A simple, closed-form expression for the time-domain reflection coefficient for a pulsed TE10-mode wave incident on a dielectric material discontinuity in a rectangular waveguide is presented. This formula may be used to represent the transient field reflected or transmitted by a dielectric-filled waveguide section, which is useful in material characterization routines. An exponential function approximation to the reflection coefficient is presented, and the formula is validated both numerically and experimentally.
2. Klapka, J. L., "Influence of wall losses on energy flow center velocity of pulses in waveguides," IEEE Trans. Microwave Theory Tech., Vol. 18, No. 10, 689-696, October 1970.
3. Giakos, G. C. and T. K. Ishii, "Rapid pulsed microwave propagation," IEEE Microwave and Guided Wave Lett., Vol. 1, No. 12, 374-375, December 1991.
4. Kristensson, G., "Transient electromagnetic wave propagation in waveguides," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 5-6, 645-671, 1995.
5. Kralj, D., L. Mei, T. T. Hsu, and L. Carin, "Short-pulse propagation in a hollow waveguide: Analysis, optoelectronic measurement, and signal processing," IEEE Trans. Microwave Theory Tech., Vol. 43, No. 9, 2144-2150, September 1995.
6. Stenius, P. and B. York, "On the propagation of transients in waveguides," IEEE Ant. Propagat. Mag., Vol. 37, No. 2, 39-44, April 1995.
7. Dvorak, S. L., "Exact, closed-form expressions for transient fields in homogeneously filled waveguides," IEEE Trans. Microwave Theory Tech., Vol. 42, No. 11, 2164-2170, November 2004.
8. Omar, A. S. and A. H. Kamel, "Frequency- and time-domain expressions for transfer functions and impulse responses related to the waveguide propagation," IEE Proc. Antennas Propagat., Vol. 151, No. 1, 21-25, February 2004.
9. Bernekorn, P., A. Karlsson, and G. Kristensson, "Propagation of transient electromagnetic waves in inhomogeneous and dispersive waveguides," Journal of Electromagnetic Waves and Applications, Vol. 10, No. 9, 1263-1286, 1996.
10. Thirios, E. C., D. I. Kaklamani, and N. K. Uzunoglu, "Pulse compression using a periodically loaded dispersive waveguide," Progress In Electromagnetics Research, PIER 48, 301-333, 2004.
11. Norgren, M. and S. He, "Reconstruction of the constitutive parameters for an Ω material in a rectangular waveguide," IEEE Trans. Microwave Theory Tech., Vol. 43, No. 6, 1315-1321, June 1995.
12. Gupta, S., A. Bhattacharya, K. S. Ranga Rao, and A. Chakrabarty, "A simple method for measuring the dielectric constant of solids," IEEE Trans. Instrument. and Meas., Vol. 49, No. 1, 66-70, February 2000.
13. Wang, Y. and M. N. Asfar, "Measurement of complex permittivity of liquids using waveguide techniques," Progress In Electromagnetics Research, PIER 42, 131-142, 2003.
14. Challa, R. K., D. Kajfez, J. R. Gladden, and A. Z. Elsherbeni, "Permittivity measurement with a non-standard waveguide by using TRL calibration and fractional linear data fitting," Progress In Electromagnetics Research B, Vol. 2, 1-13, 2008.
15. Hasar, U. C., "Thickness-independent automated constitutive parameters extraction of thin solid and liquid materials from waveguide measurements," Progress In Electromagnetics Research, PIER 92, 17-32, 2009.
16. Moradi, G. and A. Abdipour, "Measuring the permittivity of dielectric materials using STDR approach," Progress In Electromagnetics Research, PIER 77, 357-365, 2007.
17. 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.
18. Butrym, A. Y. and M. N. Legenkiy, "Charge transport by a pulse E-wave in a waveguide with conductive medium," Progress In Electromagnetic Research B, Vol. 15, 325-346, 2009.
19. Emig, T., "Propagation of an electromagnetic pulse through a waveguide with a barrier: A time domain solution within classical electrodynamics," Phys. Rev. E, Vol. 54, No. 5, 5780-5787, November 1996.
20. Ramo, S., J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communications Electronics, 3rd edition, Wiley, New York, 1994.
21. Campbell, G. A. and R. M. Foster, Fourier Integrals for Practical Applications, 2nd edition, D. Van Nostrand Co., New York, 1951.
22. Abramowitz , M. and I. S. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.
23. Zhang, S. J. and J. Jin, Computation of Special Functions, John Wiley & Sons, New York, 1996.
24. Rothwell, E. J., "Exponential approximations of the Bessel functions I0(x), I1(x), J0(x), J1(x), Y0(x) and H0(x), with application to electromagnetic scattering, radiation, and diffraction," IEEE Antennas Prop. Mag., Vol. 51, No. 3, 138-147, 2009.