CROSSTALK BETWEEN COAXIAL CONDUCTORS 363 



available. When the efifects are integrated it is found that the far-end 

 crosstalk is quite a complicated function of length and of the tertiary 

 and coaxial propagation and impedance characteristics.^ However, 

 if the coaxial units are in actual contact as in the case of the coaxial 

 cable to be considered here, the formula for the far-end crosstalk F^ 

 expressed as a current ratio is quite simple, namely, 



Z ^ 



where Z33 = Z373 is the series impedance per unit length of the circuit 

 composed of one coaxial outer conductor with return on the other. 

 Thus, for this component, the far-end crosstalk is directly proportional 

 to length. This simple relation results from the fact that the inter- 

 mediate circuit, being continuously shorted, has such high attenuation 

 that no interaction crosstalk between elementary lengths can exist. 



We shall now consider the crosstalk contribution due to the longi- 

 tudinal voltage ei/2 acting along both coaxial outer conductors in 

 parallel. Suppose that a sheath is placed symmetrically around the 

 two coaxials but insulated from them as shown in Sketch (d) of Fig. 1 . 

 The longitudinal voltage sends a current around the circuit composed 

 of the two parallel outer conductors with sheath return equal to 

 H = ei/(2)(2Zi), where Z4 is the characteristic impedance of this 

 circuit. Half of this longitudinal current flows on the disturbed 

 coaxial outer conductor in opposition to the balanced current is flowing 

 there. 



Following previous procedure it can be shown that in the elementary 

 length a crosstalk current i2c — iiZapdl/4Z will flow in the disturbed 

 coaxial circuit.® Other elementary lengths are also afl"ected by ii thus 

 producing interaction crosstalk. When the effects are integrated over 

 a length / the far-end crosstalk for this component is found to be as 

 follows : 



ri = 



I6ZZ4 



21 74^ 



74 74'' — y^ 



2(742 + 72) e-'-y*-y'>^ e-(74+y)2 



(742 — 72)2 (^y^ - -j,)2 (^^ _j_ ^)2 



(2) 



where 74 is the propagation constant of the sheath-outer conductor 

 circuit. If the sheath is in actual contact with the coaxial units the 



^ See equation (40) in the Schelkunoff-Odarenko paper in Bell Sys. Tech. Jour., 

 April, 1937. 



* The subscript "c" in {20 relates this current to the "mode c" current used by 

 Carson and Hoyt in their paper of July, 1927. 



