A power supply power supply comprising a DC voltage supply, a control unit and a plurality of high voltage channels is suggested. Each high voltage channel includes an inverter, a resonance circuit, atransformer, and a rectifier. The resonance circuit cooperates with the inverter. The inverter is formed by a first switching unit and a second switching unit whereby a voltage of a first polarity can be applied to the resonance circuit in a first switching state, whereas a voltage of a second polarity can be applied to the resonance circuit in a second switching state. The switching states can be switched by the control unit in such a manner that in a first mode of an operation for high output power, the output power can be adjusted by changing the switching frequency in the range of the resonance frequency. In a second mode of operation for low output power, the output power can be adjusted by changing the duration of the switching state at an essentially constant switching frequency, which is at least a predetermined factor lower than the resonance frequency of the resonance circuit. In addition to that a method for operating this kind of power supply with particularly low output power is proposed.