Rational Modeling Algorithm for Passive Microwave Structures and Systems

  • Dirk Deschrijver
  • Tom Dhaene
  • Oliver Salazar Celis
  • Annie Cuyt
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)


An efficient identification method is proposed for passive rational approximation of frequency domain responses. The method is applied to compute a transfer function from tabulated S-parameter data of a multiport microwave filter. Numerical results validate the robustness and efficacy of the modeling approach.


Rational Approximation Iteration Step Very Large Scale Integration Quarter Wavelength Rational Transfer Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Min, S.-H.: “Automated Construction of Macromodels from Frequency Data for Simulation of Distributed Interconnect Networks”, PhD thesis, Georgia Institute of Technology, USA, 2004Google Scholar
  2. 2.
    Choi, K.-L.: “Embedded Passives using Rational Functions in Multi-Layered Substrates”, PhD thesis, Georgia Institute of Technology, USA, 1999Google Scholar
  3. 3.
    Li, E.P., Wei, X.C., Cangellaris, A.C., Liu, E.X., Zhang, Y.J., D’Amore, M., Kim, J., Sudo, T.: “Progress review of electromagnetic compatibility analysis technologies for packages, printed circuit boards, and novel interconnects”. IEEE Trans. Electromagn. C. 52(2), 248–265 (2010)CrossRefGoogle Scholar
  4. 4.
    Saraswat, D., Achar, R., Nakhla, M.: “Enforcing Passivity for Rational Function Based Macromodels of Tabulated Data ”. IEEE Conference on Electrical Performance of Electronic Packaging (EPEP 2003), pp. 295–298. Princeton, NJ (2003)Google Scholar
  5. 5.
    Lefteriu, S., Antoulas, A.C.: “A new approach to modeling multiport systems from frequency-domain data”. IEEE Trans. Comp. Aided Des. Integrated Circ. Syst. 29(1), 14–27 (2010)CrossRefGoogle Scholar
  6. 6.
    Cuyt, A.: “Nonlinear Numerical Methods and Rational Approximation”. D. Reidel Publishing Company, Dordrecht (1988)zbMATHCrossRefGoogle Scholar
  7. 7.
    Mutnury, B.: “Macromodeling of Nonlinear Driver and Receiver Circuits ”, PhD thesis, Georgia Institute of Technology, GA, USA, 2005Google Scholar
  8. 8.
    Gustavsen, B., Semlyen, A.: “Rational approximation of frequency domain responses by vector fitting”. IEEE Trans. Power Deliv. 14(3), 1052–1061 (1999)CrossRefGoogle Scholar
  9. 9.
    Gustavsen, B.: “Improving the pole relocating properties of vector fitting”. IEEE Trans. Power Deliv. 21(3), 1587–1592 (2006)CrossRefGoogle Scholar
  10. 10.
    Deschrijver, D., Mrozowski, M., Dhaene, T., De Zutter, D.: “Macromodeling of multiport systems using a fast implementation of the vector fitting method”. IEEE Microw. Wireless Compon. Lett. 18(6), 383–385 (2008)CrossRefGoogle Scholar
  11. 11.
    Deschrijver, D., Gustavsen, B., Dhaene, T.: “Advancements in iterative methods for rational approximation in the frequency domain”. IEEE Trans. Power Deliv. 22(3), 1633–1642 (2007)CrossRefGoogle Scholar
  12. 12.
    Saraswat, D., Achar, R., Nakhla, M.S.: “Global passivity enforcement algorithm for macromodels of interconnect subnetworks characterized by tabulated data”. IEEE Trans. Very Large Scale Integration (VLSI) Syst. 13(7), 819–832 (2005)Google Scholar
  13. 13.
    Grivet-Talocia, S., Ubolli, A.: “A comparative study of passivity enforcement schemes for linear lumped macromodels”. IEEE Trans. Adv. Packag. 31(4), 673–683 (2008)CrossRefGoogle Scholar
  14. 14.
    Dhaene, T., Deschrijver, D., Stevens, N.: “Efficient algorithm for passivity enforcement of s-parameter based macromodels”. IEEE Trans. Microw. Theor. Tech. 57(2), 415–420 (2009)CrossRefGoogle Scholar
  15. 15.
    Deschrijver, D., Haegeman, B., Dhaene, T.: “Orthonormal vector fitting: A robust macromodeling tool for rational approximation of frequency domain responses”. IEEE Trans. Adv. Packag. 30(2), 216–225 (2007)CrossRefGoogle Scholar
  16. 16.
    Hendrickx, W., Deschrijver, D., Dhaene, T.: “Some remarks on the vector fitting iteration”. Post-Conference Proceedings of EMCI 2004, Mathematics in Industry, pp. 134–138. Springer, Berlin (2006)Google Scholar
  17. 17.
    Deschrijver, D., Dhaene, T.: “A note on the multiplicity of poles in the vector fitting macromodeling method”. IEEE Trans. Microw. Theor. Tech. 55(4), 736–741 (2007CrossRefGoogle Scholar
  18. 18.
    Grivet-Talocia, S.: “Passivity enforcement via perturbation of Hamiltonian matrices”. IEEE Trans. Circ. Syst. I, 51(9), 1755–1769 (2004)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Deschrijver, D., Dhaene, T.: “Fast passivity enforcement of s-parameter macromodels by pole perturbation”. IEEE Trans. Microw. Theor. Tech. 57(3), 620–626 (2009)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Boyd, S., Balakrishnan, V., Kabamba, P.: “A bisection method for computing the H inf norm of a transfer matrix and related problems”. Math. Contr. Signals Syst. 2, 207–219 (1989)Google Scholar
  21. 21.
    Zhang, Z., Wong, N.: “Passivity check of S-parameter descriptor systems via s-parameter generalized hamiltonian methods”. IEEE Trans. Adv. Packag. 33(4), 1034–1042 (2010)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Chinea, A., Grivet-Talocia, S., Deschrijver, D., Dhaene, T., Knockaert, L.: “On the construction of guaranteed passive macromodels for high-speed channels”. Design, Automation and Test in Europe (2010), Dresden, Germany, pp. 1142–1147, March 2010Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dirk Deschrijver
    • 1
  • Tom Dhaene
    • 1
  • Oliver Salazar Celis
    • 2
  • Annie Cuyt
    • 2
  1. 1.Ghent University – IBBTGhentBelgium
  2. 2.University of AntwerpAntwerpBelgium

Personalised recommendations