his paper presented a novel unconditional stable FDTD (US-FDTD) algorithm for solving the transient response of uniform or nonuniform multiconductor transmission line with arbitrary coupling status. Analytical proof of unconditional stability and detailed analysis of numerical dispersion are presented. The precise split-time-step scheme has been introduced to eliminate the restriction of the Courant-Friedrich-Levy (CFL) condition. Compared to the conventional USFDTD methods, the proposed approach generally achieves lower phase velocity error for coarse temporal resolution. So larger time scales can be chosen for the transient simulation to achieve accurate results efficiently. Several examples of coupled uniform and nonuniform lines are presented to demonstrate the accuracy, stability, and efficiency of the proposed model.
"An Unconditional Stable 1D-FDTD Method for Modeling Transmission Lines Based on Precise Split-Step Scheme," Progress In Electromagnetics Research,
Vol. 135, 245-260, 2013. doi:10.2528/PIER12103007
1. Eudes, , T., B. Ravelo, and A. Louis, "Transient response characterization of the high-speed interconnection RLCG-model for the signal integrity analysis," Progress In Electromagnetics Research, Vol. 112, 183-197, 2011.
2. Carlsson, , J., , "A FDTD program for computing responses on branched multi-conductor transmission lines," SP Swedish National Testing and Research Insitute, SP Report, 1998.
3. Yilmaz, , A. E., J. M. Jin, and E. Michielssen, "A TDIE-based asynchronous electromagnetic-circuit simulator," IEEE Micro. Wireless Compo. Lett., Vol. 16, No. 3, 122-124, 2006.. doi:10.1109/LMWC.2006.869861
4. Yang, , C. Y. and V. Jandhyala, "A time-domain surface integral technique for mixed electromagnetic and circuit simulation," IEEE Trans. Adv. Packag., Vol. 28, No. 4, 745-753, 2005. doi:10.1109/TADVP.2005.848389
5. Xu, , K., , Z. H. Fan, D. Z. Ding, and R. S. Chen, "GPU accelerated unconditional stable Crank-Nicolson FDTD method for the analysis of three-dimensional microwave circuits," Progress In Electromagnetics Research, Vol. 102, 381-395, 2010. doi:10.2528/PIER10020606
6. Wang, R., J. M. Jin, and , "A flexible time-stepping scheme for hybrid ¯eld-circuit simulation based on the extended time-domain FEM ," IEEE Trans. Adv. Packag., Vol. 33, No. 4, 769-776, 2010. doi:10.1109/TADVP.2010.2044411
7. Djordjeric, , A. R. , T. K. Sarkar, and , "Analysis of time response of lossy multiconductor transmission line networks," IEEE Trans. Microw. Theory Tech., Vol. 35, No. 10, 898-908, 1987. doi:10.1109/TMTT.1987.1133776
8. Griffith, , J. R., M. S. Nakhla, and , "Time-domain analysis of lossy coupled transmission lines," IEEE Trans. Microw. Theory Tech. , Vol. 38, No. 10, 1480-1486, 1990. doi:10.1109/22.58689
9. Xu, , Q. W. , P. Mazumder, and , "Accurate modeling of lossy nonuniform transmission lines by using differential quadrature methods," IEEE Trans. Microw. Theory Tech.,, Vol. 50, 2233-2246, 2002. doi:10.1109/TMTT.2002.803440
10. Tang, , M. , J. F. Mao, and , "Transient analysis of lossy nonuniform transmission lines using a time-step integration method," Progress In Electromagnetics Research, Vol. 69, 257-266, 2007.. doi:10.2528/PIER06123001
11. Jaehoon, , J., H. Ic-Pyo, and N. Robert, "The time domain propagator method for lossless multiconductor quasi-TEM lines," IEEE Trans. Adv. Packag., Vol. 32, No. 3, 619-626, 2009. doi:10.1109/TADVP.2009.2022016
12. Bagci, , H., A. E. Yilmaz, and E. Michielssen, , "An FFT-accelerated time-domain multiconductor transmission line simulator," IEEE Trans. Electrom. Compat., Vol. 52, No. 1, 199-214, 2010. doi:10.1109/TEMC.2009.2036602
13. Tang, M. , J. F. Mao, and , "Finite-difference analysis of interconnects with frequency-dependent parameters based on equivalent circuit models ," IEEE Trans. Adv. Packag., Vol. 33, No. 2, 457-467, 2010. doi:10.1109/TADVP.2009.2033200
14. Trakadas, , P. T. , C. N. Capsalis, and , "Validation of a modified FDTD method on non-uniform transmission lines," Progress In Electromagnetics Research, Vol. 31, 311-329, 2001. doi:10.2528/PIER00071705
15. Chiu, C.-N., I.-T. Chiang, and , "A fast approach for simulation long-time response of high-speed dispersive and lossy interconnects terminated with nonlinear loads," Progress In Electromagnetics Research, Vol. 91, 153-171, 2009. doi:10.2528/PIER09021502
16. Afrooz, , K. , A. Abdipour, and , "Effcient method for time-domain analysis of lossy nonuniform multiconductor transmission line driven by a modulated signal using FDTD technique," IEEE Trans. Electrom. Compat., Vol. 54, No. 2, 482-494, 2012. doi:10.1109/TEMC.2011.2161765
17. Tang, , M. , J. F. Mao, and , "A precise time-step integration method for transient analysis of lossy nonuniform transmission lines," IEEE Trans. Electrom. Compat., Vol. 50, No. 1, 166-174, 2008. doi:10.1109/TEMC.2007.913222
18. Jia, L., , W. Shi, and J. Guo, "Arbitrary-difference precise-integration method for the computation of electromagnetic transients in single-phase nonuniform transmission line," IEEE Trans. Power Deliv., Vol. 23, No. 3, 1488-1494, 2008. doi:10.1109/TPWRD.2008.919187
19. Bai, Z. M., X. K. Ma, and G. Sun, , "A low-dispersion realization of precise integration time-domain method using a fourth-order accurate finite difference scheme," IEEE Trans. Antenn. Propag.,, Vol. 59, No. 4, 1311-1320, 2011. doi:10.1109/TAP.2011.2109673
20. Higham, , N. J., , "The scaling and squaring method for the matrix exponential revisited," SIAM J. Matrix Anal. Appl., Vol. 26, 1179-1193, 2005. doi:10.1137/04061101X
21. Kong, , Y. D. , Q. X. Chu, and , "High-order split-step unconditionally-stable FDTD methods and numerical analysis," IEEE Trans. Antenn. Propag., Vol. 59, No. 9, 3280-3289, 2011. doi:10.1109/TAP.2011.2161543
22. Pereda, , J. A., , et al., "Analyzing the stability of the FDTD technique by combining the von Neumann method with the Routh-Hurnitz criterion," IEEE Trans. Microw. Theory Tech., Vol. 49, 377-381, 2001. doi:10.1109/22.903100
23. Wang, J., , B. Zhou, L. Shi, C. Gao, and B. Chen, "A novel 3-D weakly conditionally stable FDTD algorithm," Progress In Electromagnetics Research, Vol. 130, 525-540, 2012..
24. Kong, Y. D. , Q. X. Chu, and , "Reduction of numerical dispersion of the six-stages split-step unconditionally-stable FDTD method with controlling parameters," Progress In Electromagnetics Research, Vol. 122, 175-196, 2012. doi:10.2528/PIER11082512
25. Dou, , L., J. Dou, and , "Sensitivity analysis of lossy nonuniform multiconductor transmission lines with nonlinear terminations," IEEE Trans. Adv. Packag., Vol. 33, No. 2, 492-497, 2010.. doi:10.1109/TADVP.2009.2035439
26. Boulejfen, , N., , A. B. Kouki, and F. M. Ghannouchi, "Frequency-and time-domain analysis of nonuniform lossy coupled transmission lines with linear and nonlinear terminations," IEEE Trans. Microw. Theory Tech., Vol. 48, No. 3, 367-379, 2000.. doi:10.1109/22.826835
27. Afrooz, K., , A. Abdipour, A. Tavakoli, and M. Movahhedi, "Time domain analysis of active transmission line using FDTD technique (application to microwave/mm-wave transistors)," Progress In Electromagnetics Research, Vol. 77, 309-328, 2007. doi:10.2528/PIER07081401