646 



BELL SYSTEM TECHNICAL JOURNAL 



Thus, if we wish we may write (14.70) in the form 



tanh^ 



where 



P. = _^^!^ _ p (14.72) 



Pe = (l/0)[(ei/e)i/2 tanh [(ei/e)!/^ d -tanh 6] (14.73) 



The quantities on the right of (14.72) refer to the circuit in the absence of 

 electrons; if there are no electrons P« = and (14.72) yields the circuit 



0.1 



// 



r / 



/ 

 • 



Fig. 14.8 — Suppose we compare the circuit admittance for the structure of Fig. 14.1 

 with that used in earlier calculations. Here the solid curve is proportional to the difference 

 of the Hi's for the finned structure and for the central space (the impressed current) di- 

 vided by £, . The dashed curve is the simple expression (6.1) used earlier fitted in mag- 

 nitude and slope. 



waves. Thus, P, may be regarded as the equivalent of an added current * 

 at the wall, such that 



^4-=^Ve/.P. 



(14.74) 



Now, the root giving the increasing wave, the one we are most interested 

 in, occurs a little way from the pole, where (ei/e)^'^ may be reasonably 

 large if Q is large. It would seem that one of the best comparisons which 

 could be made would be that between the approximate analysis and a very 

 broad beam case, for which B is very large. In this case, we may take ap- 

 proximately, away from 6 = 6, 



(14.75) 



tanh [(€i/€)i/2 6] = tanh 6 = 1 



Pe = iMe)[{e,/eyi-^ - 1 



A 



Pe = (1/6) 



1 - 



(6. - ey 



m 



(14.76) 



