Homogenization of electrical networks including voltage-to-voltage amplifiers

We derive the homogenized model of periodic electrical networks which inclu des resistive devices, voltage-to-voltage amplifiers, sources of tension an d sources of current. On the one hand, in considering the homogenized probl em, general conditions are stated insuring the existence and uniqueness of the solution. They are formulated in function of the network topology. On t he other hand, the two-scale transformation introduced by Arbogast, Douglas and Hornung is adapted to the context of electrical networks. New two-scal e convergence results, inspired by the principle of Allaire's two-scale con vergence, are shown in this context. In particular, the two-scale convergen ce for the tangential derivative on a network is established. Following the se results, two models of homogenized networks are derived. The first one b elongs to a general framework whereas the second one does not.