OPEN-WIRE CROSSTALK 23 



indicates such a parallel. In calculating the crosstalk coupling 

 between a terminal of circuit a and a terminal of circuit b, the parallel 

 may be divided into a series of thin transverse slices. One such 

 slice of thickness d is indicated on the figure. The coupling in each 

 slice is calculated and, then, the total coupling between circuit terminals 

 due to all the slices. 



In Fig. 2A circuit a is considered to be the disturber and to be 

 energized at the left-hand end. In the single slice indicated, a trans- 

 mission current will be propagated along circuit a and will cause 

 crosstalk currents in circuit b at both ends of the slice. In this slice, 

 therefore, the left-hand end of circuit a may be considered to be 

 coupled to the two ends of circuit b through the transmission paths 

 flab and fab- The path «„& is called the near-end crosstalk coupling 

 and the path fab is called the far-end crosstalk coupling. 



The presence of a tertiary circuit, such as c of Fig. 2B, changes 

 both the near-end and the far-end coupling between a and b in the 

 transverse slice. In addition to the direct couplings «„& and fab there 

 are indirect couplings fiacb and/„c6 by way of circuit c. 



The transverse crosstalk coupling between a terminal of a disturbing 

 circuit and a terminal of a disturbed circuit is defined as the coupling 

 between these points due to all the small couplings in all the thin 

 transverse slices including indirect couplings in each slice by way of 

 other circuits. (There are also indirect couplings involving more 

 than one slice and these are not included in the transverse crosstalk 

 coupling.) 



In computations of transverse crosstalk coupling it is convenient to 

 distinguish between the direct and indirect components. The direct 

 component considers only the currents and charges in the disturbing 

 circuit while the indirect component takes account of certain charges 

 in tertiary circuits resulting from transmission over the disturbing 

 circuit. The tertiary circuits may be circuits used for transmission 

 purposes or any other circuits which can be made up of combinations 

 of wires on the line or of these wires and ground. If there are only 

 two pairs on the line as in Fig. 2A there are still tertiary circuits, 

 namely, the "phantom" circuit consisting of pair a as one side of the 

 circuit and pair b as the return and the "ghost" circuit consisting of 

 all four wires with ground return. In a multi-wire line many of the 

 tertiary circuits involve the wires of the disturbing circuit. If these 

 tertiary circuits did not exist the currents at any point in the two 

 wires of the disturbing circuit would be equal and opposite. The 

 presence of the tertiary circuits makes these currents unequal and it 

 is convenient to divide the actual currents into two components, i.e., 



