Vol. 86
Latest Volume
All Volumes
PIERL 119 [2024] PIERL 118 [2024] PIERL 117 [2024] PIERL 116 [2024] PIERL 115 [2024] PIERL 114 [2023] PIERL 113 [2023] PIERL 112 [2023] PIERL 111 [2023] PIERL 110 [2023] PIERL 109 [2023] PIERL 108 [2023] PIERL 107 [2022] PIERL 106 [2022] PIERL 105 [2022] PIERL 104 [2022] PIERL 103 [2022] PIERL 102 [2022] PIERL 101 [2021] PIERL 100 [2021] PIERL 99 [2021] PIERL 98 [2021] PIERL 97 [2021] PIERL 96 [2021] PIERL 95 [2021] PIERL 94 [2020] PIERL 93 [2020] PIERL 92 [2020] PIERL 91 [2020] PIERL 90 [2020] PIERL 89 [2020] PIERL 88 [2020] PIERL 87 [2019] PIERL 86 [2019] PIERL 85 [2019] PIERL 84 [2019] PIERL 83 [2019] PIERL 82 [2019] PIERL 81 [2019] PIERL 80 [2018] PIERL 79 [2018] PIERL 78 [2018] PIERL 77 [2018] PIERL 76 [2018] PIERL 75 [2018] PIERL 74 [2018] PIERL 73 [2018] PIERL 72 [2018] PIERL 71 [2017] PIERL 70 [2017] PIERL 69 [2017] PIERL 68 [2017] PIERL 67 [2017] PIERL 66 [2017] PIERL 65 [2017] PIERL 64 [2016] PIERL 63 [2016] PIERL 62 [2016] PIERL 61 [2016] PIERL 60 [2016] PIERL 59 [2016] PIERL 58 [2016] PIERL 57 [2015] PIERL 56 [2015] PIERL 55 [2015] PIERL 54 [2015] PIERL 53 [2015] PIERL 52 [2015] PIERL 51 [2015] PIERL 50 [2014] PIERL 49 [2014] PIERL 48 [2014] PIERL 47 [2014] PIERL 46 [2014] PIERL 45 [2014] PIERL 44 [2014] PIERL 43 [2013] PIERL 42 [2013] PIERL 41 [2013] PIERL 40 [2013] PIERL 39 [2013] PIERL 38 [2013] PIERL 37 [2013] PIERL 36 [2013] PIERL 35 [2012] PIERL 34 [2012] PIERL 33 [2012] PIERL 32 [2012] PIERL 31 [2012] PIERL 30 [2012] PIERL 29 [2012] PIERL 28 [2012] PIERL 27 [2011] PIERL 26 [2011] PIERL 25 [2011] PIERL 24 [2011] PIERL 23 [2011] PIERL 22 [2011] PIERL 21 [2011] PIERL 20 [2011] PIERL 19 [2010] PIERL 18 [2010] PIERL 17 [2010] PIERL 16 [2010] PIERL 15 [2010] PIERL 14 [2010] PIERL 13 [2010] PIERL 12 [2009] PIERL 11 [2009] PIERL 10 [2009] PIERL 9 [2009] PIERL 8 [2009] PIERL 7 [2009] PIERL 6 [2009] PIERL 5 [2008] PIERL 4 [2008] PIERL 3 [2008] PIERL 2 [2008] PIERL 1 [2008]
2019-08-15
On the Mutual Inductance Between Non-Coaxial Coplanar Circular Loops
By
Progress In Electromagnetics Research Letters, Vol. 86, 83-89, 2019
Abstract
A simple and efficient explicit solution is derived for the mutual inductance of two non-coaxial coplanar circular loops, which is valid in the quasi-static as well as non-quasi-static frequency ranges. The solution is obtained by rigorously evaluating the Sommerfeld Integral describing the inductance, starting from expanding the integrand into a power series of the loop radius. As a result, a sum of simpler integrals is obtained, and term-by-term analytical integration is straightforwardly performed. The inductance is finally expressed as a series of spherical Hankel functions, with algebraic coefficients depending on the electrical size of the loops. Conducted numerical tests lead to conclude that, accuracy being equal, the proposed expression offers advantages in terms of time cost over conventional numerical integration techniques.
Citation
Marcello Salis, and Marco Muzi, "On the Mutual Inductance Between Non-Coaxial Coplanar Circular Loops," Progress In Electromagnetics Research Letters, Vol. 86, 83-89, 2019.
doi:10.2528/PIERL19061203
References

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

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

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

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

5. 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

6. Conway, J. T., "Analytical and semi-analytical solutions for the force between circular loops in parallel planes," IEEE Transactions on Magnetics, Vol. 49, 4817-4823, 2013.
doi:10.1109/TMAG.2013.2245912

7. Conway, J. T., "Inductance calculations for noncoaxial coils using Bessel functions," IEEE Transactions on Magnetics, Vol. 43, 1023-1034, 2007.
doi:10.1109/TMAG.2006.888565

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

9. 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

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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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.

19. Parise, M., "Transverse magnetic field of infinite line source placed on ground surface," Electronics Letters, Vol. 51, No. 19, 1478-1480, 2015.
doi:10.1049/el.2015.0636

20. 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.

21. 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

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

23. 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

24. 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.
doi:10.1109/8.481642

25. 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.
doi:10.1049/iet-map.2016.0590

26. 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.
doi:10.1109/10.503178

27. 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.
doi:10.1155/2015/187806

28. 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.
doi:10.1007/s00024-004-2586-2

29. 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.

30. 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.
doi:10.1109/TEMC.2018.2790265

31. 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.
doi:10.1186/BF03351764

32. 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.
doi:10.1109/LAWP.2011.2148190

33. 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.
doi:10.1163/156939311797164945

34. Parise, M. and S. Cristina, "High-order electromagnetic modeling of shortwave inductive diathermy effects," Progress In Electromagnetics Research, Vol. 92, 235-253, 2009.
doi:10.2528/PIER09022608

35. Rosa, E. B. and L. Cohen, "Formulae and tables for the calculation of mutual and self-inductance," Bull. Bureau Standards, Vol. 5, 1-132, 1908.
doi:10.6028/bulletin.103

36. Snow, C., Formulas for Computing Capacitance and Inductance, (Circular of the Bureau of Standards No. 544), U. S. Govt. Printing Office, Washington DC, 1954.

37. Parise, M., "A highly accurate analytical solution for the surface fields of a short vertical wire antenna lying on a multilayer ground," Waves in Random and Complex Media, Vol. 28, 49-59, 2018.
doi:10.1080/17455030.2017.1319990

38. Balanis, C. A., Antenna Theory: Analysis and Design, 4th Ed., John Wiley & Sons, New York, 2016.

39. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 2007.

40. 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.
doi:10.1016/j.aeue.2016.02.004

41. 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

42. 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.
doi:10.1109/TAP.2015.2478958

43. 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. 28, No. 8, 932-942, 2014.
doi:10.1080/09205071.2014.897653

44. 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.
doi:10.1109/22.310584