210 BELL SYSTEM TECHNICAL JOURNAL 



in these wires may be not quite equal and opposite. As a result, 

 voltages will be induced in wires 3 and 4 but these will be equal and 

 there will be no crosstalk current in pair 3-4. By the reciprocal 

 theorem the crosstalk between the two pairs will also be zero when 

 pair 3-4 is the disturber. 



Arrangement B is nearly non-inductive. In this case if pair 1-2 is 

 the disturber and the currents in the two wires are not quite equal and 

 opposite due to the presence of the ground, unequal voltages will be 

 induced in wires 3 and 4 and there will be a crosstalk current in this 

 pair. This effect could be minimized by transposing both pairs at 

 the same points. They would not require relative transpositions since 

 equal and opposite currents in pair 1-2 will induce no voltage in either 

 wire 3 or wire 4. 



With pair 3-4 as the disturber, equal and opposite currents will 

 result in equal voltages induced in wires 1 and 2. These voltages 

 cause a phantom current in phantom 1-2/3-4. This phantom current 

 will divide between wires 3 and 4 but can not induce unequal voltages 

 in wires 1 and 2 because 1 and 2 are equally distant from either 3 or 4. 

 The crosstalk coefficient is, therefore, zero both for the direct effect 

 and for the indirect effect of the phantom. However, the indirect 

 effect of the ground or other conductors is not zero and may require 

 transpositions. 



Arrangement C is non-inductive for direct crosstalk. It is not 

 non-inductive in regard to the indirect effect of the phantom 1-2/3-4. 

 Equal and opposite currents in pair 1-2 induce equal voltages in wires 

 3 and 4. The resulting equal phantom currents in wires 1 and 2 of 

 phantom 1-2/3-4 will induce unequal voltages in pair 3-4. 



When there are many pairs on a line it is not possible to make all 

 combinations strictly non-inductive even for direct crosstalk. With 

 perfect wire spacing the larger values of direct crosstalk per mile 

 could be greatly reduced, however, and appreciable reductions could 

 be obtained in the indirect effect which is usually controlling in far-end 

 crosstalk. 



Wire sag deviations must be considered, however. If a given 

 number of "non-inductive" pairs are placed in the pole head area 

 normally occupied by the same number of pairs with conventional 

 configuration, the crosstalk due to sag deviations is likely to be more 

 serious with the "non-inductive" pairs than with conventional pairs. 

 For the same pole head area, the number of transpositions and, 

 therefore, the "pole spacing" crosstalk could be reduced if non- 

 inductive arrangements were used. The tests to date indicate, 

 however, that the total crosstalk would not be reduced because of 

 increased "sag difference" crosstalk. 



