OPEN-WIRE CROSSTALK 45 



In this expression K is the frequency in kilocycles and Tc = «c + j^c 

 is the propagation constant of the tertiary circuit c. On a multi-wire 

 line there would be numerous tertiary circuits with various values of 7. 

 With practicable wire sizes the attenuation constants indicated by a 

 are small compared with the phase change constants indicated by /3. 

 Measurements of crosstalk indicate that the values of jS are all in 

 the neighborhood of the value given by the expression irK/90. This 

 corresponds to a speed of propagation of 180,000 miles per second 

 which is about the average for the present carrier frequency range. 

 Neglecting the attenuation constants : 



.- .tK 

 Ic =JI3 =J-9Q-. 



T — — • ^Tr/^gj, 

 ~ -^ 90 ' 



This relation is much used in transposition design. As noted above, 

 the indirect component of Fab should, strictly speaking, be used to 

 obtain lab- In most cases, however, the total value of Fab may be 

 used since this total is determined largely by the indirect component. 



Type Unbalance 



A conception important in transposition design is that of "type 

 unbalance." This conception will now be explained and the general 

 method of computation will be discussed. 



As we have seen, any two open-wire circuits tend to crosstalk into 

 each other due to coupling between them. By transposing the circuits, 

 the coupling in any short length of line is nearly balanced in another 

 short length by a second coupling of about the same size but about 

 opposite in phase. This balancing is never perfect and there is always 

 a residual unbalanced coupling due to (1) attenuation and change in 

 phase of the disturbing transmission current and resulting crosstalk 

 currents as they are propagated along the circuits and (2) irregularities 

 in the spacing of the transpositions and irregularities in the spacings 

 between the various wires. The term "type unbalance" has been 

 chosen to indicate the residual unbalance caused by propagation 

 effects. It is expressed as an "equivalent untransposed length," that 

 is, the type unbalance times the crosstalk per mile gives the residual 

 crosstalk due to propagation effects assuming no constructional 

 irregularities. 



The method of computing the type unbalance for near-end crosstalk 

 will now be discussed. The part of the near-end crosstalk due to 

 interaction between all the different thin slices of line may be ignored 



