Power supply comprising: - a transformer comprising a primary intended to be connected to a voltage source and having a leakage inductance (L F), the transformer being intended to be passed through by a magnetizing current (i M), - a control circuit for the magnetizing current (i M) intended to switch between: • a magnetizing state wherein the control circuit is intended to allow the magnetizing current (i M) to increase, and • a demagnetizing state wherein the control circuit is intended to reduce the magnetizing current (i M), - a control device for the control circuit intended to switch the control circuit alternatively from the magnetizing state to the demagnetizing state in order to respectively alternate a magnetization phase and a demagnetization phase, the control device being intended to cause the magnetization phase to last during a magnetization time (T F), - an output capacitor (C S) connected to a secondary of the transformer so as to form a resonant circuit with the leakage inductance (L F), the voltage between the terminals of the output capacitor (C S) corresponding to the output voltage (V S) of the power supply, characterised in that the magnetization time (T F) and the value of the output capacitor (C S) are such that, over a portion, referred to as the resonance portion, of the magnetization phase, the output voltage (V S) describes a sine wave portion and, starting from an initial value (V S0) below the median value of the sine wave, passes through said median value. - a transformer comprising a primary intended to be connected to a voltage source and having a leakage inductance (L F), the transformer being intended to be passed through by a magnetizing current (i M), - a control circuit for the magnetizing current (i M) intended to switch between: • a magnetizing state wherein the control circuit is intended to allow the magnetizing current (i M) to increase, and • a demagnetizing state wherein the control circuit is intended to reduce the magnetizing current (i M), - a control device for the control circuit intended to switch the control circuit alternatively from the magnetizing state to the demagnetizing state in order to respectively alternate a magnetization phase and a demagnetization phase, the control device being intended to cause the magnetization phase to last during a magnetization time (T F), - an output capacitor (C S) connected to a secondary of the transformer so as to form a resonant circuit with the leakage inductance (L F), the voltage between the terminals of the output capacitor (C S) corresponding to the output voltage (V S) of the power supply, • a magnetizing state wherein the control circuit is intended to allow the magnetizing current (i M) to increase, and • a demagnetizing state wherein the control circuit is intended to reduce the magnetizing current (i M), - a control device for the control circuit intended to switch the control circuit alternatively from the magnetizing state to the demagnetizing state in order to respectively alternate a magnetization phase and a demagnetization phase, the control device being intended to cause the magnetization phase to last during a magnetization time (T F), - an output capacitor (C S) connected to a secondary of the transformer so as to form a resonant circuit with the leakage inductance (L F), the voltage between the terminals of the output capacitor (C S) corresponding to the output voltage (V S) of the power supply,