Skip to main content
SpringerLink
Log in

Structure-Preserving-Based Model-Order Reduction of Parameterized Interconnect Systems

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In recent years, the continued miniaturization of VLSI circuits leads to the need for more efficient simulation of large-scale linear dynamical systems with ever-increasing state-space dimension. The linear dynamical systems in VLSI circuit simulation are RC or RCL models of the VLSI circuit’s interconnected system. Model-order reduction is an important technique to reduce such a high complexity. Along the technology scaling, the indetermination in the manufacturing process causes variations in the critical dimensions and interlevel dielectric thickness of interconnects, which could make the system performance unpredictable and produce a significant parametric yield loss. An efficient exploitation of these design activities results in a parameterized model-order reduction technique able to reduce large systems of equations with respect to all of the variable parameters of the circuit, (i.e., resistance, capacitance, and inductance). For this purpose, we propose a novel parameterized model-order reduction method for interconnect variation systems, which is based on an efficient and reliable combination of invariable structure-preserving model-order reduction (SPMOR) methods and variable parameter retaining schemes. It is referred to as a parameterized interconnect model-order reduction via structure-preserving algorithm. The SPMOR model yields the same form of the original state equation and preserves the passivity of the parameterized RC and RLC networks, like the well-known passive reduced-order interconnect algorithm for nonparameterized RC and RLC networks. The most important benefit it entails is the ability to preserve the probability characteristic of the original interconnect systems. Pertinent numerical examples are proposed to validate the proposed SPMOR approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. E. Acar, S. Nassif, Y. liu, L.T. Pileggi, Time-domain simulation of variational interconnect models, in Proceedings of the International Symposium Quality Electronic Dessign (2002) pp. 419–424

  2. M. Ahmadloo, A. Dounavis, Parameterized model order reduction of electromagnetic systems using multiorder arnoldi. IEEE Trans. Adv. Packag. 33(4), 1012–1020 (2010)

    Article  Google Scholar 

  3. U. Baur, P. Benner, Model reduction for parametric systems using balanced truncation and interpolation. Automatisierungstechnik 57(8), 411–420 (2009)

    Article  Google Scholar 

  4. U. Baur, P. Benner, A. Greiner, J.G. Korvink, J. Lienemann, C. Moosmann, Parameter preserving model order reduction for MEMS applications. Math. Comput. Model. Dyn. Syst. 8(7), 1–20 (2010)

    MATH  Google Scholar 

  5. J.P. Berrut, R. Baltensperger, H.D. Mittelmann, Recent developments in barycentric rational interpolation. Trends Appl. Constr. Approx. 151, 27–51 (2005)

    MathSciNet  MATH  Google Scholar 

  6. L. Codecasa, A novel approach for generating boundary condition independent compact dynamic thermal networks of packages. IEEE Trans. Compon. Packag. Technol. 28(4), 593–604 (2005)

    Article  Google Scholar 

  7. L. Daniel, O.C. Siong, L.S. Chay, K.H. Lee, J. Whilte, A multiparameter moment-matching model-reduction approach for generation geometrically parameterized interconnect approach for generating geometrically parameterized interconnect performance models. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 23(5), 678–693 (2004)

    Article  Google Scholar 

  8. V.H.O. Farle, R.D. Edlinger, An Arnoldi type algorithm for parametric finite element modeling of microwave components. PAMM 5(1), 655–656 (2005)

    Article  Google Scholar 

  9. P.I.O. Farle, V. Hill, R.D. Edlinger, Ordnungsreduktion linearer zeitinvarianter finite element modelle mit multivariater poly nomierller parametrierung. Automatiseirungstechnik 54(4), 161–169 (2006)

    Google Scholar 

  10. L. Feng, Parameter independent model order reduction. Math. Comput. Simul. 68(3), 221–234 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Z. Feng, P. Li, Performance-oriented statistical parameter reduction of parameterized systems via reduced rank regression, in Proceedings of the IEEE/ACM International Conference on Compututer-Aided Design (2006), pp. 868–875

  12. L.H. Feng, E.B. Rudnyi, J.G. Korvink, Preserving the film coefficient as a parameter in the compact thermal model for fast electrothermal simulation. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 24(12), 1838–1847 (2005)

    Article  Google Scholar 

  13. F. Ferranti, G. Antonini, T. Dhaene, L. Knockaert, Guaranteed passive parameterized model order reduction of the partial element equivalent circuit method. IEEE Trans. Electromagn. Compat. 52(4), 974–984 (2010)

    Article  Google Scholar 

  14. F. Ferranti, G. Antonini, T. Dhaene, L. Knockaert, A. Ruehli, Physics-based passivity-preserving parameterized model order reduction for PEEC circuit analysis. IEEE Trans. Compon. Packag. Manuf. Technol. 1(3), 399–409 (2011)

    Article  MATH  Google Scholar 

  15. F. Ferranti, M. Nakhla, G. Antonini, Interpolation-based parameterized model order reduction of delayed systems. IEEE Trans. Microw. Theory Tech. 60(3), 431–440 (2012)

    Article  Google Scholar 

  16. R. Freund, SPRIM: structure-preserving reduced-order interconnect macromodeling, in IEEE/ACM International Conference on Computer-Aided Design (Los Alanmos, 2004), pp. 80–87

  17. R.W. Freund, Passive reduced order models for interconnect simulation and their computation via Krylov-subspace algorithms, In Proceedings of the 36th ACM/IEEE Design Automation Conference (New York, 1999), pp. 195–200

  18. R.W. Freund, Krylov-subspace methods for reduced order modeling in circuits simulation. J. Comput. Appl. Math. 123(1–2), 395–421 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  19. P.K. Gunupudi, R. Khazaka et al., Passive parameterized time-domain macromodels for high-speed transmission line networks. IEEE Trans. Microw. Theory Tech. 51(12), 2347–2354 (2003)

    Article  Google Scholar 

  20. P. Gunupudi, R. Khazaka, M. Nakhla, Analysis of transmission line circuits using multidimensional model reduction techniques. IEEE Trans. Adv. Packag. 25(2), 174–180 (2002)

    Article  Google Scholar 

  21. P. Heydari, M. Pedram, Model-order reduction using variational balanced truncation with spectral shaping. IEEE Trans. Circuits Syst. I Regul. Pap. 53(4), 879–891 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  22. A. Klimke, Sparse Grid Interpolation Toolbox-User’s Guide, in IANS report, University of Stuttgart (2007)

  23. Y.T. Li, Z. Bai, Y. Su, X. Zeng, Model order reduction of parameterized interconnect network via a two-directional arnoldi process. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 27(9), 1571–1582 (2008)

    Article  Google Scholar 

  24. X. Li, P. Li, L.T. Pileggi, Parameterized interconnect order reduction with explicit-and-implicit multi-parameter moment matching for inter/introdie variations, in Proceedings of the IEEE/ACM International Conference on Computer-Aided Design (2005), pp. 806–812

  25. P. Li, F. Liu, X. Li, L. and etc, Modeling interconnect variability using efficient parametric model order reduction, in Proceedings of the IEEE/ACM Design, Automation and Test in Europe (2005), pp. 958–963

  26. F. Lihong, Parameter independent model order reduction. Math. Comput. Simul. 68, 221–234 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  27. Y. Liu, L.T. Pileggi, A.J. Strojwas, Model order-reduction of RCL interconnect including variational analysis, in Proceedings of the 36th IEEE/ACM Design Automation Conference (1999), pp. 201–206

  28. N. Mi, B. Yan, S. X.-D. Tan, J. Fan, H. Yu, General block structure-preserving reduced order modeling of linear dynamic circuits, in Proceedings of the 8th International Symposium on Quality Electronic Design (2007)

  29. C. Moosmann. ParaMOR: Model Order Reduction for Parameterized MEMS Application, Ph.D. Dissertation, University of Freiburg—IMTEK, (2007)

  30. C. Moosmann, E.B. Rudnyi, J.G. Korvink, A. Greiner, Parameter preserving model order reduction of a flow meter, in Proceedings of Nanotech 2005, vol. 3 ( Anaherm 2005), pp. 684–687

  31. E.E. Nigussie, Variation Tolerant On-Chip Interconnects (Springer, New York, 2012)

    Book  Google Scholar 

  32. A. Odabasioglu, M, Celik, L.T. Pileggi, PRIMA: passive reduced-order interconnect macromodeling algorithm, in International Conference on Computer-Aided Design (Los Alamitos, 1997), pp. 58–65

  33. M. Orshansky, S.R. Nassif, D. Boning, Design for Manufacturability and Statistical Design: A Constructive Approach (Springer, New York, 2008)

    Google Scholar 

  34. J.R. Phillips, Variational interconnect analysis via PMTBR, in Proceedings of the IEEE/ACM International Conference on Compututer-Aided Design (2004), pp. 872–879

  35. J.R. Phillips, L.M. Silveira, Poor man’s TBR: a simple modle reduction scheme. IEEE Trans. Comput. Aided Des. Integr. Circuits Ssyst. 24(1), 43–55 (2005)

    Article  Google Scholar 

  36. L.T. Pillage, R.A. Rohrer, Asymptotic waveform evaluation for timing analysis. IEEE Trans. comput. Aided Des. 9(4), 352–366 (1990)

    Article  Google Scholar 

  37. M. Sampath, A. Dounavis, R. Khazaka, Parameterized model order reduction techniques for FEM based full wave analysis. IEEE Trans. Adv. Packag. 32(1), 2–12 (2009)

    Article  Google Scholar 

  38. K.C. Sou, A. Megretski, L. Daniel, A quasi-convex optimization approach to parameterized model order reduction. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 27(3), 456–469 (2008)

    Article  Google Scholar 

  39. S.G. Talocia, S. Acquadro, M. Bandinu, F.G. Canavero, I. Kelander, M. Rouvala, A parameterization scheme for lossy transmission line macromodels with application to high speed interconnects in mobile devices. IEEE Trans. Electromagn. Compat. 49(1), 18–24 (2007)

    Article  Google Scholar 

  40. J. Wang, P. Ghanta, S. Vrudhula, Stochastic analysis of interconnect performance in the presence of process variations, in Proceding of the IEEE/ACM International Conference on Comutuer-Aided Design (2004), pp. 880–886

  41. J.M. Wang, O.A. Hafiz, J. Li, A linear fractional transform based model for interconnect parametric uncertainty, in Proceedings of the 41st IEEE/ACM Dessign, Auttomation Conference (2004), pp. 375–380

  42. D.S. Weile, E. Michielssen, E. Grimme, K. Gallivan, A method for generating rational interpolant reduced order models of two-parameter linear systems. Appl. Math. Lett. 12, 93–102 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  43. M.R. Wohlers, Lumped and Distributed Passive Networks (Academic Press, New York, 1969)

    MATH  Google Scholar 

Download references

Acknowledgements

This research is supported by “The Fundamental Research Funds for the Central Universities” (Grant No. HIT.NSRIF.2016107).

Author information

Authors and Affiliations

  1. School of Information and Electrical Engineering, Harbin Institute of Technology at Weihai, Weihai, China

    Xinsheng Wang

  2. School of Information Science and Engineering, Zhejiang University Ningbo Institute of Technology, Ningbo, China

    Mingyan Yu

  3. International Micro-Electronic Center, Harbin Institute of Technology at Weihai, Weihai, China

    Chenxu Wang

Authors
  1. Xinsheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mingyan Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chenxu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinsheng Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Yu, M. & Wang, C. Structure-Preserving-Based Model-Order Reduction of Parameterized Interconnect Systems. Circuits Syst Signal Process 37, 19–48 (2018). https://doi.org/10.1007/s00034-017-0561-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-017-0561-2

Keywords

Search

Navigation