Miic.ii. /.v/Tc/'.f.vc/. i\ ir.iri iii iiks 71 



(-(in< lit ions, will slmw ih.il llii> is ilit- \n\wr nl ilic Iwd ciil-olT lri'i|iii-iii-ii's 

 (fx). lli.U is 



r,= ' . (29) 



2jrv /.iC 

 Hs o<iiiatinn Zi AZ- In —I in t.-(|uali(>ii (27) thr iippiT (iil-nrf frc- 

 (liii'iu-y (/•) is found lt> lu' 



■'' 27r\ C,t'2(L,+4Lj)" 



(30) 



For these exjilicit relations for /i. /■.. an(i/„, cfiuation (2(1) may be 

 rewritten 



When d is zero this eciuatioii heeonies, for the iion-(lissipati\e case 



4Z 



From the precediii;j; formul.n' .uul trom tlu- lurxes shown in I'igs. 

 11 and 12, it is possible to read directly the attenuation constant and 

 the phase constant for the structure shown in Fig. 13, at any fre- 

 quency, provided the values of /i,/: and /x are known. The formulae 

 for the dissipative case are of use mainly throughout the transmission 

 bands and near the frequency /». Elsewhere, the formulae for 

 Zi'4Z-> for the non-dissipative structure may be employed without 

 undue error. The preceding formulae have been derived in a direct 

 manner, but may be obtained more simply by considering the structure 

 of Fig. 13 to be a derived form of the structure 3 — 2 in Table II. 



In order to minimize reflection loss effects, it is, as a rule, desirable 

 to terminate a filter in an impedance ccjual to the image impedance 

 of the filter at the mid-frequency," (Jm) or at some other important 

 frequency. From equation (6) and the values of Zi and Zj, the mid- 

 series image impedance (Zu), at the mid-frequency in the non-dissipa- 

 tive case is 



" Dcfine<i as the geometric mean of the two cut-ofT frequencies /i and ft; or /, 



