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BELL SYSTEM TECHNICAL JOURNAL 



14.5 Comparison with Previous Theory 



We will compare our field solution with the theory presented earlier by 

 comparing separately circuit effects and electronic effects. 



14.6a Comparison of Circuit Equations 



According to Chapter VI the field induced in an active mode by the current 

 i should be 



-6-4-2 2 4 6 



OJ/COq 



Fig. 14.7 — In a plot such as that of Fig. 14.5, the horizontal line for the fins may not 

 intersect the solid line for the central space at all. Particularly, this will be true as the 

 central space is made very narrow. There will still be an increasing and a decreasing wave, 

 however. Suppose, now, that the finned structure is lossy. We find that the gain in db of 

 the increasing wave will vary with frequency as shown. Here oio is the resonant frequency 

 of the slots in the finned structure. 



whence 



E. = 



jO'R 



{e\ - e') 



(14.60) 



where i? is a positive constant proportional to {E-/I3-P). 



Suppose that in Fig. 14.2 we have at y = d not only the current jBE^ 

 flowing in the wall admittance, but an additional current i given by (14.60) 

 as well. Then instead of (14.28) we have 



1 



^oCVe/M) JE, 



+ P = - 



tanh id' - do) 



2\l/2 



id' - el)'" 



For simplicity, let 9o « 6. Then we obtain from (14.61) 



/— /— / ,^ tanh 0\ „ 



(14.61) 



(14.62) 



