Homogenization of linear spatially periodic electronic circuits

Michel Lenczner

doi:10.3934/nhm.2006.1.467

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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

Michel Lenczner^1,

1.
Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695

Received: February 2006

Revised: June 2006

Published: September 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 74Q05, 94C99; Secondary: 78M35.

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