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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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

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 Google Scholar

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 Google Scholar

Prof. Cheng-Nan Chiu

Dr. I-Ting Chiang