306 BELL SYSTEM TECHNICAL JOURNAL 



Formukis for the series il/i/'-type are 



Si//(w, ni') = z , 



+ 



mm'zik 4inm' 



r> Zok 



nr 





cosh Tj,{))i, m') = 1 + 



4m' '^'' w'(l - m-') 

 2mhn'\Uu + iVk) 



1 + (1 - ni^nr){Uk + iVt) 



and 



R[\ + (1 - mW^)(;7, + zF,)] 



W-ik{m, m') = 



[1 + (1 - W')(t/, + iF,)]Vl + f/;t + ^'F, 



where < w ^ 1, and < An' ^ 1. 

 As a limiting value, W^kijn, m' = 1) = W^k- 

 For the shunt MM'-type 



Zik"(m, m') = 



' + 



mm'zik m'{\ — m^) . Am' 



m{\ — m' ) m{\ — m' ) 



Z'lk {m, m ) = —. r -u + ■ / -2/:, 



Anim mm 



cosh Tk{m, m') = same formula as in (15), 



i?[l + (1 - m'){Uk + iVk)yi + Uk + JF, 

 [1+ (1 - 7nhn'^)(Uk+ iVkU 



TFu(w, ^;i') = ,-.,.. ., /2 



and 



Vl+ f/. + ^'F, 



where as before < ;;z ^ 1, and < m' ^1. A limiting value here 

 is WuOn, m' = 1) = TFu- 



The J/.l/'-type wave-filters have structural designs which can be 

 inferred from their respective mid-half sections of Fig. 8; they may 

 have characteristics such as illustrated in Fig. 9 where the parame- 



