MAXIMALLY-FLAT FILTERS IN WAVEGUIDE 



697 



tuned circuit situated across the middle of a short length of transmission 

 line. This short length of transmission Une is added in order to account for 

 an excess of phase shift associated with the resonant cavity, but it can read- 

 ily be absorbed in the connecting line which otherwise would have been an 

 odd quarter wavelength long. 



The similarity between resonant cavities and resonant lumped circuits 

 enables one to use the known art of designing lumped element filters to de- 



RESONANT 

 CAVITY 



Z + 2Z =-^ 



Fig. 9 — A resonant cavity is approximately equivalent to a resonant circuit shunted 

 across a short length of transmission line. 



Yq line 



TAN 



2tt£ 



Q = 



ARC TAN -|- 



Vb44- 4B2 



ARC TAN 



2 ARC SIN 



Vb'* + 4B2 



Fig. 10— The resonant wavelength and the loaded Q of a cavity depend upon the 

 normahzed susceptance of the end obstacles and their separation. 



sign filters which use resonant cavities, provided that the selectivity, the 

 resonant frequency and the excess phase shift of the resonant cavity are 

 known. 



Resonant Wavelength and Loaded Q of Cavities 



These properties can best be derived by considering one of the usual types 

 of cavities, which consists of two obstacles or discontinuities separated by a 

 length of transmission line. Such a cavity is shown schematically in Fig. 

 10. The obstacles at each end are assumed to be equal, and to have an 

 unvarying susceptance BYq , where Fo is the surge admittance of the con- 



