150 



BELL SYSTEM TECHNICAL JOURNAL 



O 160 



< 200 



5 10 20 30 50 100 200 300 500 1000 2000 



FREQUENCY IN KILOCYCLES PER SECOND 



Fig. 2 — Direct near-end crosstalk in a system of three coaxial conductors. 



to the electromotive force in the section kl, to be given by the expression 



E 



dVf = ■;^Zi2e-^2ie^^2-y0^dx. 



(16) 



Integrating this over the total length / we obtain the total voltage 

 induced at the far end 



Vt = E 



Zii e-T2' - g-Ti 



2Zi 7i - 72 



and the far-end crosstalk from circuit (1) into circuit (2) is 



Vf Zi2 1 - e(^i-T2)^ 



Fl2 = 



£e-Ti^ 2Zi 72 



7i 



(17) 



(18) 



If two similar lines are considered, with equal propagation constants 

 and the characteristic impedances, equation (18) becomes 



F = 



Vf _ Z,2 

 Ee-y^ 2Zo 



(19) 



The far-end crosstalk is proportional to the length of the line at all 

 frequencies. 



Inasmuch as we have ignored the reaction of the induced currents 

 upon the disturbing line, the foregoing equations must be regarded as 

 approximations. Under practical conditions these approximations are 



