MUTUAL IMPEDANCES OF GROUND-RETURN CIRCUITS 629 



the currents, either at fundamental frequency or at any harmonic fre- 

 quency, in any of the lines can be resolved into components, some of 

 which are entirely confined to the wires while another component flows 

 in a circuit composed of all the wires as one side with the ground as a 

 return path. The work which is described in this paper deals with 

 the magnitude of the induced voltages on exposed telephone lines 

 caused by the latter component. It has been directed to two ends, 

 first, the establishment of an experimental basis for the study of the 

 physical factors involved in the inductive coupling of ground-return 

 circuits, and second, the development of practical methods to enable 

 the advance calculation of the mutual impedances of power and tele- 

 phone lines. The work is accordingly presented in two parts; first are 

 given the results of tests made at a field laboratory in which testing 

 conditions could be controlled, and second, tests in which the practical 

 side of the problem was investigated are described. 



Cross Keys Tests and Theoretical Background 



Cross Keys Tests. An extended series of measurements was made at 

 a field laboratory operated by the subcommittee near Cross Keys, New 

 Jersey, about 20 miles southeast of Camden. A single conductor, 

 located about 34 ft. above the ground and 8500 ft. in length, was avail- 

 able for the disturbing circuit. For disturbed circuits, 500-ft. lengths 

 of insulated wire were laid on the earth parallel to the disturbing con- 

 ductor, at several separations, as shown on Fig. 1. Grounds were pro- 



.iGROUNO CONNECTION 



-4850'- 



DISTURBING LINE 



:500>< 



-3150'- 



GENERATOR 



OHi" 



LINE DATA 

 DISTURBING DISTURBED 



HEIGHT 34 FT 

 LENGTH 8500 FT 



SEPARATIONS 



21.5 FT. 



56.1 FT. 



101.4 FT 



200 FT. 



500 FT. 



1000 FT. 





 500 FT. 



-"^DISTURBED 

 / LINES 



SCALE IN F£ET 



500 1000 



1 ■ ■ ■ ■ I ■ ■ ■ ■ I 



SETUP FOR GRADIENT MEASUREMENTS 

 ■4500' 



GROUND CONNECTION 



H I 



GRADIENTS WERE 

 MEASURED ALONG 

 DOTTED LINES 



-ao-|ii' 



Fig. 1 — Cross Keys tests — experimental setup. 



vided at the ends of each line. Ground-return current was transmitted 

 over the disturbing line at 60 cycles from a commerical source, or at 

 frequencies between 100 and 1000 cycles from a vacuum-tube oscillator 

 with power amplifier. The measuring instrument was an a.-c. poten- 

 tiometer, equipped with suitable filters so that the observations were 

 unaffected by the presence of harmonics in the disturbing current. 

 At several frequencies within the range from 60 to 1000 cycles the 



