The rectifier includes two input paths configured to receive an alternating input voltage and two output paths configured to provide a direct output voltage. A switched-mode rectifying path is connected between one of the input paths and one of the output paths and comprises at least two semiconductor elements with controllable paths; the controllable paths are series-connected with each other. An auxiliary output node is disposed between the controllable paths of the two semiconductor elements in the rectifying path and provides an auxiliary node voltage. A controllable output path is connected downstream of one of the two output paths and comprises a semiconductor element with a controllable path, wherein the controllable path of the semiconductor element of the controllable output path is controlled by a signal representing the auxiliary node voltage.