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
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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