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BELL SYSTEM TECHNICAL JOURNAL 



14.9. The propagation constants obtained in Chapters II and VIII represent 

 such intersections of approximate circuit and electronic curves, such as the 

 dotted lines of Fig. 14.8 and 14.9. Propagation constants obtained by field 

 solutions represent intersections of the more nearly exact circuit and elec- 

 tronic curves such as the solid curves of Figs. 14.8 and 14.9. 

 If we plot a circuit curve giving 



as given by (14.65) (the right-hand side of 14.75) and an electronic curve 

 giving 



0.4 



0.2 



-0.2 



Fig. 14.10 — The curves of Fig. 14.5 may be replaced by those of Fig. 14.6. Here the 

 curve which is concave upward represents the circuit susceptance and the other curve 

 represents the electronic susceptance (as in Fig. 14.9). 



as given by (14.73) (the left-hand side of (14.72)), the plot, which is shown 

 in Fig. 14.10, contains the same information as the plot of Fig. 14.5 for which 

 00 , Q» and A are the same. In Fig. 14.10, however, one curve represents the 

 circuit without electrons and the other represents the added effect of the 

 electrons. 



We have seen that the approximate expressions of Chapter VII fit the 

 broad-beam curves well for real propagation constants (real values of Q) 

 (Fig. 14.8 and 14.9). Hence, we expect that complex roots corresponding to 

 the increasing waves which are obtained using the approximate expressions 

 will be quite accurate when the circuit curve is not too far from the electronic 

 curve for real values of Q\ that is, when the parameters (electron velocity, 

 for instance) do not differ too much from those values for which the circuit 

 curve is tangent to the electronic curve. 



Unfortunately, the behavior of a function for values of the variables far 



