An oscillator comprises an inverter, with a resonator connected between an input and an output of the inverter. A transistor external to the inverter is connected in a current mirror mode with a transistor of the inverter so that the inverter's transistor copies the current of the external transistor. The external transistor has its drain terminal connected to the gate terminals of the inverter's transistor and of the external transistor. A current source is connected to the gate terminal of the inverter's transistor, and a switch is connected between the drain and gate terminals of the external transistor. Circuitry controls the switch so as to open the connection between the drain and gate terminals of the external transistor at the beginning of a start-up phase of the oscillator.