A micro-system, for example a micro-sensor, includes a resonator 10 with vibrating element(s) 11 receiving an excitation signal E of a loop 20 for automatic gain control, as a function of an amplitude setpoint (C) and providing as output a signal y(t) defined by a peak amplitude having a nominal value A0 dependent on the said setpoint and a resonant frequency. The micro-sensor integrates a circuit for measuring a quality factor of the resonator based on a measurement of an attenuation of the output signal during a momentary phase of cutoff of the excitation signal E applied to the resonator. This circuit for measuring the quality factor is configured so as to activate the excitation signal cutoff phase, for a duration of cutoff Td such that at the end of the cutoff phase, the peak amplitude of the output signal is attenuated by factor to the nominal peak amplitude A0 at the start of the cutoff phase, by a factor k with 1