. The Bell System technical journal . .0018 j: ^ \ \ _ . bp^ X 1000 Fig. 1—Mutual impedance gradient at earths surface parallel to an infinitestraight wire on the earths surface; real component; two-layer earth Xi = IOX2;b and y in feet, frequency in cycles per second, conductivities in abmhos per cm. Figures 1 and 2 show, respectively, the real and imaginary parts ofthe mutual impedance gradient parallel to an infinite straight wire forthe conductivity ratio X2/X1 = ; Figs. 3 and 4 show the same MUTUAL IMPEDANCE OF GROUNDED WIRES 167 quantities for X2/X1 = 10. When the depth b a


. The Bell System technical journal . .0018 j: ^ \ \ _ . bp^ X 1000 Fig. 1—Mutual impedance gradient at earths surface parallel to an infinitestraight wire on the earths surface; real component; two-layer earth Xi = IOX2;b and y in feet, frequency in cycles per second, conductivities in abmhos per cm. Figures 1 and 2 show, respectively, the real and imaginary parts ofthe mutual impedance gradient parallel to an infinite straight wire forthe conductivity ratio X2/X1 = ; Figs. 3 and 4 show the same MUTUAL IMPEDANCE OF GROUNDED WIRES 167 quantities for X2/X1 = 10. When the depth b approaches the Hmitszero and infinity, the ground condition approaches the hmits ofhomogeneous ground of conductivities X2 and Xi, respectively. Byreference to Figs. 2 and 4 it will be seen that there is a wide range inwhich the curves for other values of the depth are parallel to these. \ \\ \\ \\\ iv\ I m \ \\ V ^ k ^ ^ , UJ _lO o ct UJ °- LiJ 2 (T ^ O Fig. 2—Imaginary component of mutual impedance gradientfor conditions of Fig. 1. limiting curves so that for a given frequency a properly chosen homo-geneous ground conductivity leads to equivalent results. The equiva-lent conductivity varies with the frequency, increasing or decreasingwith increasing frequency according as Xi is greater or less than X2;this variation of apparent homogeneous conductivity with frequencyhas been frequently observed in results obtained from mutual im- 168 BELL SYSTEM TECHNICAL JOURNAL 00014 ~>. ^, y /^ o a 00012 -^^ 4>o- / ^ ^ — —■ ---:.. Q- u ■^ 4 . - / / 1 ^ ~^ 2 ^ .... y 00006 10-2 ^ in 5 00004 ,y I 00002 ? JiH^ 0 5 10 Fig. 3—Two-layer earth X2 = lOXi; real component of mutualimpedance gradient. 50


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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1