26 BELL SYSTEM TECHNICAL JOURNAL 



the values of these frequencies, the wave-filter structures may have 

 from three to six elements per section. 



In the six element pair/ioo and/ 2 » are unrestricted except that they 

 must lie within their respective attenuating bands. These wave- 

 filters are the general ones including the others. A relation found 

 to exist here is 



l-m\_ fUl 



l-ml fLfL 



which has been incorporated in the formulae. The three element 

 structures, of which there are two pairs, come from putting /i» = 

 and / 2 oo =ji in one case, /ioo —j\ and / 2oo = co in the other. Those 

 having four elements are the "constant k," where /ioo=0 and 

 /2» = 00 , and the two similar appearing pairs in one of which / 2o0 =/ 2) 

 and in the other f ix =/i. Two pairs of five element structures exist, 

 one with fi x =0 and the other with / 2 « = 00 . It is of interest to 

 point out that m 2 =l in all of the band pass wave-filters where / l0O =0, 

 and Wi = l where / 2 » = 00 , showing that in these cases certain of the 

 elements will be like those of the " constant k " wave-filter. Also, 

 in the limiting cases where a frequency of infinite attenuation co- 

 incides with a critical frequency, the attenuation constant increases 

 from zero at this frequency to a finite limiting value at the other 

 extreme of the attenuating band. 



The M-type band pass wave-filters are given by putting rai = ra 2 = m. 

 Choosing / 2 oo as the independent frequency, the formulae simplify to 



m = 





a = a 



4m V f x fj (43) 



4 _ c _l-« V, ,/./ 



4m 

 and Jioo — 7 — 



/2a0 



Part III. Composite Wave-Filters 



The preceding parts of this paper have considered wave-filters as 

 made up of a series of uniform sections. We know, however, from 

 this discussion that the propagation constants of certain general 



