volume | PIER Journals

Abstract

The traditional magnetic field integral equation has been generalized to the study of antenna radiation and coupling problems with the feeding lines included. A rigorous proof of the uniqueness of the new magnetic field integral equation has been presented. Some numerical examples have been expounded to demonstrate the validity of the new magnetic field integral equation formulation.

1. Harrington, R. F., Field Computation by Moment Methods, IEEE Press, 1993.

2. Mittra, R., Computer Techniques for Electromagnetics, Pergamon Press, 1973.

3. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, Oxford University Press, 1998.

4. Umashankar, K. and A. Taflove, Computational Electromagnetics, Artech House, 1993.

5. Morita, N., N. Kumagai, and J. R. Mautz, Integral Equation Methods for Electromagnetics, Artech House, 1990.

6. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, 1990.

7. Chew, W. C., Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, 2001.

8. Jones, D. S., Methods in Electromagnetic Wave Propagation, Oxford University Press, 1979.

9. Albertsen, N. C., J. E. Hansen, and N. E. Jensen, "Computation of radiation from wire antennas on conducting bodies," IEEE Trans. Antennas and Propagat., Vol. 22, No. 2, 200-206, 1974.
doi:10.1109/TAP.1974.1140783 Google Scholar

10. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas and Propagat., Vol. 30, No. 3, 409-417, 1982.
doi:10.1109/TAP.1982.1142818 Google Scholar

11. Wilton, D. R., S. M. Rao, A. W. Glisson, and D. H. Schaubert, "Potential integrals for uniform and linear source distributions on polygonal polyhedral domains," IEEE Trans. Antennas and Propagat., Vol. 32, No. 3, 276-281, 1984.
doi:10.1109/TAP.1984.1143304 Google Scholar

12. Graglia, R. D., "On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle," IEEE Trans. Antennas and Propagat., Vol. 41, No. 10, 1448-1455, 1993.
doi:10.1109/8.247786 Google Scholar

13. Bluck, M. J., M. D. Pocock, and S. P. Walker, "An accurate method for the calculation of singular integrals arising in timedomain integral equation analysis of electromagnetic scattering," IEEE Trans. Antennas and Propagat., Vol. 45, No. 12, 1793-1798, 1997.
doi:10.1109/8.650197 Google Scholar

14. Järvenpää, S., M. Taskinen, and P. Ylä-Oijala, "Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedral," Int. J. Numer. Meth. Engng., Vol. 58, 1149-1165, 2003.
doi:10.1002/nme.810 Google Scholar

15. Ubeda, E. and J. M. Rius, "Novel monopolar MFIE MoMdiscretization for the scattering analysis of small objects," IEEE Trans. Antennas and Propagat., Vol. 54, No. 1, 50-57, 2006.
doi:10.1109/TAP.2005.861529 Google Scholar

16. Jung, B. H., Y. S. Chung, and T. K. Sarkar, "Timedomain EFIE, MFIE and CFIE formulations using Laguerre polynomials as temporal basis functions for the analysis of transient scattering from arbitrarily shaped conducting structures," Progress Electromagn. Res., Vol. 39, 1-45, 2003.
doi:10.2528/PIER02083001 Google Scholar

17. Zhang, Y., T. J. Cui, W. C. Chew, and J.-S. Zhao, "Magnetic field integral equation at very low frequencies," IEEE Trans. Antennas and Propagat., Vol. 51, No. 8, 1864-1871, 2003.
doi:10.1109/TAP.2003.814753 Google Scholar

18. Miano, G. and F. Villone, "A surface integral formulation of Maxwell equations for topologically complex conducting domains," IEEE Trans. Antennas and Propagat., Vol. 53, No. 12, 4001-4013, 2005.
doi:10.1109/TAP.2005.859898 Google Scholar

19. Peterson, A. F. and M. M. Bibby, "Higher-order numerical solutions of the MFIE for the linear dipole," IEEE Trans. Antennas and Propagat., Vol. 52, No. 10, 2684-2691, 2004.
doi:10.1109/TAP.2004.834407 Google Scholar

20. Carr, M., E. Topsakal, and J. L. Volakis, "A procedure for modeling material junctions in 3-D surface integral equation approaches," IEEE Trans. Antennas and Propagat., Vol. 52, No. 5, 1374-1379, 2004.
doi:10.1109/TAP.2004.827247 Google Scholar

21. Mautz, J. R. and R. F. Harrington, "H-field, E-field, and combined-field solutions for conducting bodies of revolution," Arch. Elektron., Vol. 32, 19-164, 1978. Google Scholar

22. Yaghjian, A. D., "Augmented electric-and-magnetic integral equations," Radio Sci., Vol. 16, No. 12, 987-1001, 1981. Google Scholar

23. Peterson, A. F., "The interior resonance problem associated with surface integral equations of electromagnetics: numerical consequences and a survey of remedies," Electromagnetics, Vol. 10, No. 7, 293-312, 1990. Google Scholar

24. Correia, L. M., "A comparison of integral equations with unique solution in the resonance region for scattering by conduction bodies," IEEE Trans. Antennas and Propagat., Vol. 41, No. 1, 52-58, 1993.
doi:10.1109/8.210115 Google Scholar

25. Klein, C. and R. Mittra, "Stability of matrix equations arising in electromagnetics," IEEE Trans. Antennas and Propagat., Vol. 21, No. 6, 902-905, 1973.
doi:10.1109/TAP.1973.1140627 Google Scholar

26. Albert, G. E. and J. L. Synge, "The general problem of antenna radiation and the fundamental integral equation with application to an antenna of revolution-Part 1," Quart. Appl. Math., Vol. 6, No. 4, 117-131, 1948. Google Scholar

27. Waterman, P. C., "Matrix formulation of electromagnetic scattering," Proc. IEEE, Vol. 53, No. 8, 806-812, 1965.

28. Waterman, P. C., "Symmetry, unitarity, and geometry in electromagnetic scattering," Phys. Rev., Vol. D3, 825-839, 1971. Google Scholar

29. AL-Badwaihy, K. A. and J. L. Yen, "Extended boundary condition integral equations for perfectly conducting and dielectric bodies: formulation and uniqueness," IEEE Trans. Antennas and Propagat., Vol. 23, No. 4, 546-551, 1975.
doi:10.1109/TAP.1975.1141100 Google Scholar

30. Morita, N., "Another method of extending the boundary condition for the problem of scattering by dielectric cylinders," IEEE Trans. Antennas and Propagat., Vol. 27, No. 1, 97-99, 1979.
doi:10.1109/TAP.1979.1142024 Google Scholar

31. Colton, D. and R. Kress, Integral Equation Methods in Scattering Theory, John Wiley, 1983.

32. Colton, D. and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer-Verlag, 1998.

33. Geyi, W. and W. Hongshi, "Solution of the resonant frequencies of a cavity resonator by boundary element method," IEE Proc., Vol. 135, No. 6, 361-365, 1988.

34. Wu, T. T. and R. W. P. King, "Transient response of linear antennas driven from a coaxial line," IEEE Trans. Antenna and Propagat., Vol. 11, No. 1, 17-23, 1963.
doi:10.1109/TAP.1963.1137980 Google Scholar

35. Maloney, J. G., G. S. Smith, and W. R. Scott, Jr., "Accurate computation of the radiation from simple antennas using the finite-difference time-domain method," IEEE Trans. Antennas and Propagat., Vol. AP-38, No. 7, 1059-1068, 1990.
doi:10.1109/8.55618 Google Scholar

36. Geyi, W., "A time-domain theory of waveguide," Progress Electromagn. Res., Vol. 59, 267-297, 2006.
doi:10.2528/PIER05102102 Google Scholar

37. Marcuvitz, N., Waveguide Handbook, Peter Peregrinus Ltd, 1993.

38. MacPhie, R. H. and A. I. Zaghloul, "Radiation from a rectangular waveguide with infinite flange-exact solution by the correlation matrix method," IEEE Trans. Antenna and Propagat., Vol. 28, 497-503, 1980.
doi:10.1109/TAP.1980.1142376 Google Scholar

39. Jan, I. C., R. F. Harrington, and J. R. Mautz, "Aperture admittance of a rectangular aperture and its use," IEEE Trans. Antennas and Propagat., Vol. 39, 423-425, 1991.
doi:10.1109/8.76346 Google Scholar

40. Mailloux, R. J., "Radiation and near-field coupling between two collinear open-ended waveguides," IEEE Trans. Antennas and Propagat., Vol. 17, 49-55, 1969.
doi:10.1109/TAP.1969.1139354 Google Scholar

Dr. Geyi Wen