MUTUAL IMPEDANCES OF GROUND-RETURN CIRCUITS 635 



disturbing and disturbed circuits. For the calculation of the mutual 

 inductance formulas and graphs requiring only a knowledge of the 

 mutual arrangement of the wire parts of the disturbing and disturbed 

 circuits with respect to each other and the earth are given. The mu- 

 tual inductance is independent of earth resistivity. While these for- 

 mulas are, of course, strictly applicable only for direct currents, it is to 



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0.2 



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 o 



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a 



UJ 

 Q. 



in 



2 

 I 



o 



0.1 



07 



0.05 

 04 



o 



2 0.03 

 < 



Q 

 Ul 

 Q. 



2 0.02 



< 



D 



D 

 2 



0.01 



0.007 



005 



20 



30 



50 100 200 300 



HORIZONTAL SEPARATION IN FEET 



500 



1000 



Fig. 7 — Cross Keys tests. Ground plane theory. Comparison of measured and 



calculated values of mutual impedance. 



be expected that at sufficiently low frequencies the ground-current 

 distribution would not differ appreciably from that for direct current, 

 and hence for these frequencies, these calculated d.-c. mutual resistance 

 and inductance should approximate the actual values. In the paper 

 referred to, some experimental results at frequencies of 25 and 60 cycles 

 supporting this point of view are presented. 



The experimental curves of Fig. 2, which were obtained from meas- 

 urements at Cross Keys on the 500-ft. disturbed lines near the middle of 

 the 8500-ft. disturbing line, indicate a pronounced increase in mutual 

 resistance with increase in frequency in the range from 60 to 1000 



