volume | PIER Journals

Abstract

This paper presents an efficient approach for analyzing the longtime response of high-speed dispersive and lossy interconnects terminated with nonlinear loads. In this approach, a fast real-time convolution algorithm with computational cost st O(N log²N) is suggested to tackle the long-time analysis of the high-speed dispersive and lossy interconnects, which are modeled by S-parameters. In addition, the acquirement of the S-parameters is recommended to adopt wideband closed-form formulas. The time response of a microstrip line with a nonlinear load is shown as a practical example. The dominant parameters affecting the response of this microstrip line is observed and discussed in detail. The approach demonstrates its efficiency and accuracy in the analysis.

1. Hall, S. H., G. W. Hall, and J. A. McCall, High-speed Digital System Design — A Handbook of Interconnect Theory and Design Practices, Wiley, New York, 2000.

2. Young, B., Digital Signal Integrity — Modeling and Simulation with Interconnects and Packages, Prentice Hall, London, 2001.

3. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media," IEEE Trans. Antennas Propag., Vol. 14, No. 5, 302-307, 1966.

4. Kunz, K. S. and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics, CRC Press, Boca Raton, FL, 1993.

5. Mardare, D. and J. LoVetri, "The finite-difference time-domain solution of lossy MTL networks with nonlinear junctions," IEEE Trans. Electromagn. Compat., Vol. 37, No. 5, 252-259, 1995.
doi:10.1109/15.385890

6. Taflove, A., Computational Electrodynamics: The Finite Difference Time Domain Method, Artech House, Norwood, MA, 1995.

7. Orlandi, A. and C. R. Paul, "FDTD analysis of lossy, multiconductor transmission lines terminated in arbitrary loads," IEEE Trans. Electromagn. Compat., Vol. 38, No. 3, 388-399, 1996.
doi:10.1109/15.536069

8. Djordjevic, A. R., T. K. Sarkar, and R. F. Harrington, "Analysis of lossy transmission lines with arbitrary nonlinear terminal networks," IEEE Trans. Microwave Theory Tech., Vol. 34, No. 6, 660-666, 1986.
doi:10.1109/TMTT.1986.1133414

9. Schutt-Aine, J. E. and R. Mittra, "Scattering parameter transient analysis of transmission lines loaded with nonlinear terminations," IEEE Trans. Microwave Theory Tech., Vol. 36, No. 3, 529-539, 1988.
doi:10.1109/22.3545

10. Winklestein, D., M. B. Steer, and R. Pomerieau, "Simulation of arbitrary transmission line networks with nonlinear terminations," IEEE Trans. Circuit Syst., Vol. 38, No. 4, 418-422, 1991.
doi:10.1109/31.75398

11. Komuro, T., "Time-domain analysis of lossy transmission lines with arbitrary terminal networks," IEEE Trans. Circuit Syst., Vol. 38, No. 10, 1160-1164, 1991.
doi:10.1109/31.97535

12. Chang, F. Y., "Waveform relaxation analysis of nonuniform lossy transmission lines characterized with frequency-dependent parameters," IEEE Trans. Circuit Syst., Vol. 38, No. 10, 1484-1500, 1991.
doi:10.1109/31.108502

13. Gu, Q., D. M. Sheen, and S. M. Ali, "Analysis of transients in frequency-dependent interconnections and planar circuits with nonlinear loads," IEEE Proc.-H, Vol. 139, No. 2, 38-44, 1992.

14. Mao, J. F. and Z. F. Li, "Analysis of the time response of nonuniform multiconductor transmission lines with a method of equivalent cascaded network chain ," IEEE Trans. Microwave Theory Tech., Vol. 40, No. 5, 948-954, 1992.
doi:10.1109/22.137402

15. Maio, I., S. Pignari, and F. Canavero, "Influence of the line characterization on transient analysis of nonlinearly loaded lossy transmission lines," IEEE Trans. Circuit Syst. I, Vol. 41, No. 3, 197-209, 1994.
doi:10.1109/81.273919

16. Huang, C. C., "Analysis of multiconductor transmission lines with nonlinear terminations in frequency domain," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 8, 1069-1083, 2005.
doi:10.1163/156939305775526142

17. Antonini, G., "A dyadic Green's function based method for the transient analysis of lossy and dispersive multiconductor transmission lines ," IEEE Trans. Microwave Theory Tech., Vol. 56, No. 4, 880-895, 2008.
doi:10.1109/TMTT.2008.919651

18. Chiang, I. T. and W. C. Chew, "Fast real-time convolution algorithm for microwave multiport networks with nonlinear terminations ," IEEE Trans. Circuit Syst. II, Vol. 52, No. 7, 370-375, 2005.
doi:10.1109/TCSII.2005.850410

19. Chiang, I. T. and W. C. Chew, "Fast real-time convolution algorithm for transients of nonlinearly-terminated microwave multiport circuits," Microwave Opt. Tech. Lett., Vol. 39, No. 4, 280-282, 2003.
doi:10.1002/mop.11190

20. Hairer, E., C. Lubich, and M. Schliche, "Fast numerical solution of nonlinear Volterra convolution equations," SIAM J. Sci. Stat. Comput., Vol. 6, 532-541, 1985.

21. Edwards, T. C. and M. B. Steer, Foundations of Interconnect and Microstrip Design, Wiley, New York, 2000.

22. Kobayashi, M., "A dispersion formula satisfying recent requirements in microstrip CAD," IEEE Trans. Microwave Theory Tech., Vol. 36, No. 8, 1246-1250, 1988.
doi:10.1109/22.3665

23. York, R. A. and R. C. Compton, "Experimental evaluation of existing CAD models for microstrip dispersion," IEEE Trans. Microwave Theory Tech., Vol. 38, No. 3, 327-328, 1990.
doi:10.1109/22.45354

24. Hammerstad, E. and O. Jensen, "Accurate models for microstrip computer-aided design," IEEE MTT-S Int. Microwave Symp. Dig., 407-409, 1980.

25. Bahl, I. J. and R. Garg, "Simple and accurate formulas for a microstrip with finite strip thickness," Proc. IEEE, Vol. 65, No. 11, 1611-1612, 1977.
doi:10.1109/PROC.1977.10783

26. Collin, R. E., Foundations for Microwave Engineering, 2nd Ed., McGraw-Hill, New York, 1992.

27. Denlinger, E. J., "Losses of microstrip lines," IEEE Trans. Microwave Theory Tech., Vol. 28, No. 6, 513-522, 1980.
doi:10.1109/TMTT.1980.1130112

Prof. Cheng-Nan Chiu

Dr. I-Ting Chiang