146 



BELL SYSTEM TECHNICAL JOURNAL 



ings are in series, as are the secondary windings, and are connected as 

 shown in Fig. 4, for example. The relative direction of each secon- 

 dary winding is the same, whereas the relative directions of the primary 

 windings are reversed. With the cores in mid-position, the voltages 

 induced in the two secondaries are equal in magnitude but opposite in 

 phase, and the net induced voltage in the disturbed circuit is zero. 

 As the cores are moved toward the left the respective components of 

 the voltage induced in circuit 3-7-8-4 increase in a counter-clockwise 

 direction and decrease in a clockwise direction, the net result being a 

 voltage in a counter-clockwise direction. Such a setting of the balanc- 



2 — 



Is 



DISTURBING 

 CIRCUIT 



I ^ 



■^W^ 



Rs 



AAAr 



SHUNT 



L.R 



^wy^ 



A^^- 



■VA ^mu- 



DISTURBED 

 CIRCUIT 



e 



■nm^ 



Fig. 4 — Schematic of a simple balancing coil designed to produce a complex mutual 



impedance. 



ing coil would be used to counteract a clockwise crosstalk voltage, the 

 amount of departure of the cores from mid-position being dependent 

 on the magnitude of the crosstalk voltage being counteracted. Move- 

 ment of the cores toward the right produces the opposite effect 



This device, disregarding any proximity effects therein and the 

 effects of the shunt, acts to set up a net voltage e which is in phase 

 quadrature with the disturbing current /. Hence, 



e — — jwml, 



(1) 



in which m is the net mutual inductance of the device. To obtain the 

 required mutual impedance characteristic, the primary (or secondary) 

 windings of the coil are shunted by an inductive resistance. Let the 

 effective self-inductance and resistance of the line windings (primaries) 

 be denoted by L and R, respectively, and the current through these 

 windings by /«,. Let the effective self-inductance and resistance of the 

 shunt be denoted by Lg and Rs, respectively. At balance, that is. 



