OPEN- WIRE CROSSTALK 



237 



Interaction Crosstalk Coefficient 

 It was assumed in the discussion of crosstalk coefficients that the 

 "interaction crosstalk coefficient" NacN ch^Q"^ was nearly equal to 

 — IFijclK. This relation is deduced below, for a representative 

 tertiary circuit c, from the expressions for Fi and Nd given by equations 

 (3) and (6) above. Nac may be obtained by using the expressions 

 for Ne and Nd given by equations (1) and (3) above. In these equa- 

 tions, subscript c should be substituted for subscript b. The expression 

 for Nac becomes: 



Nac = - jirZaTacCcW^, 



1 + 



Jajc 



Deriving a similar approximate expression for Net: 



F- C 

 N N JO-s = _ i_L ^ JrfL 



1 + 



_7ol 



laic 



1 + 



70^ 



Iclh 



This assumes Zcj<JiCc = Zc(Gc + jirCc) which is 7c. 

 Crosstalk measurements indicate that the ratio of 70 to 7a or 7b or 

 7c is about .97 at carrier frequencies and CajCJ about 1 .02. Therefore : 



NacNcb\0-' = 



Fijc 

 2K 



1.02(1.94)2 = - 2Fi7c/i^ approx. 



The above discussion covers the case of a single tertiary circuit c. 

 In the practical case the known crosstalk coefficient Fi includes the 

 effect of a large number of tertiary circuits which have various values 

 of 7c. Obtaining the interaction crosstalk coefficient from the ex- 

 pression — IFadK involves assuming a representative value of 7,.. 

 At carrier frequencies 7c is about equal to j^c which for all important 

 tertiary circuits is in the neighborhood of JTrK/90. 



A known value of the crosstalk coefficient Fi expresses the effects 

 of the electric fields of many tertiary circuits in one infinitesimal slice 

 and includes the alteration of the field of any one tertiary circuit due 

 to the presence of the others. The interaction crosstalk coefficient 

 involves consideration of both electric and magnetic fields. In any 

 one slice, the electric field of a tertiary circuit determines its crosstalk 

 into the disturbed circuit but the current in the tertiary circuit at the 

 end of the slice is determined by both the electric and magnetic fields 

 of the disturbing circuit. The tertiary circuit current is transmitted 

 into another slice and sets up electric and magnetic fields which both 

 contribute to the crosstalk current in the disturbed circuit. 



