GENKRALIZKD TELEGRAPHIST'S EQUATIONS 789 



Hence, the F's and /'s correspond to the voltages and currents in (■()ui)lcd 

 transmission lines. 



In an expanded form equations (12) are 



^^(") 1 T/ ^^["1 ti V dT(n) ^r dr[n] 

 — -r— + y [n] -- - , ii„ = V (n) — — Vln] " T" , 



ei du e-> dv €•> dv ei du 



Eu — V^n) 1— + V[n] --„-, Ev = V(n) T^ — V [n] 



(15) 



Ci du e-i dv Co dv C] du 



To these we add the following expansions for the longitudinal compo- 

 nents of E and H 



E, = X(«)T%.(„)(2)7\„)0/, r), //, = X(«]A',[n](2)7^[.)(M, v). (lO) 



Equations of this form satisfy automatically the boundary conditions 

 on E, and //, . The multipliers X;. have been inserted arbitrarily in order 

 to make the phj^sical dimensions of the second factors to correspond to 

 those of \'oltage and current. 



Let us now write Maxwell's equations in an expanded form 



dE. dE,, . „ dH, dH„ . ^ 



e-i dv dz e-i dv dz 



dE^ dE, . a//„ dH, . ^ , „. 



dz 61 du dz 6] du 



—^-— - ^„ = -J^eiCoB, , —- • - — = JUC1C2D, . 



du dv du dv 



Substituting from (15) and (16) hi the left column of (17), we find 

 62 dv dz e-i dv dz exdu 



„ dTf^n) . dYjn-) dT(n) . dV[„] dT[n] . „ , . 



ei du dz ei du dz e-idv > v / 



y d'T(n) _ y A /^!r ^Zinl\ _ T/ ^'^(n) _ x. d ( Cl dT [n]\ 



'""'dudv '"'auU'a^/ ^'"^d^Td^ ^"^a^U^'aT/ 



(20) 

 = —jojeieiBg. 



In view of (4) the last equation reduces to 



X[n]V[n]Tln] = -jc^B^. (21) 



