Vol. 136
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2013-01-22
Second-Order Formulation for the Quasi-Static Field from a Vertical Electric Dipole on a Lossy Half-Space
By
Progress In Electromagnetics Research, Vol. 136, 509-521, 2013
Abstract
Improved quasi-static expressions are derived for the time-harmonic electromagnetic (EM) field components excited by a vertical electric dipole (VED) lying on the surface of a flat and homogeneous lossy half-space. An analytical procedure is developed that allows to evaluate the complete integral representations for the fields, once the non-oscillating part of the integrand in the expression of the magnetic vector potential is replaced with its quadratic approximation for small values of the free-space wavenumber. The advantage of the proposed second-order quasi-static approximations resides in the possibility of relaxing the assumption of highly conducting half-space. This makes it possible to overcome the limitations implied by the previously published zeroth-order formulation, whose validity is restricted to extremely low frequencies for poorly conducting media. Numerical results are presented to illustrate the reduction of relative percent error arising from using the improved quasi-static field expressions.
Citation
Mauro Parise, "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
References

1. Sommerfeld, A. N., "Propagation of waves in wireless telegraphy," Annalen der Physik, 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, Ltd., 1966.

3. 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

4. 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

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

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

7. 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

8. Bannister, P. R., "Quasi-static fields of dipole antennas at the earth's surface," Radio Science, Vol. 1, No. 11, 1321-1330, 1966.

9. 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

10. 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

11. Zhang, M. and A. Alden, "Calculation of whole-body SAR from a 100MHz dipole antenna," Progress In Electromagnetics Research, Vol. 119, 133-153, 2011.
doi:10.2528/PIER11052005

12. Li, Z. X., G.-F. Li, J.-B. Fan, and Y. Yin, "Quasi-static complex image method for a current point source in horizontally stratified multilayered earth," Progress In Electromagnetics Research B, Vol. 34, 187-204, 2011.

13. Mowete, A. I., A. Ogunsola, and L. Sandrolini, "A quasi-static theory for dielectric-coated thin-wire antenna structures," Progress In Electromagnetics Research Letters, Vol. 20, 45-54, 2011.

14. Kong, J. A., Electromagnetic Wave Theory, John Wiley & Sons, New York, 1986.

15. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990.

16. Radi, Y., S. Nikmehr, and S. Hosseinzadeh, "A rigorous treatment of vertical dipole impedance located above lossy DPS, MNG, ENG, and DNG half-space," Progress In Electromagnetics Research, Vol. 116, 107-121, 2011.

17. Mahmood, A., A. Illahi, A. A. Syed, and Q. A. Naqvi, "Scattering of an arbitrarily oriented electric dipole field from an infinitely long dB circular cylinder," Progress In Electromagnetics Research M, Vol. 24, 15-27, 2012.

18. Ghaffar, A., N. Mehmood, M. Shoaib, M. Y. Naz, A. Illahi, and Q. A. Naqvi, "Scattering of a radially oriented hertz dipole field by a perfect electromagnetic conductor (PEMC) sphere," Progress In Electromagnetics Research B, Vol. 42, 163-180, 2012.

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

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

21. Priestley, H. A., Introduction to Integration, Oxford University Press, Oxford, 1997.

22. 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

23. Gustavsen, B. and A. Semlyen, "Rational approximation of frequency domain responses by vector fitting," IEEE Trans. Power Delivery, Vol. 14, No. 3, 1052-1061, 1999.
doi:10.1109/61.772353