58 BELL SYSTEM TECHNICAL JOURNAL 



circuits of the phantoms or between a side circuit and a phantom 

 circuit is complicated by the fact that the phantom transpositions 

 cause the side circuits to change pin positions. Near-end and far-end 

 type unbalances have been computed, however, which take account 

 of this "pin shift" effect of the phantom circuits. In general, the 

 use of phantom circuits seriously limits the crosstalk reduction which 

 may be obtained by transpositions. Phantom circuits are often 

 uneconomic since they seriously restrict the number of carrier fre- 

 quency channels which may be operated over a given pole line. 



As indicated by Fig. 15 A the values of type unbalance times fre- 

 quency have marked maximum and minimum values when they are 

 plotted against frequency or length. The maximum values are usually 

 reduced by increasing the number of transpositions in a given length. 

 When there are a number of circuits on the line it is usually necessary 

 that the propagation of current between successive transposition poles 

 does not change the phase by more than about five degrees. Since 

 the phase change is about two degrees per mile per kilocycle the 

 maximum transposition interval in miles is about 2.5//^ where Fis the 

 frequency in kilocycles. This means .25 mile or 1300 feet at 10 

 kilocycles and .06 mile or 300 feet at 40 kilocycles. 



It does not follow, however, that the least maximum value of type 

 unbalance for a range of frequencies is obtained by using the greatest 

 number of transpositions for a given number of transposition poles. 

 This is illustrated by Fig. 15A which shows that the least maximum 

 value is obtained with no transpositions rather than with one trans- 

 position. The total crosstalk current at a terminal is composed of 

 numerous elements of various magnitudes and phase relations. The 

 vector sum of these elements tends to be small at particular frequencies 

 with no transpositions at all and it is important to preserve this 

 tendency as much as possible when choosing an arrangement of 

 transpositions. The vector sum of the elements can never be made 

 zero since this would require that the circuits have no attenuation 

 and infinite speed of propagation. This sum and, therefore, the type 

 unbalances can be made very small, however, by choosing a suitable 

 transposition arrangement and making the interval between trans- 

 position poles very small. In practice, the values of type unbalance 

 times frequency for adjacent circuits are restricted to values much 

 less than those of Fig. 15A. 



