

 the gain of this tube will be less than that of a lossless tube of the same 

 total length by about the reduction of the gain of the increasing wave in 

 lossy section. 



Suppose that the electromagnetic energy of the circuit is suddenly ab- 

 sorbed at a distance beyond the input measured by CN. This might be 

 done by severing a helix and terminating the ends. The a-c velocity and 

 convection current will be unaffected in passing the discontinuity, but the 

 circuit voltage drops to zero. For d = b = QC = 0, Fig. 9.6 shows the 

 ratio of Vi , the amplitude of the increasing wave beyond the break, to 

 V, the amplitude the increasing wave would have had if there were no break. 

 We see that for CN greater than about 0.2 the loss due to the break is not 



