CROSSTALK BETWEEN COAXIAL TRANSMISSION LINES 155 



The factor 5/ used in the above formulae is given by the expression 



273 1 — e-(Tl-T2)i 1 — e-(T3-72)i 



Sf 



-(72— 7i)' 



Tl 



72 73^ - 7l^ 



(73 - 7i)(73 



\ — g(73+72>' 



(73 + 7i)(73 + 72) 



-72) 



g-(73+7l)^ 



(39) 



When both coaxial pairs are similar and placed symmetrically with 

 respect to the intermediate conductors we obtain the following expres- 

 sion for the far-end crosstalk between two coaxial conductors via an 

 intermediate circuit: 



F' = 





273/ 



1 _ g-(73-7)i 1 _ e-(y 3+1)1 



73 



(73 - 7)' 



(73 + 7)' 



For small / the expression for the far-end crosstalk becomes 



^Z,Z,' 



(40) 



(41) 



which is the same as (34) for the near-end crosstalk. 



For large / and provided the attenuation of the intermediate circuit 

 is greater than that of the coaxial circuit we have 



F' = 



4Z0Z3 



273/ 2(73^^ + 7^) 



,^ - 7^ (73^ - I'Y 



(42) 



Finally, letting 73 approach 7 and considering a limiting case when 

 attenuation of the intermediate circuit is equal to attenuation of either 

 of the coaxial conductors we obtain 



F' = 



(ZnY 

 4Z,Z, 



11 1 — e-27 



_ 4- 1/2 _ ^ 



27^2 47' 



-J 



(43) 



If the intermediate transmission line is short-circuited a large 

 number of times per wave-length its propagation constant 73 becomes 

 very large on the average. The equation (37) becomes, then, 



and 



Sf- 

 Fm' = 



2[1 - e-(-y2-7i)^] 

 (72 - 7i)73 



Z13Z32 1 - g^n-72)^ 

 2Z1Z373 72 — 7i 



(44) 



(45) 



The indirect crosstalk becomes direct with the mutual impedance 

 given by the expression 



Z13Z23 Z13Z23 



Z12 



^373 



(46) 



