Towards Abstract Analysis Techniques for Range Based System Simulations

  • Florian Schupfer
  • Michael Kärgel
  • Christoph Grimm
  • Markus Olbrich
  • Erich Barke
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 106)


Traditionally multi-run simulations are used for evaluating the correctness and behavior of electronic systems. The necessary high number of simulation runs restricts the evaluation performance, especially when also considering varying parameter sets. To solve this performance issue range based modeling and simulation techniques have emerged. They enhance the nominal system model by a range symbol covering the additional parameter deviations and when simulated provides the range based system response in one simulation run. The simulation of such a deviated system model results in a system response consisting of a nominal value superimposed by a set of ranges. These ranges define an area where all output signals, effected by the deviating parameter values confidently reside in. Transforming the range based signals from a time domain to a frequency domain representation significantly increases the analysis capabilities and provides a broader insight into the system’s behavior. This transformation operation for range based signals is defined and discussed within this work. A Discrete Fourier Transform is computed for range based signals and finally the method is discussed and interpreted on frequency spectrums of two examples.


Discrete Fourier Transform Partial Deviation Transformation Operation Affine Form Frequency Domain Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been supported by the Austrian WWTF project MARC under contract no. ICT08_012 and the German BMBF under project no. 01 M 3087.


  1. 1.
    Antreich, K., Gräb, H., Wieser, C.: Practical Methods for Worst-Case and Yield Analysis of Analog Integrated Circuits. International Journal of High Speed Electronics and Systems 4(3), 261–282 (1993)CrossRefGoogle Scholar
  2. 2.
    Grabowski, D., Grimm, C., Barke, E.: Ein Verfahren zur Effizienten Analyse von Schaltungen mit Parametervariationen. In: Tagungsband GI/ITG/GMM – Workshop Modellierung und Verifikation ’03. Dresden (2006)Google Scholar
  3. 3.
    Grabowski, D., Grimm, C., Barke, E.: Semi-Symbolic Modeling and Simulation of Circuits and Systems. In: International Symposium on Circuits and Systems 2006 (ISCAS 2006). IEEE Press, Kos, Greece (2006). DOI 10.1109/ISCAS.2006.1692752Google Scholar
  4. 4.
    Grabowski, D., Olbrich, M., Barke, E.: Ac-analyse analoger schaltungen mit affiner arithmetik. In: GMM/ITG (ed.) Analog 2008, vol. Entwicklung von Analogschaltungen mit CAE-Methoden, pp. 63–68. VDE (2008). 6 VG-Wort pagesGoogle Scholar
  5. 5.
    Grabowski, D., Olbrich, M., Barke, E.: Analog circuit simulation using range arithmetics. In: ASP-DAC ’08: Proceedings of the 2008 Asia and South Pacific Design Automation Conference, pp. 762–767. IEEE Computer Society Press, Seoul, Korea (2008)Google Scholar
  6. 6.
    Grabowski, D., Olbrich, M., Grimm, C., Barke, E.: Range Arithmetics to Speed up Reachability of Analog Systems. In: Forum on specification and Design Languages, FDL 2007, pp. 38–43 (2007)Google Scholar
  7. 7.
    Grimm, C., Heupke, W., Waldschmidt, K.: Refinement of Mixed-Signal Systems with Affine Arithmetic. In: Design, Automation and Test in Europe 2004 (DATE ’04). IEEE Press (2004)Google Scholar
  8. 8.
    Grimm, C., Heupke, W., Waldschmidt, K.: Analysis of Mixed-Signal Systems with Affine Arithmetic. IEEE Transactions on Computer Aided Design of Circuits and Systems 24(1), 118–123 (2005). DOI 10.1109/TCAD.2004.839469(410)24CrossRefGoogle Scholar
  9. 9.
    Heupke, W., Grimm, C., Waldschmidt, K.: Semi-symbolic simulation of nonlinear systems. In: Forum on Specification and Design Languages 2005 (FDL’05). ECSI, Lausanne (2005)Google Scholar
  10. 10.
    Heupke, W., Grimm, C., Waldschmidt, K.: Advances in Specification and Design Languages for SoC, chap. Modeling Uncertainty in Nonlinear Systems with Affine Arithmetic, pp. 198–213. Springer-Verlag (2006)Google Scholar
  11. 11.
    M.Andrade, J.Comba, J.Stolfi: Affine arithmetic (extended abstract). In: INTERVAL ’94. St. Petersburg, Russia (1994)Google Scholar
  12. 12.
    Messine, F., Touhami, A.: A General Reliable Quadratic Form: An Extension of Affine Arithmetic. Reliable Computing 12(3), 171–192 (2006)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Moore, R.E.: Interval Analysis. Prentice-Hall, Eaglewood Cliffs, NJ (1966)MATHGoogle Scholar
  14. 14.
    Rafaila, M., Grimm, C., Decker, C., Pelz, G.: Sequential design of experiments for effective model-based validation of electronic control units. e&i Elektrotechnik und Informationstechnik 127, 164–170 (2010)Google Scholar
  15. 15.
    Rubinstein, R.: Simulation and the Monte Carlo Method. John Wiley&Sons, Inc., New York, NY, USA (1981)CrossRefMATHGoogle Scholar
  16. 16.
    Schupfer, F., Grimm, C.: Towards more Dependable Verification of Mixed-Signal Systems. In: Verification over discrete-continuous boundaries, no. 10271 in Dagstuhl Seminar Proceedings (2010)Google Scholar
  17. 17.
    Schupfer, F., Kärgel, M., Grimm, C., Olbrich, M., Barke, E.: Towards Abstract Analysis Techniques for Range Based System Simulations. In: Proceedings of the 2010 Gorum on specification & Design Languages, FDL 2010, pp. 159–164 (2010)Google Scholar
  18. 18.
    Shou, H., Lin, H., Martin, R., Wang, G.: Modified Affine Arithmetic Is More Accurate than Centered Interval Arithmetic or Affine Arithmetic. In: Martin(Eds.), Lecture Notes in Computer Science 2768, Mathematics of Surfaces, Springer-Verlag, pp. 355–365. Springer (2003)Google Scholar
  19. 19.
    Singhee, A., Rutenbar, R.A.: Statistical Blockade: A Novel Method for Very Fast Monte Carlo Simulation of Rare Circuit Eevents, and its Application. In: Design, Automation Test in Europe Conference Exhibition, 2007. DATE‘07, pp. 1–6 (2007)Google Scholar
  20. 20.
    Vachoux, A., Grimm, C., Einwich, K.: Analog and Mixed-Signal Modeling with SystemC-AMS. In: International Symposium on Circuits and Systems 2003 (ISCAS ’03). IEEE Press, Bangkok, Thailand (2003)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Florian Schupfer
    • 1
  • Michael Kärgel
    • 2
  • Christoph Grimm
    • 1
  • Markus Olbrich
    • 2
  • Erich Barke
    • 2
  1. 1.Institute of Computer TechnologyVienna University of TechnologyViennaAustria
  2. 2.Institute of Microelectronic SystemsLeibniz University of HannoverHannoverGermany

Personalised recommendations