The rectified non-linear response of a clean, time-reversal symmetric, undoped semiconductor to an ac electric field includes a well known intrinsic shift current. In a recent work we demonstrated that, when Kramers degeneracy is broken, a distinct second order rectified response appears due to Bloch state anomalous velocities in a system with an oscillating Fermi surface. This effect has been termed the resonant photovoltaic effect (RPE). It manifests itself as a resonant galvanic current peak at the interband absorption threshold in doped semiconductors or semimetals with approximate particle-hole symmetry. In this manuscript we present a detailed theory of this effect, and we evaluate the RPE for a model of the surface states of a magnetized topological insulator.