Automated Macromodelling for Simulation of Signals and Noise in Mixed-Signal/RF Systems

  • Jaijeet Roychowdhury

Abstract

During the design of electronic circuits and systems, particularly those for RF communications, the need to abstract a subsystem from a greater level of detail to one at a lower level of detail arises frequently. One important application is to generate simple, yet accurate, system-level macromodels that capture circuit-level non-idealities such as distortion. In recent years, computational (“algorithmic”) techniques have been developed that are capable of automating this abstraction process for broad classes of differential-equationbased systems (including nonlinear ones). In this paper, we review the main ideas and techniques behind such algorithmic macromodelling methods.

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References

  1. [1]
    A. Demir, E. Liu, A.L. Sangiovanni-Vincentelli and I. Vassiliou. Behavioral simulation techniques for phase/delay-locked systems. In Proceedings of the Custom Integrated Circuits Conference 1994, pages 453–456, May 1994.Google Scholar
  2. [2]
    E. Chiprout and M.S. Nakhla. Asymptotic Waveform Evaluation. Kluwer, Norwell, MA, 1994.Google Scholar
  3. [3]
    A. Costantini, C. Florian, and G. Vannini. Vco behavioral modeling based on the nonlinear integral approach. IEEE International Symposium on Circuits and Systems, 2:137–140, May 2002.Google Scholar
  4. [4]
    D. Schreurs, J. Wood, N. Tufillaro, D. Usikov, L. Barford, and D.E. Root. The construction and evaluation of behavioral models for microwave devices based on time-domain large-signal measurements. In Proc. IEEE IEDM, pages 819–822, December 2000.Google Scholar
  5. [5]
    A. Demir, A. Mehrotra, and J. Roychowdhury. Phase noise in oscillators: a unifying theory and numerical methods for characterization. IEEE Trans. Ckts. Syst.–I: Fund. Th. Appl., 47:655–674, May 2000.Google Scholar
  6. [6]
    A. Demir and J. Roychowdhury. A Reliable and Efficient Procedure for Oscillator PPV Computation, with Phase Noise Macromodelling Applications. IEEE Trans. Ckts. Syst.–I: Fund. Th. Appl., pages 188–197, February 2003.Google Scholar
  7. [7]
    P. Feldmann and R.W. Freund. Efficient linear circuit analysis by Padé approximation via the Lanczos process. IEEE Trans. CAD, 14(5):639–649, May 1995.Google Scholar
  8. [8]
    R.W. Freund and P. Feldmann. Efficient Small-signal Circuit Analysis And Sensitivity Computations With The Pvl Algorithm. Proc. ICCAD, pages 404–411, November 1995.Google Scholar
  9. [9]
    K. Gallivan, E. Grimme, and P. Van Dooren. Asymptotic waveform evaluation via a lanczos method. Appl. Math. Lett., 7:75–80, 1994.MathSciNetCrossRefGoogle Scholar
  10. [10]
    W. Gardner. Introduction to Random Processes. McGraw-Hill, New York, 1986.Google Scholar
  11. [11]
    E.J. Grimme. Krylov Projection Methods for Model Reduction. PhD thesis, University of Illinois, EE Dept, Urbana-Champaign, 1997.Google Scholar
  12. [12]
    A. Hajimiri and T.H. Lee. A general theory of phase noise in electrical oscillators. IEEE J. Solid-State Ckts., 33:179–194, February 1998.Google Scholar
  13. [13]
    J. Phillips, L. Daniel, and L.M. Silveira. Guaranteed passive balancing transformations for model order reduction. In Proc. IEEE DAC, pages 52–57, June 2002.Google Scholar
  14. [14]
    J-R. Li and J. White. Efficient model reduction of interconnect via approximate system gramians. In Proc. ICCAD, pages 380–383, November 1999.Google Scholar
  15. [15]
    J. Wood and D.E. Root. The behavioral modeling of microwave/RF ICs using nonlinear time series analysis. In IEEE MTT-S Digest, pages 791–794, June 2003.Google Scholar
  16. [16]
    K. Francken, M. Vogels, E. Martens, and G. Gielen. A behavioral simulation tool for continuous-time /spl Delta//spl Sigma/ modulators. In Proc. ICCAD, pages 229–233, November 2002.Google Scholar
  17. [17]
    J. Katzenelson and L.H. Seitelman. An iterative method for solution of nonlinear resistive networks. Technical Report TM65-1375-3, AT&T Bell Laboratories.Google Scholar
  18. [18]
    K.J. Kerns, I.L. Wemple, and A.T. Yang. Stable and efficient reduction of substrate model networks using congruence transforms. In Proc. ICCAD, pages 207–214, November 1995.Google Scholar
  19. [19]
    K. Kundert. Predicting the Phase Noise and Jitter of PLL-Based Frequency Synthesizers. www.designers-guide.com, 2002.Google Scholar
  20. [20]
    K.S. Kundert, J.K. White, and A. Sangiovanni-Vincentelli. Steady-state methods for simulating analog and microwave circuits. Kluwer Academic Publishers, 1990.Google Scholar
  21. [21]
    L. Hongzhou, A. Singhee, R. Rutenbar, and L.R. Carley. Remembrance of circuits past: macromodeling by data mining in large analog design spaces. In Proc. IEEE DAC, pages 437–442, June 2002.Google Scholar
  22. [22]
    L.M. Silveira, M. Kamon, I. Elfadel, and J. White. A coordinate-transformed Arnoldi algorithm for generating guaranteed stable reduced-order models of RLC circuits. In Proc. ICCAD, pages 288–294, November 1996.Google Scholar
  23. [23]
    M. Kamon, F. Wang, and J. White. Generating nearly optimally compact models from Krylov-subspace based reduced-order models. IEEE Trans. Ckts. Syst.-II: Sig. Proc., pages 239–248, April 2000.Google Scholar
  24. [24]
    M. F. Mar. An event-driven pll behavioral model with applications to design driven noise modeling. In Proc. Behav. Model and Simul.(BMAS), 1999.Google Scholar
  25. [25]
    N. Dong and J. Roychowdhury. Piecewise Polynomial Model Order Reduction. In Proc. IEEE DAC, pages 484–489, June 2003.Google Scholar
  26. [26]
    N. Dong and J. Roychowdhury. Automated Extraction of Broadly-Applicable Nonlinear Analog Macromodels from SPICE-level Descriptions. In Proc. IEEE CICC, October 2004.Google Scholar
  27. [27]
    L.W. Nagel. SPICE2: a computer program to simulate semiconductor circuits. PhD thesis, EECS Dept., Univ. Calif. Berkeley, Elec. Res. Lab., 1975. Memorandum no. ERL-M520.Google Scholar
  28. [28]
    O. Narayan and J. Roychowdhury. Analysing Oscillators using Multitime PDEs. IEEE Trans. Ckts. Syst.-I: Fund. Th. Appl., 50(7):894–903, July 2003.MathSciNetGoogle Scholar
  29. [29]
    A. Nayfeh and B. Balachandran. Applied Nonlinear Dynamics. Wiley, 1995.Google Scholar
  30. [30]
    E. Ngoya and R. Larchevèque. Envelop transient analysis: a new method for the transient and steady state analysis of microwave communication circuits and systems. In Proc. IEEE MTT Symp., 1996.Google Scholar
  31. [31]
    A. Odabasioglu, M. Celik, and L.T. Pileggi. PRIMA: passive reduced-order interconnect macromodelling algorithm. In Proc. ICCAD, pages 58–65, November 1997.Google Scholar
  32. [32]
    A. Odabasioglu, M. Celik, and L.T. Pileggi. PRIMA: passive reduced-order interconnect macromodelling algorithm. IEEE Trans. CAD, pages 645–654, August 1998.Google Scholar
  33. [33]
    Fujisawa Ohtsuki and Kumagai. Existence theorems and a solution algorithm for piecewise linear resistor networks. SIAM J. Math. Anal., 8, February 1977.Google Scholar
  34. [34]
    P. Li and L. Pileggi. NORM: Compact Model Order Reduction of Weakly Nonlinear Systems. In Proc. IEEE DAC, pages 472–477, June 2003.Google Scholar
  35. [35]
    P. Vanassche, G. Gielen, and W. Sansen. Constructing symbolic models for the input/output behavior of periodically time-varying systems using harmonic transfer matrices . In Proc. IEEE DATE Conference, pages 279–284, March 2002.Google Scholar
  36. [36]
    J. Phillips. Model Reduction of Time-Varying Linear Systems Using Approximate Multipoint Krylov-Subspace Projectors. In Proc. ICCAD, November 1998.Google Scholar
  37. [37]
    J. Phillips. Projection-based approaches for model reduction of weakly nonlinear, time-varying systems. IEEE Trans. CAD, 22(2):171–187, February 2000.Google Scholar
  38. [38]
    J. Phillips. Projection frameworks for model reduction of weakly nonlinear systems. In Proc. IEEE DAC, June 2000.Google Scholar
  39. [39]
    L.T. Pillage and R.A. Rohrer. Asymptotic waveform evaluation for timing analysis. IEEE Trans. CAD, 9:352–366, April 1990.Google Scholar
  40. [40]
    T.L. Quarles. Analysis of Performance and Convergence Issues for Circuit Simulation. PhD thesis, EECS Dept., Univ. Calif. Berkeley, Elec. Res. Lab., April 1989. Memorandum no. UCB/ERL M89/42.Google Scholar
  41. [41]
    R. Freund. Passive reduced-order models for interconnect simulation and their computation via Krylov-subspace algorithms. In Proc. IEEE DAC, pages 195–200, June 1999.Google Scholar
  42. [42]
    R. Freund and P. Feldmann. Reduced-order modeling of large passive linear circuits by means of the SyPVL algorithm. In Proc. ICCAD, pages 280–287, November 1996.Google Scholar
  43. [43]
    M. Rewienski and J. White. A Trajectory Piecewise-Linear Approach to Model Order Reduction and Fast Simulation of Nonlinear Circuits and Micromachined Devices. In Proc. ICCAD, November 2001.Google Scholar
  44. [44]
    M. Rosch and K.J. Antreich. Schnell stationäre simulation nichtlinearer schaltungen im frequenzbereich. AEÜ, 46(3):168–176, 1992.Google Scholar
  45. [45]
    J. Roychowdhury. MPDE methods for efficient analysis of wireless systems. In Proc. IEEE CICC, May 1998.Google Scholar
  46. [46]
    J. Roychowdhury. Reduced-order modelling of linear time-varying systems. In Proc. ICCAD, November 1998.Google Scholar
  47. [47]
    J. Roychowdhury. Reduced-order modelling of time-varying systems. IEEE Trans. Ckts. Syst.-II: Sig. Proc., 46(10), November 1999.Google Scholar
  48. [48]
    J. Roychowdhury. Analysing circuits with widely-separated time scales using numerical PDE methods. IEEE Trans. Ckts. Syst.-I: Fund. Th. Appl., May 2001.Google Scholar
  49. [49]
    W. Rugh. Nonlinear System Theory - The Volterra-Wiener Approach. Johns Hopkins Univ Press, 1981.Google Scholar
  50. [50]
    Y. Saad. Iterative methods for sparse linear systems. PWS, Boston, 1996.Google Scholar
  51. [51]
    M. Schetzen. The Volterra and Wiener Theories of Nonlinear Systems. John Wiley, 1980.Google Scholar
  52. [52]
    M. Schwab. Determination of the steady state of an oscillator by a combined time-frequency method. IEEE Trans. Microwave Theory Tech., 39:1391–1402, August 1991.Google Scholar
  53. [53]
    J. L. Stensby. Phase-locked loops: Theory and applications. CRC Press, New York, 1997.Google Scholar
  54. [54]
    S.X.-D Tan and C.J.-R Shi. Efficient DDD-based term generation algorithm for analog circuit behavioral modeling. In Proc. IEEE ASP-DAC, pages 789–794, January 2003.Google Scholar
  55. [55]
    S.X.-D Tan and C.J.-R Shi. Efficient DDD-based term generation algorithm for analog circuit behavioral modeling. In Proc. IEEE DATE Conference, pages 1108–1009, March 2003.Google Scholar
  56. [56]
    S.X.-D Tan and C.J.-R Shi. Efficient very large scale integration power/ground network sizing based on equivalent circuit modeling. IEEE Trans. CAD, 22(3):277–284, March 2003.Google Scholar
  57. [57]
    R. Telichevesky, K. Kundert, and J. White. Efficient steady-state analysis based on matrix-free krylov subspace methods. In Proc. IEEE DAC, pages 480–484, 1995.Google Scholar
  58. [58]
    P. Vanassche, G.G.E. Gielen, and W. Sansen. Behavioral modeling of coupled harmonic oscillators. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, 22(8):1017–1026, August 2003.Google Scholar
  59. [59]
    W. Daems, G. Gielen, and W. Sansen. A ?tting approach to generate symbolic expressions for linear and nonlinear analog circuit performance characteristics. In Proc.—IEEE DATE Conference, pages 268–273, March 2002.Google Scholar
  60. [60]
    L. Wu, H.W. Jin, and W.C. Black. Nonlinear behavioral modeling and simulation of phase-locked and delay-locked systems. In Proceedings of IEEE CICC, 2000, pages 447–450, May 2000.Google Scholar
  61. [61]
    X. Huang, C.S. Gathercole, and H.A. Mantooth. Modeling nonlinear dynamics in analog circuits via root localization. IEEE Trans. CAD, 22(7):895–907, July 2003.Google Scholar
  62. [62]
    X. Lai and J. Roychowdhury. Capturing injection locking via nonlinear phase domain macromodels. IEEE Trans. MTT, 52(9):2251–2261, September 2004.CrossRefGoogle Scholar
  63. [63]
    X. Lai and J. Roychowdhury. Fast, accurate prediction of PLL jitter induced by power grid noise. In Proc. IEEE CICC, May 2004.Google Scholar
  64. [64]
    X. Lai, Y. Wan and J. Roychowdhury. Fast PLL Simulation Using Nonlinear VCO Macromodels for Accurate Prediction of Jitter and Cycle-Slipping due to Loop Non-idealities and Supply Noise. In Proc. IEEE ASP-DAC, January 2005.Google Scholar
  65. [65]
    Y. Qicheng and C. Sechen. A uni?ed approach to the approximate symbolic analysis of large analog integrated circuits. IEEE Trans. Ckts. Syst.-I: Fund. Th. Appl., pages 656–669, August 1996.Google Scholar
  66. [66]
    Z. Bai, R. Freund, and P. Feldmann. How to make theoretically passive reduced-order models passive in practice. In Proc. IEEE CICC, pages 207–210, May 1998.Google Scholar
  67. [67]
    L. A. Zadeh and C. A. Desoer. Linear System Theory: The State-Space Approach. McGraw-Hill Series in System Science. McGraw-Hill, New York, 1963.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Jaijeet Roychowdhury
    • 1
  1. 1.University of MinnesotaMinneapolis

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