692 



BELL SYSTEM TECHNICAL JOURNAL 



When the filter characteristic is given by equation 13, the relationship be- 

 tween 12, the frequency parameter, and the standing wave ratio can be ex- 

 pressed as 



i^T = 2^ . (17) 



This is shown graphically in Fig. 5, where the standing wave ratio is given 

 in db ( 20 logio -^f^ ). This graph is used as an aid in the design of filters of 



100 

 80 

 60 



40 



20 



O 

 til 

 O 10 



Z 8 



> 

 4 



< 



z 

 < 



W 1.0 

 1-0.8 



a 0.6 



z 



0.4 



0.2 





0.01 0.02 0.04 



4 6 8 10 20 40 60 100 



0.1 0.2 0.4 0.6 1.0 2 



Fig. 5 — Input standing wave ratio of maximally-flat filters. 



this type, where the requirements are given in terms of the standing wave 

 ratio. From this information the number of filter branches and the selec- 

 tivity of the total filter can be determined, either from equation 17 or from 

 Fig. 5. 



Distributed Branches 



It has been assumed that the mutual impedances of successive branches 

 are all zero. At low frequencies this limitation may not be a serious one 

 and the practical realization of the expected filter characteristics is accom- 

 plished by shielding properly one branch from another. However, as the 



