220 BELL SYSTEM TECHNICAL JOURNAL 



Hi to We- If the crosstalk is due to irregularities the exact values of 

 11 can not be calculated but from the data collected on the crosstalk 

 due to irregularities, the r.m.s. of all possible values may be estimated, 



W 10 DECIBELS NET LOSS H 



KlOdbLOSS*- ■• — lOdb — »■ -• — lOdb — *■ •• — lOdb — •■ ■• — lOdb- 



E F 



Fig. 29 — Crosstalk between repeatered circuits. 



Letting n equal the r.m.s. value of Wi, etc., and using probability 

 theory we may write: 



i?2 = ^2 + ^2^ + • • • + re^, 



where R is the r.m.s. of all possible values of the near-end crosstalk 

 at ^. If ri = r2, etc. 



R = rV6. 



The chance of the overall crosstalk deviating from R by any specified 

 amount may be estimated by probability methods. It will be noted 

 that the crosstalk in six repeater sections tends to be more severe 

 than that in one section by \^ or, in other words, that the crosstalk 

 varies as the square root of the length. If the use of repeaters were 

 avoided by using more copper, for the same overall loss the crosstalk 

 would be practically the same as with the repeatered circuits. With 

 the arrangement of repeaters shown it is not the use of repeaters which 

 causes the increase in crosstalk but rather the increase in circuit length 

 without corresponding increase in circuit loss. For a given circuit 

 length, circuit loss and wire size, other arrangements of repeaters may 

 cause greater or less crosstalk. 



If the repeaters of Fig. 29 are spaced farther apart, say 15 db 

 instead of 10, there will be three line repeaters of 15 db gain each and 

 terminal repeaters will be necessary to supply a terminal gain of 5 db 

 in order to obtain a net loss of 10 db. The near-end crosstalk would 

 be reduced by about V4 -t- \'6 or 1.8 db because there are only four 

 repeater sections but the terminal repeaters would ampUfy the near-end 

 crosstalk by 5 db. The net increase would be 3.2 db. From the 

 standpoint of near-end crosstalk, it is thus seen that close spacing 

 between repeaters is very desirable. 



