  The precise determination of the universality classes in self-organized
critical phenomena (SOC) is still an unsolved problem. Different SOC models
like sandpile, linear interface depinning, and the Barkhausen effect have been
investigated independently. In the present work we demonstrate that these
models can all be mapped into a linear interface depinning model driven at
constant rate. The model is found to belong to the universality class of
constant force linear interface depinning above the depinning transition, with
an upper critical dimension d_c=4. Results are compared with numerical
simulations, experiments, and previous theoretical works reported in the
literature. In this way we demonstrate a precise connection between different
SOC models which display the same universal beha
