Resonant power converters and inverters include a self-oscillating feedback loop coupled from a switch output to a control input of a switching network comprising one or more semiconductor switches. The self-oscillating feedback loop sets a switching frequency of the power converter and comprises a first intrinsic switch capacitance coupled between a switch output and a control input of the switching network and a first inductor. The first inductor is coupled in-between a first bias voltage source and the control input of the switching network and has a substantially fixed inductance. The first bias voltage source is configured to generate an adjustable bias voltage applied to the first inductor. The output voltage of the power converter is controlled in a flexible and rapid manner by controlling the adjustable bias voltage.