Fullwave volumetric Maxwell solver using conduction modes

ABSTRACT

We present a gridless method for solving the interior problem for a set of conductors in an homogeneous dielectric, at sufficiently high frequencies, valid for conductor lengths that are not small compared to the minimum wavelength, and transverse dimensions that are large compared to the skin depth. For IC applications, we cover the regime 10--100 GHz and the inclusion of all relevant wire dimensions. We decompose the Electromagnetic-field in terms of the eigenfunctions of the Helmholtz equation for three dimensional current distributions inside the conductors. Using a relatively small number of modes per conductor we obtain results comparable to filament or mesh decompositions using a much larger dimensionality for the resulting linear problem. The method is an extension to the fullwave regime of a method introduced in [1].

REFERENCES

• 1: Luca Daniel , Alberto Sangiovanni , Jacob White, Using conduction modes basis functions for efficient electromagnetic anaysis of on-chip and off-chip interconnect, Proceedings of the 38th conference on Design automation, p.563-566, June 2001, Las Vegas, Nevada, United States [doi>10.1145/378239.379024]
• 2: W.C. Chew , E. Michielssen , J. M. Song , J. M. Jin, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Inc., Norwood, MA, 2001
• 3: K. Nabors and J. White, "Fastcap: a multipole accelerated 3-d capacitance extraction program," vol. 10, no. 11, pp. 1441--1459, 1991.
• 4: M. Kamon, M. J. Tsuk, and J. White, "Fasthenry: A multipole-accelerated 3-d inductance extraction program," IEEE Trans. Microwave Theory Tech., vol. 42, no. 9, pp. 1750--1758, Sept. 1994.
• 5: Z. Zhu, B. Song, and J. White, "Algorithms in fastimp: a fast and wide-band impedance extraction program for complicated 3-d geometries," vol. 24, pp. 981--998, July 2005.
• 6: J.-S. Zhao and W. C. Chew, "Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies," in Antennas and Propagation, IEEE Transactions on, vol. 48, Oct 2000, pp. 1635--1645.
• 7: Xin Hu , Jung Hoon Lee , Jacob White , Luca Daniel, Analysis of full-wave conductor system impedance over substrate using novel integration techniques, Proceedings of the 42nd annual conference on Design automation, June 13-17, 2005, Anaheim, California, USA [doi>10.1145/1065579.1065620]
• 8: J. Jackson, Classical Electrodynamics. New York: John Wiley and Sons, Inc., 1962.
• 9: L. Daniel, "Simulation and modeling techinques for signal integrity and electromagnetic interference on high frequency electronic systems," Ph.D. dissertation, University of California at Berkeley, 2003.
• 10: William H. Press , Brian P. Flannery , Saul A. Teukolsky , William T. Vetterling, Numerical recipes: the art of scientific computing, Cambridge University Press, New York, NY, 1986
• 11: Gene H. Golub , Charles F. Van Loan, Matrix computations (3rd ed.), Johns Hopkins University Press, Baltimore, MD, 1996
• 12: X. Hu, L. Daniel, and J. White, "Partitioned conduction modes in surface integral equation-based impedance extraction," in Electrical Performance of Electronic Packaging, Oct 2003, pp. 355--358.

INDEX TERMS

Primary Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.2 Design Aids

Additional Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS
      B.7.1 Types and Design Styles
  B.8 Performance and Reliability
      B.8.2 Performance Analysis and Design Aids
  B.m MISCELLANEOUS
      Subjects: Design management

General Terms:
Design, Performance