  Given a supervector bundle $E = E_0\oplus E_1 \to M$, we exhibit a
parametrization of Quillen superconnections on $E$ by graded connections on the
Cartan-Koszul supermanifold $(M;\Omega (M))$. The relation between the
curvatures of both kind of connections, and their associated Chern classes, is
discussed in detail. In particular, we find that Chern classes for graded
vector bundles on split supermanifolds can be computed through the associated
Quillen superconnections.
