Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth

Hanan Shehata Shoeib

doi:doi:10.11648/j.ajam.20190704.11

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Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth

Hanan Shehata Shoeib

Published in American Journal of Applied Mathematics (Volume 7, Issue 4)

Received: 14 July 2019 Accepted: 27 August 2019 Published: 9 September 2019

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Abstract

In a recent study, the classical problem of a circular loop antenna carrying a uniform current on the Earth's surface has been revisited, with a scope for deriving Closed-form formulae for the generated magnetic and electric far fields by a vertical magnetic dipole (VMD) located at certain height above the surface of a planar two-layer conducting earth, with a high degree of accuracy. The solution is obtained by reducing the field integrals to combinations of known Sommerfeld integrals (SIs), which is advantageous over the previous numerical and analytical-numerical approaches, and its usage takes negligible computation time. Numerical simulations are performed and illustrated by figures for different values of the frequency to show the accuracy of the obtained field expressions and to investigate the behavior of the above surface ground fields in a wide frequency range. Results can be used to evaluate numerical solutions of more complicated modeling algorithms, for application to mobile communication and will be useful for remote sensing especially when the transmitter is close to the surface.

Published in	American Journal of Applied Mathematics (Volume 7, Issue 4)
DOI	10.11648/j.ajam.20190704.11
Page(s)	90-97
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Far-field, Vertical Magnetic Dipole (VMD) Radiation, Circular Loop Antenna, Planar Layered Conducting Earth, Sommerfeld Integral (SI)

References

[1]	R. K. Moore and W. E. Blair, “Dipole radiation in a conducting half space,” Journal of Research of the National Bureau of Standards Section D: Radio Propagation, vol. 65, no. 6, pp. 547–563, 1961.
[2]	A. Banos, “Dipole Radiation in the Presence of a Conducting Half-Space,” Pergamon Press, Oxford, NY, USA, 1966.
[3]	J. R. Wait, “The electromagnetic fields of a horizontal dipole in the presence of a conducting half-space,” Can. J. Phys., vol. 39, pp. 1017-1028, 1961.
[4]	J. A. Kong, “Electromagnetic Wave theory,” John Wiley & Sons, New York, NY, USA, 1986.
[5]	J. R. Wait, “Electromagnetic waves in stratified media,” Pergamon Press, New York, NY, USA, 1970.
[6]	W. C. Chew, J. A. Kong, “Electromagnetic field of a dipole on a two layer earth”, Geophys., vol. 46, pp. 309-315, 1981.
[7]	S. H. Ward and G. W. Hohmann, “Electromagnetic theory for geophysical applications,” in Electromagnetic Methods in Applied Geophysics, vol. 1, chapter 4, pp. 130–311, Society of Exploration Geophysicists, Tulsa, Okla, USA, 1988.
[8]	R. E. Colline, “Antennas and Radio Wave Propagation,” New York, McGraw–Hill, 1985.
[9]	Y. Long, H. Jiang and Y. Lin “Electromagnetic field due to loop antenna in a borehole,” IEEE Trans. Geosci. Remote Sensing, vol. 34, pp. 33-35, Jan. 1996.
[10]	A. Arutaki and J. Chiba, “Communication in a three-layered conducting media with a vertical magnetic dipole,” IEEE Trans. Antennas Propagat., vol. 28, pp. 551-556, July 1980.
[11]	A. Sommerfeld, “Partial differential equations in physics,” Academic Press. New York and London, 1964.
[12]	W. C. Chew, “A quick way to approximate a Sommerfeld–Wely-Type integral,” IEEE. Trans. Antennas Propagat., vol. 36, no. 11, pp. 1654-1657, Nov. 1988.
[13]	Y. Long, H. Jiang and B. Rembold, “Far-Region Electromagnetic Radiation with a Vertical Magnetic Dipole in Sea,” IEEE Trans. Antennas Propagat., vol. 49, no. 6, pp. 992-996, June 2001.
[14]	P. R. Bannister, “The image theory of electromagnetic fields of a horizontal electric dipole in the presence of conducting half–space,” Radio Sci., vol. 17, no. 5, pp. 1095-1102, Sept.-Oct. 1982.
[15]	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, pp. 57-69, 2017.
[16]	J. A. Stratton, “Electromagnetic Theory,” New York, McGraw-Hill, 1941.
[17]	D. S. Jones, “The Theory of Electromagnetism,” London, U. K.: Pergamon, 1964.
[18]	M. Abramowitz and I. A. Stegun, “Handbook of Mathematical Functions,” New York: Dover, 1972.

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APA Style

Hanan Shehata Shoeib. (2019). Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth. American Journal of Applied Mathematics, 7(4), 90-97. https://doi.org/10.11648/j.ajam.20190704.11

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ACS Style

Hanan Shehata Shoeib. Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth. Am. J. Appl. Math. 2019, 7(4), 90-97. doi: 10.11648/j.ajam.20190704.11

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AMA Style

Hanan Shehata Shoeib. Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth. Am J Appl Math. 2019;7(4):90-97. doi: 10.11648/j.ajam.20190704.11

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@article{10.11648/j.ajam.20190704.11,
  author = {Hanan Shehata Shoeib},
  title = {Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth},
  journal = {American Journal of Applied Mathematics},
  volume = {7},
  number = {4},
  pages = {90-97},
  doi = {10.11648/j.ajam.20190704.11},
  url = {https://doi.org/10.11648/j.ajam.20190704.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20190704.11},
  abstract = {In a recent study, the classical problem of a circular loop antenna carrying a uniform current on the Earth's surface has been revisited, with a scope for deriving Closed-form formulae for the generated magnetic and electric far fields by a vertical magnetic dipole (VMD) located at certain height above the surface of a planar two-layer conducting earth, with a high degree of accuracy. The solution is obtained by reducing the field integrals to combinations of known Sommerfeld integrals (SIs), which is advantageous over the previous numerical and analytical-numerical approaches, and its usage takes negligible computation time. Numerical simulations are performed and illustrated by figures for different values of the frequency to show the accuracy of the obtained field expressions and to investigate the behavior of the above surface ground fields in a wide frequency range. Results can be used to evaluate numerical solutions of more complicated modeling algorithms, for application to mobile communication and will be useful for remote sensing especially when the transmitter is close to the surface.},
 year = {2019}
}

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TY  - JOUR
T1  - Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth
AU  - Hanan Shehata Shoeib
Y1  - 2019/09/09
PY  - 2019
N1  - https://doi.org/10.11648/j.ajam.20190704.11
DO  - 10.11648/j.ajam.20190704.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 90
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PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20190704.11
AB  - In a recent study, the classical problem of a circular loop antenna carrying a uniform current on the Earth's surface has been revisited, with a scope for deriving Closed-form formulae for the generated magnetic and electric far fields by a vertical magnetic dipole (VMD) located at certain height above the surface of a planar two-layer conducting earth, with a high degree of accuracy. The solution is obtained by reducing the field integrals to combinations of known Sommerfeld integrals (SIs), which is advantageous over the previous numerical and analytical-numerical approaches, and its usage takes negligible computation time. Numerical simulations are performed and illustrated by figures for different values of the frequency to show the accuracy of the obtained field expressions and to investigate the behavior of the above surface ground fields in a wide frequency range. Results can be used to evaluate numerical solutions of more complicated modeling algorithms, for application to mobile communication and will be useful for remote sensing especially when the transmitter is close to the surface.
VL  - 7
IS  - 4
ER  -

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Author Information

Hanan Shehata Shoeib

Department of Basic Sciences, College of Education, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia

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APA Style

Hanan Shehata Shoeib. (2019). Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth. American Journal of Applied Mathematics, 7(4), 90-97. https://doi.org/10.11648/j.ajam.20190704.11

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ACS Style

Hanan Shehata Shoeib. Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth. Am. J. Appl. Math. 2019, 7(4), 90-97. doi: 10.11648/j.ajam.20190704.11

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AMA Style

Hanan Shehata Shoeib. Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth. Am J Appl Math. 2019;7(4):90-97. doi: 10.11648/j.ajam.20190704.11

Copy | Download

@article{10.11648/j.ajam.20190704.11,
  author = {Hanan Shehata Shoeib},
  title = {Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth},
  journal = {American Journal of Applied Mathematics},
  volume = {7},
  number = {4},
  pages = {90-97},
  doi = {10.11648/j.ajam.20190704.11},
  url = {https://doi.org/10.11648/j.ajam.20190704.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20190704.11},
  abstract = {In a recent study, the classical problem of a circular loop antenna carrying a uniform current on the Earth's surface has been revisited, with a scope for deriving Closed-form formulae for the generated magnetic and electric far fields by a vertical magnetic dipole (VMD) located at certain height above the surface of a planar two-layer conducting earth, with a high degree of accuracy. The solution is obtained by reducing the field integrals to combinations of known Sommerfeld integrals (SIs), which is advantageous over the previous numerical and analytical-numerical approaches, and its usage takes negligible computation time. Numerical simulations are performed and illustrated by figures for different values of the frequency to show the accuracy of the obtained field expressions and to investigate the behavior of the above surface ground fields in a wide frequency range. Results can be used to evaluate numerical solutions of more complicated modeling algorithms, for application to mobile communication and will be useful for remote sensing especially when the transmitter is close to the surface.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth
AU  - Hanan Shehata Shoeib
Y1  - 2019/09/09
PY  - 2019
N1  - https://doi.org/10.11648/j.ajam.20190704.11
DO  - 10.11648/j.ajam.20190704.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 90
EP  - 97
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20190704.11
AB  - In a recent study, the classical problem of a circular loop antenna carrying a uniform current on the Earth's surface has been revisited, with a scope for deriving Closed-form formulae for the generated magnetic and electric far fields by a vertical magnetic dipole (VMD) located at certain height above the surface of a planar two-layer conducting earth, with a high degree of accuracy. The solution is obtained by reducing the field integrals to combinations of known Sommerfeld integrals (SIs), which is advantageous over the previous numerical and analytical-numerical approaches, and its usage takes negligible computation time. Numerical simulations are performed and illustrated by figures for different values of the frequency to show the accuracy of the obtained field expressions and to investigate the behavior of the above surface ground fields in a wide frequency range. Results can be used to evaluate numerical solutions of more complicated modeling algorithms, for application to mobile communication and will be useful for remote sensing especially when the transmitter is close to the surface.
VL  - 7
IS  - 4
ER  -

Copy | Download