A power switching converter includes a switch coupled to an input terminal through a primary winding of a transformer and a control circuit configured to drive the switch to provide a regulated output signal at a secondary winding of the transformer. A wake up circuit is provided to force the switching-on of the switch when the power converter enters in a burst mode. The wake up circuit includes a transmitting section coupled to the secondary winding and a receiving section coupled to an auxiliary winding of the transformer and the control circuit. The transmitting section is configured to provide a wake up signal communicated in a wireless manner to the receiving section when the output signal falls below a threshold value.