Scattering Analysis of Antenna by Using Ludwig Based Hybrid Method

Abstract

Solving an electromagnetic problem can be handled in two phases. These are modelling the setup and carrying out the numeric evaluations. Throughout this study, the structure is modelled by Bézier surfaces and the antenna used is meshed with triangular patches. For the calculation part, the method of moments and physical optics (MoM-PO) hybrid method is implemented. While the calculations related with antenna are actualized by using MoM equations, the ones related with structure are obtained by using PO equations. Modified Ludwig’s Algorithm is applied to calculate the current integral for the PO-region. This gives the ability to obtain successful results when the antenna is both close and far from the structure. Overall the stated modelling and calculation technique gives accurate results and saves time and memory in comparison with MoM. 

Keywords

• B-spline surfaces,Ludwig’s Algorithm,Method of moments,Physical optics,Scattering problems,Ludwig’s Algorithm

References

1. [1] Djordjevic, M. and Notaros, B.M., “Higher order hybrid method of moments-physical optics modelling technique for radiation and scattering from large perfectly conducting surfaces,” IEEE Trans. on Antennas and Propag., 53(2): 800-813, (2005).
2. [2] Hodges, R. E. and Rahmat-Samii, Y., “An iterative current-based hybrid method for complex structures,” IEEE Trans. Antennas Propagat., 45: 265–276, (1997).
3. [3] Jakobus, U. and Landstorfer, F. M., “Improved PO-MM hybrid formulation for scattering from three-dimensional perfectly conducting bodies of arbitrary shape,” IEEE Trans. Antennas Propagat., 43(2): 162–169, (1995).
4. [4] Gordon, W. B., “Far-field approximation to the Kirchoff-Helmholtz representations of scattered field,” IEEE Trans. Antennas Propagat., 23: 864–876, (1975).
5. [5] Ludwig, A., “Computation of radiation patterns involving numerical double integration,” IEEE Trans. Antennas Propag., 16(6): 767–769, (1968).
6. [6] Filon, L. N. G., “On a quadrature formula for trigonometric integrals” Proc. Royal Soc. Edinburgh, 49: 38–47, (1928).
7. [7] Levin, D., “Procedures for computing one and two dimensional integrals of functions with rapid irregular oscillations,” Math. Comput,. 38(158): 531–538, (1982).
8. [8] Iserles, A. and Nørsett, S.P., “Quadrature methods for multivariate highly oscillatory integrals using derivatives,” Math. Comp., 75: 1233-1258, (2006).

9. [9] Wu, Y. M., Jiang, L. J., Sha, W. E. I. and Chew, W. C., “The Numerical Steepest Descent Path Method for Calculating Physical Optics Integrals on Smooth Conducting Quadratic Surfaces,” IEEE Trans. Antennas Propag., 61(8): 1483–4193, (2013).
10. [10] Zhang, J., Yu, W. M., Zhou, X. Y. and Cui, T. J., “Efficient Evaluation of the Physical-Optics Integrals for Conducting Surfaces Using the Uniform Stationary Phase Method,” IEEE Transactions On Antennas and Propagation, 60: 2398–2408, (2012).
11. [11] Perez, J. and Cátedra, M. F., “Application of physical optics to the RCS computation of bodies modeled with NURBS surfaces,” IEEE Trans. Antennas Propagat., 42: 1404–1411, (1994).
12. [12] Conde, O. M., Pérez, J., and Catedra, M. F., “Stationary phase method application for the analysis of radiation of complex 3-D conducting structures,” IEEE Trans. Antennas Propag., 49(5): 724–731, (2001).
13. [13] Chen, M., Zhang, Y., Zhao, X.W. and Liang, C. H., “Analysis of antenna around NURBS surface with hybrid MoM-PO technique,” IEEE Trans. Antennas Propag., 55(2): 407–413, (2007).
14. [14] Wang, M., Chen, M. and Liang, C., “Ludwig algorithm’s improvement and its application on NURBS-PO method,” IEEE Inter. Symp. On Microwave, Antenna, Propag. and EMC Techn.for Wireless Comm., 258-260, (2005).
15. [15] Xiang, F. and Donglin, S., “Polynomial representation of NURBS and its application to high frequency scattering prediction,” Chinese Journal of Aero., 23: 235-239, (2010).
16. [16] Wang, M., Wang, N. and Liang, C.H., “Problem of singularity in Ludwig’s algorithm,” Microwave and Optical Tech. Letters, 49: 400–403, (2007).
17. [17] Yardım, F.E., Akçam, N. and Bayraktar, M., “Shielding effect analysis of various configurations of the square patch elements,” Gazi University Journal of Science, 30(2): 123–132, (2017).