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2013-05-23
On the Success of Electromagnetic Analytical Approaches to Full Time-Domain Formulation of Skin Effect Phenomena
By
Progress In Electromagnetics Research M, Vol. 31, 29-43, 2013
Abstract
Maxwell equations can be used to formulate an analytical full time-domain theory of skin effect phenomena in circular cylindrical conductors without any detour into the frequency domain. The paper shows how this can be done and concomitantly provides the means to determine the time-varying per unit length voltage drop along the conductor from a given time-varying conductor current. The developed relationship between voltage and current is not very complicated and led the authors to examine the reasons why it has never been utilized in transient analysis, nor given special emphasis in the literature. Those reasons are thoroughly examined and the conclusion is that the conditions required for the application of a purely time-domain skin effect theory are very restrictive.
Citation
Jose Antonio Marinho Brandao Faria, and Malcolm Stuart Raven, "On the Success of Electromagnetic Analytical Approaches to Full Time-Domain Formulation of Skin Effect Phenomena," Progress In Electromagnetics Research M, Vol. 31, 29-43, 2013.
doi:10.2528/PIERM13042405
References

1. Maxwell, J. C., Treatise on Electricity and Magnetism, Articles 689, 690, Vol. 2, Oxford University Press, Oxford, UK, 1892.

2. Dwight, H., "Skin effect in tubular and flat conductors," AIEE Trans., Vol. 37, Part II, 1379-1403, 1918.

3. Cockcroft, J., "Skin effect in rectangular conductors at high frequencies," Proc. Roy. Soc., Vol. 122, 533-542, 1929.
doi:10.1098/rspa.1929.0038

4. Arnold, A., "The alternating current resistance of tubular conductors," J. IEE, Vol. 78, 580-593, 1936.

5. Wheeler, H. A., "Formulas for the skin-effect," Proc. IRE, Vol. 30, 412-424, 1942.
doi:10.1109/JRPROC.1942.232015

6. Silvester, P., "The accurate calculation of skin effect in conductors of complicated shape," IEEE Trans. Power App. Syst., Vol. 87, 735-742, 1968.
doi:10.1109/TPAS.1968.292187

7. Waldow, P. and I. Wolff, "The skin-effect at high frequencies," IEEE Trans. Microw. Theory Tech., Vol. 33, 1076-1081, 1985.
doi:10.1109/TMTT.1985.1133172

8. Morgan, V., R. Findlay, and S. Derrah, "New formula to calculate the skin effect in isolated tubular conductors at low frequencies," EE Proc. Sci. Meas. Technol., Vol. 147, 169-171, 2000.
doi:10.1049/ip-smt:20000420

9. Mingli, W. and F. Yu, "Numerical calculations of internal impedance of solid and tubular cylindrical conductors under large parameters," IEE Proc. Generation Trans. Distrib., Vol. 151, 67-72, 2004.
doi:10.1049/ip-gtd:20030981

10. Gatous, O. M. and J. Pissolato, "Frequency-dependent skin-effect formulation for internal resistance and internal inductance of a solid cylindrical conductor," IEE Proc. Microw. Ant. and Propag., Vol. 151, 212-216, 2004.
doi:10.1049/ip-map:20040469

11. Coufal, O., "Current density in a long solitary tubular conductor," J. Physics A: Math. Theory, Vol. 41, No. 4, 145401-14, 2008.

12. Lovric, D., V. Boras, and S. Vujevic, "Accuracy of approximate formulas for internal impedance of tubular cylindrical conductors for large parameters," Progress In Electromagnetics Research M, Vol. 16, 171-184, 2011.

13. Faria, J. A., "A matrix approach for the evaluation of the internal impedance of multilayered cylindrical structures," Progress In Electromagnetics Research B, Vol. 28, 351-367, 2011.

14. Faria, J. A., "Skin effect in inhomogeneous Euler-Cauchy tubular conductors," Progress In Electromagnetics Research M, Vol. 18, 89-101, 2011.

15. Faria, J. A., "A circuit approach for the electromagnetic analysis of inhomogeneous cylindrical structures," Progress In Electromagnetics Research B, Vol. 30, 223-238, 2011.

16. Yen, C., Z. Fazarinc, and R. L. Wheeler, "Time-domain skin-effect model for transient analysis of lossy transmission lines," Proc. IEEE, Vol. 70, 750-757, 1982.

17. Tripathi, V. K. and J. B. Rettig, "A SPICE model for multiple coupled microstrips and other transmission lines," IEEE Trans. Microw. Theory Tech., Vol. 33, 1513-1518, 1985.
doi:10.1109/TMTT.1985.1133248

18. Costache, G., "Finite element method applied to skin-effect problems in strip transmission lines," IEEE Trans. Microw. Theory Tech., Vol. 35, 1009-1013, 1987.
doi:10.1109/TMTT.1987.1133799

19. Djordjevic, A. R., T. K. Sarkar, and E. F. Harrington, "Time-domain response of multiconductor transmission lines," Proc. IEEE, Vol. 75, 643-764, 1987.

20. Tsuk, M. and J. Kong, "A hybrid method for the calculation of the resistance and inductance of transmission lines with arbitrary cross sections," IEEE Trans. Microw. Theory Tech., Vol. 39, 1338-1347, 1991.
doi:10.1109/22.85409

21. Chang, E. C. and S. Kang, "Computationally efficient simulation of a lossy transmission line with skin effect by using numerical inversion of Laplace transform," IEEE Trans. Circuits and Syst., Vol. 39, 861-868, 1992.

22. Paul, C. R., Analysis of Multiconductor Transmission Lines, Wiley, New York, USA, 1994.

23. Dular, P., R. V. Sabariego, and L. Krahenbuhl, "Subdomain finite element method for efficiently considering strong skin and proximity effects ," IEEE Trans. Mag., Vol. 44, 738-741, 2008.
doi:10.1109/TMAG.2007.915817

24. Dedkova, J. and L. Brancik, "Laplace transform and FDTD approach applied to MTL simulation," PIERS Online, Vol. 4, No. 1, 16-20, 2008.

25. Giacoletto, L. J., "Frequency- and time-domain analysis of skin effects," IEEE Trans. Mag., Vol. 32, 220-229, 1996.
doi:10.1109/20.477574

26. Faria, J. A., Electromagnetic Foundations of Electrical Engineering, Wiley, Chichester, UK, 2008.
doi:10.1002/9780470697498

27. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, "Vandermonde matrices and Toeplitz matrices," umerical Recipes: The Art of Scientific Computing, Vol. 3rd, Cambridge Univ. Press, Cambridge, UK, 2007.

28. Knuth, D. E. and T. K. Buckholtz, "Computation of tangent, Euler, and Bernoulli numbers," Math. Comput., Vol. 21, 663-688, 1967.