MAXIMALLY-FLAT FILTERS IN WAVEGUIDE 



689 



Written in terms of the wavelengths this becomes 



Xo 





1 



(6) 



This equation is a convenient one to use later in the discussion on resonant 

 cavities. 



The normalized admittance of a single-shunt branch terminated by a re- 

 sistance R can be expressed in terms of its resonant frequency and its Q; 

 thus 



YR= 1+ J2Q, 



a-f)- 



(7) 



Similarly, the normahzed impedance of a single-series branch terminated 

 by a resistance R can be written 



R 



= ^+J2Qr['T 



iir'i)^ 



(8) 



The use of the term loaded Q thus has the advantage that expressions for 

 normalized admittance and normalized impedance of shunt and series reso- 

 nant circuits respectively are identical, as are also the corresponding expres- 

 sions for their insertion loss functions. 



Loss functions of complete filters can likewise be expressed in terms of a 

 loaded Q defined for the complete filter. For example, the loss function of 

 the particular type of filter called a "Maximally-flat" filter is given"* 



= 1 + 



(9) 



where n is the number of resonant branches in the filter, and/, is the cutoff 

 frequency of the filter (half power points). 



In consequence of the concept of loaded Q of the total filter, the loss 

 function can be expressed as 



Po 

 Pl 

 where the total Qt oi the filter is 



1 



1 + 



Hi-'M 



(10) 



Qt = 



(11) 



