CABLE CROSSTALK 183 



force acting in each filament of the other conductor and causes a 

 further redistribution of the current in that conductor over and above 

 that due to the above mentioned skin effect. This additional altera- 

 tion in current distribution is known as the proximity effect. 



The resultant current distribution can no longer be symmetrical 

 about the axis of either wire. The current in the return wire sets up 

 greater back-electromotive forces in the filaments of the other wire 

 which are close to it than in the more remote filaments. These back- 

 electromotive forces tend to act in opposition to those set up by the 

 current in the wire itself since the current in the return wire is opposite 

 in sign. Hence, the proximity of the return wire reduces the counter- 

 electromotive force acting in the filaments closest to it in the other 

 wire more than it does in the filaments farther away. This results in 

 higher current density in the sides of the wires adjacent to each other. 



The current distribution due to the combined action of skin and 

 proximity effects is shown for a pair of rqund copper wires in space in 

 Figs. 1-A and 1-B.^ The wires are No. 19 A.W.G. and are separated a 

 distance equivalent to that between wires in 19-gauge cable pairs. 

 The current distribution at 56 kilocycles is shown in Fig. 1-A and at 

 112 kilocycles in Fig. 1-B. It is seen that the tendency at the higher 

 frequencies is for the current to concentrate on the sides of the wires 

 adjacent to each other. With perfect conductors the current would 

 all be on the surface of the wires and for this wire spacing would be 

 distributed as shown in Fig. 1-C.^ With actual conductors this distri- 

 bution is approached as the frequency increases toward the highest 

 conceivable wire communication frequency. 



In addition to this unsymmetrical distribution of current with 

 respect to magnitude the currents in various filaments in the conductor 

 may be considerably out of phase with the current at the center. 

 This phase shift may be quite unsymmetrical as indicated for three 

 wire diameters in Figs. 2-A and 2-B. While similar phase shifts occur 

 when only skin effect is present, such shifts are symmetrical about 

 the center of the wire so that the currents at all points in a thin 

 concentric ring have the same phase. Figure 2-A shows the phase 

 shift at 56 kilocycles and Fig. 2-B the phase shift at 112 kilocycles. 

 It is seen that the tendency at the higher frequencies is for the currents 

 at different points on the surface to become in phase with each other. 

 At infinite frequency the surface currents would be in phase. 



^ The current distribution and phase change at 56 and 112 kilocycles were com- 

 puted from formulas given by Harvey L. Curtis in Bureau of Standards Scientific 

 Paper No. 374, entitled, "An Integration Method of Deriving the Alternating 

 Current Resistance and Inductance of Conductors." 



" This distribution was calculated by Ray S. Hoyt. 



