Skip to main content
SpringerLink
Log in

Surrogate-Based Circuit Design Centering

  • Chapter
Book cover Surrogate-Based Modeling and Optimization

Abstract

Circuit design centering is one of the most important problems concerning the optimal design of circuits. Circuit design centering seeks nominal values of designable circuit parameters that maximize the probability of satisfying the design specifications (yield function). Design centering can be performed geometrically by finding the center of the feasible region (region in the designable parameter space where the design specifications are satisfied), or by maximizing the yield function explicitly. For all cases, the high expense of circuit simulations required obstructs the design centering process, especially for microwave circuits. To overcome this, computationally cheap surrogate-based models (e.g., space mapping, response surfaces, kriging, and neural networks) can be used for approximating the response functions or the yield function itself. In this chapter the design centering problem is formulated as an optimization problem, and the estimation of the yield function through several sampling techniques is explained. The difficulties facing the design centering process, especially for microwave circuits, are discussed, and the role of surrogate-based models in overcoming these difficulties is demonstrated. Special interest is devoted to space mapping surrogates and microwave circuit design centering. Some of the important surrogate-based circuit design centering approaches are reviewed with an overview of their theoretical bases. Tutorial and practical circuit examples are given to show the effectiveness of these approaches.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abdel-Malek, H.L., Bandler, J.W.: Yield optimization for arbitrary statistical distributions: part I—theory. IEEE Trans. Circuits Syst. 27, 245–253 (1980)

    Article  MATH  Google Scholar 

  2. Abdel-Malek, H.L., Hassan, A.S.O.: The ellipsoidal technique for design centering and region approximation. IEEE Trans. Comput.-Aided Des. 10, 1006–1014 (1991)

    Article  Google Scholar 

  3. Abdel-Malek, H.L., Hassan, A.S.O., Bakr, M.H.: Statistical circuit design with the use of a modified ellipsoidal technique. Int. J. Microw. Millimeter Waves Comput.-Aided Eng. 7, 117–129 (1997)

    Article  Google Scholar 

  4. Abdel-Malek, H.L., Hassan, A.S.O., Bakr, M.H.: A boundary gradient search technique and its application in design centering. IEEE Trans. Comput.-Aided Des. 18(11), 1654–1661 (1999)

    Article  Google Scholar 

  5. Abdel-Malek, H.L., Hassan, A.S.O., Soliman, E.A., Dakroury, S.A.: The ellipsoidal technique for design centering of microwave circuits exploiting space-mapping interpolating surrogates. IEEE Trans. Microw. Theory Tech. 54(10), 3731–3738 (2006)

    Article  Google Scholar 

  6. Allen, P.E., Holberg, D.R.: CMOS Analog Circuit Design, 2nd edn. Oxford University Press, Oxford (2002)

    Google Scholar 

  7. Antreich, K.J., Graeb, H.E., Wieser, C.U.: Circuit analysis and optimization driven by worst-case distances. IEEE Trans. Comput.-Aided Des. 13, 57–71 (1994)

    Article  Google Scholar 

  8. Bakr, M.H., Bandler, J.W., Madsen, K., Søndergaard, J.: An introduction to the space mapping technique. Optim. Eng. 2, 369–384 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bandler, J.W., Abdel-Malek, H.L.: Optimal centering, tolerancing and yield determination via updated approximations and cuts. IEEE Trans. Circuits Syst. 25, 853–871 (1978)

    Article  Google Scholar 

  10. Bandler, J.W., Chen, S.H.: Circuit optimization: the state of the art. IEEE Trans. Microw. Theory Tech. 36, 424–443 (1988)

    Article  Google Scholar 

  11. Bandler, J.W., Seviora, R.E.: Computation of sensitivities for noncommensurate networks. IEEE Trans. Circuit Theory CT-18, 174–178 (1971)

    Article  Google Scholar 

  12. Bandler, J.W., Zhang, Q.J., Song, J., Biernacki, R.M.: FAST gradient based yield optimization of nonlinear circuits. IEEE Trans. Microw. Theory Tech. 38, 1701–1710 (1990)

    Article  Google Scholar 

  13. Bandler, J.W., Biernacki, R.M., Chen, S.H., Grobelny, P.A., Hemmers, R.H.: Space mapping technique for electromagnetic optimization. IEEE Trans. Microw. Theory Tech. 42, 2536–2544 (1994)

    Article  Google Scholar 

  14. Bandler, J.W., Cheng, Q.S., Dakroury, S.A., Hailu, D.M., Madsen, K., Mohamed, A.S., Pedersen, F.: Space mapping interpolating surrogates for highly optimized EM-based design of microwave devices. In: IEEE MTT-S Int. Microwave Symp. Dig., Fort Worth, TX, vol. 3, pp. 1565–1568 (2004)

    Google Scholar 

  15. Bandler, J.W., Cheng, Q.S., Dakroury, S.A., Mohamed, A.S., Bakr, M.H., Madsen, K., Søndergaard, J.: Space mapping: the state of the art. IEEE Trans. Microw. Theory Tech. 52, 337–361 (2004)

    Article  Google Scholar 

  16. Broyden, C.G.: A class of methods for solving nonlinear simultaneous equations. Math. Comput. 19, 577–593 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  17. Cheng, Q.S., Bandler, J.W., Koziel, S., Bakr, M.H., Ogurtsov, S.: The state of the art of microwave CAD: EM-based optimization and modeling. Int. J. RF Microw. Comput.-Aided Eng. 20, 475–491 (2010)

    Article  Google Scholar 

  18. Conn, A.R., Toint, Ph.L.: An algorithm using quadratic interpolation for unconstrained derivative free optimization. In: Di Pillo, G., Giannes, F. (eds.) Nonlinear Optimization and Applications, pp. 27–47. Plenum Publishing, New York (1996)

    Google Scholar 

  19. Conn, A.R., Scheinberg, K., Toint, Ph.L.: A derivative free optimization algorithm in practice. In: Proceedings of 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis, MO (1998)

    Google Scholar 

  20. De Boor, C., Ron, A.: Computational aspects of polynomial interpolation in several variables. Math. Comput. 58, 705–727 (1992)

    MATH  Google Scholar 

  21. De Klerk, E.: Aspects of Semidefinite Programming: Interior-Point Algorithms and Selected Applications. Kluwer Academic, New York (2002)

    MATH  Google Scholar 

  22. Director, S.W., Hachtel, G.D., Vidigal, L.M.: Computationally efficient yield estimation procedures based on simplicial approximation. IEEE Trans. Circuits Syst. 25, 121–130 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  23. Elias, N.J.: Acceptance sampling: an efficient accurate method for estimating and optimizing parametric yield. IEEE J. Solid-State Circuits 29, 323–327 (1994)

    Article  Google Scholar 

  24. Fortran90 Software Repository. http://www.nag.co.uk/nagware/examples.asp

  25. Giunta, A.A., Wojtkiewicz, S.F. Jr., Eldred, M.S.: Overview of modern design of experiments methods for computational simulations. In: Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV (2003). AIAA-2003-0649

    Google Scholar 

  26. Graeb, H.: Analog Design Centering and Sizing. Springer, Amsterdam (2007)

    Google Scholar 

  27. Hassan, A.S.O.: Normed distances and their applications in optimal circuit design. Optim. Eng. 4, 197–213 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  28. Hassan, A.S.O.: Design centering and region approximation via primal-dual interior-point technique. J. Eng. Appl. Sci. 51(2), 195–212 (2004)

    Google Scholar 

  29. Hassan, A.S.O., Rabie, A.A.: Design centering using parallel-cuts ellipsoidal technique. J. Eng. Appl. Sci. 47, 221–239 (2000)

    Google Scholar 

  30. Hassan, A.S.O., Abdel-Malek, H.L., Rabie, A.A.: Design centering and polyhedral region approximation via parallel-cuts ellipsoidal technique. Eng. Optim. 36(1), 37–49 (2004)

    Article  MathSciNet  Google Scholar 

  31. Hassan, A.S.O., Abdel-Malek, H.L., Rabie, A.A.: None-derivative design centering algorithm using trust region optimization and variance reduction. Eng. Optim. 38, 37–51 (2006)

    Article  MathSciNet  Google Scholar 

  32. Hassan, A.S.O., Mohamed, A.S., El-Sharabasy, A.Y.: Statistical microwave circuit optimization via a non-derivative trust region approach and space mapping surrogates. In: IEEE MTT-S Int. Microw. Symp. Dig., Baltimore, MD, USA (2011)

    Google Scholar 

  33. Hassan, A.S.O., Abdel-Naby, A.: A new hybrid method for optimal circuit design using semi-definite programming. Eng. Optim. 1–16 (2011)

    Google Scholar 

  34. Hocevar, D.E., Lightner, M.R., Trick, T.N.: A study of variance reduction techniques for estimating circuit yields. IEEE Trans. Comput.-Aided Des. 2(3), 180–192 (1983)

    Article  Google Scholar 

  35. Hocevar, D.E., Lightner, M.R., Trick, T.N.: An extrapolated yield approximation for use in yield maximization. IEEE Trans. Comput.-Aided Des. 3, 279–287 (1984)

    Article  Google Scholar 

  36. Keramat, M., Kielbasa, R.: A study of stratified sampling in variance reduction techniques for parametric yield estimations. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 45(5), 575–583 (1998)

    Article  Google Scholar 

  37. Koziel, S., Bandler, J.W., Madsen, K.: A space-mapping frame work for engineering optimization: theory and implementation. IEEE Trans. Microw. Theory Tech. 54(10), 3721–3730 (2006)

    Article  Google Scholar 

  38. Marcuvitz, N.: Waveguide Handbook, 1st edn. McGraw-Hill, New York (1951)

    Google Scholar 

  39. Matthaei, G.L., Young, L., Jones, E.M.T.: Microwave Filters, Impedance-Matching Networks, and Coupling Structures, 1st edn. McGraw-Hill, New York (1964)

    Google Scholar 

  40. McKay, M.D., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in analysis of output from a computer code. Technometrics 21(2), 239–245 (1979)

    MathSciNet  MATH  Google Scholar 

  41. Metropolis, N., Ulam, S.: The Monte-Carlo method. J. Am. Stat. Assoc. 44, 335–341 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  42. Moré, J.J., Sorensen, D.C.: Computing a trust region step. SIAM J. Sci. Stat. Comput. 4(3), 553–572 (1983)

    Article  MATH  Google Scholar 

  43. Powell, M.J.D.: UOBYQA. Unconstrained optimization by quadratic approximation. Math. Program. 92, 555–582 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  44. Powell, M.J.D.: The NEWUOA software for unconstrained optimization without derivatives. In: Di Pillo, G., Roma, M. (eds.) Large-Scale Nonlinear Optimization, pp. 255–297. Springer, New York (2006)

    Chapter  Google Scholar 

  45. Powell, M.J.D.: Developments of NEWUOA for unconstrained minimization without derivatives. Technical Report, DAMTP 2007INA05, Department of Applied Mathematics and Theoretical Physics, Cambridge University, UK (2007)

    Google Scholar 

  46. Sapatnekar, S.S., Vaidya, P.M., Kang, S.: Convexity-based algorithms for design centering. IEEE Trans. Comput.-Aided Des. 13(12), 1536–1549 (1994)

    Article  Google Scholar 

  47. Sauer, Th., Xu, Y.: On multivariate Lagrange interpolation. Math. Comput. 64, 1147–1170 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  48. Seifi, A., Ponnambalam, K., Vlach, J.: A unified approach to statistical design centering of integrated circuits with correlated parameters. IEEE Trans. Circuits Syst. 46, 190–196 (1999)

    Article  Google Scholar 

  49. Singhal, K., Pinel, J.F.: Statistical design centering and tolerancing using parametric sampling. IEEE Trans. Circuits Syst. 28, 692–702 (1981)

    Article  Google Scholar 

  50. Soliman, E.A., Bakr, M.H., Nikolova, N.K.: An adjoint variable method for sensitivity calculations of multiport devices. IEEE Trans. Microw. Theory Tech. 52, 589–599 (2004)

    Article  Google Scholar 

  51. Soliman, E.A.: Rapid frequency sweep technique for MoM planar solvers. IEE Proc. Microw. Antennas Propag. 151, 277–282 (2004)

    Article  Google Scholar 

  52. Soliman, E.A., Bakr, M.H., Nikolova, N.K.: Accelerated gradient-based optimization of planar circuits. IEEE Trans. Antennas Propag. 53, 880–883 (2005)

    Article  Google Scholar 

  53. Styblinski, M.A., Oplaski, L.J.: Algorithms and software tools for IC yield optimization based on fundamental fabrication parameters. IEEE Trans. Comput.-Aided Des. 5, 79–89 (1986)

    Article  Google Scholar 

  54. Toh, K.-C.: Primal-dual path-following algorithms for determinant maximization problems with linear matrix inequalities. Comput. Optim. Appl. 14, 309–330 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  55. Vandenberghe, L., Boyd, S., Wu, S.-P.: Determinant maximization with linear matrix inequality constraints. SIAM J. Matrix Anal. Appl. 19, 499–533 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  56. Vandenberghe, L., Boyd, S.: Applications of semidefinite programming. Appl. Numer. Math. 29, 283–299 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  57. Wojciechowski, J.M., Vlach, J.: Ellipsoidal method for design centering and yield estimation. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 12, 1570–1579 (1993)

    Article  Google Scholar 

  58. Wojciechowski, J., Opalski, L., Zantyniski, K.: Design centering using an approximation to the constraint region. IEEE Trans. Circuits Syst. 51(3), 598–607 (2004)

    Article  Google Scholar 

  59. Yu, T., Kang, S.M., Hajj, I.N., Trick, T.N.: Statistical performance modeling and parametric yield estimation of MOS VLSI. IEEE Trans. Comput.-Aided Des. 6, 1013–1022 (1987)

    Article  Google Scholar 

  60. Zaabab, A.H., Zhang, Q.J., Nakhla, M.: A neural network modeling approach to circuit optimization and statistical design. IEEE Trans. Microw. Theory Tech. 43, 1349–1358 (1995)

    Article  Google Scholar 

  61. Zhao, W., De, A., Donoro, D.G., Zhang, Y., Sarkar, T.K.: Antenna optimization by using NEWUOA. In: IEEE Antennas, Propag. Int. Symp., APSURSI 09 (2009)

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank Prof. Slawomir Koziel, School of Science and Engineering, Reykjavik University, for his invitation to contribute to this book. The authors also would like to acknowledge the contributions to the original work by Prof. Hany Abdel-Malek, Dr. Azza Rabie, Dr. Sameh Dakroury, Dr. Ahmed Abdel-Naby, and Eng. Ahmed El-Sharabasy, Faculty of Engineering, Cairo University, which have been reviewed in this chapter.

Author information

Authors and Affiliations

  1. Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza, 12211, Egypt

    Abdel-Karim S. O. Hassan & Ahmed S. A. Mohamed

Authors
  1. Abdel-Karim S. O. Hassan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmed S. A. Mohamed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdel-Karim S. O. Hassan .

Editor information

Editors and Affiliations

  1. , Engineering Optimization & Modeling Cent, Reykjavik University, Menntavegur 1, Reykjavik, 101, Iceland

    Slawomir Koziel

  2. School of Science and Engineering, Engineering Optimization & Modeling, Reykjavik University, Menntavegur 1, Reykjavik, 101, Iceland

    Leifur Leifsson

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Hassan, AK.S.O., Mohamed, A.S.A. (2013). Surrogate-Based Circuit Design Centering. In: Koziel, S., Leifsson, L. (eds) Surrogate-Based Modeling and Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7551-4_2

Download citation

Publish with us

Policies and ethics

Search

Navigation