volume | PIER Journals

Abstract

This paper presents an accurate analytical explicit expression for the self-inductance of a flat pancake round coil made up of concentric turns. The expression is obtained by converting the semi-infinite integral representation for the mutual inductance between two arbitrary turns of the coil into a finite integral, and then by expanding the integrand into a series of Legendre polynomials. As a result, a sum of simpler integrals is obtained, whose analytical evaluation is straightforward. The self inductance is finally expressed as the sum of logarithmic functions, describing the contributions from the self-inductances of the single turns, plus the mutual-inductance terms originating from all the possible pairs of turns of the coil, each one given by a power series of the ratio between the radii of the turns. Numerical simulations are performed to illustrate the advantages of the proposed solution.

1. Trivino-Cabrera, A., J. Aguado, and J. M. Gonzalez, "Analytical characterisation of magnetic field generated by ICPT wireless charger," Electronics Letters, Vol. 53, 871-873, 2017.
doi:10.1049/el.2017.0968 Google Scholar

2. Fu, M., H. Yin, and C. Ma, "Megahertz multiple-receiver wireless power transfer systems with power flow management and maximum efficiency point tracking," IEEE Trans. Microwave Theory Techniques, Vol. 65, 4285-4293, 2017.
doi:10.1109/TMTT.2017.2689747 Google Scholar

3. Niitsu, K., Y. Sugimori, Y. Kohama, K. Osada, N. Irie, H. Ishikuro, and T. Kuroda, "Analysis and techniques for mitigating interference from power/signal lines and to sram circuits in cmos inductive-coupling link for low-power 3-d system integration," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, Vol. 19, 1902-1907, 2011.
doi:10.1109/TVLSI.2010.2056711 Google Scholar

4. Kwiat, D., S. Saoub, and S. Einav, "Calculation of the mutual induction between coplanar circular surface coils in magnetic resonance imaging," IEEE Transactions on Biomedical Engineering, Vol. 39, 433-436, 1992.
doi:10.1109/10.135536 Google Scholar

5. Angelidis, P., K. Vassiliadis, and G. D. Sergiadi, "Lowest mutual coupling between closely spaced loop antennas," IEEE Transactions on Antennas and Propagation, Vol. 39, 949-953, 1991.
doi:10.1109/8.86914 Google Scholar

6. Zhdanov, M. S., Geophysical Electromagnetic Theory and Methods, Elsevier, Amsterdam, 2009.

7. Parise, M., V. Tamburrelli, and G. Antonini, "Mutual impedance of thin-wire circular loops in near-surface applications," IEEE Transactions on Electromagnetic Compatibility, Vol. 61, 558-563, 2019.
doi:10.1109/TEMC.2018.2816030 Google Scholar

8. Paul, C. R., Inductance: Loop and Partial, John Wiley & Sons, Hoboken, NJ, USA, 2010.

9. Parise, M., "Fast computation of the forward solution in controlled-source electromagnetic sounding problems," Progress In Electromagnetics Research, Vol. 111, 119-139, 2011.
doi:10.2528/PIER10101409 Google Scholar

10. Parise, M., "Exact electromagnetic field excited by a vertical magnetic dipole on the surface of a lossy half-space," Progress In Electromagnetics Research B, Vol. 23, 69-82, 2010.
doi:10.2528/PIERB10060707 Google Scholar

11. Farquharson, C. G., D. W. Oldenburg, and P. S. Routh, "Simultaneous 1D inversion of loop-loop electromagnetic data for magnetic susceptibility and electrical conductivity," Geophysics, Vol. 68, No. 6, 1857-1869, 2003.
doi:10.1190/1.1635038 Google Scholar

12. Parise, M., "Efficient computation of the surface fields of a horizontal magnetic dipole located at the air-ground interface," International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 29, 653-664, 2016.
doi:10.1002/jnm.2120 Google Scholar

13. Wait, J. R., "Mutual electromagnetic coupling of loops over a homogeneous ground," Geophysics, Vol. 20, No. 3, 630-637, 1955.
doi:10.1190/1.1438167 Google Scholar

14. Beard, L. P. and J. E. Nyquist, "Simultaneous inversion of airborne electromagnetic data for resistivity and magnetic permeability," Geophysics, Vol. 63, No. 5, 1556-1564, 1998.
doi:10.1190/1.1444452 Google Scholar

15. Parise, M., "Quasi-static vertical magnetic field of a large horizontal circular loop located at the earth’s surface," Progress In Electromagnetics Research Letters, Vol. 62, 29-34, 2016.
doi:10.2528/PIERL16053003 Google Scholar

16. Ward, S. H. and G. W. Hohmann, "Electromagnetic theory for geophysical applications," Electromagnetic Methods in Applied Geophysics, Theory --- Volume 1, 131-308, edited by M. N. Nabighian, SEG, Tulsa, Oklahoma, 1988. Google Scholar

17. Spies, B. R. and F. C. Frischknecht, "Electromagnetic sounding," Electromagnetic Methods in Applied Geophysics, Volume 2, 285-426, edited by M. N. Nabighian, SEG, Tulsa, Oklahoma, 1988. Google Scholar

18. Parise, M., "Second-order formulation for the quasi-static field from a vertical electric dipole on a lossy half-space," Progress In Electromagnetics Research, Vol. 136, 509-521, 2013.
doi:10.2528/PIER12112508 Google Scholar

19. Tiwari, K. C., D. Singh, and M. K. Arora, "Development of a model for detection and estimation of depth of shallow buried non-metallic landmine at microwave x-band frequency," Progress In Electromagnetics Research, Vol. 79, 225-250, 2008.
doi:10.2528/PIER07100201 Google Scholar

20. Telford, W. M., L. P. Geldart, and R. E. Sheriff, Applied Geophysics, Cambridge University Press, 1990.
doi:10.1017/CBO9781139167932

21. Parise, M., "An exact series representation for the EM field from a circular loop antenna on a lossy half-space," IEEE Antennas and Wireless Prop. Letters, Vol. 13, 23-26, 2014.
doi:10.1109/LAWP.2013.2296149 Google Scholar

22. Werner, D. H., "An exact integration procedure for vector potentials of thin circular loop antennas," IEEE Transactions on Antennas and Propagation, Vol. 44, 157-165, 1996. Google Scholar

23. Parise, M., "Full-wave analytical explicit expressions for the surface fields of an electrically large horizontal circular loop antenna placed on a layered ground," IET Microwaves, Antennas & Propagation, Vol. 11, 929-934, 2017. Google Scholar

24. Zierhofer, C. M. and E. S. Hochmair, "Geometric approach for coupling enhancement of magnetically coupled coils," IEEE Transactions on Biomedical Engineering, Vol. 43, 708-714, 1996. Google Scholar

25. Parise, M., "On the surface fields of a small circular loop antenna placed on plane stratified earth," International Journal of Antennas and Propagation, Vol. 2015, 1-8, 2015. Google Scholar

26. Singh, N. P. and T. Mogi, "Electromagnetic response of a large circular loop source on a layered earth: A new computation method," Pure and Applied Geophysics, Vol. 162, 181-200, 2005. Google Scholar

27. Wait, J. R., "Fields of a horizontal loop antenna over a layered half-space," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 10, 1301-1311, 1995. Google Scholar

28. Parise, M. and G. Antonini, "On the inductive coupling between two parallel thin-wire circular loop antennas," IEEE Transactions on Electromagnetic Compatibility, Vol. 60, No. 6, 1865-1872, 2018. Google Scholar

29. Singh, N. P. and T. Mogi, "Effective skin depth of EM fields due to large circular loop and electric dipole sources," Earth Planets Space, Vol. 55, 301-313, 2003. Google Scholar

30. Parise, M., "A study on energetic efficiency of coil antennas used for RF diathermy," IEEE Antennas and Wireless Propagation Letters, Vol. 10, 385-388, 2011. Google Scholar

31. Parise, M., "On the use of cloverleaf coils to induce therapeutic heating in tissues," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 11–12, 1667-1677, 2011. Google Scholar

32. Parise, M. and S. Cristina, "High-order electromagnetic modeling of shortwave inductive diathermy effects," Progress in Electromagnetics Research, Vol. 92, 235-253, 2009. Google Scholar

33. Bregg, R. K., Horizons in Polymer Research, Nova Publishers, New York, 2005.

34. Vafeas, P., A. Skarlatos, T. Theodoulidis, and D. Lesselier, "Semi-analytical method for the identification of inclusions by air-cored coil interaction in ferromagnetic media," Mathematical Methods in the Applied Sciences, Vol. 41, 6422-6442, 2018. Google Scholar

35. Vafeas, P., G. Perrusson, and D. Lesselier, "Low-frequency scattering from perfectly conducting spheroidal bodies in a conductive medium with magnetic dipole excitation," International Journal of Engineering Science, Vol. 47, 372-390, 2009. Google Scholar

36. Vafeas, P., P. K. Papadopoulos, and D. Lesselier, "Electromagnetic low-frequency dipolar excitation of two metal spheres in a conductive medium," Journal of Applied Mathematics, Vol. 2012, 1-37, Article ID 628261, 2012. Google Scholar

37. Watson, G. N., A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1994.

38. Parise, M., "Exact EM field excited by a short horizontal wire antenna lying on a conducting soil," AEU --- International Journal of Electronics and Communications, Vol. 70, No. 5, 676-680, 2016. Google Scholar

39. Parise, M., Transverse magnetic field of infinite line source placed on ground surface, Vol. 51, No. 19, 1478-1480, Electronics Letters, 2015.

40. Parise, M., "Improved Babylonian square root algorithm-based analytical expressions for the surface-to-surface solution to the Sommerfeld half-space problem," IEEE Transactions on Antennas and Propagation, Vol. 63, 5832-5837, 2015. Google Scholar

41. Hayek, S. I., Advanced Mathematical Methods in Science and Engineering, 2nd Ed., Chapman and Hall/CRC, 2010.

42. Parise, M., "An exact series representation for the EM field from a vertical electric dipole on an imperfectly conducting half-space," Journal of Electromagnetic Waves and Applications, Vol. 2, No. 8, 932-942, 2014. Google Scholar

43. Kamon, M., M. J. Tsuk, and J. K. White, "FASTHENRY: A multipole accelerated 3-D inductance extraction program," IEEE Transactions on Microwave theory and techniques, Vol. 42, No. 9, 1750-1758, 1994. Google Scholar

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Dr. Marco Muzi