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Networks and Heterogeneous Media

2006, Volume 1, Issue 3: 467-494. doi: 10.3934/nhm.2006.1.467
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Homogenization of linear spatially periodic electronic circuits

  • 1.
    Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695
  • Received: 01 February 2006 Revised: 01 June 2006

  • Primary: 74Q05, 94C99; Secondary: 78M35.

  • In this paper we establish a simplified model of general spatially periodic linear electronic analog networks. It has a two-scale structure. At the macro level it is an algebro-differential equation and a circuit equation at the micro level. Its construction is based on the concept of two-scale convergence, introduced by the author in the framework of partial differential equations, adapted to vectors and matrices. Simple illustrative examples are detailed by hand calculation and a numerical simulation is reported.

    Citation: Michel Lenczner. Homogenization of linear spatially periodic electronic circuits[J]. Networks and Heterogeneous Media, 2006, 1(3): 467-494. doi: 10.3934/nhm.2006.1.467

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  • In this paper we establish a simplified model of general spatially periodic linear electronic analog networks. It has a two-scale structure. At the macro level it is an algebro-differential equation and a circuit equation at the micro level. Its construction is based on the concept of two-scale convergence, introduced by the author in the framework of partial differential equations, adapted to vectors and matrices. Simple illustrative examples are detailed by hand calculation and a numerical simulation is reported.


  • This article has been cited by:

    1. N. Ratier, M. Lenczner, 2009, Simulation of large-scale periodic circuits by a homogenization method, 978-1-4244-4159-4, 1, 10.1109/ESIME.2009.4938413
    2. Scott Cogan, Hui Hui, Michel Lenczner, Emmanuel Pillet, Nicolas Rattier, Youssef Yakoubi, 2013, 9781118557815, 149, 10.1002/9781118557815.ch6
    3. Matthieu Brassart, Michel Lenczner, A two-scale model for the periodic homogenization of the wave equation, 2010, 93, 00217824, 474, 10.1016/j.matpur.2010.01.002
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  • © 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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