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BELL SYSTEM TECHNICAL JOURNAL 



5. Band Pass Wave-Filter, Type h\C\L 2 , Fig. 5. 



w 

 A n {t) = —,Jn(y) sin (x + wtt/2) 



(5a) 



where x = u m t, y — wt/2 and the filter elements are determined by 



L\ =2wik/W(i)2\ Ci=w/2k(X> 2 m ' t Li= — jr— 2 — k. 



JL, 2C, 



o — nswr^ 



-npm^- 



Fig.5 



The approximate formulas for y>n are 



w I 2 



■^ «(0 - — L *» \ — cos (<l*y — 8») sin (x + wtt/2) (5b) 



Wm« \ Try 



A MX )_[sin(* — g n y + 9„ + wir/2)+sin(* + g„y — e n 4-n7r/2)l (5c) 



2w m k 



and ultimately 



A„(t) C o^^A[ s in(x-y + 4 -^- 1 7 r)+sin^+y-V4)]. (5d) 

 6. Band Pass Wave-Filter, Type L\L 2 C 2 , Fig. 6. 



111! 



A„(t) =^ [/„(y) sin (x-rnr/2)- 7iCy) cos (x-nr/2)] (6a) 





L, 



o- 



T__. 



Fig. 6 



where x = u m t; y = wt/2; J„(y) =d/dy J„(y), and 



U = 



2k 



^1 + ^2 



; L 2 = w^/2cji 2 ; C 2 = 2/wk. 



