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Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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Comparison between Frequency Domain and Time Domain Methods for Parameter Reconstruction on Nonuniform Dispersive Transmission Lines

By J. Lundstedt and M. Norgren

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Abstract:
In this paper, we present two methods for the inverse problem ofreconstructing a parameter profile ofa nonuniform and dispersive transmission line - one frequency domain and one time domain method. Both methods are based on the wave splitting technique, but apart from that the methods are mathematically very different. The time domain analysis leads to hyperbolic partial differential equations and an inverse method based on solving implicit equations. The frequency domain analysis leads instead to Riccati differential equations and an inverse method based on optimization. The two methods are compared numerically by simulating a reconstruction ofa soil moisture profile along a flat band cable. A heuristic model ofthe dispersion characteristics ofa flat band cable in moist sand is derived. We also simulate the effect parasitic capacitances at the cable ends has on the reconstructions. The comparison shows that neither method outperforms the other. The time domain method is numerically much faster whereas the frequency domain method is much faster to implement. An important conclusion is also that it is crucial to model the connector parasitic capacitances correctly - especially ifthere are impedance mismatches at the connectors.

Citation: (See works that cites this article)
J. Lundstedt and M. Norgren, "Comparison Between Frequency Domain and Time Domain Methods for Parameter Reconstruction on Nonuniform Dispersive Transmission Lines," Progress In Electromagnetics Research, Vol. 43, 1-37, 2003.
doi:10.2528/PIER03020301
http://www.jpier.org/PIER/pier.php?paper=0302031

References:
1. Lundstedt, J. and S. Ström, "Simultaneous reconstruction oft wo parameters from the transient response of a nonuniform LCRG transmission line," J. Electro. Waves and Applic., Vol. 10, 19-50, 1996.

2. Lundstedt, J. and S. He, "A time domain optimization technique for the simultaneous reconstruction of the characteristic impedance, resistance and conductance ofa transmission line," J. Electro. Waves and Applic., Vol. 10, 581-601, 1996.

3. Norgren, M. and S. He, "An optimization approach to the frequency-domain inverse problem for a nonuniform LCRG transmission line," IEEE Transactions on Microwave Theory and Techniques, Vol. 44, 1503-1507, 1996.
doi:10.1109/22.536038

4. Norgren, M. and S. He, "Optimal designs for nonuniform LCRG transmission lines," J. Electro. Waves and Applic., Vol. 10, 1113-1127, 1996.

5. Kristensson, G., S. Rikte, and A. Sihvola, "Mixing formulas in the time domain," J. Opt. Soc. Am. A, Vol. 15, 1411-1422, 1998.

6. Scaife, B. K. P., Principles of Dielectrics, Clarendon Press, Oxford, 1989.

7. Hellberg, R. and A. Karlsson, "Design o freflectionless media for transient electromagnetic waves," Inverse Problems, Vol. 11, 147-164, 1995.
doi:10.1088/0266-5611/11/1/008

8. Kristensson, G. and R. J. Krueger, "Direct and inverse scattering in the time domain for a dissipative wave equation. Part 4: Use ofphase velocity mismatches to simplify inversions," Inverse Problems, Vol. 5, 375-388, 1989.
doi:10.1088/0266-5611/5/3/010

9. Fuks, P., A. Karlsson, and G. Larson, "Direct and inverse scattering from dispersive media," Inverse Problems, Vol. 10, 555-571, 1994.
doi:10.1088/0266-5611/10/3/005

10. Polak, E., Computational Methods in Optimization, Academic Press, 77 New York and London, 1971.


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