A control device controls a rectifier of a switching converter that is supplied with an input voltage and provides an output current. The rectifier is configured to rectify the output current of the converter and has at least one transistor. The control device, when the at least one transistor is turned off, provides a slow discharge path to ground in a normal operation condition and provides a fast discharge path to ground for discharging the control terminal of the at least one transistor in response to detecting a zero cross event of the current flowing through said at least one transistor.