516 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



TYPE UNBALANCE CROSSTALK 



Crosstalk is measured in terms of a current ratio between the disturb- 

 ing and disturbed circuits at the point of observation. Crosstalk between 

 open-wire circuits is also generally computed in terms of a current ratio 

 (cu) but it is also convenient to refer to it in terms of a coupling loss 

 (db). The coupling in crosstalk units (cu) is the product of three terms: 

 a coefficient dependent on wire configuration; a type unbalance depend- 

 ent on transposition patterns; and frequency. The coefficient represents 

 the coupling between relatively untransposed circuits of a specified 

 length (1 mile) at a specific frequency (1 kc). The type unbalance is a 

 measure of the inability to completely cancel out crosstalk by intro- 

 ducing transpositions because of interaction effects between the two 

 halves of the exposure and because of propagation effects, primarily 

 phase shift. Type unbalance is expressed in terms of a residual unbalance 

 in miles and the frequency is expressed in kilocycles. 



The coefficients applicable to lines built in accordance with certain 

 standardized specifications are available in tabular form. When it is 

 desired to obtain coefficients for other types of line, it is possible to 

 compute approximate values which may be modified by correction 

 factors to indicate the relationship between the computed values and 

 measurements on carefully constructed lines. 



Expressions for near-end type unbalance for certain simple types of 

 exposures are developed and the formulas for all types of exposures are 

 given. In addition, the values for near-end type unbalance are tabulated 

 at 30° line angle intervals for lines where the propagation angle is iu 

 2,880° or less. 



The principal component of far-end crosstalk between well transposed 

 circuits results from compound couplings involving tertiary circuits. 

 Again the expressions are developed for some of the exposures involving 

 a few transpositions and the procedure for obtaining the formulas for 

 any type of exposure is shown. Formulas are included for the types of 

 exposures encountered in normal practice and the numerical values of 

 far-end type unbalance are given at 30° intervals for line angles up to 

 2,880°. 



SUMMATION OF CROSSTALK 



The procedures referred to thus far evaluate the crosstalk occurring 

 within a limited length of line known as a transposition section. In 

 practice, however, a line is transposed as a series of sections. It is neces- 

 sary, therefore, to determine how the crosstalk arising within the several 



