A new method is presented for analysis of transient electromagnetic fields in regular structures with abrupt discontinuities. The method is based on mode expansion of the fields in the Time Domain. The modes propagate independently in the regular parts of the structure and are coupled at the discontinuity. The main idea consists in solving 1D FDTD equations for each independent mode channel in the regular waveguides and using mode-matching at the junction cross-section in order to relate the mode amplitudes in all the channels at the same time instant via imposing boundary conditions. As examples the problems of pulse signal diffraction at a step discontinuity in a parallel-plate waveguide, diffraction at a junction of circular and coaxial waveguides, and pulse radiation of a bi-conical antenna are considered. The latter problem is treated as a junction of two conical lines (one of which is the free space) that are regular in spherical coordinates.
Maxim N. Legenkiy,
"Method of Mode Matching in Time Domain," Progress In Electromagnetics Research B,
Vol. 22, 257-283, 2010. doi:10.2528/PIERB10043003
1. Rao, S. M., Time Domain Electromagnetics, Department of Electrical Engineering, Aubum University, Aubum, AL, 1999.
2. Taflove, A. and S. Hagness, Computational Eletrodynamics: The Finite-Difference Time-Domain Method, 2 Ed., Artech House, 2000.
3. Pozar, D. M., Microwave Engineering, 2 Ed., University of Massachusetts at Amherst, 1998.
4. Marcuvitz, N., Waveguide Handbook, Peter Peregrinus Ltd, 1993.
5. Mittra, R. and S. Lee, Analytical Techniques in the Theory of Guided Waves, University of Illinois, New York, 1971.
6. Kisunko, G. V., Electrodynamics of Hollow Systems, VKAS, Leningrad, USSR, 1949 (in Russian).
7. Borisov, V. V., "Electromagnetic field of a current with arbitrary time dependence distributed on the surface of a sphere," Radiophysics and Quantum Electronics, Vol. 19, No. 12, 1291-1298, 1976. doi:10.1007/BF01034030
8. Borisov, V. V., "Nonperiodic electromagnetic fields in a sectoral horn," Radiotekhnika and Elektronika, Vol. 28, 450-460, Mar. 1983 (in Russian).
9. Borisov, V. V., "Excitation of nonperiodic fields in a conical horn," Radiotekhnika and Elektronika, Vol. 30, 443-447, Mar. 1985 (in Russian).
10. Borisov, V. V., Transients in Waveguides, Publishing House of Leningrad State University, Leningrad, 1991 (in Russian).
11. Tretyakov, O. A., "Mode basis method," Radiotekhnika and Elektronika, Vol. 31, No. 6, 1071-1082, 1986 (in Russian).
12. Tretyakov, O. A., "Evolutionary equations for the theory of waveguides," IEEE Antennas and Propagation Society, AP-S International Symposium (Digest), Vol. 3, 1973-1976, 1994.
13. Tretyakov, O. A., "Evolutionary waveguide equations," Radiotekhnika and Elektronika, Vol. 34, No. 5, 917-926, 1989.
14. Tretyakov, O. A., "Essentials of nonstationary and nonlinear electromagnetic field theory," Analytical and Numerical Methods in Electromagnetic Wave Theory, 572, Science House Co, Ltd, Tokyo, Hashimoto M., Idemen M., Tretyakov O. A.,1993.
15. Nikitskiy, S. B., O. A. Tretyakov, and K. M. Yemelyanov, "Electromagnetic step signal propagation in lossy waveguide," Telecommunications and Radio Engineering, Vol. 51, No. 2, 149-159, 1997.
16. Kristensson, G., "Transient electromagnetic wave propagation in waveguides," Journal of Electromagnetic Waves and Applications, Vol. 9, 645-671, 1995. doi:10.1163/156939395X00866
17. Geyi, W., "A time-domain theory of waveguide," Progress In Electromagnetics Research, Vol. 59, 267-297, 2006.
18. Tretyakov, O. A. and S. V. Chumachenko, "Oscillations in a resonator flled with a time-varying dielectric medium," Telecommunications and Radio Engineering, Vol. 52, No. 6, 36-45, 1998.
19. Butrym, A. Y., Y. Zheng, and O. A. Tretyakov, "Transient diffraction on a permittivity step in a waveguide: Closed-form solution in time domain," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 7, 861-876, 2004. doi:10.1163/156939304323105709
20. Butrym, A. Y. and M. N. Legenkiy, "Charge transport by a pulse E-wave in a waveguide with conductive medium," Progress In Electromagnetics Research B, Vol. 15, 325-346, 2009. doi:10.2528/PIERB09050703
21. Butrym, A. Y. and B. A. Kochetov, "Mode basis method for spherical TEM-transmission lines and antennas," Proc. International Conference on Antenna Theory and Techniques (ICATT-07), 243-245, Sevastopol, 2007.
22. Aksoy, S. and O. A. Tretyakov, "Study of a time variant cavity system," Journal of Electromagnetic Waves and Applications , Vol. 16, No. 11, 1535-1553, 2002. doi:10.1163/156939302X00985
23. Tretyakov, O. A. and F. Erden, "Temporal cavity oscillations caused by a wide-band waveform," Progress In Electromagnetics Research B, Vol. 6, 183-204, 2008. doi:10.2528/PIERB08031222
24. Geyi, W., "Time-domain theory of metal cavity resonator," Progress In Electromagnetics Research, Vol. 78, 219-253, 2008. doi:10.2528/PIER07090605
25. Antyufeyeva, M. S., A. Y. Butrym, and O. A. Tretyakov, "Transient electromagnetic fields in cavity with dispersive double negative medium," Progress In Electromagnetics Research M, Vol. 8, 51-65, 2009. doi:10.2528/PIERM09062307
26. Aksoy, S. and O. A. Tretyakov, "Evolution equations for analytical study of digital signals in waveguides," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 12, 263-270, 2004.
27. Butrym, A. Y. and B. A. Kochetov, "Time domain mode basis method for a waveguide with transverse inhomogeneous multiconnected cross-section. 1. The general theory of method," Radio Physics and Radio Astronomy, Vol. 14, No. 2, 162-173, 2009 (in Russian).
28. Butrym, A. Y. and B. A. Kochetov, "Time domain mode basis method for a waveguide with transverse inhomogeneous multiconnected cross-section. 2. Example of numerical implementation of the method," Radio Physics and Radio Astronomy, Vol. 14, No. 3, 266-277, 2009 (in Russian).
29. Dumin, A. N., "Radiation of transient localized waves from an open-ended coaxial waveguide with infinite flange," Telecommunications and Radio Engineering, Vol. 53, No. 6, 30-34, 1999.
30. Tretyakov, O. A. and A. N. Dumin, "Emission of nonstationary electromagnetic fields by a plane radiator," Telecommunications and Radio Engineering, Vol. 54, No. 1, 2-15, 2000.
31. Shlivinski, A. and E. Heyman, "Time-domain near-field analysis of short-pulse antennas. Part I: Spherical wave (multipole) expansion," IEEE Trans. Antennas Propag., Vol. 47, No. 2, 271-279, Feb., 1999. doi:10.1109/8.761066
32. Tretyakov, O., A. Dumin, O. Dumina, and V. Katrich, "Modal basis method in radiation problems," Proc. Int. Conf. on Math. Methods in Electromagnetic Theory (MMET-2004), 312-314, Dnepropetrovsk, Ukraine 2004.
33. Dumin, O. M., O. O. Dumina, and V. O. Katrich, "Propagation of spherical transient electromagnetic wave through radially inhomogeneous medium," Proc. Int. Conf. on Ultrawideband and Ultrashort Impulse Signals (UWBUSIS-2006), 276-278, Sevastopol,Ukraine, Sep.18-22, 2006.
34. Butrym, A. Y. and B. A. Kochetov, "Mode expansion in time domain for conical lines with angular medium inhomogeneity," Progress In Electromagnetics Research B, Vol. 19, 151-176, 2010. doi:10.2528/PIERB09102606
35. Zheng, Y., B. A. Kochetov, and A. Y. Butrym, "Finite difference scheme in time domain and analytical solution for Klein-Gordon equation," Bulletin of Karazin Kharkiv National University, No. 712, ``Radiophysics and Electronics,'' No. 10, 91-94, 2006 (in Russian).
36. Butrym, A. Y. and M. N. Legenkiy, "Comparison of absorbing boundary conditions for numerical analysis of periodic structures," Proc. of International Conference on Antenna Theory and Techniques, 239-242, Sevastopol, Ukraine, Sep.17-21, 2007.
37. Uher, J., J. Bornemann, and U. Rosenberg, Waveguide Components for Antenna Feed Systems: Theory and CAD, Artech House, Boston, 1993.
38. Kirilenko, A. A., V. I. Tkachenko, L. A. Rud, and D. Y. Kulik, "The mode-matching technique and fast numerical models of arbitrary coordinate waveguide objects," Quasi-optical Control of Intense Microwave Transmission, 41-53, J. L. Hirshfield and M. I. Petelin (eds.), Springer, Netherlands, 2005.
39. Kirilenko, A. A., D. Y. Kulik, and V. I. Tkachenko, "General scheme of the mode-matching technique as a basis for generalized solutions to the internal boundary-value problems," Telecommunications and Radio Engeneering, Vol. 60, No. 12, 159-170, 2003.
40. Legenkiy, M., Y. Zheng, and A. Butrym, "Mode matching in time domain," Proceedings of UWBUSIS, 225-227, Sevastopol, Ukraine, Sep.15-19, 2008.
41. Butrym, A., B. Kochetov, and M. Legenkiy, "Numerical analysis of simple TEM conical-like antennas using mode matching in time domain," Proceedings of EuCAP 2009, 3471-3475, Berlin, 2009.
42. Bornemann, J., "On the acceleration of the coupled-integralequations technique and its application to multistub Eplane discontinuities," Journal of Electromagnetic Waves and Applications, Vol. 13, 539-554, 1999.
43. Amari, S., A. Motamedi, J. Bornemann, and R. Vahldieck, "Global edge-conditioned basis functions from local solutions of Maxwell's equations," IEEE MTT-S International Microwave Symposium Digest, 1373-1376, Denver, USA, 1997.
44. Damaschke, J. M., S. Amari, and J. Bornemann, "Fast and accurate mode-spectrum analysis of waveguide structures using a new set of edge-conditioned basis functions," International Journal of RF and Microwave Computer-aided Engineering, Vol. 8, No. 3, 215-225, 1998. doi:10.1002/(SICI)1099-047X(199805)8:3<215::AID-MMCE5>3.0.CO;2-I
45. Luo, S. and Z. Chen, "An efficient modal FDTD for absorbing boundary conditions and incident wave generator in waveguide structures," Progress In Electromagnetic Research, Vol. 68, 229-246, 2007. doi:10.2528/PIER06090506
46. Sirenko, Y. K., "Exact `absorbing' conditions in outer initial boundary-value problems of electrodynamics of nonsinusoidal waves. Part 3. Compact inhomogeneities in free space," Telecommunications and Radio Engineering, Vol. 57, No. 12, 1-31, 2002.
47. Lo, Y. T. and S. W. Lee, Antenna Handbook. Volume 1 Fundamentals and Mathematical Techniques, Chapman & Hall, New York, 1993.
48. Gustafsson, B., H.-O. Kreiss, and J. Oliger, Time-dependent Problems and Difference Methods, Willey-Interscience, New York, 1995.
49. Samaddar, S. N. and E. L. Mokole, "Biconical antennas with unequal cone angles," IEEE Trans. Antennas Propagat., Vol. 46, 181-193, Feb., 1998. doi:10.1109/8.660962