Monte Carlo Simulation Using VHDL-AMS

  • Ekkehart-Peter Wagner
  • Joachim Haase


Monte Carlo simulation is widely used in Spice-like circuit simulators. It allows to obtain statistical information derived from estimates of the random variability of circuit parameters. Multiple simulation runs are carried out with different sets of parameters. VHDL-AMS provides flexible possibilities to specify nominal and tolerance values and their distributions. Correlation between parameters can easily be taken into account. This is especially important if behavioral models are considered. The paper describes requirements and implementation aspects of the Monte Carlo simulation using VHDL-AMS.


Monte Carlo simulation VHDL-AMS 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Box, G.E.P., and Draper, N.R. (1987). Empirical Model-Building and Response Surfaces. New York: John Wiley & Sons.Google Scholar
  2. Box, G.E.P., and M.E. Muller. “A Note on the Generation of Random Normal Deviates,” Annals Math. Stat. 29(1958), pp. 610–611.Google Scholar
  3. Christen, E. “Statistical Modeling,” Available: Scholar
  4. Esbaugh, K.S. “Generation of correlated parameters for statistical circuit simulation,” Trans. on CAD 11(1992)10, pp. 1198–1206.Google Scholar
  5. Forsythe, G.E. (1972). Von Neumann’s comparison method for random sampling from the normal and other distributions. Report CS-TR-72-254. Stanford University. Available: Scholar
  6. Graham, W.N. “A Comparison of Four Pseudo Random Number Generators Implemented in Ada,” ACM SIGSIM Simulation Digest 22(1992)2, pp. 3–18.Google Scholar
  7. IEEE Standard VHDL Analog and Mixed-Signal Extensions (IEEE Std 1076.1-1999). Approved 18 March 1999. Available: Scholar
  8. IEEE Standard VHDL Mathematical Packages (IEEE Std 1076.2-1996). Approved 19 September 1996.Google Scholar
  9. Karvanen, J. “Generation of Correlated Non-Gaussian Random Variables from Independent Components,” Proc. 4th Int. Symposium on Independent Component Analysis and Blind Signal Separation ICA 2003, April 2003, Nara (Japan), pp. 769–774.Google Scholar
  10. L’Ecuyer, P. “Efficient and Portable Combined Random Number Generators,” Communications of the ACM 31(1988)6, pp. 742–774.MathSciNetCrossRefGoogle Scholar
  11. Monnerie, G., N. Lewis, D. Dallet, H. Levi, and Robbe, M. “Modelling of transient noise sources with VHDL-AMS and normative spectral interpretation,” Proc. Forum on Specification & Design Languages FDL’03, September 23–26, 2003, Frankfurt/M., pp. 108–119.Google Scholar
  12. O’Connor P.D.T. (2002). Practical Reliability Engineering. Chichester: John Wiley & Sons Ldt.Google Scholar
  13. Schrüfer, E. (1990). Signalverarbeitung. München-Wien: Carl Hanser Verlag.Google Scholar
  14. Shared Variable WG (IEEE PAR 1076a) Homepage. Available: Scholar
  15. SystemVision. Mentor Graphics Corp. Product Information. Available: Scholar
  16. Vlach, J., and K. Singhal (1994). Computer Methods for Circuit Analysis and Design. New York: Van Nostrand Reinhold.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Ekkehart-Peter Wagner
    • 1
  • Joachim Haase
    • 2
  1. 1.Siemens VDO Automotive AGRegensburgGermany
  2. 2.Fraunhofer-Institut Integrierte SchaltungenBranch Lab EAS DresdenGermany

Personalised recommendations