Stability, causality, and passivity in electrical interconnect models

IEEE Transactions on Advanced Packaging

Volumn 30, Issue 4, 2007, Pages 795-808

  Triverio, Piero ^a   Grivet Talocia, Stefano ^a   Nakhla, Michael S ^b   Canavero, Flavio G ^a   Achar, Ramachandra ^b  

^a POLITECNICO DI TORINO   (Italy)

^b CARLETON UNIVERSITY   (Canada)

Author keywords

Bilateral Laplace transform; Causality; Dispersion relations; High speed interconnects; Linear systems; Modeling; Passivity; Stability

Indexed keywords

COMPUTER AIDED DESIGN; COMPUTER SIMULATION; FREQUENCY DOMAIN ANALYSIS; INTERCONNECTION NETWORKS; LAPLACE TRANSFORMS; LINEAR SYSTEMS; TIME DOMAIN ANALYSIS;

BILATERAL LAPLACE TRANSFORM; ELECTRICAL INTERCONNECT MODEL;

ELECTRONICS PACKAGING;

EID: 36349002964     PISSN: 15213323     EISSN: None     Source Type: Journal    
DOI: 10.1109/TADVP.2007.901567     Document Type: Article

References (56)

1. M. Nakhla and R. Achar, "Simulation of high-speed interconnects," Proc. IEEE, vol. 89, no. 5, pp. 693-728, May 2001.
2. M. Celik, L. Pileggi, and A. Obadasioglu, IC Interconnect Analysis Boston, MA: Kluwer, 2002.
3. B. Gustavsen and A. Semlyen, "Rational approximation of frequency domain responses by vector fitting," IEEE Trans. Power Delivery, vol. 14, no. 3, pp. 1052-1061, Jul. 1999.
4. A. Semlyen and B. Gustavsen, "Vector fitting by pole relocation for the state equation approximation of nonrational transfer matrices," Circuits Syst. Signal Process, vol. 19, no. 6, pp. 549-566, 2000.
5. B. Gustavsen and A. Semlyen, "A robust approach for system identifi- cation in the frequency domain," IEEE Trans. Power Delivery, vol. 19, no. 3, pp. 1167-1173, Jul. 2004.
6. C. K. Sanathanan and J. Koerner, "Transfer function synthesis as a ratio of two complex polynomials," IEEE Trans. Automat. Contr., vol. 8, no. 1, pp. 56-58, Jan. 1963.
7. W. Beyene and J. Schutt-Ainé, "Accurate frequency-domain modeling and efficient circuit simulation of high-speed packaging interconnects," IEEE Trans. Microwave Theory Tech., vol. 45, no. 10, pp. 1941-1947, Oct. 1997.
8. K. L. Choi and M. Swaminathan, "Development of model libraries for embedded passives using network synthesis," IEEE Trans. Circuits Syst. II, vol. 47, no. 4, pp. 249-260, Apr. 2000.
9. M. Elzinga, K. Virga, L. Zhao, and J. L. Prince, "Pole-residue formulation for transient simulation of high-frequency interconnects using householder LS curve-fitting techniques," IEEE Trans. Comp. Packag. Manufact. Technol., vol. 23, no. 1, pp. 142-147, Mar. 2000.
10. M. Elzinga, K. Virga, and J. L. Prince, "Improve global rational approximation macromodeling algorithm for networks characterized by frequency-sampled data," IEEE Trans. Microwave Theory Tech., vol. 48, no. 9, pp. 1461-1467, Sep. 2000.
11. J. Morsey and A. C. Cangellaris, "PRIME: Passive realization of interconnects models from measures data," in Proc. IEEE 10th Topical Meeting Electr. Perf. of Electron. Packag., 2001, pp. 47-50.
12. S. Grivet-Talocia and M. Bandinu, "Improving the convergence of vector fitting in presence of noise," IEEE Trans. Electromagnetic Compatibility, vol. 48, no. 1, pp. 104-120, Feb. 2006.
13. D. Deschrijver and T. Dhaene, "Broadband macromodeling of passive components using orthonormal vector fitting," Electron. Lett., vol. 41, no. 21, pp. 1160-1161, Oct. 2005.
14. IdEM 2.4, [Online]. Available: http://www.emc.polito.it
15. F. H. Branin, "Transient analysis of lossless transmission lines," Proc. IEEE, vol. 55, pp. 2012-2013, 1967.
16. A. J. Gruodis and C. S. Chang, "Coupled lossy transmission line characterization and simulation," IBM J. Res. Development, vol. 25, pp. 25-41, 1981.
17. D. B. Kuznetsov and J. E. Schutt-Aine, "Optimal transient simulation of transmission lines," IEEE Trans. Circuits Syst.-I, vol. 43, no. 1, pp. 110-121, Jan. 1996.
18. S. Lin and E. S. Kuh, "Transient simulation of lossy interconnects based on recursive convolution formulation," IEEE Trans. Circuits Syst.-I, vol. 39, no. 6, pp. 879-892, Jun. 1992.
19. A. Semlyen and A. Dabuleanu, "Fast and accurate switching transient calculations on transmission lines with ground using recursive convolution," IEEE Trans. Power Apparatus Syst., vol. 94, pp. 561-571, 1975.
20. S. Grivet-Talocia, H. M. Huang, A. E. Ruehli, F. Canavero, and I. M. Elfadel, "Transient analysis of lossy transmission lines: An effective approach based on the method of characteristics," IEEE Trans. Advanced Packaging, vol. 27, no. 1, pp. 45-56, Feb. 2004.
21. N. Nakhla, A. Dounavis, R. Achar, and M. S. Nakhla, "DEPACT: Delay extraction-based passive compact transmission-line macromodeling algorithm," IEEE Trans. Adv. Packaging, vol. 28, no. 1, pp. 13-23, Feb. 2005.
22. R. Mandrekar and M. Swaminathan, "Causality enforcement in transient simulation of passive networks through delay extraction," in Proc. 9th IEEE Workshop Signal Propagation on Interconnects, Garmisch-Partenkirchen, Germany, May 10-13, 2005.
23. E. Gad, C. Chen, M. Nakhla, and R. Achar, "A passivity checking algorithm for delay-based macromodels of lossy transmission lines," in Proc. 9th IEEE Workshop on Signal Propagation on Interconnects, May 10-13, 2005, pp. 125-128.
24. E. Gad, C. Chen, M. Nakhla, and R. Achar, "Passivity verification in delay-based macromodels of electrical interconnects," IEEE Trans. Circuits Syst.-I, vol. 52, no. 10, pp. 2173-2187, Oct. 2005.
25. A. H. Zemanian, "An N-port realizability theory based on the theory of distributions," IEEE Trans. Circuit Theory, vol. CT-10, pp. 265-274, Oct. 1963.
26. M. R. Wohlers, Lumped and Distributed Passive Networks. New York: Academic, 1969.
27. D. C. Youla, L. J. Castriota, and H. J. Carlin, "Bounded real scattering matrices and the foundations of linear passive network theory," IRE Trans. Circuit Theory, vol. CT-6, pp. 102-124, Mar. 1959.
28. A. V. Oppenheim and A. S. Willsky, Signals and Systems. Englewood Cliffs, NJ: Prentice-Hall, 1983.
29. A. H. Zemanian, "Realizability theory for continuous linear systems," in Mathematics in Science and Engineering. New York: Academic, 1972, vol. 97, pp. XV-231.
30. E. J. Beltrami, "Linear dissipative systems, nonnegative definite distributional kernels, and the boundary values of bounder-real and positive-real matrices," J. Math. Analysis Applic., vol. 19, pp. 231-246, 1967.
31. H. A. Kramers, "La diffusion de la lumière par les atomes," in Collected Scientific Papers. Amsterdam, The Netherlands: North-Holland, 1956.
32. R. Krönig, "On the theory of dispersion of x-rays," J. Opt. Soc. Amer., vol. 12, pp. 547-557, 1926.
33. N. M. Nussenzveig, Causality and Dispersion Relations. New York: Academic, 1972.
34. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd ed. London, U.K.: Oxford Univ. Press, 1948.
35. G. W. Milton, D. J. Eyre, and J. V. Mantese, "Finite frequency range Kramers Krönig relations: Bounds on the dispersion," Phys. Rev. Lett., vol. 79, pp. 3062-3065, 1997.
36. K. R. Waters, J. Mobley, and J. G. Miller, "Causality-imposed (Kramers-Krönig) relationships between attenuation and dispersion," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 52, pp. 822-833, 2005.
37. K. F. Palmer, M. Z. Williams, and B. A. Budde, "Multiply subtractive Kramers-Krönig analysis of optical data," Appl. Opt., vol. 37, no. 13, pp. 2660-2673, May 1998.
38. V. Lucarini, J. J. Saarinen, and K. Peiponen, "Multiply subtractive generalized Kramers-Krönig relations: Application on third-harmonic generation susceptibility on polysilane," J. Chem. Phys., vol. 119, no. 21, pp. 11 095-11 098, Dec. 2003.
39. F. M. Tesche, "On the use of the Hilbert transform for processing measured CW data," IEEE Trans. Electromagn. Compat., vol. 34, pp. 259-266, 1992.
40. P. Triverio and S. Grivet-Talocia, "A robust causality verification tool for tabulated frequency data," in Proc. 10th IEEE Workshop Signal Propagation on Interconnects, Berlin, Germany, May 9-12, 2006.
41. P. Triverio and S. Grivet-Talocia, "On checking causality of bandlimited sampled frequency responses," in Proc. 2nd Conf. Ph.D. Research in Microelectronics and Electronics (PRIME), Otranto, LE, Italy, June 12-15, 2006, pp. 501-504.
42. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1996.
43. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, "Linear matrix inequalities in system and control theory," in SIAM Studies in Applied Mathematics. Philadelphia, PA: SIAM, 1994.
44. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
45. C. P. Coelho, J. Phillips, and L. M. Silveira, "A convex programming approach for generating guaranteed passive approximations to tabulated frequency-data," IEEE Trans. Computed-Aided Design Integrated Circuits Syst., vol. 23, no. 2, Feb. 2004.
46. H. Chen and J. Fang, "Enforcing bounded realness of S parameter through trace parameterization," in Proc. 12th IEEE Topical Meeting Electrical Performance of Electronic Packaging, Princeton, NJ, Oct. 27-29, 2003, pp. 291-294.
47. B. Dumitrescu, "Parameterization of positive-real transfer functions with fixed poles," IEEE Trans. Circuits Syst.-I, vol. 49, no. 4, pp. 523-526, Apr. 2002.
48. B. Gustavsen and A. Semlyen, "Enforcing passivity for admittance matrices approximated by rational functions," IEEE Trans. Power Syst., vol. 16, no. 1, pp. 97-104, Mar. 2001.
49. R. Achar, P. K. Gunupudi, M. Nakhla, and E. Chiprout, "Passive interconnect reduction algorithm for distributed/measured networks," IEEE Trans. Circuits Syst. II, vol. 47, no. 4, pp. 287-301, Apr. 2000.
50. D. Saraswat, R. Achar, and M. Nakhla, "Enforcing passivity for rational function based macromodels of tabulated data," in Proc. 12th IEEE Topical Meeting Electrical Performance of Electronic Packaging, Princeton, NJ, Oct. 27-29, 2003, pp. 295-298.
51. D. Saraswat, R. Achar, and M. Nakhla, "A fast algorithm and practical considerations for passive macromodeling of measured/simulated data," IEEE Trans. Components, Packaging and Manufacturing Technol., vol. 27, pp. 57-70, Feb. 2004.
52. D. Saraswat, R. Achar, and M. Nakhla, "Global passivity enforcement algorithm for macromodels of interconnect subnetworks characterized by tabulated data," IEEE Trans. VLSI Syst., vol. 13, no. 7, pp. 819-832, Jul. 2005.
53. S. Grivet-Talocia, "Enforcing passivity of macromodels via spectral perturbation of hamiltonian matrices," in Proc. 7th IEEE Workshop on Signal Propagation on Interconnects, Siena, Italy, May 11-14, 2003, pp. 33-36.
54. S. Grivet-Talocia, "Passivity enforcement via perturbation of Hamiltonian matrices," IEEE Trans. Circuits Syst.-I, vol. 51, no. 9, pp. 1755-1769, Sep. 2004.
55. S. Grivet-Talocia and A. Ubolli, "On the generation of large passive macromodels for complex interconnect structures," IEEE Trans. Adv. Packaging, vol. 29, no. 1, pp. 39-54, Feb. 2006.
56. S. Grivet-Talocia, "Improving the efficiency of passivity compensation schemes via adaptive sampling," in Proc. 14th IEEE Topical Meeting Electrical Performance of Electronic Packaging, Austin, TX, Oct. 24-26, 2005, pp. 231-234.