54 PEI.l. SYSTr.M TllCIISIC.tl. JOIKX.IL 



The real part of the transfer constant, that is, tlie attenuation con- 

 stant, is expressed by the above ilefmition in napiers or hyperbolic- 

 radians and the imaginary part, tliat is, the phase constant, is ex- 

 presse<I in circular radians. The practical luiit of attenuation here 



^^ — vww — r — \w\/v — ^- 



Z.^ 2. ^Zj Zi 5Z, 



Z 4 



Fig. 2 — Generalized Syimnetrical T Network Connected to Impedances Equal to 



Its Image Impedances 



used is the transmission unit* (1 y'(' = .ll")13 napicr). It can be 

 demonstratwl that the transfer constant, (), of the T network shown 

 in Fig. 1 is 



e = tanh '*/^- = lanh '^ 



= cosh"' 



{Za+ZcKZb+Zc) 

 1{Za+ZcKZb+Zc) 



(5) 



Zc' 



in which Z„, and Zu are, as previously defined, the open and short- 

 circuit impedances of the network. The ratio Zsc/Zoc is the same at 

 Ixjth ends of any pa.ssive network. 



Principles of Generalized Symmetrical Netuvrks. (^insider now the 

 impedance and propagation characteristics of the generalized sym- 

 metrical structure shown in Fig. 2. On account of the s>nimetry of 

 the structure, the image impedances at both ends are identical, and 

 from e{|uation ('.i) or (4) their value may be shown' to be 



Z, = ^Z.Z,(l-H^). (6) 



In the case of a s\inmelrical 7' structure, such as is shown in Fig. 2, 

 the impe<lance Z/ is called the mid-series image impedance. The 

 significance of this term will be evident, if the series-shunt type of 



* \V. H. Martin, "The Transmissum l"nit and Telephone Transmission Reference 

 .System," Bfll .Sys. Teth. Jour., July, 1924; Jour. .4. /. E. E., Vol. 4.?, p. 504, 1924. 



» Zobcl, O. J., "Theory and Design of Uniform and Composite Electric Wave- 

 Kilters." Bell Syit. Tech. Jour., Jan., 1923. 



