An oscillator circuit comprises a crystal oscillator and an inverter. The input of the inverter is connected to the first terminal of the crystal oscillator and the output of the inverter is connected to the second terminal of the crystal oscillator, oscillator circuit is arranged to operate the inverter in its linear operating region. An amplitude regulator has an input connected to the input of the inverter, arranged to provide a first supply current IAREG to the inverter, where the magnitude of the first supply current is inversely dependent on a magnitude of a voltage at the inverter input. A digital-to-analogue converter is arranged to provide a second supply current IDAC to the inverter having a magnitude determined by a digital signal applied to a digital input of the digital-to-analogue converter.