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Homogenization of an electric circuit. (Homogénéisation d’un circuit électrique.) (French) Zbl 0887.35016
Summary: We derive the homogenized model of a periodic electric circuit including resistive devices, tension sources, and current sources. The model derivation is based on a two-scale convergence which is based on the two-scale transform introduced by [T. Arbogast, J. Douglas, and U. Hornung, SIAM J. Math. Anal. 21, 823–836 (1990; Zbl 0698.76106)]. The present two-scale convergence leads to the same results as the usual two-scale convergence introduced by Allaire. However, its statement is more general; in particular, it allows us to define easily the strong two-scale convergence, and it may be applied to functions defined on some periodical manifolds. Since electric circuits are considered as one-dimensional manifolds, the last point leads to the desired model.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
94C15 Applications of graph theory to circuits and networks
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