Mlll-.ll. IMHCT.IXCr. I\ ll.irii IILTERS 57 



slant. riif I.i>l f.n tor li,i> l«t«ii i .illcd ilu' inlenution factor. The 

 \aluf of till" ri'dfiiiKii I.U lor i> t\ idtiilK .» fimrtion sim()l\- of the ratio 

 of the iiniHil.mres iiuoKed, while the ahsoliile \aliie of tlie transfer 

 factor is t ' wliere .1 is the re.il |M>rtion of the transfer constant and 

 hence is the attenuation constant. 'Pile \alue of the interaction 

 factor is seen to i)e unity eitlier when Z i^ = Zr or whvn Zt^=Zs. It 

 also approaches unity if the vahie of O is sufficiently large. 



In the case of a symmetrical structure, such as is shown in I'ip;. 2, 

 or Fii;. 4, Zi,=Zi.=Zi and e(iuation (10) reduces to 



h ^ ( Z s+Zr \ (VTzJZs) ( V-IZiZr ) 

 U- V y/AZsZR' \ Z/+Z5 / ^ Z,+Zr I 



Xt-ex ,y y \y 7 , • (12) 



1 _ ( Zi-Zr \ / Zi-Zs \ ^^, 



\Z, + Zr)\Z,+Zs) 



If the structure is symmetrical, and if, furthermore, the sending-end 

 impedance Zs is equal to the rccciving-cnd impedance Zr. equation 

 (12) becomes 



7^.-* ^{z,+ZRr-^. ( Z,-zr \^ _^; ^'^> 



\Z,+Zr) ' 



The preceding formulae make it possible to calculate rigorously 

 the transmission loss caused by any network whose image impedances 

 and transfer constant are both known. In the symmetrical case, if 

 Zi=Zs = Zr, the transmission loss is determined simply by the \alue 

 of the attenuation constant. In general, in the attenuation range 

 of freciuencies, the value of 6 of a wave filter is relatively large and 

 the interaction factor is substantially unity. Consequently, the 

 transmission loss caused by any filler in its attenuation range is de- 

 pendent practically only upon the value of the attenuation constant 

 and the reflection losses between Zs and Z/,, Zr and Z/,, and Zs 

 and Zr, respectively. Throughout most of the transmission range 

 of a filter, its image impedances may be nuide very closely equal to the 

 terminating impedances so that the transmission loss caused by the 

 filter in this range is dependent simply upon its attenuation constant. 

 In the intervening range, between the attenuated and the non-at- 

 tenuated bands, the transfer factor, the reflection factors and the 

 interaction factor must all be taken into account.^ 



' Zobel, O. J., "Transmission Characteristics of Electric Wave-Filters," Bell Sys. 

 Tech. Jour., Oct., 1924. 



