28 BELL SYSTEM TECHNICAL JOURNAL 



For like circuits, like impedance mismatches and like near-end 

 crosstalk couplings at the two ends of the line, these two additional 

 far-end crosstalk currents are of equal importance. Similar reflection 

 effects will occur at any intermediate points in the lines having im- 

 pedance irregularities. Since the far-end crosstalk coupling can be 

 much more readily reduced by transpositions than the near-end 

 crosstalk coupling this reflection crosstalk effect is important in 

 practice. It is, therefore, necessary to carefully design the terminal 

 and intermediate apparatus and cables to minimize impedance mis- 

 matches as far as practicable. 



In calculation of crosstalk coupling it is ordinarily assumed that 

 the two wires of a circuit are electrically similar or "balanced " (except 

 as regards crosstalk from other wires). This is substantially true in 

 practice except for accidental deviations, such as resistance differences 

 due to poor joints and leakage differences due to cracked insulators, 

 foliage, etc. Resistance differences may be of considerable practical 

 importance and are said to cause resistance unbalance crosstalk. The 

 following discussion indicates the general nature of this effect. 



As discussed in connection with Fig. 1, the external field of the 

 disturbing circuit is minimized by the opposing effects of substantially 

 equal and opposite currents or charges in the two wires of the circuit. 

 The two wires may be considered as two separate circuits, each having 

 its return in the ground. At any point in the line these two wires 

 would normally have practically equal and opposite voltages with 

 respect to ground. These voltages would normally cause almost equal 

 and opposite currents in the two wires. If the resistance of one wire 

 is increased due to a bad joint, the current in that wire is reduced and 

 the currents in the two wires are no longer equal and opposite. The 

 external field of the two wires and the resulting voltage induced in the 

 disturbed circuit are, therefore, altered. If this voltage had previously 

 been practically cancelled out by means of transpositions, the alter- 

 ation in the field would increase the crosstalk current at the terminal 

 of the disturbed circuit. 



A resistance unbalance in the disturbed circuit will have a similar 

 effect as indicated by Fig. 4A. This figure shows a short length d of 

 two long paralleling circuits. Equal and opposite transmission cur- 

 rents in the disturbing circuit 1-2 are indiceited by /. Equal crosstalk 

 currents in the two wires of the disturbed circuit 3-4 at one end of the 

 short length are indicated by i. It is assumed that these crosstalk 

 currents have been made substantially equal by transpositions in other 

 parts of the line. Since the currents in wires 3 and 4 are equal and 

 in the same direction, there will be no current in a receiver connected 



