We report on a broadband GaAs/AlAs superlattice detector for THz radiation; a THz field reduces the current through a superlattice, which is carried by miniband electrons, due to modulation of the Bloch oscillations of the miniband electrons. We studied the detector response, by use of a free electron laser, in a large frequency range (5-12 THz). The responsivity showed strong minima at frequencies of infrared active phonons of the superlattice. A theoretical analysis of the detector delivers an understanding of the role of phonons and gives a characterization of the responsivity. (C) 2001 American Institute of Physics.