The invention relates to a power supply unit with an inverter which co-operates with a resonant circuit (L, C) and can be controlled so as to adjust the output power by means of a control unit (6). The power supply unit is characterized notably by the fact that it is formed by a first and a second switching unit (S1, S4; S2, S3) whereby a voltage of a first polarity can be applied to the resonant circuit (L, C) in a first switching state and a voltage of a second polarity can be applied thereto in a second switching state, the switching states being switchable by the control unit (6) in such a manner that in a first mode of operation for low output powers the output power can be adjusted by changing the duration of the switching states at an essentially constant switching frequency fs which is at least a predetermined factor lower than the resonance frequency fres of the resonant circuit, and that in a second mode of operation for high output powers the output power can be adjusted by changing the switching frequency in the range of the resonance frequency.