516 BELL SYSTEM TECHNICAL JOURNAL 



wires. The total mode-c current 2/c along the two wires in parallel 

 is calculable from -qc through the mode-c parameters (7c, Kc, and 

 terminal impedances) of the system ; while the mode-a or loop current 

 {la and — la in the two wires respectively) is calculable from r}a through 

 the mode-a parameters (7a, Ka, and terminal impedances). The 

 connection of each current constituent with the corresponding field 

 constituent, through the corresponding parameters, is formally the 

 same as for the one-wire line (treated in the preceding subsection). 



Finally, it may be remarked that the assumption of balance (bi- 

 lateral symmetry) for the two-wire line is essential to the above sim- 

 plicity; for otherwise each mode of the impressed field would produce 

 components of both modes of efi^ects, instead of only the appropriate 

 single mode of effects. 



Illustrative Special Case 



For illustration it will suffice to choose the simple case of a balanced 

 two-wire line terminated at each end in its mode-c and mode-a char- 

 acteristic impedances simultaneously. That is, the line consisting of 

 the two wires in parallel, with ground return, is terminated at each 

 end in the mode-c characteristic impedance Kc ; while the loop circuit 

 is terminated at each end in the mode-a characteristic impedance Ka. 

 (Evidently these two modes of terminating can be simultaneously 

 accomplished by means either of a balanced T-network or of a 

 balanced H-network at each end.) 



Let/i(A;) and/2(:x;) denote the axial impressed electric forces at any 

 point X in wires No. 1 and No. 2 respectively; and let them be 

 resolved into mode-c and mode-a constituents fc{x) and ja{x), respec- 

 tively, such that 



Ic{x) = hlh{x)+h{xn (61) 



faix) =Mx) -Mx), (62) 



in accordance with equations (57) and (58). Similarly, let Fi{x) and 

 F2{x) denote the impressed potentials at point x; and let them be 

 resolved likewise, so that 



Fc(x) = i[Fi(x) + F,(xn (63) 



Faix) = Fx(x) - F2{x). (64) 



Thus, formulas (49), • • • (54) of the one-wire line are seen to be 

 formally applicable to the balanced two-wire line, for calculating 

 separately the two modes of currents. This is with the understanding 

 that they give the sum of the mode-c currents in the two wires, hence 

 twice the mode-c current in each wire; and that they give the loop 



