MA XI MA LLY-FLA T FILTERS IN WA VEGUIDE 711 



The short-circuited admittances of half the cavity and half the tuned cir- 

 cuit are 



Ysci = j{Bi - cot ^i) (Al) 



Yscx = -j cot e, (A2) 



while the open-circuited admittances are 



Yoci = j{B, -h tan ^i) (A3) 



(A4) 



(A5) 



(A6) 

 2 cot $1 - Bi 

 Solving for Bx we have 



B^ = -5i(^i sin ISi - 2 cos 2^i) (A7) 



which becomes 



S. = VB\ + 4Bf sin |-' (^ - l) 



where 



Equation A9 gives the requirements for resonance. 

 The expression for the loaded Q is 



2x/ 



2ir^ _2ia 



\gc2 \el 



(A8) 



- — = arc tan ^- . (A9) 



(AlO) 



