Broadband Rational Macromodeling Based on the Adaptive Frequency Sampling Algorithm and the Partial Element Equivalent Circuit Method

The increasing operating frequencies in modern designs call for broadband macromodeling techniques. The problem of computing high-accuracy simulation models for high-speed interconnects is of great importance in the modeling arena. Nowadays, many full-wave numerical techniques are available that provide high accuracy, often at a significant cost in terms of memory storage and computing time. Furthermore, designers are usually only interested in a few electrical quantities such as port voltages and currents. So, model order reduction techniques are commonly used to achieve accurate results in a reasonable time. This paper presents a new technique, based on the partial element equivalent circuit method, which allows to generate reduced-order models by adaptively selecting the complexity (order) of the macromodel and suitable frequency samples. Thus, the proposed algorithm allows to limit the computing time while preserving the accuracy. Validation examples are given.

[1]  R. Coifman,et al.  The fast multipole method for the wave equation: a pedestrian prescription , 1993, IEEE Antennas and Propagation Magazine.

[2]  Zhaojun Bai,et al.  Error bound for reduced system model by Pade approximation via the Lanczos process , 1999, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[3]  T. Dhaene,et al.  Broadband Macromodels for Retarded Partial Element Equivalent Circuit (rPEEC) Method , 2007, IEEE Transactions on Electromagnetic Compatibility.

[4]  Roger F. Harrington,et al.  Field computation by moment methods , 1968 .

[5]  Ramachandra Achar,et al.  Simulation of high-speed interconnects , 2001, Proc. IEEE.

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

[7]  A. Ruehli.  Equivalent Circuit Models for Three-Dimensional Multiconductor Systems , 1974 .

[8]  R.W. Freund,et al.  Efficient Small-signal Circuit Analysis And Sensitivity Computations With The Pvl Algorithm , 1994, IEEE/ACM International Conference on Computer-Aided Design.

[9]  Uwe Beyer,et al.  Data exploration with reflective adaptive models , 1996 .

[10]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[11]  A. Semlyen,et al.  Rational approximation of frequency domain responses by vector fitting , 1999 .

[12]  E. K. Miller,et al.  Model-based parameter estimation in electromagnetics. I. Background and theoretical development , 1998 .

[13]  Roland W. Freund,et al.  Small-Signal Circuit Analysis and Sensitivity Computations with the PVL Algorithm , 1996 .

[14]  Ahmed A. Kishk,et al.  MODEL-BASED PARAMETER ESTIMATION IN ELECTROMAGNETICS:III--Applications to EM Integral Equations , 1998 .

[15]  Mattan Kamon,et al.  A mixed nodal-mesh formulation for efficient extraction and passive reduced-order modeling of 3D interconnects , 1998, Proceedings 1998 Design and Automation Conference. 35th DAC. (Cat. No.98CH36175).

[16]  Jianming Jin,et al.  Fast solution methods in electromagnetics , 1997 .

[17]  Andreas C. Cangellaris,et al.  Hybrid electromagnetic modeling of noise interactions in packaged electronics based on the partial-element equivalent-circuit formulation , 1997 .

[18]  Andreas C. Cangellaris,et al.  PRIME: passive realization of interconnect models from measured data , 2001, IEEE 10th Topical Meeting on Electrical Performance of Electronic Packaging (Cat. No. 01TH8565).

[19]  Giulio Antonini,et al.  SPICE equivalent circuits of frequency-domain responses , 2003 .

[20]  Vikram Jandhyala,et al.  Oct-tree-based multilevel low-rank decomposition algorithm for rapid 3-D parasitic extraction , 2004, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[21]  H. Reichl,et al.  Time-domain modeling of lossy substrates with constant loss tangent , 2004, Proceedings. 8th IEEE Workshop on Signal Propagation on Interconnects.

[22]  Giulio Antonini,et al.  Time Domain Modeling Of PCB Discontinuities , 2003 .

[23]  T. Dhaene,et al.  Adaptive rational modeling algorithm for EM-based S-parameter data , 2002 .

[24]  Bjørn Gustavsen.  Computer Code for Rational Approximation of , 2002 .

[25]  Albert E. Ruehli,et al.  The modified nodal approach to network analysis , 1975 .

[26]  Stefano Grivet-Talocia,et al.  Passivity enforcement via perturbation of Hamiltonian matrices , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  S. Grivet-Talocia,et al.  Transient analysis of lossy transmission lines: an efficient approach based on the method of Characteristics , 2004, IEEE Transactions on Advanced Packaging.

[28]  Dirk Deschrijver,et al.  Adaptive Building of Accurate and Stable PEEC Models for EMC Applications , 2006 .

[29]  D. Wilton,et al.  Transient scattering by conducting surfaces of arbitrary shape , 1991 .

[30]  E. K. Miller,et al.  Using model-based parameter estimation to increase the efficiency of computing electromagnetic transfer functions , 1989 .

[31]  B. Gustavsen,et al.  Improving the pole relocating properties of vector fitting , 2006, 2006 IEEE Power Engineering Society General Meeting.

[32]  M. Bleszynski,et al.  AIM: Adaptive integral method for solving large‐scale electromagnetic scattering and radiation problems , 1996 .

[33]  G. Antonini,et al.  Including dispersive dielectrics in PEEC models , 2003, Electrical Performance of Electrical Packaging (IEEE Cat. No. 03TH8710).

[34]  E. Miller,et al.  Pole extraction from real-frequency information , 1980, Proceedings of the IEEE.

[35]  Peter Russer,et al.  Full-wave modeling and automatic equivalent-circuit generation of millimeter-wave planar and multila , 1999 .

[36]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .

[37]  E. K. Miller,et al.  Model-based parameter estimation in electromagnetics. II. Applications to EM observables , 1998 .

[38]  Jian-Ming Jin,et al.  The Finite Element Method in Electromagnetics , 1993 .

[39]  A. Ruehli,et al.  A method for reduced-order modeling and simulation of large interconnect circuits and its application to PEEC models with retardation , 2000 .

[40]  Giulio Antonini,et al.  PEEC Equivalent Circuits for Dispersive Dielectrics , 2004 .

[41]  Roland W. Freund,et al.  Efficient linear circuit analysis by Pade´ approximation via the Lanczos process , 1994, EURO-DAC '94.

[42]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[43]  M. S. Sarto,et al.  A new model for the FDTD analysis of the shielding performances of thin composite structures , 1999 .

[44]  Bjorn Gustavsen.  Frequency-dependent modeling of power transformers with ungrounded windings , 2004 .

[45]  L. Greengard.  The Rapid Evaluation of Potential Fields in Particle Systems , 1988 .

[46]  B. Kolundžija,et al.  Entire-domain Galerkin method for analysis of metallic antennas and scatterers , 1993 .

[47]  P. Dooren,et al.  Asymptotic Waveform Evaluation via a Lanczos Method , 1994 .

[48]  Andreas C. Cangellaris,et al.  Progress in the methodologies for the electrical modeling of interconnects and electronic packages , 2001, Proc. IEEE.

[49]  Jiming Song,et al.  Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects , 1997 .

[50]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[51]  A. Ruehli,et al.  Efficient Capacitance Calculations for Three-Dimensional Multiconductor Systems , 1973 .

[52]  T. Dhaene,et al.  Efficient GA-inspired macro-modeling of general LTI multi-port systems , 2004, Proceedings. 8th IEEE Workshop on Signal Propagation on Interconnects.

[53]  Paul Van Dooren,et al.  A rational Lanczos algorithm for model reduction , 1996, Numerical Algorithms.

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

[55]  Albert E. Ruehli,et al.  Circuit models for 3D structures with incident fields , 1993, 1993 International Symposium on Electromagnetic Compatibility.

[56]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[57]  K. Sertel,et al.  Multilevel fast multipole method solution of volume integral equations using parametric geometry modeling , 2001, IEEE Transactions on Antennas and Propagation.

[58]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[59]  D. Wilton,et al.  Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces , 1980 .

[60]  Johnson J. H. Wang.  Generalized Moment Methods in Electromagnetics: Formulation and Computer Solution of Integral Equations , 1991 .

[61]  Anestis Dounavis,et al.  Passive model reduction of multiport distributed interconnects , 2000 .

[62]  Jacob K. White,et al.  A precorrected-FFT method for electrostatic analysis of complicated 3-D structures , 1997, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[63]  R. Weigel,et al.  On the synthesis of equivalent circuit models for multiports characterized by frequency-dependent parameters , 2002, 2002 IEEE MTT-S International Microwave Symposium Digest (Cat. No.02CH37278).

[64]  Michel Nakhla,et al.  Passive interconnect reduction algorithm for distributed/measured networks , 2000 .

[65]  Lawrence T. Pileggi,et al.  Asymptotic waveform evaluation for timing analysis , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[66]  Jiming Song,et al.  Multilevel fast‐multipole algorithm for solving combined field integral equations of electromagnetic scattering , 1995 .

[67]  Albert E. Ruehli,et al.  Speeding Up PEEC Partial Inductance Computations Using a QR-Based Algorithm , 2007, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[68]  T. Dhaene,et al.  Adaptive frequency sampling algorithm for fast and accurate S-parameter modeling of general planar structures , 1995, Proceedings of 1995 IEEE MTT-S International Microwave Symposium.