24 



BELL SYSTEM TECHNICAL JOURNAL 



Taking the first term of the right member as typical, it may be trans- 

 formed through (29) to the form 



R- 



1 



1 



az L + bz c azL.bzc i2TvjaC 2 k+ 

 R 2 + R 2 



(37) 



t2rfc- 



which is the impedance of an anti-resonant component having an 



inductance, -^, and a capacity, aC 2k . Similarly each of the other two 



o 



terms of (36) represents the impedance due to an anti-resonant com- 

 ponent, in one case of elements -§- and cC% k , and in the other of ele- 

 ct 



ments -j- and eC<i k . 



The shunt impedance may by (29) and (31) be put in the form 

 R 2 R 2 



222 



Zu miZ L + ni2rz L zc 

 rzL+zc 

 1 



(38) 



i2TfmiC 2 k + 



i^f—1 



1 



ra 2 i2wjni2rC2k 



and is the impedance of a capacity ra x Ci k in parallel with a resonant 



The structure 



component of inductance — ^ and capacity mirC^k 



m 2 



corresponding to 212 and 222 is shown in Fig. 9. 



mfizk 



Fig. 9 — General Mid-Shunt Equivalent Low-and-Band Pass Wave-Filter 



The method of reducing these general wave-filters to the desired 

 lower class wave-filters will now be taken up briefly. The resulting 

 structures and formulae are given in Appendix II, where the two 

 wave-filters having identical propagation constants are considered 



