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BELL SYSTEM TECHNICAL JOURNAL 



and that when r' = I\ and K' = K 2 , 



1 





and 



(25) 



Zi = Z<i. 



In both cases it is apparent that for equivalent results the lattice 

 type requires more elements than the ladder type and is, therefore, 

 not as economical. 



Part II. Design of Low-and-Band Pass Wave-Filters and 

 Reduction to Wave-Filters of Lower Class 



The foregoing theory of design can be applied separately to the 

 design of wave-filters of each class in general use, which classes are 

 the low pass, high pass, low-and-high pass, and band pass. However, 



Lik 



o OXftO^ 





L 2k=Uc 



2k 



Fig. 7 — "Constant k" Low-and-Band Pass Wave-Filter 



instead of such individual treatment designs will first be derived for 

 low-and-band pass wave-filters which are wave-filters of higher class 

 than these four classes and include the latter as particular cases. The 

 simplifications in structure and formulae which result upon their 

 reduction to the lower classes will be considered later. 



Low-and-Band Pass Wave- Filters 



The structure of the " constant k " low-and-band pass wave-filter 

 as derived from the attenuation requirements has the form of Fig. 7. 

 Since this form may be obtained from that given in Fig. 2 by assuming 

 the critical frequency, / 3 , in the latter to be infinite, we may under 

 this assumption refer to Fig. 2 for the impedance and attenuation 

 characteristics corresponding to Fig. 7. 



The series impedance z Vz expressed as a function of frequency is 



hk = i2irfL lk (l + 



l-4r 2 PrL lk C lk 



), 



(26) 



