224 BELL SYSTEM TECHNICAL JOURNAL 



APPENDIX 



Calculation of Crosstalk Coefficients 



This appendix will first cover methods of calculating the coefficients 

 of transverse crosstalk coupling. It is necessary to calculate both 

 near-end and far-end crosstalk coefficients which involve both direct 

 and indirect components of transverse crosstalk coupling. Coefficients 

 for the direct and for the indirect components will be derived separately 

 and then combined to obtain the total coefficients. 



Ordinarily, the indirect effect cannot be readily computed with good 

 accuracy and the total coefficients are usually measured. As previ- 

 ously noted, the method of computing the indirect effect can be used 

 with fair accuracy, however, and it is useful in cases where measure- 

 ments are impracticable. 



The crosstalk between frequently transposed circuits may be 

 calculated with the aid of the above coefficients of transverse coupling 

 and in addition an "interaction crosstalk coefficient" relating to 

 interaction crosstalk coupling of the most important type. The 

 relation of this interaction coefficient to the far-end coefficient of 

 transverse coupling is also discussed herein. 



Direct Crosstalk Coefficients 



Figure 30 indicates the definitions of the direct crosstalk coefficients 



used in computing the direct component of the transverse crosstalk 



coupling. This figure shows a thin transverse slice in a parallel 



between two long circuits a and h, the thickness of the slice being the 



P'ig. 30 — Crosstalk in a single infinitesimal length. 



infinitesimal length dx. Circuit a is energized from the left, the 

 current entering dx being la. Propagation of la through dx results in 

 near-end and far-end currents in and i/ in circuit b at the ends of dx. 

 Since the coefficients are the crosstalk per mile per kilocycle, the 

 near-end coefficient A^ and the far-end coefficient F may be expressed 



