# Angular Effect of Virtual Vertices Inserted to Treat The Boundary Edges on an Infinite Conducting Surface

• Hwang, Ji-Hwan (Dept. of Electronic Information & Communication Engineering, Hongik University) ;
• Kweon, Soon-Koo (Dept. of Electronic Information & Communication Engineering, Hongik University) ;
• Oh, Yisok (Dept. of Electronic Information & Communication Engineering, Hongik University)
• Accepted : 2013.02.27
• Published : 2013.03.31
• 60 7

#### Abstract

This study presents the angular effects of virtual vertices inserted for effective treatment of the boundary edge laid on an infinite conducting surface in a half-space scattering problem. We investigated the angular effects of virtual vertices by first computing the radar cross section (RCS) of a specific scatterer; i.e., a tilted conducting plate in contact with the ground surface, by inserting the virtual vertex in half-space. Here, the electric field integral equation is used to solve this problem with various virtual vertex angles (${\theta}_{\nu}$) and conducting plate inclination angles (${\theta}_r$) ranging from $0^{\circ}$ to $180^{\circ}$. The effects of the angles ${\theta}_{\nu}$ and ${\theta}_r$ on the RCS computation are clearly shown with numerical results with and without the virtual vertices in free- and half-spaces.

#### Keywords

Electric Field Integral Equation (EFIE);Half-Space Scattering;Image Theory;RWG Basis;Virtual Vertex

#### References

1. S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., vol. AP-30, no. 3, pp. 409-418, May 1982.
2. Pasi Yla-Oijala, Matti Taskinen, "Calculation of CFIE impedance matrix elements with RWG and n${\times}$ RWG functions," IEEE Trans. Antennas Propag., vol. 51, no. 8, pp. 1837-1846, Aug. 2003. https://doi.org/10.1109/TAP.2003.814745
3. Y. Q. Hu, J. J. Ding, D. Z. Ding, and R. S. Chen, "Analysis of electromagnetic scattering from dielectric objects above a lossy half-space by multiresolution preconditioned multilevel fast multipole algorithm," IET Microw. Antennas Propag., vol. 4, Iss. 2, pp. 232- 239, 2010. https://doi.org/10.1049/iet-map.2008.0265
4. J. -H. Hwang, Y. Oh, "Investigation of the effect of boundary edges placed on an infinite conducting surface and effective treatment using virtual vertices," IEEE Antennas and Wireless Propagation Letters, vol. 11, pp. 913-916, Aug. 2012. https://doi.org/10.1109/LAWP.2012.2212172
5. Y. Oh, Y. M. Jang, and K. Sarabandi, "Full-wave analysis of microwave scattering from short vegetation: an investigation on the effect of multiple scattering," IEEE Trans. Geosci. Remote Sensing, vol. 40, no. 11, pp. 2522-2526, Nov. 2002. https://doi.org/10.1109/TGRS.2002.805085
6. I. V. Lindell, E. Alanen, "Exact image theory for the sommerfield half-space problem, part I: vertical magnetic dipole," IEEE Trans. Antennas Propag., vol. AP-32, no. 2, pp. 126-133, Feb. 1984.
7. I. V. Lindell, E. Alanen, "Exact image theory for the sommerfield half-space problem, part II: Vertical electric dipole," IEEE Trans. Antennas Propag., vol. AP-32, no. 8, pp. 841-847, Aug. 1984.
8. W. C. Gibson, The Method of Moments in Electromagnetics, Chapman & Hall/CRC, Boca Raton, FL, pp. 161-270, 2008.
9. D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-bundak, and C. M. Butler, "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domain," IEEE Trans. Antennas Propag., vol. AP-32, no. 3, pp. 276- 281, May 1984.
10. C. T. Tai, Dyadic Green Functions in Electromagnetic Theory, IEEE Press, NJ, 2nd Edition, pp. 92- 95, 1994.
11. G. T. Ruck, D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook, New York: Plenum, pp. 141-159, 1970.

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