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Temporal Cavity Oscillations Caused by a Wide-Band Waveform

By Oleg Tretyakov and Fatih Erden
Progress In Electromagnetics Research B, Vol. 6, 183-204, 2008


Excitation of the electromagnetic fields by a wide-band current surge, which has a beginning in time, is studied in a cavity bounded by a closed perfectly conducting surface. The cavity is filled with Debye or Lorentz dispersive medium. The fields are presented as the modal expansion in terms of the solenoidal and irrotational cavity modes with the time-dependent modal amplitudes, which should be found. Completeness of this form of solution has been proved earlier. The systems of ordinary differential equations with time derivative for the modal amplitudes are derived and solved explicitly under the initial conditions and in compliance with the causality principle. The solutions are obtained in the form of simple convolution (with respect to time variable) integrals. Numerical examples are exhibited as well.


Oleg Tretyakov and Fatih Erden, "Temporal Cavity Oscillations Caused by a Wide-Band Waveform," Progress In Electromagnetics Research B, Vol. 6, 183-204, 2008.


    1. Camp, M. and H. Garbe, "Susceptibility of personal computer systems to electromagnetic pulses with double exponential character," Advances in Radio Science, Vol. 2, 63-69, 2004.

    2. Savic, M. S., "Estimation of the surge arrester outage rate caused by lightning overvoltages," IEEE Trans. on Power Delivery, Vol. 20, No. 1, 116-122, 2005.

    3. Zhen, J., S. C. Hagness, J. H. Booske, S. Mathur, and M. L. Meltz, "FDTD analysis of a Gigahertz TEM cell for ultra-wideband pulse exposure studies of biological specimens," IEEE Trans. on Biomedical Eng., Vol. 53, No. 5, 780-789, 2006.

    4. Camp, M. and H. Garbe, "Parameter estimation of double exponential pulses (EMP, UWB) with least squares and nelder mead algorithm," IEEE Trans. on EM Compatibility, Vol. 46, No. 4, 675-678, 2004.

    5. Tretyakov, O. A., Analytical and Numerical Methods in Electromagnetic Wave Theory, M. Hashimoto, M. Idemen, O. A. Tretyakov (eds.), Chapter 3, Science House Co., Ltd., 1993.

    6. Tretyakov, O. A., Evolutionary equations for the theory of waveguides, Proc. IEEE AP-S Int. Symp. Dig., 2465-2471, Seattle, WA, 1994.

    7. 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.

    8. 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.

    9. Aksoy, S. and O. A. Tretyakov, "The evolution equations in study of the cavity oscillations excited by a digital signal," IEEE Trans. Antennas Propag., Vol. 52, No. 1, 263-270, 2004.

    10. Aksoy, S., M. Antyufeyeva, E. Basaran, A. A. Ergin, and O. A. Tretyakov, "Time-domain cavity oscillations supported by a temporally dispersive dielectric," IEEE Trans. Microw. Theory Tech., Vol. 53, No. 8, 2465-2471, 2005.

    11. Weyl, H., "The method of orthogonal projection in potential theory," Duke Math. J., Vol. 7, 411-444, 1940.

    12. http://math.fullerton.edu/mathews/n2003/matrixexponential/MatrixExponentialBib/Links/MatrixExponentialBib lnk 2.html.