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BELL SYSTEM TECHNICAL JOURNAL 



necting transmission line. This type of cavity is resonant when the rela- 

 tion is satisfied^ • ^"^ 



tan 



IttI 



(31) 



where Xo is the resonant wavelength in the transmission line, 

 I is the length of the cavity 

 B is the normalized susceptance of the end obstacles. 

 This resonance occurs at any number of wavelengths, but the 1st or 2nd 

 longest wavelength at which resonance occurs is in the region which is usu- 

 ally of greatest interest. 



The selectivity in this region is determined also by the value of the nor- 

 malized susceptance, B, of the obstacles, and is given by the relation (See 

 Appendix I) 



arc tan •= 



(32) 



2 arc sin 



\/B^ + 452 



This selectivity is based upon the wavelength, not the frequency parameter. 

 In terms of the wavelength in the transmission line this is 



2jd 



<aO 



\ci — \c2 



m 



2irt lirt 



where \gQ is the wavelength of resonance in the transmission line and \gc 

 is the wavelength at the half power points. If the phase velocity in the 

 transmission line does not vary with frequency, then the selectivity can be 

 expressed simply in terms of either the wavelength or the frequency since 



/o / X Xo 



(34) 



However, when the velocity in the transmission line varies with frequency, 

 equation 34 does not hold true, and the expression relating the two parame- 

 ters is more complicated. In the case of the rectangular waveguide 



X. = 



vT^^ 



(35) 



where c is the velocity of light in vacuum, few is the cutoff frequency of the 



c 

 waveguide, jew — 'Z' and a is the width of the waveguide. 



