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A novel digital oscillator for MEMS, based on bandpass sigma-delta modulation is presented. Short pulses of force of the same amplitude maintain the oscillation and their associated bit-stream output serves to know the oscillation frequency of the resonator, which for low mechanical losses is very close to the natural frequency. Position sensing requirements are extremely simplified because at each sampling time it is only necessary to know whether the resonator position is above or below the steady state position. Continuous-time simulations are presented which show the behavior of the oscillator for a reference MEMS resonator and different sampling frequencies.