342 BELL SYSTEM TECHNICAL JOURNAL 



This method of analysis, when applied to the twin coaxial cable 

 described in the companion paper by Messrs. Booth and Odarenko, 

 gave results in good agreement with the measured crosstalk. 



In this analysis it was assumed that all the tertiary circuits could be 

 combined and considered as a single circuit. Although no evidence 

 has been found that with the types of structure studied so far, better 

 accuracy would result from the further refinement of considering two 

 or more dissimilar tertiary circuits with coupling between them, 

 there is one case of practical importance which cannot be handled with 

 the single-tertiary analysis. This case is that of the interaction cross- 

 talk (that is, the crosstalk by way of a tertiary circuit) between two 

 adjoining lengths of coaxial cable, when, at the junction, part of the 

 tertiary conductors are short-circuited to the outer coaxial conductors 

 while the remaining tertiary conductors continue through with no 

 discontinuity. This problem might be of importance where, at a 

 repeater, the outer coaxial conductors and the sheath are bonded to- 

 gether, but paper-insulated pairs in the same sheath provide an un- 

 interrupted tertiary circuit. The near-end crosstalk under such condi- 

 tions might also differ significantly from the values indicated by the 

 single-tertiary analysis. 



The two-tertiary analysis is too long to be given here in detail, and 

 hence has been outlined only to such an extent as to indicate the 

 derivation of the formulas for interaction crosstalk when one of the 

 tertiaries is short circuited and the other terminated in its character- 

 istic impedance. The formula for near-end crosstalk under this condi- 

 tion is given without derivation. 



I — Identical Coaxial Lines Symmetrically Placed 

 WITH Respect to a Single Tertiary 



The first case we shall consider herein is that of any number of 

 identical coaxial lines with the outer coaxial conductors in continuous 

 electrical contact and symmetrically placed with respect to a single 

 tertiary circuit, such as that which might be provided by a sheath sur- 

 rounding the coaxial lines and insulated from the outer coaxial con- 

 ductors, or by a surrounding layer of paper-insulated pairs. Through- 

 out we shall assume that the reaction of the induced currents upon the 

 disturbing line is negligible. 



Following a nomenclature analogous to that of the Schelkunoff- 

 Odarenko paper,^ we will designate by Z12 the mutual impedance per 

 unit length between any two coaxial lines in the presence of the other 

 coaxial lines but in the absence of any other conductors. The mutual 



^ Bell System Technical Journal, April, 1937. 



