Homogenization of an electric circuit. (Homogénéisation d’un circuit électrique.) (French) Zbl 0887.35016

Lenczner, Michel

C. R. Acad. Sci., Paris, Sér. II, Fasc. b 324, No. 9, 537-542 (1997).

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

Keywords:

periodic electric circuit; two-scale convergence; two-scale transform

Citations:

Zbl 0698.76106