CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 153 

 Using the expressions (23) and (24), we obtain 



Vn — E „ „ Sn, (28) 



w 



here 



Jo 



S„ = e-y^y 



g-JlV — g— )'32/ g-TlJ/ — e'>'3yg-('>'3+Tl> ' 



73 - Ti 73 + 7i 



Integrating (29) we have 



273 1 — e-(T2+Tl)' 1 _ g-(73+T2)i 



dy. (29) 



5: 



7i + 72 73^ - 7i^ (73 - 7i)(73 + 72) 



1 _ g(73-72)' 



(73 + 7i)(73 - 72) 



Thus, the near-end crosstalk from circuit (I) into circuit (2) via the 

 intermediate circuit (3) is given by the expression 



In a similar manner we can derive the following expression for the 

 near-end crosstalk from circuit (2) into circuit (1) via the intermediate 

 circuit (3) : 



iV,/=|^^5„. (31b) 



'±/S2Z,3 



The factor 5„ present in (31&) is the same as in (31a), being symmetrical 

 with respect to the subscripts 1 and 2 as a close inspection of the 

 formula (30) would prove. Zu — Z31 and Z23 = Z32 by the reciprocity 

 theorem. 



For the case of two similar coaxial pairs with equal characteristic 

 impedances Zq and propagation constants 7, and symmetrically placed 

 with respect to the intermediate line, so that Z13 = Z32, we have 



^, ^ (Zi3)^ r 73 1 - e~'y' _ 1 - 2g-(^3+T)^ 4- g-27^ 



4Z0Z3 [7 73^- 7^ 73^ - 7^ 



(32) 



Now for short lengths we may use again the approximation 



e-a = 1 - a + ^a\ (33) 



The expression in the brackets of (32) then becomes equal to P and the 



