HOMOGENIZATION OF ELECTRICAL NETWORKS INCLUDING VOLTAGE-TO-VOLTAGE AMPLIFIERS

Abstract

We derive the homogenized model of periodic electrical networks which includes resistive devices, voltage-to-voltage amplifiers, sources of tension and sources of current. On the one hand, in considering the homogenized problem, general conditions are stated insuring the existence and uniqueness of the solution. They are formulated in function of the network topology. On the other hand, the two-scale transformation introduced by Arbogast, Douglas and Hornung is adapted to the context of electrical networks. New two-scale. convergence results, inspired by the principle of Allaire's two-scale convergence, are shown in this context. In particular, the two-scale convergence for the tangential derivative on a network is established. Following these results, two models of homogenized networks are derived. The first one belongs to a general framework whereas the second one does not.