Progress in the methodologies for the electrical modeling of interconnects electronic packages

Proceedings of the IEEE

Volumn 89, Issue 5, 2001, Pages 740-771

  Ruehli, Albert E ^a,b   Cangellaris, Andreas C ^a,b  

^a IBM RESEARCH   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Electrical modeling; Electromagnetic; Finite difference; Full wave; Interconnect; Model order reduction; Partial element; Passivity; TEM; Transmission lines

Indexed keywords

EID: 0001105495     PISSN: 00189219     EISSN: None     Source Type: Journal    
DOI: 10.1109/5.929652     Document Type: Article

References (157)

1. G. Katopis et al, "MCM technology and design for thé S/390 G5 server," IBM J. Res. Develop., Nov. 1999.
2. B. Archambeault, O. Ramahi, and C. Brench, EMI/EMC Computational Modeling Handbook, Norwell, MA: Kluwer, 1998.
3. A. E. Ruehli and A. C. Cangellaris, ''Application of the partial element requivalent circuit (PEEC) method to realistic printed circuit board problem," in Proc. IEEE Int. Syrnp. Electromagnetic Compatibility, Denver, CO, Aug. 1998, pp. ! 82-187.
4. A. E. Ruehli, "Survey of computer-aided electrical analysis of integrated circuit interconnections," IBM J. Res. Develop., vol. 23, pp. 626-639, Nov. 1979.
5. D. Sylvester and K. Keutzer, "Impact of small process geometries," Proc. IEEE, vol. 89, pp. 467189, Apr. 2001.
6. J. Cong, "An interconnect-centric design flow for nanometer technologies," Proc. IEEE, vol. 89, pp. 505-528, Apr. 2001.
7. E. Friedman. "Clock distribution networks," Proc. IEEE, vol. 89, pp. 665-692, May 2001.
8. D. Sylvester and C. Hu, "Analytical modeling and characterization of deep submicromster interconnect," Proc. IEEE, vol. 89, pp. 634-664; May 2001.
9. F. Cuignet, S. Delnias-Bendhia, and E. Sicard, "The challenge of signal integrity in deep-submicrometer CMOS technology," Proc. IEEE, vol.89, pp. 556-573, Apr. 2001.
10. W. Kao, C.-Y. Lo, M. Basel, and R. Singh, "Parasitic extraction: Current state of the art and future trends," Proc. IEEE. vol. 89, pp. 729-739, May 2001.
11. D. Burnett, Finite Element Analysis. Reading, MA: Addison-Wesley, 1997.
12. J. Jin, The Finite Element Method in Electromagnetics. New York: Wiley, 1993.
13. T. Itoh, G. Peiosi, and P. P. Silvester, Eds., Finite Element Sofnvare for Microwave Engineering. New York: Wiley, 1996.
14. S. McCormick, Multigrid Methods. Philadelphia, PA: SIAM, 1997, vol. 3, SIAM Frontier Series.
15. S. V. Polstyanko, G. Peng, and J.-R Lee, "Algebraic multigrid method for solving FEM matrix equations for 3D static problems," IEEE Trans. Magn., vol. 14, pp. 1183-1186, May 1999.
16. A. Taflove, Advances in Computational Eleclrodnamics. Norwell, MA: Aitech House, 1998.
17. K. S. Yee. "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propagea., vol. 14, pp. 302-307, May 1966.
18. A. Taflove and S. C. Hagness, Computational Electrodynamics. Norwell, MA: Artech House, 2000.
19. Y. Zhu, A. C. Cangellaris, and J. L. Prince, "Macro-elements for efficient finite element simulation of small geometries features in waveguide components," IEEE Trans. Microwave Theory Tech., vol. 42, Dec. 2000.
20. J. P. Bcrenger, "A multiwire formalism for the FDTD method," IEEE Trans. Electwmagn. Compat., vol. 42, pp. 257-264, Aug. 2000.
21. T. Narniki. "A new FDTD algorithm based on alternative direction implicit method," IEEE Trans, Microwave Theory Tech., vol. 47, pp. 2003-2007, Aug. 1999.
22. _, "3-D ADI-FDTD method-Unconditionally stable time-domain algorithm for solving lull vector Maxwell's equations," IEEE Trans. Microwave Theory Tech., vol. 48, pp. 1743-1748, Oct. 2000.
23. G. Li u and S. D. Gedney, "Perfectly matched layer media for an unconditionally stable three-dimensional ADI-FDTD method," IEEE Microwave Guided Wave Lett., vol. 10, pp. 261-263, July 2000.
24. G. Krön, "Equivalent circuit for the field equations of Maxwell," Proc. IKE, vol. 32, no. 289, 1944.
25. I. J. Craddoek and C. J. Railton, "Application of a circuit-based approach to ensuring the stability of modified finite difference time domain algorithms," in Proc. litt. Zürich Symp. EMC, vol. 11, Zürich, Switzerland, Feb. 1997.
26. Y. Tsuei, A. C. Cangellaris, and J. L. Prince, "Rigorous electromagnetic modeling of chip-to-package first-level interconnections," IEEE Trans. Comp. Hybrids Manufact. Techno'., vol. 41, pp. 876-833, Dec. 1993.
27. Y.-S. Tsuei, "Incorporating of linear/nonlinear lumped circuit models in a full-wave electromagnetic simulator for transient electromagetic analysis of high-speed electronic systems," Ph.D. dissertation, Dept. Electromag. and Computer Engineering, Univ. Arizona, 1996.
28. K.-P. Ma, M. Chen, B. Houshmand, Y. Qian, and T. Itoh, "Global time-domain full-wave analysis of microwave circuits involving highly nonlinear phenomena and EMC effects," IEEE Trans. Microwave Theory Tech., vol. 47, pp. 859-866, June 1999.
29. G. N. Tait and S. H. Jones, "Transient simulation of millimeter-wave circuits incorporating numerical device modeling," IEEE Trans. Microwave Theory Tech., vol. 47, pp. 877-881, 1999.
30. J. Fang, Y. Chen, and Z. Wu, "Modeling of electrical properties of power/ground planes in electronics packaging," in Proc. Ira. Symp. Microel. Package und PCB Technology, Beijing, China, Sept. 1994, pp. 74-83.
31. M. J. Choi K.-P. Hwang, and A. Cangellaris, "Direct generation of SPICE-compatible passive reduced-order models of ground/power planes," in Electr. Components and Technology Conf., vol. 50, Las Vegas, NV, May 2000, pp. 775-780.
32. W. J. R. Hoef'er, "The transmission line matrix (TLM) method," in Numerical Techniques for Microwave and Millimeter Wave Passive Structures, T. Itoh, Ed. New York: Wiiey, 1989.
33. C. Christopoulos, An Introduction to the Transmission-Line Modelling (TLMMethod). Piscatawa>, NJ: IEEE Press, 1992.
34. T. Mangold and P. Russer, "Modeling of multichip module interconnections by the TLM method and system identification," in Proc. Eur. Microwave Conf., vol. 27, Jerusalem, Israel, Sept. 1997, pp. 538-543.
35. C. Christopoulos and P. Russer, "Application of TLM to EMC problems," in NATO AS! Series; Serie..1: /': Computer and System. Sciences, N. K. Uzungoglu, K. S. Xikita. and D. I, Kakamani, Eds: Applied Computational Electromagnetics: State of the Art and Future Trends, Feh. 1999, vol. 12.
36. L. Pierantoni, S. Lindenmeier, and P. Russer. "A combination of integral equation method and FD/TLM method for efficient solution of EMC problems," in Proc. Eur. Microwave Conf., Jerusalem, Israel, 1997, pp. 608-613.
37. V. Sjankar, A. Mohammadian, and W. F. Hall, "A time-domain finite-volume treatment for the Maxwell equations," Electromagnetics,vol. 10, pp. 127-145, 1990.
38. N. Vladsen, ''Divergence preserving discrete surface integral methods for Maxwell's equations using nonorthogonal unstructured grids," in Lawrence Livermore National Laboratory.
39. S. D. Gedney and F. Lansing, "Explicit time-domain solution of Maxwell's equations using nonorthogonal and unstructured grids," in Computational Electromagnetics: The Finite-Difference Time Domain Method, A. Taflove, Ed. Norwood, MA: Artech House.
40. R. Schuhrnann and T. Weiland, "An improved implementation of nonorthogonal FDTD using triangular fillings," in Proc. IEEE Antennas Prop. Soc. Int. Symp., vol. 35, Atlanta, GA, 1998, pp. 600-603.
41. D. J. Riley. C. D. Turner, and J. D. Kotulski, "Transient applications of sub-cell wire and slot models to unstructured tetrahedral-element meshes," in Proc. IEEE Antennas Prop. Soc. Inf. Symp., vol. 35, Atlanta, GA, 1998, pp. 592-595.
42. R. F. Harrington, Field Computation by Moment Methods. New York: Macmillan, 1968.
43. A. W. Glisson and D. R. Wilson, "Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces," IEEE Trans. Antennas Propagea., vol. 28. pp. 593-603, 1980.
44. S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., vol. AP-30, pp. 40918, May 1982.
45. B. M. Kolundzija and B. D. Popvic, "Entire-domain Galerkin method for analysis of metallic antennas and scatterers," Proc. /nst. Elect. Eng., pt. H, vol. 1, pp. 1-10, Jan. 1990.
46. B. 3. Rubin and S. Daijavad, "Radiation and scattering from structures involving finite-size dielectric regions," in IEEE APS Int. Symp., 1990.
47. M. Kimme! and H. Singer, "A modular formulation for electromagnetic transmission through shields of arbiträr)' shape using the method of moments," in Proc. IEEE Int. Symp. Electromagnetic Compatibility, Atlanta, GA, Aug. 1995, pp. 208-213.
48. A. E. Ruehli and P. A. Brennan, "Efficient capacitance calculations for three-dimensional multiconduetor systems," IEEE Trans. Microwave Theory Tech., vol. MTT-21. pp. 76-82, Feb. 1973.
49. A. E. Ruehli, "Inductance calculations in a complex integrated circuit environment," IBM J. Res. Develop., vol. 16, pp. 470-481, Sept. 1972.
50. _. "Equivalent circuit models for three dimensional multiconductor systems," IEEE Trans. Microwave Theory Tech., vol. MTT-22, pp. 216-221, Mar. 1974.
51. W. Pinello, A. C. Cangeliaris, and A. E. Ruehli, "Hybrid electromagnetic modeling of noise interactions in packaged electronics based on the partial-element equivalent circuit formulation," IEEE Trans. Microwave Theory Tech., vol. MTT-45, pp. 1889-1896, Oct. 1997.
52. G. Wellenberg and A. Görisch, "Analysis of 3-D interconnect structures with PEEC using SPICE," IEEE Trans. Electmmagn. Cornpat., vol. 41, pp. 412-417, Nov. 1999.
53. A. Ruehli and H. Heeb, "Circuit models for three-dimensional geometries including dielectrics," IEEE Trans. Microwave Theory Tech., vol. 40, pp. 1507-1516, Jui> 1992.
54. C. Ho, A. Ruehli, and P. Brennan, "The modified nodal approach to network analysis," IEEE Tram. Circuits Svst.. pp. 504-509, June 1975.
55. A. Bellen, N. Guglielmi, and A. Ruehli, "Methods for linear systems of circuit delay differential equations of neutral type," IEEE Trans. Circuits Syst.,'vol. 46, pp. 212-216, Jan. 1999.
56. A. E. Ruehli, W. P. Pinello, and A. C. Cangellaris, "Comparison of differential and common mode response for short transmission line using PEEC models," in Dig. Electr. Perf. Electronic Packaging, vol. 5, Napa. CA, Nov. 1996, pp. 169-171.'
57. G. Coen and D. De Zutter, "Reduction of circuit complexity using tensor analysis of networks," in Proc. Int. Zürich Symp. EMC, vol. 11, Zürich, Switzerland, Feb. 1997.
58. P. A. Brennan, N. Raver, and A. E. Ruehli, "Three-dimensional inductance computations with partial element equivalent circuits," IBMJ. Res. Develop., vol. 23, pp. 661-668, Nov. 1979.
59. L. M. Silveira, M. iCamon, and J. White, "Direct computations of reduced-order models for circuit simulation of 3D interconnect structures," in Dig. Electr. Perf. Electronic Packaging, Monterey, CA, Nov. 1994.
60. L. W. Nagel, "SPICE: A computer program to simulate semiconductor circuits," Electr. Res. Lab. Rep. ERL M520, Univ. California, Berkeley, May 1975.
61. W. T. Weeks, A. J. Jirnenez, G. W. Mahoney, D. Mehta, H. Quasemzadeh, and T. R. Scott, "Algorithms for ASTAP-A network analysis program," IEEE Trans. Circuit Theory, vol. CT-20, pp. 628-634, Nov. 1973.
62. S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics. New York: Wiley, 1994.
63. R. E. Coffin, Field Theory of Guided Waves. Piscataway, NJ: IEEE Press, 1991.
64. C. Paul, Analysis of Mulnconductor Transmission Lines. New York: Wiley, 1992.
65. A. Deutsch el al, "Frequency-dependent crosstalk simulation for on-chip interconnects," IEEE Trans. Antennas Prnpagat., vol. 22, pp. 292-308, Aug. 1999.
66. M. Gribbons, A. C. Cangellaris, and J. L. Prince, "Finite-difference time-domain analysis of pulse propagation in multichip module interconnects," IEEE Trans. Coinp. Hybrids Mannfcct. Technol., vol. 16, pp. 490-498, Aug. 1993.
67. A. C. Cangellaris, M. Gribbons, and J. L. Prince, "Electrical characteristics of multichip module interconnects with perforated reference planes," IEEE Trans. Comp. Hybrids Manufacl. Technol., vol. 16, pp. 113-118, Feb. 1993.
68. H. A. Wheeler, "Formulas for the skin effect," in Proc. IRE, Sept. 1942, pp. 412-24.
69. N. S. Nahman and D. R. Holt, "Transient analysis of coaxial cables using the skin effect approximation n+bi/[,s )," IEEE Trans. Circuit Theory; vol. CT-19, pp. 443-451, 1972.
70. C. S. Yen, Z. Fazarinc, and R. L. Wheeler, "Time-domain skin-effect model for transient analysis of lossy transmission lines," Proc. IEEE, vol. 70, pp. 750-757, July 1982. '
71. M. Kamon. F. Wang, and J. White, "Recent improvements for fast inductance extraction and simulation," in Dig. Electr. Perf. Electronic Packaging, vol. 7, West Point, NY, Oct. 1998, pp. 281-284.
72. M. J, Tsuk and J. Au Kong, "A hybrid method for the calculation of the resistance and inductance of transmission lines with arbitrary cross sections," IEEE Trans, Microwave Theory Tech., vol. 39, pp. 1338-1347, Aug. 1991.
73. B.-T. Lee, E. Tuncer, and D. P. Neikirk, "Efficient 3-D series impedance extraction using effective internal impedance," in Dig. Electr. Perf. Electronic Packaging, vol. 4, Portland, OR. Nov. 1995, pp. 292-222.
74. B.-T. Lee and D. P. Neikirk, "Minimum segmetation in (he surface ribbon method for series impedance calculation of microstrip lines," in Dig. Electr. Perf. Electronic Packaging, vol. 5, Napa, CA, Oct. 1996,"pp. 233-235.
75. K. Coperich, A. Ruehli, and A. Cangeliaris, "Enhanced skin effect for partial-element equivalent circuit (PEEC) models," IEEE Trans. Microwave Theory Tech., vol. 48, pp. 1435-1442, Sept. 2000.
76. J. Cain, "Asynchronous GB/s signaling for digital communications," in Dig. Elecir. Perf. Electronic Packaging, vol. 9, Scottsdale, AZ, Oct. 2000, pp. 13-16.
77. J. D.Jackson, Classical Electrodynamics. New York: Wiley, 1975.
78. D. Pozar, Microwave Engineering. New York: Wiley, 1998.
79. J. Zheng, Y.-C. Hahrn, V. K. T'ripathl. and A. Weisshaar, "CAD-oriented equivalent circuit modeling of on-chip interconnects on lossy silicon substrate," IEEE Trans. Microwave Tkevry Tech., vol. 48, pp. 1443-1451. Sept 2000.
80. [SO] J. E. Schutt-Aine and R. Mittra, "Xonlinear transient analysis of coupled transmission lines," IEEE Tram. Circuit.', Syst.. pp. 959-967, July 1989.
81. A. E. Ruehli, Ed., Circuit Analysis, Simulation and Design, Par! 2. Amsterdam, The Netherlands; Elsevier, 1987.
82. D. B. Kuznetsov and J. E. Schutt-Aine, "Optimal transient simulation of transmission lines," IEEE Trans. Circuits Syst., vol. 43, pp. 110-121. Feb. 1996.
83. D, Winkelstein, M. B. Sieer, and R. Pomerlau. "Simulation cf arbitrary transmission line networks with nonlinear terminations," IEEE Trans. Circuits Syst., pp. 418-422, Apr. 1991.
84. Z. Bai, A. Orlandi. and W. T. Smith, "Moment matching method for numerical solution of MTL equations in interconnect analysis," J. Compul. Appl. Math., vol. 86, pp. 3-16, 1997.
85. K. S. D. Oh, "Accurate transient simulation of transmission lines with skin effect," IEEE Trans. Computer-Aided Design, vol. 19, pp. 389-396, Mar. 2000.
86. J. Morsley, K. Coperich, V. Okhmatovski, A. C. Cangeilaris, and 4. Ruehii, "A new broadband transmission line model for accurate simulation of dispersive interconnects," in Electr. Packaging Technology Conf., vol. 3, Singapore, Dec. 2000. pp. 345-351.
87. B. Shanker, A. A. Ergin, K. Aygun, and E. Michielssen, "Analysis of transient electromagnetic scattering from closed surfaces using a combined field intégra! equation," IEEE Trans. Antennas Propagat., vol. 48, pp. 1064-1074, June 2000.
88. P. D. Smith, "Instabilities in time marching methods for scattering: Cause and rectification," Electromagnetics, vol. iO, pp. 439-451, 1990.
89. W. Liniger and A. Ruehli, "Time domain integration methods for electric field integral equations," in Proc, Im. Zürich Symp. EMC, vol. 10, Zürich, Switzerland, Mar. 1995, pp. 209-214.
90. E. Michielssen, \V. C. Chew, K. Aygun, H. Y. Chao, A. Ergin, V. Jandhyala, B. Shanker. J. M. Song, and J. S. Zhao. "Fast algorithms for the electromagnetic simulation of planar structures," in Proc. IEEE Int. Symp. Electromagnetic Compatibility, Denver, CO, Aug. 1998, pp. 172-176.
91. J. Garrett, A. E. Ruehli, and C. R. Paul, "Accuracy and stability improvements of integral equation models using the partial element equivalent circuit PEEC approach," IEEE Trans. Antennas Propagat., vol. 46, pp. 1824-1831, Dec. 1998.
92. A. A. Ergin, B. Shanker, and E. Michielssen, "Fast evaluation of transient wave fields using diagonal translation operators," J. Compitt. Phys., vol. 146, pp. 157-180, 1998.
93. _, "The plane wave time domain algorithm for the fast analysis of transient wave phenomena," IEEE Trans. Antennas Propagat., vol. 41, pp. 39-52, Aug. 1999.
94. K. Aygun, B. Shanker, and E. Michelssen, "Analysis of nonlinearly loaded antennas and circuits using the multilevel plane wave time domain algorithm," in Int. Conf. EM in Advanced Applications, Torino, Italy, Sept. 1999, pp. 741-744.
95. K. Aygun, B. Shanker, A. A. Ergin, and E. Michielssen, "Analysis of shielding enclosures using the multilevel plane wave time domain algorithm,", Seattle, \VA. Aug. 1999.
96. M. J. Bluck and S. P. Walker, "Time-domain analysis of large threedimensional electromagnetic scattering problems," IEEE Trans. Antennas Propagat., vol. 45, pp. 894-901, May 1997.
97. B. Gustavsen and A. Semlyen, "Rational approximation of frequency domain responsed by vector fitting," IEEE Trans. Power Delivery, vol. 14, pp. 1052-1061, July 1999.
98. W. T. Beyene and J. E. Schutt-Aine, "Accurate frequency-domain modeling and efficient circuit simulation of high-speed packaging interconnects." IEEE Trans. Microwave Theor? Tech., vol. 45, pp. 1141-1147, Oct. 1997.
99. (99] S. Lin and E. S. Kuh, "Transient simulation of lossy interconnects based on recursive convolution formulation," IEEE Trans. Circuits Syst. I, vol. 39, Nov. 1992.
100. M. Xu, Y. Ji, T. H. Hubing, T. P. Van Doren, and 1. L. Drewniak, "Development of a closed-form expression for the input impedance of power-ground plane structures," in Proc. IEEE Int. Symp. Electromagnetic Compatibility, Washington, DC, Aug. 2000, pp. 77-82.
101. R. Achar and M. Nakhla, "Simulation of High-Speed Interconnects," Proc. IEEE, vol. 89, pp. 693-728, May 2001.
102. R. Barreit et al. Templates for the Solution of Linear Systems. Philadelphia, PA: SIAM Books, 1994.
103. IEEE Computational Sei. Eng., July 1998, vol. 5. Special Issue on Fast Multipole Methods.
104. W. C. Chew et ai, "Fasi solution methods in electromagnetics," IEEE Trans. Antennas Prvpagat., vol. 45, pp. 533-543, Mar. 1997.
105. .1. Phillips and J. K. White, "Efficient capacitance extraction of 3D structures using generalized pre-corrected FFT methods," in Dig. Eli-cir. Pert'. Electronic Packaging, Monterey, CA, Nov. 1994.
106. J.R- Phillips. "Error and complexity analysis for a collocation-grid projection plus pre-corrected-FFT allgorithm for solving potential integral equations with Laplace or Helmholz kernels," in Proc. Cooper Mountain ConJ. Mn'tigrid Methods, Copper Mountain, CO, Mar. 1995.
107. E. Bleszynski, M. Bleszynski. and T. Jaroszewicz, "AIM: Adaptive integral method for solving large-scale scattering and radiation problemt" Xumerial Algorithms, vol. 31, no. 5, pp. 1225-1251, 1996.
108. F. Ling, "Fast electromagnetic modeling of multilayer microstrip antennas and circuits," Ph.D. dissertation, ECE Dept., Univ. Illinois Urbana-Champaign, 2000.
109. Y. L. Le Coz and R. B. Iverson, "A stochastic algorithm for high speed capacitance extraction in integrated circuits," IEEE Trans. Microwave Theory Tech., vol. 40, pp. 1507-1516, July 1992.
110. J G. Wang, G. Pan, and B. K. Gilben, "A hybrid wavelet expansion and boundary element analysis for multiconductor transmission lines in multilayered dielectric media," IEEE Trans. Microwave Theory Tech., vol. 43, pp. 664-675, Mar. 1995.
111. W. L. Gölik, "Wavelet packets for fast solution of electromagnetic integral equations," IEEE Trans. Antennas Proposal., vol. 46, pp. 618-624. May 1998.
112. H. Deng and H. Ling, "Fast solution of electromagnetic integral equations using adaptive wavelet packet transform," IEEE Trans. Antennas Pmpagat., vol. 47, pp. 674-682, Apr. 1999.
113. O. Wang and G. Pan, "Full-wave analysis of microstnp floating line structures by wavelet expansion method." IEEE Trans. Microwave Theory Tech., vol. 43, pp. 131-142, Jan. 1995.
114. K. Sabet and L. P. B. Kaethi, "Analysis of integrated millimeter-wave and submillimeter-wave guides using orthogonal wavelet expansions," IEEE Trans. Microwave Theory Tech., vol. 42, pp. 2412-2422, Dec. 1994.
115. _, "An integral formulation of two- and three-dimensional dielectric structures and orthonormal multiresolution expansions," Int. J. Numer. Modeling, vol. 11. pp. 3-19, Jan./Feb. 1998.
116. A. Caproni, F. Cervelli, M. Mongiardo, L. Tarricone, and F. Malucelli, "Bandwidth reduced full-wave simulation of lossless and thin planar microstrip circuits," / Appl. Comput. Electromagn. Soc., vol. 13, no. 2, pp. 197-204, 1998.
117. F. Chen and D. Suter, "Using fast multipole method to accelerate spline evaluations," IEEE Comput. Sei. Eng., July 1998.
118. V. Rokhlin, "Rapid solution of integral equations of classical potential theory," j. Comput. Phys., vol. 60, pp. 187-207, Sept. 1985.
119. K. Nabors and J. White, "FastCap: A multipole accelerated 3D capacitance extraction program," IEEE Trans. Computer-Aided Design, voi. 10. pp. 1447-1459, 1991,
120. K. Nabors, F. T. Korsmeycr, F. T. Leighton, and J. White, "Preconditioned, adaptive, multipole-accelerated iterative methods for three-dimensional first-kind integral equations of potential theory," Siam J. Sei. Slat. Comput., vol. 15, pp. 723-735, Mar. i994.
121. M. Kamon, M. J. Tsuk, and J. White, "Fasthenry: A multipole-accelerated 3-D inductance extraction program," in Proc. Design Automation Conf., Jane 1993, pp. 678-683.
122. M. Bachtold, M. Spasojevic, C. Large, and P. B. Ljung, "A system for full-chip and critical net parasitic extraction for USLI interconnects using a fast 3-D field solver," IEEE Trans. Computer-Aided Design, vol. 19, pp. 325-338, Mar. 2000.
123. N. Engheta, W. D. Murphy, V. Rokhlin, and M. S. Vassilou, "The fast muitipole method (FMM)," in PIERS, July 1991.
124. R. Coif man, V. Rokhlin, and S. Wandzura, "The fast multipole method: A pedestrian description," IEEE Antennas Propage,!. Mag., vol. 35, pp. 7-12, 1993.
125. C. C. Lu and W. C. Chew, "A multilevel algorithm for solving a boundary integral equation of wave scattering." Microw. Opt. Technoi. Let!., vol. 7, pp. 456-470, July 1994.
126. J. .VI. Song and W. C. Chew, "Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering," Micro. Opt. Technoi. Lett., vol. 10, 1995.
127. J. M. Song, C. C. Liu, and W. C. Chew, "MLFMA for electromagnetic scattering for large complex objects," IEEE Tram,. Antennas Propagat, vol. 45, pp. 1488-1893, Oct. 1997.
128. L. Greengard, J. Huang, V. Rokhlin. and S. Wandzura, "Accelerating fast mullipole methods for the Helmholtz equation at low frequencies." IEEE Compn!. Sei. Eng. Meg., July 1998.
129. M. Burton and S. Kashyap, "A study of a recent moment-method algorithm that is accurate to very low frequencies," J. Appl. Comput. Electrnmagn. Soc., vol. 10, pp. 58-68, 1995.
130. W. Wu. A. W. Güssen, and D. Kajfez, "A study of two numeric-ill solution procedures for the electric field integral equations at low frequencies," J. Appl. CompuL Electromagr,. Soc.. vol. 10, no. 3, pp. 69-80, 1995.
131. W. Chew and J. S. Zhao, "Solving the electric field integral equation at very low frequencies," in Int. Conf. EM Advanced Applications, Torino, Italy, Sept. 1999, pp. 725-728.
132. V. K. Tripalhi and J. B. Reitig, "A spice model for multiple coupled micrcstrips and other transmission lines," IEEE '1'rans. Microwave Theory Tech.. vol. MTT-33, pp. 1513-1518, 1985.
133. M Celik. A. C. Cangellaris, and A. Yaghmour, "An all-purpose transmission-line model for interconnect simulation in SPICE," IEEE Trans. Microwave Theory Tech.. vol. 45, pp. 1857-1867, Oct. 1997.
134. W. Pincllo, "Application of the partial element equivalent circuit method for advanced package modeling,'1, Hiiton Head Island, SC, July 1998.
135. J. É. Bracken, D.-K. Sun, and Z. J. Cendes, "S-domain methods for simultaneous time and frequency characterization of electromagnetic devices," IEEE Trans. Microwave Theory Tech., vol. 46, pp. 1277-1290, Sept. 1998.
136. E. Christoffersen, M. Ozkar, M. B. Steer, M. G. Case, and M. Rodwell, "State-variable-based transient analysis using convolution," IEEE Trans. .Microwave Theory Tech., vol. 47, pp. 882-889, June 1999.
137. A. C. Cangeliaris, M. Celik, S. Pasha, and L. Zhao, "Electromagnetic model order reduction for system level modeling," IEEE Trans. Microwave Theory Tech., vol. 47, pp. 840-850, June 1999.
138. A. C. Cangellaris and L. Zhao. "Model order reduction techniques for electromagnetic macromodeling based on finite methods," Int. J. Numer. Modeling, vol. 13, pp. 181-197. 2000.
139. L. T. Pillage and R. A. Rohrer, "Asymptotic waveform evaluation for timing analysis," IEEE Trans. Computer-Aided Design, vol. 9, pp. 352-366, 1990.
140. S. P. McCormick and J. Alien, "Waveform moment methods for improved interconnection analysis," in Proc. Design Automation Conf., vol.27, 1990.
141. A. E. Ruehli, H. Heeb, E. Bracken, and R. Rohrer, "Three dimensional circuit oriented electromagnetic modeling for VLSI interconnects." in Proc. Packaging, Interconnects. Optoelectronics for the Design of Parallel Computers Workshop, Mar. 1992.
142. R. W. Freund and P. Feldmann, "Efficient small-signal circuit analysis and sensitivity computations with the PVL algorithm," in Proc. IEEE Int. Conf Computer-Aided Design, San Jose. CA, Nov. 1994.
143. R. du Cloux, W. J. de Graaf, G. P. J. F. M. Maas, and R. W. van der Veeken, "EMC simulations and measurements," in Proc. In!. Zürich Symp. EMC, vol. 10, Zürich. Switzerland, Mar. 1995, pp. 185-190.
144. K. Gallivan, E. Grimme, and P. Van Dooren, "A rational Lanczos algorithm for model reduction," Numer. Algorithms, vol. 12, pp. 33-63, 1996.
145. E. Chiprout and M. S. Nakhla, Asymptotic Waveform Evaluation, Norwell, MA: Kluwer. 1994.
146. J. Cullum, A. Ruehli, and T. Zhang, "Model reduction for PEEC models including retardation," in Dig. Electi: Perf. Electronic Packaging, vol. 7, West Point. NY, Oct. 1998, pp. 287-290.
147. N. Marques, M. Kamon, J. White, and L. M. Silvera, "A mixed nodal-mesh formulation for efficient extraction and passive reducedorder modeling of 3D interconnects," in Proc. Design Automation Conf., vol. 35, San Francisco, CA, June 1998.
148. A. Odabasioglu, M. Celik, and L. T. Pileggi, "Prima: Passive reduced-order interconnect macromodeiing algorithm," IEEE Trans. Compuler-Aided Design, vol. 17, pp. 645-653, 1998.
149. R. Rohrer and H. Nostrati, "Passivity considerations in stability studies of numerical integration algorithms," IEEE Trans. Circuits Syst., pp. 857-866, Sept."l981.
150. A. C. Cangellaris and M. Igarashi, "Rules for robust generation of accurate reduced-order models of high-speed coupled interconnections," in 50th Electronic Components and Technology Conf., Las Vegas, NV, May 2ÖÜO, pp. 502-507.
151. M. J. Choi and A. Cangelîaris, "A quasi three-dimensional distributed electromagnetic model for complex pcnver distribution networks," in Electr. Components and Technology Conf., vol. 51, Orlando. FL, May 2001.
152. M Celik and L. Pileggi, "Simulation of lossy multiconductor transmission lines using backward Euler integration," IEEE Trans. Circuits Syst., vol. 45, pp. 238-243, Mar. 1998.
153. M. S. Xahka, R. Acfaar, A. Dounavis, and X. Li, "passive closed-form transmission-line model for general-purpose circuit simulators," IEEE Trans. Microwave Theory Tech., vol. 47, pp. 2450-2459, Dec. 1999.
154. C. R. Paul, introduction to Electromagnetic Compatibility. New York: Wiley, 1992.
155. M. Zunoubi, K. C. Donepudi, J.-M. Jin, and W. C. Chew, "Efficient time-domain and frequency-domain finite element solution of Maxwell's équation using spectral Lanc7os algorithm," IEEE Trans Microwave Theory Tech., vol. 46, pp. 1141-1149, Aug. 1998.
156. L. Zhao and A. C. Cangelîaris, "Reduced-order modeling of electromagnetic field interactions in unbounded domains truncated by perfect matched layers," in Microwave and Opt. Technol. Lett., vol. 11, Hilton Head Island, SC, Jan. 1998, pp. 62-66.
157. S. Grivet-Talocia and F. Canavero, "Weak boundary treatment for high-order transient analysis of MTL's," in Proc. IEEE Int. Symp. Electromagnetic Compatibility, Washington, DC, Aug. 2000, pp. 409-414.