The Bell System Technical Journal 



Vol. XIV April, 1935 No. 2 



Cable Crosstalk — Effect of Non-Uniform Current 

 Distribution in the Wires 



By R. N. HUNTER and R. P. BOOTH 



When wires are close to each other as they are in cable, the mutual in- 

 ductance coupling between pairs is not a simple number, constant at all fre- 

 quencies. Because of the non-uniform and non-symmetrical distribution 

 of current over the cross-sections of the conductors the "effective mutual 

 inductance" is of the form M = Ma +jMb where both Ma and Mb vary 

 with frequency. This paper discusses the results of certain measurements 

 which have been made of the effective mutual inductance between straight 

 wires and between cable pairs over a wide range of frequencies extending up 

 to a million cycles. This is of interest in connection with crosstalk problems 

 in cable carrier telephone systems. 



TTOR many years it has been recognized that non-uniform distribu- 

 -■- tion of current over the cross-section of a conductor reduces the 

 efficiency of transmission in either power or communication circuits. 

 With direct current or with alternating current of very low frequency 

 the current is distributed almost uniformly. As the frequency in- 

 creases, the current distribution becomes more and more non-uniform. 



If the two conductors of a circuit are remote from each other the 

 high-frequency current distribution in either conductor is practically 

 symmetrical with respect to its center, the density of the current being 

 lowest in the center of the conductor and highest near the surface of 

 the conductor. If, however, the conductors are close together, the 

 high-frequency current distribution in either conductor is unsym- 

 metrical due to the proximity of the other conductor. This is known 

 as the proximity effect. 



It is probably not well known that this proximity effect may have 

 an important bearing on the crosstalk between communication circuits.^ 

 While the effect is negligible in open-wire circuits, it is quite marked in 

 cable circuits. This paper describes an investigation of the influence 



^ This effect was mentioned in the Carson-Hoyt paper on " Propagation of Periodic 

 Currents Over a System of Parallel Wires," in the Bell System Technical Journal of 

 July, 1927. 



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