volume | PIER Journals

Abstract

In a previous work, improved full-wave analytical expressions have been derived for the Sommerfeld Integrals (SIs) describing electromagnetic radiation from a short vertical straight wire located in close proximity to a conductive soil. Such formulas ensure high accuracy of the result of the computation, as well as time savings with respect to conventional techniques used to evaluate the SIs, but unfortunately may be used only when both source and field points are located at the air-medium interface. The scope of this paper is to overcome the limitations implied by the previous approach, and provide series-form expressions for the generated field components that are valid for an arbitrarily stratified medium and for any position of the vertical wire antenna and observation point in the air space above it. The expressions follow from the analytical evaluation of the integral representation for the magnetic vector potential, performed through contour integration after substituting an equivalent pole set for each branch cut of the integrand. Validity, efficiency and accuracy of the developed formulas are illustrated through numerical examples.

1. Sommerfeld, A., "On the propagation of waves in wireless telegraphy," Annals of Physics, Vol. 81, 1135-1153, 1926.
doi:10.1002/andp.19263862516

2. Banos, A., Dipole Radiation in the Presence of a Conducting Half-space, Pergamon Press, 1966.

3. Durrani, S. H., "Air to undersea communication with electric dipoles," IRE Transactions on Antennas and Propagation, Vol. 10, 524-528, 1962.
doi:10.1109/TAP.1962.1137912

4. Moore, R. K. and W. E. Blair, "Dipole radiation in a conducting half space," Journal of Research of the National Bureau of Standards-D Radio Propagation, Vol. 65D, No. 6, 547-563, 1961.
doi:10.6028/jres.065D.065

5. Wait, J. R., "The electromagnetic fields of a horizontal dipole in the presence of a conducting half-space," Canadian Journal of Physics, Vol. 39, 1017-1028, 1961.
doi:10.1139/p61-111

6. Bannister, P. R., "Quasi-static fields of dipole antennas at the earth’s surface," Radio Science, Vol. 1, 1321-1330, 1966.
doi:10.1002/rds19661111321

7. King, R. W. P., M. Owens, and T. T. Wu, Lateral Electromagnetic Waves: Theory and Applications to Communications, Geophysical Exploration, and Remote Sensing, Springer-Verlag, 1992.

8. King, R. W. P., S. S. Sandler, and L. C. Shen, "The electromagnetic field of a vertical electric dipole over the earth or sea," IEEE Transactions on Antennas and Propagation, Vol. 42, 382-389, 1994.
doi:10.1109/8.280725

9. King, R. W. P., "Electromagnetic field of a vertical dipole over an imperfectly conducting halfspace," Radio Science, Vol. 25, 149-160, 1990.
doi:10.1029/RS025i002p00149

10. 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

11. Wait, J. R., Electromagnetic Waves in Stratified Media, Pergamon Press, 1970.

12. 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

13. Kong, J. A., Electromagnetic Wave Theory, John Wiley & Sons, 1986.

14. Ward, S. H. and G. W. Hohmann, "Electromagnetic theory for geophysical applications," Electromagnetic Methods in Applied Geophysics, Vol. 1, 130-311, Society of Exploration Geophysicists, Tulsa, OK, 1988.

15. Balanis, C. A., "Antenna Theory: Analysis and Design," John Wiley & Sons, 1997.

16. Wait, J. R., "Radiation from a vertical electric dipole over a stratified ground," Transactions of the IRE — Antennas and Propagation, Vol. 1, No. 1, 9-11, 1953.
doi:10.1109/T-AP.1953.27320

17. Wait, J. R., "Influence of a sub-surface insulating layer on electromagnetic ground wave propagation," IEEE Transactions on Antennas and Propagation, Vol. 14, No. 6, 755-767, 1966.
doi:10.1109/TAP.1966.1138776

18. Wait, J. R., "Asymptotic theory for dipole radiation in the presence of a lossy slab lying on a conducting half-space," IEEE Transactions on Antennas and Propagation, Vol. 15, No. 5, 645-648, 1967.
doi:10.1109/TAP.1967.1138993

19. Kong, J. A., L. C. Shen, and L. Tsang, "Field of an antenna submerged in a dissipative dielectric medium," IEEE Transactions on Antennas and Propagation, Vol. 25, No. 6, 887-889, 1977.
doi:10.1109/TAP.1977.1141703

20. Fuller, J. A. and J. R. Wait, "A pulsed dipole in the earth," Transient Electromagnetic Fields, 237-269, Springer, New York, 1976.

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

22. 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

23. 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, No. 12, 5832-5837, 2015.
doi:10.1109/TAP.2015.2478958

24. 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

25. Patterson, T. N. L., "The optimum addition of points to quadrature formulae," Mathematics of Computation, Vol. 22, 847-856, 1968.
doi:10.1090/S0025-5718-68-99866-9

Dr. Mauro Parise

Prof. Giulio Antonini