690 



BELL SYSTEM TECHNICAL JOURNAL 



For convenience, the bracketed term of equation 9 may be called 12, a 

 frequency parameter, whence 



./o U -1 

 and the loss function becomes 



(12) 



^ = 1 + (ur. 



XL 



(13) 



20 



0.2 



0.1 



0.1 0.2 0.4 0.6 1 10 lO*^ 10^ lO'* 



Fig. 4^-Insertion loss of maximally-flat filters. 



Maximally-Flat Filters 



The loss function for maximally-flat filters as given in equation 13 is 

 plotted in Fig. 4 where the insertion loss in db is used on the ordinate and 

 12" is used on the abscissa. 



The ladder network which gives rise to this loss function consists of n 

 resonant branches, as shown in Fig. 3, that are all tuned to the same fre- 

 quency, but whose selectivities, or loaded Q's, are tapered from one end of 

 the filter to the other according to the positive imaginary parts of the In 

 roots of - 1, according to the theories of Bennett^ and DarUngton.^ These 

 roots are expressed thus 



sin 



\ In ) 



