A New Approach to Passivity Preserving Model Reduction: The Dominant Spectral Zero Method

A new model reduction method for circuit simulation is presented, which preserves passivity by interpolating dominant spectral zeros. These are computed as poles of an associated Hamiltonian system, using an iterative solver: the subspace accelerated dominant pole algorithm (SADPA). Based on a dominance criterion, SADPA finds relevant spectral zeros and the associated invariant subspaces, which are used to construct the passivity preserving projection. RLC netlist equivalents for the reduced models are provided.

[1]  M. Ronald Wohlers,et al.  I – Linear Systems , 1969 .

[2]  Thomas Kailath,et al.  Linear Systems , 1980 .

[3]  Andras Varga,et al.  Enhanced Modal Approach for Model Reduction , 1995 .

[4]  Lawrence T. Pileggi,et al.  PRIMA: passive reduced-order interconnect macromodeling algorithm , 1997, ICCAD 1997.

[5]  Lawrence T. Pileggi,et al.  Robust and passive model order reduction for circuits containing susceptance elements , 2002, ICCAD 2002.

[6]  Me Menno Verbeek,et al.  Partial element equivalent circuit (PEEC) models for on‐chip passives and interconnects , 2002 .

[7]  Luís Miguel Silveira,et al.  Guaranteed passive balancing transformations for model order reduction , 2003, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[8]  Danny C. Sorensen,et al.  Passivity preserving model reduction via interpolation of spectral zeros , 2003, 2003 European Control Conference (ECC).

[9]  Roland W. Freund SPRIM: structure-preserving reduced-order interconnect macromodeling , 2004, ICCAD 2004.

[10]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[11]  Athanasios C. Antoulas,et al.  A new result on passivity preserving model reduction , 2005, Syst. Control. Lett..

[12]  Hao Yu,et al.  A sparsified vector potential equivalent circuit model for massively coupled interconnects , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[13]  Daniel Kressner,et al.  Numerical Methods for General and Structured Eigenvalue Problems , 2005, Lecture Notes in Computational Science and Engineering.

[14]  N. Martins,et al.  Efficient computation of transfer function dominant poles using subspace acceleration , 2006, IEEE Transactions on Power Systems.

[15]  David S. Watkins,et al.  The matrix eigenvalue problem - GR and Krylov subspace methods , 2007 .

[16]  Joost Rommes,et al.  Methods for eigenvalue problems with applications in model order reduction , 2007 .

[17]  Sheldon X.-D. Tan,et al.  Advanced Model Order Reduction Techniques in VLSI Design , 2007 .

[18]  Roxana Ionutiu,et al.  Passivity preserving model reduction in the context of spectral zero interpolation , 2008 .

[19]  Roxana Ionutiu,et al.  Passivity-Preserving Model Reduction Using Dominant Spectral-Zero Interpolation , 2008, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[20]  Fan Yang,et al.  RLC equivalent circuit synthesis method for structure-preserved reduced-order model of interconnect in VLSI , 2008 .

[21]  Zhaojun Bai,et al.  A Unified Krylov Projection Framework for Structure-Preserving Model Reduction , 2008 .

[22]  Roland W. Freund,et al.  Structure-Preserving Model Order Reduction of RCL Circuit Equations , 2008 .