MAXIMALLY-FLA T FILTERS IN WA VEGUIDE • 701 



Further explanation is needed to distinguish between these two impor- 

 tant cases. First consider the case where inductive obstacles are used. 



Tan - — is negative and the cavity length lies between a quarter and a half 



wavelength (plus any multiple of half wavelength). The selectivity, as 

 given by equation (32), is plotted on Fig. 11 for the fundamental mode. 

 The excess phase is positive, and the added lengths, f, of Fig. 9 are positive. 

 The connecting Unes between two such cavities are then slightly less than a 

 quarter wavelength (or odd multiple thereof). 



9 / 



Next consider the case where the obstacles are capacitive. Tan -- is 



positive and the cavity length lies between zero and a quarter wavelength 

 (plus any multiple of half wavelengths). The selectivity as given by equa- 

 tion (32) is plotted in Fig. 12 for cavity lengths lying between a half wave- 

 length and three quarters wavelength. The excess phase is negative and 

 the added lengths, A of Fig. 9 are negative. The connecting lines between 

 two such cavities are then sKghtly longer than a quarter wavelength (or odd 

 multiple thereof). 



SUSCEPTANCE OF OBSTACLES 



The Equations (31), (32) and (39) give the resonant wavelength, the selec- 

 tivity (in terms of wavelength) and the excess phase as functions of the nor- 

 malized susceptance of the obstacles which form the ends of the cavity, and 

 a knowledge of this susceptance as a function of the geometrical configura- 

 tion of the obstacle is necessary to complete the design of the filter. At low 

 frequencies, conventional coils and condensers can be used to form the dis- 

 continuities in the transmission line; while at high frequencies, transmission 

 line stubs can be used.^^ In the microwave region, where waveguides are 

 employed, obstacles having the shapes shown in Figures 13, 14, and 15 can 

 be used.^^ 



Inductive Vanes 



Figure 13 shows a plane metaUic obstacle, transversely located across a 

 rectangular waveguide, with a centrally located rectangular opening extend- 

 ing completely across the waveguide in a direction parallel to the electric 

 vector. For thin obstacles, the normalized susceptance can be calculated 

 from the approximate formula, ^^ 



B^ - ^ cot^ ^ (42) 



a 2a 



where X^ is the wavelength in the waveguide, a is the width of the waveguide, 

 and d is the width of the iris opening. 



