CABLE CROSSTALK 181 



currents. The mutual admittance is due almost entirely to capacitive 

 coupling, the leakance ordinarily being negligible in its effect on cross- 

 talk coupling. This capacitive coupling varies but little with fre- 

 quency and its effect on crosstalk may be balanced out by means of a 

 simple condenser. If the proximity effect were negligible, the mutual 

 impedance would be substantially that of a simple mutual inductance 

 constant with frequency. The crosstalk due to this coupling would, 

 therefore, be balanceable by means of a simple inductance coil. If, 

 however, the proximity effect is not negligible the mutual impedance 

 is due to a complex mutual inductance both of whose components 

 vary considerably with frequency. This is the case in cable circuits 

 and a complex balancing unit must be designed if the complex magnetic 

 coupling is to be accurately simulated. 



The mutual impedance, Zm, between two circuits is by definition 

 the negative ratio of the induced series voltage ^ (e) in the disturbed 

 circuit to the current (/) in the disturbing circuit. Thus, 



Since the induced voltage is proportional to the time variation of the 

 magnetic field set up by the disturbing current, it is important to 

 visualize how this field may be altered by changes in the distribution of 

 the current, /, over the cross section of the disturbing conductor. 

 Four types of current distribution will be considered and the effects 

 on Zm noted. 



In order to simplify the following qualitative explanation of the 

 effect of current distribution on mutual impedance it will be assumed 

 that in all cases the disturbed wire is a filament. When the disturbed 

 wire is finite in cross section the effect is generally similar, but more 

 complicated. 



Case I — Current Concentrated in a Filamentary 



Disturbing Wire 



In the case of a wire of infinitely small cross section the magnetic 



field due to a sinusoidal current, /, induces a voltage in another 



filamentary wire located in this field as expressed by the familiar 



equation 



e = — jooMI. 



The mutual impedance is a pure reactance equal to jwilf , where M, 



the coefficient of mutual inductance, is a pure number and independent 



of frequency. 



* This voltage is defined as being the negative of the value of an inserted electro- 

 motive force such as to bring the total current in the disturbed circuit to zero. 



