Mi'ir.ti. iMHcr.ixcii i.\ ii.iri-: iii.ii.ks ku 



Thf imptil.iiui' (if till- ^lHlllt .irm is 



Z.= -j{-L,+-[^ 



(93) 



The ratio, Zi-lZi, which controls ihi- .uicmi.itinn and i>li,isc con- 

 stants, per section, of tlie structure is 



Zi 





Cj 1 — L\C\oi' ' 



(94) 



I'rom the impedance characteristics of reactance meshes 3 and 3', as 

 illustrated in I'igs. and 43, and the coml)inetI reactance character- 



fjX 



Fig. 46 — Reactance-Frequency Characteristics of the Series and Shunt Arms of 

 the Prototype Section of Fig. 45-A 



istics of Fig. 46 for Zi, 4Z2 and — 4Z2, it will be noted thai the lower 

 cut-ofT frequency,/], is that at which Zi=0. Hence, 

 1 



/i = 



2tV'L,C," 



(95) 



Similarly, the upper cut-ofT frequency is that at which Zi = — 4Z2 or 

 JLoLi—j,'wCi=j4wL2+j4'wC2. From this relationshi|), the upper cut- 

 otT frequency is 



'' 2t\c,C2(L,-4Lj)' 



(96) 



Let /r be assumed as the frequency where Z2 is a miiiitmini, that is, 

 where u-LiCt=l. We may then write 



