56 PEI.L SYSTHM TECHNICAL JOIRXAL 



image ini|Kxl.mits al more tliaii one or a few frcc|iieiuiej. I- or a 

 gi-neralizcMl strucliirf, sutli as that of Fig. 1, operating between a 

 sctiditiii-ciid impedance Zs and a receirin'^-ciid impedance Zr, the 

 current in Zr, for an electromotive force acting in Zs, is 



h = ^HV X '^r . X xjif^-^^ X 



^s+Zr x^AZJZr Z,,+Zs Zi,+Zr 



Xt-oX y y—\ y • (9) 



Zj^ — Zr AU—/.S v^-2» 



Ninee A [Z^-Y'Zr] is the currenl (/«■) which would flow if the gcner- 

 alizetl T network were not inherled in the circuit, the ratio of the re- 

 ceived current, wiih and 'wilhoiil the network in the circuit, may l)c 

 exprcssi'd l)y the relation 



Ir ^ ( Zs+Zr \ (VJZ,^) ( ViZjTR ) 

 Ik- \^AZ^r) V Z,,+Zs ' ^ Zu+Zr ' 



Xt-OX -y y-^ jr\ • (10) 



f Zi,-ZR \/ Zj,-Zs \ 2» 

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



In general, the electromotive force does not act through a simple 

 sending-cnd im|)edance Z.s l)ut through some complex circuit. The 

 current ratio (Ir Ir) will, howe\er, he the same in either case. The 

 |)rinciple imderlying this fact is known ;is Thei'cniii's Theorem.'' 



The absolute magnitude of the current ratio, \ Ir Ir |, is a measure 

 of the transmission loss caused by the introtluction of the network. 

 The transmission loss ma\" be expressed in terms a( transmission imits 

 (7"t') l)y aid of the following relation 



rt/ = 201og,o|(^i. (11) 



Reference to e(|uatiiin (10) shows tli.il the transmission loss caused 

 by the iniriKluction of any network is composed of five factors. The 

 first three f.utors of this e(|uation ;ire all of the Siinie general type 

 with the exci'plion that the first of the three is reciprocal in nature 

 t<i the other two. These two latter factors have been called reflection 

 factors and determine the reflection losses which exist between the im- 

 [K-dances involvi^l. The fourth factor is the transfer factor and 

 expresses the current ratio which corresponds to the transfer con- 



•("a»|)er, \V. 1.., " IVIc'|ihniic rmnsfciriucrs," Transactions A. I, E. £., March, 

 1924, p. 4. Thf-vi'iiin, M. L., ".Sur un .Noiivc.iii Tlieor^nicd'Klcctrkitf Ox n.imiqiie," 

 Comptrs Rendus, vol. 97, p. 159. 1883. 



