volume | PIER Journals

Abstract

In this paper we present a Lanczos-type reduction method to simulate the low-frequency response of multiconductor transmission lines. Reduced-order models are constructed in such a way that low frequencies are approximated first. The inverse of the transmission line system matrix is then required and an explicit expression for this inverse is presented. No matrix factorization needs to be computed numerically. Furthermore, computing the action of the inverse on a vector requires an O(N) amount of work, where N is the total number of unknowns, and the inverse satisfies a particular reciprocityrelated symmetry relation as well. These two properties are exploited in a Lanczos-type algorithm to efficiently construct the low-frequency reduced-order models. Numerical examples illustrate the performance of the method.

1. Odabasioglu, A., M. Celik, and L. T. Pileggi, "PRIMA: Passive reduced-order interconnect macromodeling algorithm," IEEE Trans. on Computer-aided Design of Integrated Circuits and Systems, Vol. 17, No. 8, 645-654, Aug. 1998.
doi:10.1109/43.712097 Google Scholar

2. Pasha, S., A. C. Cangellaris, and J. L. Prince, "An all-purpose dispersive multiconductor interconnect model compatible with PRIMA," IEEE Trans. on Advanced Packaging, Vol. 24, No. 2, 126-131, May 2001.
doi:10.1109/6040.928746 Google Scholar

3. Cangellaris, A. C., M. Celik, S. Pasha, and L. Zhao, "Electromagnetic model order reduction for system-level modeling," IEEE Trans. Microwave Theory Tech., Vol. 47, No. 6, 840-850, Jun. 1999.
doi:10.1109/22.769317 Google Scholar

4. Ruehli, A. E. and A. C. Cangellaris, "Progress in the methodologies for the electrical modeling of interconnects and electronic packages," Proceedings of the IEEE, Vol. 89, No. 5, 740-771, May 2001.
doi:10.1109/5.929652 Google Scholar

5. Gunupudi, P. K., M. Nakhla, and R. Achar, "Simulation of high-speed distributed interconnects using Krylov-space techniques," IEEE Trans. on Computer-aided Design of Integrated Circuits and Systems, Vol. 19, No. 7, 799-808, Jul. 2000.
doi:10.1109/43.851995 Google Scholar

6. Cangellaris, A. C. and M. Igarashi, "Rules for robust generation of accurate reduced-order models for high-speed coupled interconnections," IEEE Transactions on Advanced Packaging, Vol. 24, No. 2, 120-125, May 2001.
doi:10.1109/6040.928745 Google Scholar

7. Celik, M. and A. C. Cangellaris, "Simulation of multiconductor transmission lines using krylov subspace order-reduction techniques," IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems, Vol. 16, No. 5, 485-496, May 1997.
doi:10.1109/43.631211 Google Scholar

8. Khalaj-Amirhosseini, M., "Closed form solutions for nonuniform transmission lines," Progress In Electromagnetics Research B, Vol. 2, 243-258, 2008.
doi:10.2528/PIERB07111502 Google Scholar

9. Remis, R. F., "Low-frequency model-order reduction of electromagnetic fields without matrix factorization," IEEE Trans. Microwave Theory Tech., Vol. 52, No. 9, 2298-2304, Sep. 2004.
doi:10.1109/TMTT.2004.834577 Google Scholar

10. Remis, R. F. and P. M. Van Den Berg, "A modified Lanczos algorithm for the computation of transient electromagnetic wavefields," IEEE Trans. Microwave Theory Tech., Vol. 45, 2139-2149, Dec. 1997.
doi:10.1109/22.643751 Google Scholar

11. Freund, R. W., "Lanczos-type algorithms for structured non-Hermitean eigenvalue problems," Proc. Cornelius Lanczos Int. Centenary Conf., 243-245, 1993. Google Scholar

12. Freund, R. W. and N. M. Nachtigal, "Software for simplified Lanczos and QMR algorithms," Appl. Numer. Math., Vol. 19, 319-341, 1995.
doi:10.1016/0168-9274(95)00089-5 Google Scholar

13. Bai, Z., "Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems," Appl. Numer. Math., Vol. 43, 9-44, 2002.
doi:10.1016/S0168-9274(02)00116-2 Google Scholar

14. Horn, R. A. and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1994.

Dr. Rob F. Remis