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LOOP ANTENNAS WITH UNIFORM CURRENT IN CLOSE PROXIMITY TO THE EARTH: CANONICAL SOLUTION TO THE SURFACE-TO-SURFACE PROPAGATION PROBLEM

By M. Parise, M. Muzi, and G. Antonini

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Abstract:
In a recent study, the classical problem of a large circular loop antenna carrying uniform current and situated at the Earth's surface has been revisited, with the scope to derive a totally analytical explicit expression for the radial distribution of the generated magnetic field. Yet, the solution arising from the study exhibits two major drawbacks. First, it describes the vertical magnetic field component only. Second, it is a valid subject to the quasi-static field assumption, which limits its applicability to the low-frequency range. The purpose of the present work is to provide the exact canonical solution to the problem, describing all the generated electromagnetic field components and valid in both the quasi-static and non-quasi-static frequency regions. These two features constitute an improvement with respect to the preceding solution. The canonical solution, which is obtained by reducing the field integrals to combinations of known Sommerfeld integrals, is seen to be also advantageous over the previous numerical and analytical-numerical approaches, since its usage takes negligible computation time. Numerical simulations are performed to show the accuracy of the obtained field expressions and to investigate the behavior of the above surface ground- and lateral-wave contributions to the fields in a wide frequency range. It is shown that in the near-zone the two waves do not predominate over each other, while the effect of the lateral wave becomes negligible only when the source-receiver distance is far greater than the skin depth in the Earth.

Citation:
M. Parise, M. Muzi, and G. Antonini, "Loop Antennas with Uniform Current in Close Proximity to the Earth: Canonical Solution to the Surface-to-Surface Propagation Problem," Progress In Electromagnetics Research B, Vol. 77, 57-69, 2017.
doi:10.2528/PIERB17042005

References:
1. Foster, D., "Loop antennas with uniform current," Proceedings of the IRE, Vol. 32, 603-607, 1944.
doi:10.1109/JRPROC.1944.233062

2. Balanis, C. A., Antenna Theory: Analysis and Design, 2nd Ed., John Wiley & Sons, New York, 1997.

3. 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

4. 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

5. 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, 2012.

6. Palacky, G. J., "Resistivity characteristics of geologic targets," Electromagnetic Methods in Applied Geophysics, Vol. 1, 52-129, edited by M. N. Nabighian, SEG, Tulsa, Oklahoma, 1988.

7. Ward, S. H. and G. W. Hohmann, "Electromagnetic theory for geophysical applications," Electromagnetic Methods in Applied Geophysics, Theory --- Volume 1, 131-308, M. N. Nabighian (ed.), SEG, Tulsa, Oklahoma, 1988.

8. 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

9. Overfelt, P., "Near fields of the constant current thin circular loop antenna of arbitrary radius," IEEE Transactions on Antennas and Propagation, Vol. 44, 166-171, 1996.
doi:10.1109/8.481643

10. 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

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

12. 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

13. Parise, M., "On the use of cloverleaf coils to induce therapeutic heating in Tissues," Journal of Electromagnetic Waves and Applications, Vol. 25, 1667-1677, 2011.
doi:10.1163/156939311797164945

14. Boerner, D. E., "Controlled source electromagnetic deep sounding: Theory, results and correlation with natural source results," Surveys in Geophysics, Vol. 13, No. 4–5, 435-488, 1992.
doi:10.1007/BF01903486

15. Shastri, N. L. and H. P. Patra, "Multifrequency sounding results of laboratory simulated homogeneous and two-Layer earth models," IEEE Trans. Geosci. Remote Sensing, Vol. 26, No. 6, 749-752, 1988.
doi:10.1109/36.7706

16. 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

17. Kong, J. A., L. Tsang, and G. Simmons, "Geophysical subsurface probing with radio-frequency interferometry," IEEE Transactions on Antennas and Propagation, Vol. 22, No. 4, 616-620, 1974.
doi:10.1109/TAP.1974.1140858

18. Singh, N. P. and T. Mogi, "Inversion of large loop transient electromagnetic data over layered earth models," Jour. Fac. Sci Hokkaido Univ. Ser. VII, Vol. 12, No. 1, 41-54, 2003.

19. 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

20. Guptasarma, D. and B. Singh, "New digital linear filters for Hankel J0 and J1 transforms," Geophysical Prospecting, Vol. 45, No. 5, 745-762, 1997.
doi:10.1046/j.1365-2478.1997.500292.x

21. 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

22. Kong, F. N., "Hankel transform filters for dipole antenna radiation in a conductive medium," Geophysical Prospecting, Vol. 55, No. 1, 83-89, 2007.
doi:10.1111/j.1365-2478.2006.00585.x

23. Parise, M., "A study on energetic efficiency of coil antennas used for RF diathermy," IEEE Antennas and Wireless Prop. Letters, Vol. 10, 385-388, 2011.
doi:10.1109/LAWP.2011.2148190

24. Alford, A. and A. Kandoian, "Ultrahigh-frequency loop antennas," Electrical Engineering, Vol. 59, 843-848, 1940.
doi:10.1109/EE.1940.6435249

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.
doi:10.1155/2015/187806

26. 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

27. Tai, C., Dyadic Green functions in electromagnetic theory, IEEE Press, New York, 1994.

28. Mosig, J. R., R. C. Hall, and F. E. Gardiol, "Numerical analysis of microstrip patch antennas," Handbook of Microstrip Antennas, J. R. James and P. S. Hall (eds.), Peter Peregrinus Ltd., London, UK, 1989.

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

30. Erdelyi, A., Tables of Integral Transforms — Vol. 2, McGraw-Hill, New York, 1954.

31. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1964.

32. 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, 676-680, 2016.
doi:10.1016/j.aeue.2016.02.004

33. 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

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

35. Davis, J. L. and A. P. Annan, "Ground-penetrating radar for high-resolution mapping of soil and rock stratigraphy," Geophysical Prospecting, Vol. 37, 531-551, 1989.
doi:10.1111/j.1365-2478.1989.tb02221.x

36. Daniels, D. J., Ground Penetrating Radar, Institution of Engineering and Technology, London, UK, 2004.
doi:10.1049/PBRA015E

37. 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

38. Telford, W. M., L. P. Geldart, and L. E. Sherif, Applied Geophysics, Cambridge University Press, Cambridge, UK, 1990.
doi:10.1017/CBO9781139167932


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