OPEN-WIRE CROSSTALK 49 



Since attenuation can be neglected, the type unbalance for a trans- 

 position section depends only on the line angle ^D. Since j8 increases 

 practically directly with frequency, a plot of type unbalance against 

 /3Z> indicates the variation of type unbalance with frequency for a 

 fixed length or the variation with length for a fixed frequency. It is 

 convenient to plot the product of type unbalance and frequency (in 

 kilocycles) since this product multiplied by the crosstalk coefficient 

 gives the crosstalk. Two such plots for near-end type unbalance 

 times frequency are shown on Fig. 15A. The plot marked P is for the 

 condition of two circuits non-transposed or transposed alike. The 

 plot marked is for the same arrangement except for one relative 

 transposition at the midpoint of the parallel.^ The figure has a 

 frequency scale corresponding to a length of eight miles as well as the 

 general ^D scale in degrees. 



It will be seen that, for the case of no relative transpositions, the 

 crosstalk varies directly with the frequency for only a short distance 

 at the start of the curve. The effect of one relative transposition is to 

 greatly reduce the crosstalk for small values of j8L. For larger values 

 the crosstalk is increased. It may be noted that the minimum values 

 shown on the curves are somewhat in error since attenuation was 

 neglected. 



The minimum values in the P curve are due to "natural transposi- 

 tions" in the non-transposed circuits. When the line angle is 180 

 degrees the crosstalk at the near-end of the disturbed circuit due to 

 the second half of the line is just 180 degrees out of phase with the 

 crosstalk due to the first half. This reversal in phase is due to the 

 phase change accompanying the propagation of current to the mid- 

 point and back. The total crosstalk due to both halves of the line 

 lengths is the same as if the crosstalk coupling in the second half were 

 translated to the near-end and the parallel without phase change but 

 one circuit was transposed at the mid-point. When the line angle is 

 360 degrees the "natural transpositions" are at the quarter points, etc. 



The near-end crosstalk between any two circuits in a transposition 

 section may be estimated by multiplying the crosstalk coefficient by 

 values of type unbalance times frequency similar to those of Fig. 15 A. 

 The total crosstalk in a succession of similar transposition sections is 

 calculated at any particular frequency by working out a factor similar 

 to the type unbalance in order to obtain the relation between the 

 crosstalk in many transposition sections and that in one section. 

 In calculating this factor, attenuation cannot be neglected since long 

 lengths of line are involved. 



* Two circuits are relatively transposed by one transposition at a given point in 

 the line. Transpositions in both circuits leave them relatively untransposed. 



