234 BELL SYSTEM TECHNICAL JOURNAL 



frequency and since N = Nd -\- Ni is largely determined by Nd, the 

 near-end coefficient N is about independent of frequency above a 

 few hundred cycles. The far-end coefficient F is about independent 

 of frequency above a few thousand cycles where it is largely determined 

 by Fi. 



The preceding discussion of indirect crosstalk coefficients covered 

 only the effect of charges in the single metallic tertiary circuit c of 

 Fig. 34. The indirect coefficient in a practical case may be estimated 

 with fair accuracy by considering all the more important tertiary 

 circuits in a similar manner. It was shown that the final voltage of 

 tertiary circuit c was zero. Similarly, the final voltage of each tertiary 

 circuit is zero. This includes any tertiary circuits involving the two 

 wires of the disturbing circuit in multiple. The average voltage of 

 the two wires of the disturbing circuit is zero and the voltage across 

 the disturbing circuit is balanced. As previously stated, this voltage 

 does not become unbalanced as a result of transverse crosstalk in any 

 infinitesimal length but it may become unbalanced due to interaction 

 crosstalk. 



The charges per unit length on the various tertiary circuits are the 

 same as those which would be caused by impressing a system of 

 voltages equal and opposite to those induced by the balanced charges 

 per unit length which would be on the two wires of the disturbing 

 circuit if this circuit were the only pair on the line. Assuming such 

 a system of impressed voltages, it is not practicable to accurately 

 compute the charges in any tertiary circuit since this depends on the 

 voltages impressed on all the tertiary circuits and the couplings 

 between the various tertiary circuits. Advantage may be taken, 

 however, of the fact that the charge on a tertiary circuit will depend 

 mostly on the voltage impressed on that circuit provided it is not 

 heavily coupled with other circuits. 



It is possible to divide the various voltages impressed on the tertiary 

 circuits into components such that (1) equal voltages are impressed 

 on wires of a "ghost" circuit composed of all the wires on the line 

 with ground return, (2) balanced voltages are impressed on each pair 

 used for transmission purposes (except the disturbed and disturbing 

 circuits) and (3) balanced voltages are impressed on each possible 

 phantom of two pairs used for transmission purposes. 



Such a system of impressed voltages and tertiary circuits is con- 

 venient for computation since the charge on any tertiary circuit 

 largely depends on the voltage impressed on that circuit. If accurate 

 calculations of the charges were practicable, a simpler system of 

 tertiary circuits could be used to obtain the same final result, i.e., 



