  We get a new expression of the microscopic renormalized energy for a pinned
Ginzburg-Landau type energy modeling small impurities. This is done by
obtaining a sharp decomposition for the minimal energy of a Dirichlet type
functional with an L $\infty$-weight. In particular we get an explicit
expression of the microscopic renormalized energy for a circular impurity. We
proceed also to the minimization of this renormalized energy in some cases.
