The switched power converter comprises a first rectifier module (11-1) connected to a first capacitor (11-2) that, in turn, is connected to an excitation module (11-3) that applies a voltage to some input terminals (PT-1, PT-2) of a piezoelectric transformer (PT). A controller device (11-3-3) governs the excitation module (11-3) in order that the piezoelectric transformer (PT) works at constant frequency and regulates the power delivered to the output of the converter by enabling/disabling the voltage applied to the terminals (PT-1, PT-2). When the piezoelectric transformer (PT) is not transferring energy between its input terminals (PT-1, PT-2) and its output terminals (PT-3, PT-4), the converter output voltage is supplied by a second capacitor included in a second filter (11-6).