146 BELL SYSTEM TECHNICAL JOURNAL 



in terms of crosstalk units, if the absolute value of the crosstalk ratio is 

 multiplied by a factor 10^. 



It is well to observe at this point that, depending upon special 

 conditions, the significant crosstalk ratio may be either the voltage 

 ratio or the current ratio or the power ratio. The power ratio, or 

 more commonly the square root of it, is usually the most important 

 but if the outputs are impressed on the grids of vacuum tubes then the 

 voltage ratio becomes the significant measure of crosstalk. However, 

 if one crosstalk ratio is known, any other crosstalk ratio can be readily 

 determined provided that the characteristics of both circuits are 

 known. Thus for the conditions of Fig. 1 the value of far-end crosstalk 

 as given by the ratio VflEe~'^^^ in the voltage ratio system will become 

 (Vf/Ee~'^i^){Zi/Z2) in the current ratio system. 



In general, the crosstalk between any two transmission lines depends 

 upon the existence of mutual impedances and mutual admittances 

 between the lines. Generally, then, one can differentiate between two 

 types of crosstalk. The first is produced by an electromotive force in 

 series with the disturbed line in consequence of mutual impedances 

 between the lines, and can be appropriately designated as the "im- 

 pedance crosstalk." The other is due to an electromotive force in 

 shunt with the disturbed line, induced by virtue of mutual admittances, 

 and can be designated as the "admittance crosstalk." The two types 

 of crosstalk are frequently referred to either as "electromagnetic 

 crosstalk" and "electrostatic crosstalk" or as "magnetic crosstalk" 

 and "electric crosstalk" ; the latter terminology is the better of the two. 



The Mutual Impedance 



Consider the simplest crosstalking system consisting of two circuits 

 only, such as shown schematically in Fig. 1. The mutual impedance 

 between two corresponding short sections of the two lines, between the 

 disturbing section ab and the disturbed section kl, for instance, will be 

 defined as the ratio of the electromotive force induced in the disturbed 

 section to the current in the disturbing section. In what follows we 

 shall assume that the coupling between the two transmission lines is 

 uniformly distributed: that is, that the mutual impedance between two 

 infinitely small sections, each of length dx is Zndx, where Z12 is inde- 

 pendent of X. The constant Z12 is the mutual impedance per unit 

 length. 



The mutual impedance between coaxial pairs will be dealt with in a 

 later section. For the present we need only assume that this im- 

 pedance can be either calculated or measured. We shall find that the 

 crosstalk is proportional to the mutual impedance, the remaining 



