582 



BELL SYSTEM TECHNICAL JOURNAL 



that we nia\' put for eiiluT of thorn the si)iiih' termimiJ loss L,„ clcfinod 

 by (6) as 



6-i" = 



2y/K«i{m)R_2\/KvAm)R\ 



K-2,(m)+R Kx2{m)+R 

 which upon the substitution of (32j gi\os 



..=.,..(1 



1± 



Vl+Uk+iVk I 



l + {l-m-) (Uk + iVk)\ 



l + {l-m^)(Uk+i Vk)\^ 



Vl + Uk + iVk 



).(34) 



Terminal Losses, Lx, villi x-"coiistaiil k" Terminations. The 

 terminations are 



3, .v-siumt of the "i-onstani k" \va\e-fiiter, (A'.vj); and 



4, .Y-serics of the "(-onslanl k" \va\'c-filtcr, (A'n). 



The .v-shunt and .v-scries characteristic impedances, Kx2 and A'^i, 

 are related b>- the formulae 



Av2 K K 



and 



Kx 1 A'.v2 = KikKik = zikZ'ik = R-, 



where K^k and A'u- are the mid-shunt and mid-series values corre- 

 sponding to x = .5. With either termination Kx2 or Kxi it is assumed 

 that the mid-part of the wave-filter begins at the mid-point, i.e., at 

 the position corresponding to K^k or A"]*:, respectively, even when x 

 is less than .5. In the latter case an impedance is theoretically added 

 which is sufficient to "build-out" the wave-filter to the mid-point, 

 and an ec|ual impi-dance is similarly subtracted from the terminal 

 impedance. 



I'or termination 3, that is Avj, the elenieiils of factor Fi, in (6) 

 ha\e the values 



11-6 = Ao,, 



Zb=z^kR/{z,k + {x-.o)R), 

 and T/h = Z2t/{z-2k + {x - .5) A) . 



l-'or tenninaiioii I, A',i. they are 



n^ = Au-, 



Zb = R + {x-.ri)z,k, 

 and I/Ib=l. 



(36) 



(37) 



