High-Order Moment-Matching MOR with Impedance Boundaries for Signal Integrity Analysis
Keywords:
MOR, Signal Integrity AnalysisAbstract
This paper presents an extension of highorder moment-matching model order reduction to frequencydependent impedance boundary conditions. Such boundary conditions are essential for accurately and efficiently modeling conductors at high frequency, where skin effect is significant. These boundary conditions involve complicated transcendental functions, whereas previous MOR methods assume polynomial dependence. Automatic differentiation is used to easily and accurately calculate the higher derivatives of such functions. Substantial improvement is shown, not only compared to discrete frequency sweeps, but also compared to non-momentmatching S matrix interpolation.
Downloads
References
R. D. Slone, R. Lee, and J.-F. Lee, “Multipoint Galerkin asymptotic waveform evaluation for model order reduction of frequency domain FEM electromagnetic radiation problems,” IEEE Trans. Antennas Propag., vol. 49, no. 10, pp. 1504–1513, Oct. 2001.
A. Odabasioglu, M. Celik, and L. T. Pileggi, “PRIMA: Passive reduced-order interconnect macromodeling algorithm,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol. 17, no. 8, pp. 645–654, Aug. 1998.
HFSS Online Help (Release 19.0), ANSYS, Inc., Canonsburg, PA, “Finite conductivity boundaries”.
O. Farle and R. Dyczij-Edlinger, “Numerically stable moment matching for linear systems parameterized by polynomials in multiple variables with applications to finite element models of microwave structures,” IEEE Trans. Antennas Propag., vol. 58, no. 11, pp. 3675–3684, Nov. 2010.
M. Bartholomew-Biggs, S. Brown, B. Christianson, and L. Dixon, “Automatic differentiation of algorithms,” J. Comput. and Appl. Math., vol. 124, no. 1, pp. 171–190, 2000.
Selected AD tools. [Online]. Available: http://www. autodiff.org/?module=Tools
Intel Math Kernel Library for Windows: Developer Guide (MKL 2018), Intel, “Obtaining Numerically Reproducible Results,”. [Online]. Available: https://software.intel.com/sites/default/ files/managed/35/53/mkl-2018-developer-guide-win.pdf
