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The paper describes a simple analytical approximation for the inductance of two-wire transmission lines of circularly cylindrical wires with proximity effect. It yields precise results up to very high frequencies, and also at all interaxial distances between the wires above some limit. Its accuracy is established by comparison to numerical computations and to measurements. It is shown that the proximity effect cannot be neglected unless the interaxial distance between the wires amounts to at least four wire diameters. Further, images of the current distribution in various situations are discussed.
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A. Sommerfeld, Elektrodynamik, Verlag Harry Deutsch, Frankfurt am Main, 1988, 4th ed. 2001.
L. D. Landau and E. M. Lifschitz, Elektrodynamik der Kontinua, Akademie-Verlag Berlin, Berlin, 5th ed. 1985, first published by edition NAUKA, Moscow, 1982.
C. R. Paul, Inductance, John Wiley & Sons, Hoboken NJ, 2010.
G.S. Smith, A Simple Derivation for the Skin Effect in a Round Wire, European Journal of Physics, vol. 35, 1-13, 2014.
A. E. Kennelly, F. A. Laws and P. H. Pierce, Experi-mental Researches on Skin Effect in Conductors, Transactions of the American Institute of Electrical Engineers, vol. XXXIV, no. 2, 1953-2021, 1915.
D. Lovrić, V. Boras, and S. Vujević, Accuracy of Ap-proximate Formulas for Internal Impedance of Tubular Cylindrical Conductors for Large Parameters, Progress in Electromagnetics Research M, vol. 16, 171-184, 2011.
M. J. Tsuk and J. A. Kong, A Hybrid Method for the Calculation of the Resistance and Inductance of Transmission Lines with Arbitrary Cross Sections, IEEE Transactions on Microwave Theory and Techniques, vol. 39, no. 8, 1338-1347, 1991.
J. R. Carson, LIV. Wave propagation over parallel wires: The proximity effect, Philosophical Magazine Series 6, 41:244, 607-633, 1921.
B.-Z. Wang, Exact Expressions for the AC Resistance and Internal Inductance of a Lossy Circular Two-Wire Transmission Line, Microwave and Optical Technolo-gy Letters, vol. 7, no. 10, 451-454, 1994.
W. T. Weeks, L. L. Wu, M. F. McAllister, and A. Singh, Resistive and Inductive Skin Effect in Rectangular Conductors, IBM Journal of Research and De-velopment, vol. 23, no. 6, 652-660, 1979.
W. M. Haynes, Th. J. Bruno, and D. R. Lide, CRC Handbook of Chemistry and Physics, 95th ed., Internet Version 2015, p. 12-41, 2015.
H. A. Aebischer and B. Aebischer, The GMD Method for Inductance Calculation Applied to Conductors with Skin Effect, submitted for publication in Advanced Electromagnetics, Jan. 2017.
E. B. Rosa, The Self and Mutual Inductances of Linear Conductors, Bulletin of the Bureau of Standards, vol. 4, no. 2, Washington, 1907.
H. A. Aebischer and B. Aebischer, Improved Formulae for the Inductance of Straight Wires, Advanced Elec-tromagnetics, vol. 3, no. 1, 31-43, 2014.