Abstract-The objective of this work is to analyze pulsed digital oscillators (PDOs), as dynamical systems. It is proved that under some conditions, the bitstream at the output of the oscillator is that of the sign of a sampled sinusoid at the resonant frequency of the resonator, and that a bijection exists between these sequences (without distinguishing between a sequence and its negated version) and those of first-order sigma-delta modulators. This provides a new and simple method of obtaining the oscillation frequency of PDOs just from their bitstream.
A novel digital oscillator topology for microelectromechanical systems (MEMS) based on bandpass sigma-delta modulation is presented. Short pulses of force of the same amplitude maintain the oscillation and the associated bit-stream output serves to know the oscillation frequency which, for low mechanical losses, is very close to the natural frequency of the MEMS resonator. 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 showing the behavior of the oscillator for different sampling frequencies and mechanical damping losses. Experimental results from an oscillator using a MEMS resonator with thermoelectric actuation and piezoresitive position sensing are presented. It is concluded that the quality of the oscillator response depends on the resonator damping losses and on the sampling frequency. The experimental results agree with the analytical and simulation results.Index Terms-Microelectromechanical systems (MEMS), oscillator, sigma-delta (6-1).
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