ML'll.ll. IMHCr.t.W li l\ ll\iri. lll.ll.Ks 



>trinlurc shown in I'iv;. H is ri'K.irdcd .is m.idr up of >.\ iiimiMrical 7' 

 lU'tworks or sfclioiis, tlu- jmirliniis of which occur .il ihc luiil-poiiils 

 of thi' si-rii's anus. 



Sup|X)so now tlial tlu- ^truclun' of Kij;- •{ is itmsidcrfd lo Ik- m.idf 

 up of syinnu-trical s- lu-tworks, or si-ctions, each of which is ri'|)ri'stMitcd 



VvVW 



AWW- 



-A/VWV- 



-j\tUh 



Kig. J — CifiUT.ilizi'il^Kii uritiit SiTics-Sluiiit Network 



3 



H, 



Hi'lZj. f 2Z, 



Z2,% Z,.^Z:. 



Fig. 4 — Generalized Syninietrical t Network Connected to Impedances Equal to 

 Its Image Impedances 



as in Fig. 4. By nu-thods similar to those empIo\etl for tiie T network 

 of Fig. 2 it can be siiown'' that the iniage impwhmce of the general- 

 ized JT network of Fig. 4 is gi\en by 



Z,= 



^ 



z,z. 



1+ 





(7) 



In this symmetrical structure the image impedance is called the mid- 

 shunt imave impedance. 



The image transfer constant of either a T or a tt symmetrical struc- 

 ture is^ 



e = ^l+jB = 2 sinh-"-y|^ = cosh-'(l+;^). 



(8) 



In discussing the generalized networks of Figs. 1, 2 and 4, it has been 

 assumed that the networks were terminated in their respective image 

 imfH-dances. In practical cases, filters must be designed to work 

 between inifK-dances which are, in general, not exactly efjual to their 



