Sensitivity of Lumped Parameters to Geometry Changes in Finite Element Models

  • Sebastian SchuhmacherEmail author
  • Carsten Potratz
  • Andreas Klaedtke
  • Herbert De Gersem
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 28)


The functional behavior of an electronic device is represented by an idealized circuit. Undesired parasitic interactions, such as electromagnetic-compatibility (EMC) problems, are modeled by additional lumped elements in the circuit. Device design parameters, e.g. partial inductances, must be optimized to improve EMC. This paper presents a sensitivity analysis method which relates changes to circuit parameters to changes to 3D model parameters.



The π-filter model used in Sect. 4.3.3 was kindly provided by Dr. Christoph Keller, Robert Bosch GmbH (CR/ARE1).


  1. 1.
    Traub, F., Hansen, J., Ackermann, W., Weiland, T.: Generation of physical equivalent circuits using 3d simulations. In: 2012 IEEE International Symposium on Electromagnetic Compatibility (EMC), pp. 486–491. IEEE, New York (2012)Google Scholar
  2. 2.
    Traub, F., Hansen, J., Ackermann, W., Weiland, T.: Automated construction of physical equivalent circuits for inductive components. In: International Symposium on Electromagnetic Compatibility (EMC Europe), Piscataway, NJ, 2013, pp. 67–72. IEEE, New York (2013)Google Scholar
  3. 3.
    Wittig, T., Schuhmann, R., Weiland, T.: Model order reduction for large systems in computational electromagnetics. Linear Algebra Appl. 415(2–3), 499–530 (2006)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Heeb, H., Ruehli, A.: Three-dimensional interconnect analysis using partial element equivalent circuits. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 39(11), 974–982 (1992)CrossRefGoogle Scholar
  5. 5.
    Bondarenko, N., Makharashvili, T., He, J., Berger, P., Drewniak, J., Ruehli, A.E., Beetner, D.G.: Development of simple physics-based circuit macromodel from PEEC. IEEE Trans. Electromagn. Compat. 58(5), 1485–1493 (2016)CrossRefGoogle Scholar
  6. 6.
    Belegundu, A.D.: Lagrangian approach to design sensitivity analysis. J. Eng. Mech. 111(5), 680–695 (1985)CrossRefGoogle Scholar
  7. 7.
    Raviart, P.-A., Sonnendrücker, E.: A hierarchy of approximate models for the Maxwell equations. Numer. Math. 73(3), 329–372 (1996)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Larsson, J.: Electromagnetics from a quasistatic perspective. Am. J. Phys. 75(3), 230–239 (2007)CrossRefGoogle Scholar
  9. 9.
    Hansen, J., Potratz, C.: Capacity extraction in physical equivalent networks. In: 2015 IEEE International Symposium on Electromagnetic Compatibility (EMC), pp. 491–496. IEEE, New York (2015)Google Scholar
  10. 10.
    Traub, F., Hansen, J., Ackermann, W., Weiland, T.: Eigenmodes of electrical components and their relation to equivalent electrical circuits. In: 2013 IEEE International Symposium on Electromagnetic Compatibility (EMC), pp. 287–293. IEEE, New York (2013)Google Scholar
  11. 11.
    Paul, C.R.: Inductance: Loop and Partial. Wiley, Oxford (2010)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Sebastian Schuhmacher
    • 1
    Email author
  • Carsten Potratz
    • 1
  • Andreas Klaedtke
    • 1
  • Herbert De Gersem
    • 2
  1. 1.Robert Bosch GmbH - Corporate ResearchRenningenGermany
  2. 2.TU DarmstadtDarmstadtGermany

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