OPEN-WIRE CROSSTALK 31 



Both of the currents Ib and if will be propagated to point C. They 

 will be attenuated or amplified alike if the circuits are similar and their 

 ratio will be unchanged. The output-to-output crosstalk at C due 

 to the length AB will, therefore, be the same as that determined for 

 point B. In other words lOH/JIc will equal IOH/JIb. The far-end 

 crosstalk between the terminals A and C, due to length AB, will be 

 IOH/JIa' This differs from the output-to-output crosstalk at C in 

 that the reference current is Ia instead of Ic. The part of the far-end 

 crosstalk between A and C due to AB is, therefore, obtained from the 

 output-to-output crosstalk at B by simply multiplying by the attenu- 

 ation ratio Ic/Ia- If the output-to-output crosstalk is expressed as 

 a loss in decibels, the far-end crosstalk is obtained by adding the net 

 loss of the complete circuit between A and C. 



Effects of Transpositions 



The eflfects of transpositions on both the transmission currents and 

 the crosstalk currents will now be discussed in a general way. The 

 general method of computing the crosstalk between circuits without 

 constructional irregularities and transposed in any manner will also 

 be outlined. 



General Principles 



If there is only one circuit on a pole line, and this is balanced and 

 free from irregularities, the communication currents will be propagated 

 along this circuit according to the simple exponential law. If a 

 current is propagated from the start of the circuit to some other point 

 at a distance L, the magnitude of the current will be reduced by the 

 attenuation factor e~"^ and the phase of the current will be retarded 

 by the angle /SL where a is the attenuation constant and (3 is the 

 phase change constant. 



If there are a number of circuits on a pole line this simple law of 

 propagation may be altered due to crosstalk into surrounding circuits. 

 This is illustrated by the curves. Fig. 6, which indicate the relation 

 between observed output-to-input current ratio and frequency for two 

 different circuits, each about 300 miles long and having 165-mil copper 

 wires. The number of decibels corresponding to the current ratio is 

 plotted rather than the ratio itself. For the simple law of propagation 

 such curves would show the number of decibels increasing smoothly 

 with frequency due to increasing losses in the line wires and insulators. 

 The upper curve is for a circuit too infrequently transposed for the 

 frequency range covered and the current ratio is abnormally small 

 at particular frequencies. The corresponding number of decibels is 

 abnormally large. The lower curve is for a circuit much more fre- 



