CROSSTALK BETWEEN COAXIAL CONDUCTORS 359 



and discussed in a previously published paper.* It was shown there 

 that the direct far-end crosstalk is directly proportional to / and the 

 direct near-end crosstalk is proportional to 



1 - e-2T' 



where / is the length and y is the propagation constant of either coaxial 

 unit. The indirect crosstalk was shown to be a more complicated 

 function of the length. 



The present paper extends this earlier work to include the case 

 where the coaxials are enclosed in a common sheath or, in the general 

 case, paralleled by any conducting material symmetrically disposed. ^ 

 When this conducting material is introduced in the neighborhood of 

 two coaxials in contact the conditions for crosstalk production are 

 naturally changed from those existing in free space. If the material 

 is uniformly distributed along the coaxials and is in continuous or 

 frequent contact with the outer conductors the summation of crosstalk 

 with length is the same as before but the magnitude is reduced. This 

 reduction is due to the fact that part of the current formerly flowing on 

 the disturbed outer conductor now flows on the new conducting 

 material instead, thus reducing the direct crosstalk coupling per unit 

 length. 



In most cables, the coaxial outer conductors are in contact but the 

 other conducting material (sheath and quads) is insulated from the 

 outer conductors. The quads must obviously be insulated for 

 normal use and the sheath is kept insulated except at the ends 

 of a repeater section in order to permit the use of insulating joints 

 for electrolysis prevention where required. This material thus pro- 

 vides an extra transmission circuit, or tertiary circuit, in which 

 tertiary currents can be propagated up and down the line. In such a 

 case the resulting crosstalk in any length consists of both the direct 

 crosstalk between the contacting coaxials and the indirect crosstalk 

 via the outer conductor-sheath and quad tertiary circuit. The gen- 

 eral formulas given in the Schelkunoff-Odarenko paper apply for 

 these components. Since the two components follow different laws 

 regarding summation with length the resultant summation is quite 

 complicated except for very short or very long lengths. 



The study of the tertiary effects on crosstalk summation is the main 

 contribution of this paper to crosstalk theory. Emphasis will be placed 

 on the development of a simple physical picture which will help one to 



* Schelkunoff-Odarenko paper in Bell Sys. Tech. Jour., April, 1937. 



^ In the interim between our tests and this publication a paper by H. Kaden 

 concerning this general subject was published in the Europaischer Fernsprechdienst, 

 no. 50. October, 1938, pp. 366-373. 



