Vol. 18
Latest Volume
All Volumes
PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2011-05-02
Skin Effect in Inhomogeneous Euler-Cauchy Tubular Conductors
By
Progress In Electromagnetics Research M, Vol. 18, 89-101, 2011
Abstract
This paper presents a novel contribution for the analysis of skin effect phenomena in inhomogeneous tubular conductors. For homogeneous tubular geometries the skin effect diffusion equation has an analytical solution described by a combination of Bessel functions, but, when the conductivity and magnetic permeability of the tubular conductor arbitrarily depend on the radial coordinate an analytical solution cannot be found. However, this work shows that closed form solutions for the electromagnetic field and conductor internal impedance do exist, provided that a specific type of radial variation of medium parameters is considered --- tubular structures like these are coined here Euler-Cauchy Structures (ECS). Analytic and computation results concerning general and particular ECS are presented, validated, and discussed. Besides its intrinsic theoretical importance, the simple closed form solutions that we have found can be of interest as benchmark tools for testing the accuracy and performance of EM field software solvers.
Citation
Jose Antonio Marinho Brandao Faria, "Skin Effect in Inhomogeneous Euler-Cauchy Tubular Conductors," Progress In Electromagnetics Research M, Vol. 18, 89-101, 2011.
doi:10.2528/PIERM11030905
References

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

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

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

4. Silvester, P., "The accurate calculation of skin effect in conductors of complicated shape," IEEE Trans. Power App. Syst., Vol. 87, No. 3, 735-742, 1968.
doi:10.1109/TPAS.1968.292187

5. Tegopoulos, J. and E. Kriezis, "Eddy current distribution in cylindrical shells of infinite length due to axial currents," IEEE Trans. Power App. Syst., Vol. 90, No. 3, 1278-1286, 1971.
doi:10.1109/TPAS.1971.292929

6. Waldow, P. and I. Wolff, "The skin-effect at high frequencies," IEEE Trans. Microw. Theory Tech., Vol. 33, No. 10, 1076-1081, 1985.
doi:10.1109/TMTT.1985.1133172

7. Costache, G., "Finite element method applied to skin-effect problems in strip transmission lines," IEEE Trans. Microw. Theory Tech., Vol. 35, No. 11, 1009-1013, 1987.
doi:10.1109/TMTT.1987.1133799

8. 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, No. 8, 1338-1347, 1991.
doi:10.1109/22.85409

9. Silveira, F. and J. Lima, "Skin effect from extended irreversible thermodynamics perspective," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 2-3, 151-160, 2010.
doi:10.1163/156939310790735787

10. Barmada, S., L. Rienzo, N. Ida, and S. Yuferev, "The use of surface impedance conditions in time domain problems: Numerical and experimental validation," Appl. Comput. Electromag. Soc. Journal, Vol. 19, No. 2, 76-83, 2004.

11. Barmada, S., L. Rienzo, N. Ida, and S. Yuferev, "Time domain surface impedance concept for low frequency electromagnetic problems. Part II: Application to transient skin and proximity effect problems in cylindrical conductors," IEE Proc. Sci. Meas. Technol., Vol. 154, No. 5, 207-216, 2005.
doi:10.1049/ip-smt:20049036

12. Rong, A. and A. Cangelari, "Note on the definition and calculation of the per-unit-length internal impedance of a uniform conducting wire," IEEE Trans. Electrom. Comp., Vol. 49, No. 3, 677-681, 2007.
doi:10.1109/TEMC.2007.903043

13. Morsey, J., V. Okhmatovski, and A. Cangelaris, "Finite-thickness conductor models for full-wave analysis of interconnects with a fast integral equation method," Proc. IEEE 11th Topical Meeting on Electrical Performance of Electronic Packaging, Monterey, USA, Oct. 2002.

14. Zutter, D., H. Rogier, L. Knockaert, and J. Sercu, "Surface current modelling of the skin effect for on-chip interconnections," IEEE Trans. Adv. Packaging, Vol. 30, No. 2, 342-349, 2007.
doi:10.1109/TADVP.2007.895984

15. Morgan, V., R. Findlay, and S. Derrah, "New formula to calculate the skin e®ect in isolated tubular conductors at low frequencies," IEE Proc. Sci. Meas. Technol., Vol. 147, No. 4, 169-171, 2000.
doi:10.1049/ip-smt:20000420

16. Mingli, W. and F. Yu, "Numerical calculations of internal impedance of solid and tubular cylindrical conductors under large parameters," IEE Proc. Generation Transm. Distribution, Vol. 151, No. 1, 67-72, 2004.
doi:10.1049/ip-gtd:20030981

17. Coufal, O., "Current density in a long solitary tubular conductor," J. Physics A: Math. Theor., Vol. 41, No. 14, 145401 (14pp), 2008.

18. Rienzo, L., S. Yuferev, and N. Ida, "Calculation of energy-related quantities of conductors using surface impedance concept," IEEE Trans. Magnetics, Vol. 44, No. 6, 1322-1325, 2008.
doi:10.1109/TMAG.2008.915850

19. Vujevic, S., V. Boras, and P. Sarajcev, "A novel algorithm for internal impedance computation of solid and tubular cylindrical conductors," Int. Rev. Electric. Eng., Vol. 4, No. 6, 1418-1425, 2009.

20. Knight, D., "Practical continuous functions and formulae for the internal impedance of cylindrical conductors,", http//www.g3ynh.info/ zdocs/comps/Zint.pdf, March 2010.

21. 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.

22. Wylie, C., Advanced Engineering Mathematics, McGraw-Hill, New York, 1975.

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

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