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BELL SYSTEM TECHNICAL JOURNAL 



errors flue to stray fields near the slots) the cutoff frequency of the wave- 

 guide without slots. Does the longitudinal frequency col have a simple 

 meaning? 



Suppose we make a model of one section of the structure, as shown in 

 Fig. 4.14. Comparing this with b of Fig. 4.10, we see that we have included 

 the section of the ridged portion between two slots, and one half of a slot 

 at each end, and closed the ends off with conducting plates C. The resonant 

 frequency of this model is wl , the longitudinal resonant frequency defined 

 above. 



We will thus liken the structure of Fig. 4.10 to the filter network of Fig. 



Fig. 4.14 — A section which will have a resonant frequency corresponding to that for tt 

 radians phase shift per section in the circuit of Fig. 4.10. 



B.= B, + 5i 





Bt = B; 



17 



Bl= 2Ci_{cU-CJi) 



Bt = 2Ct (co-OJt) 



Fig. 4.15 — The approximate variation with frequency (over a narrow l)andj of the 

 longitudinal (^/J transverse (Bt) susceptances of a filter network. 



4.12, and express the susceptances Bi and B2 in terms of two susceptances 

 Bt and Bl associated with the transverse and longitudinal resonances and 

 defined below 



Bt = -62 



Br. = 7^1 + 52/4 



(4.44) 

 (4.45) 



At the transverse resonant frequency cor , B-, ~ 0, luul at (he longitudinal 

 resonant frequency oi^ , Bl = 0. So far, the lumped-circuit representation 

 of the structure of Fig. 4.14 can be considered exact in the sense that at 

 any frequency we can assign values to Bt and A'/, which will give the correct 

 values for 6 and for V'^/P for the voltage across either the shunt or the series 

 elements (whichever we are interested in). 



