CABLE CROSSTALK 187 



for Zm in the same form as in preceding cases the bracketed expression 

 may be arbitrarily rewritten as 



miii + W2t2 + ntsH + • • • mJn = I{Ma + jMi). 

 Then, 



Zm = j<^{Ma + jMu) = - coilffc + jcoM„, 



where the mutual inductance is now considered complex and as having 

 two components such that 



M = Ma+ jMb. 



The total current in the disturbing circuit acting through the com- 

 ponent Mb of the mutual inductance sets up an induced voltage in the 

 disturbed circuit in quadrature with the induced voltage due to Ma, 

 and in the same or opposite phase as the total current in the disturbing 

 circuit. Ordinarily the phase will be opposite and the actual values of 

 Mb will be negative with respect to Ma. 



Both Ma and Mb vary with frequency. While the total current in 

 the disturbing wire is assumed constant, the unsymmetrically dis- 

 tributed currents in the various filaments change in relative magnitude 

 and phase as the frequency changes. At very low frequencies the 

 current is distributed nearly uniformly in phase and magnitude over 

 the cross-section of the wire. The mutual inductance between this 

 wire and the disturbed filamentary wire is nearly the same as the d.-c. 

 value since Ma cannot be appreciably changed from the d.-c. value and 

 Mb must be very nearly zero. At very high frequencies the major 

 part of the current flows unsymmetrically on the surface of the dis- 

 turbing wire but the filamentary surface currents are practically in 

 phase with each other. This results again in a low value of Mb 

 because the total induced voltage will be practically in phase quadra- 

 ture with the total disturbing current. However, due to the un- 

 symmetrical current distribution, the value of Ma is considerably 

 altered from its d.-c. value. At intermediate frequencies the current 

 distribution lies between these two extremes and produces corre- 

 sponding values of Ma and Mb- Since Mb is zero for both zero and 

 infinite frequency it is evident that a maximum value must be reached 

 at some intermediate frequency. 



As noted at the outset of this discussion, the disturbed circuit is 

 assumed to be a filament. In all practical cases the wires involved are 

 finite in cross section, and the reasoning outlined above must be 

 applied to each filament of the disturbed conductor in order to get 

 the total effect. 



