712 BELL SYSTEM TECHNICAL JOURNAL 



The cutoff wavelengths are obtained when Bx is equal to zb 2 and we have 

 from equation A8 



r — = -— + arc sin - — / p. , . , (A12) 



from which we obtain 



arc tan — 



0= ^.V^i + i^?arcta„|. (A13) 



This gives the loaded Q of the cavity in terms of the susceptance of the end 

 obstacles. 



To derive the length corresponding to the excess phase of the cavity, let 

 the short-circuited admittances be equal by equating equations Al and 

 A2, and let the wavelength be the resonant wavelength of the cavity, and 

 we have 



Bi - cot ^10 = - cot (9x0 . (A14) 



From equation A9 



^1=2 cot 2^10 (A15) 



so that 



But 



hence 



or 



That is 



2 cot 2^10 - cot ^10 = -cot 61x0 . (A16) 



2 cot 2^10 - cot (9io = -tan (9io (A17) 



tan ^10 = cot ^xo (A18) 



^10 + ^xo = ^ (A19) 



lir i I'kI' _ IT 



^gO 2 \gQ 2 



