MIIV.II. IMHCT.IXCr. I\ ll-.lir. III.II.RS 5.1 



imiMMl.iluc Iiinkiiii; into ilic T network at the 1 — 2 lermiii.ils will be 



Siinil.irly, if the 1 — 2 termiii.ils of tiie T network arc oonnerled to an 

 inipeilaniv Z/,, the intpeiLince lookini; into the 3 — 4 terniinais of the 



7' net work will lie , ' 



U Zi i is equal to the terminal impedance Z/,, and if, similarly, 

 Zj-i is et]iial to the terminal impedance Zj.^, the network will then be 

 terminated in such a way that, at either junction (1 — 2 or 3 — 4), the 

 impedance in the two directions is the same. In other words, at each 

 junction point, the impedance looking in one direction is the image 

 n| the impwiance looking in the opposite direction. I'nder these 

 conditions Z/, and Z/, are called the /wage impedances of the 7' not- 

 work. If equations (1) and (2) are solved explicitly for Z/, and Z/^, 

 the following expressions are obtained : 



7 I (Z.4 + Zc){ZaZb+ZaZc+ZbZc) ,,. 



^'• = \ ^^+Zc) • ^^^ 



_ I ( Zb+Zc) (ZaZb+ZaZc+ZbZc) ... 



^'^ = \ iZ^+Zc) • ^^^ 



If Zoc is the impedance looking into one end of the network with 

 the distant end open-circuited, and if Z^, is the corresponding imped- 

 ance with the distant end short-circuited, it may be shown that the 

 image impedance at either end of the network is the geometric mean 

 of Zee and Zsc- What is here termed the image impedance is, there- 

 fore, equivalent to what Kennelly has called the surge impedance.' 



The propagation characteristics of a dissymmetrical network m.iy 

 be completely expressed in terms of the transfer constant. The 

 transfer constant of any structure may be defined as one-half the 

 natural logarithm of the vector ratio of the steady-state vector volt- 

 amperes entering and leaving the network when the latter is termi- 

 nated in its image impedances. The ratio is determined by dividing 

 the value of the vector volt-amperes at the transmitting end of the 

 network by the value of the vector volt-amperes at the receiving end. 



• There is at present lack of common agreement as to the liasis of definition of 

 this term, and it is often defined upon the basis, not of open and short-circuit im- 

 pedances, but of a uniform recurrent line (See A. I. E. E. Standardization Rule 

 12054. edition of 1922). The formulae derived by the two methods are not equiva- 

 ment in the case of dissymmetrical networks. 



