148 BELL SYSTEM TECHNICAL JOURNAL 



Therefore the current at the left end of Hne (2) due to the electromotive 

 force eki is given by the expression 



{iki)n = ikie-y^' = T^^r^ e~^yi+y^>dx. (4) 



ZZ1Z2 



The contribution dVn to the potential across the left end of line (2) due 

 to crosstalk in the section dx, x cm. away from the left end of the line, is 



dVn= {Hl)nZ2 = ^ Zi2 B'^y^+y^^^dx. (5) 



Hence the total induced voltage at the near end is 



Vn= CdVn= C ^^Zi^e-^y^+y^Hx. 

 Integrating, we obtain 



(6) 



2Zi Ti + 72 

 The near-end crosstalk is thus given by the expression 



\ E J 12 2Zi 7i + 72 



If we reversed the procedure and considered the crosstalk from 

 circuit (2) into circuit (1), we would similarly obtain 



;V. = (§) =§ '--"-"'" . (9) 



\ E /21 2Z2 7i + 72 



By the reciprocity theorem, Z21 — Z^- Incidentally, if instead of 

 adopting as the definition of crosstalk the ratio of two voltages we 

 regarded it as the ratio of the induced voltage to the current through 

 the disturbing generator, we should have obtained N21 = N12. 



Finally, if the circuits are alike Zi = Z2 = Zo, 7i = 72 = 7 and the 

 near-end crosstalk is given by the expression 



We observe that the near-end crosstalk depends on length /. Two 

 limiting cases are of importance here. For a length / so small, that for 



