In this paper, a method employing both parametric excitation and harmonic forcing is applied to the excitation of a micro-ring gyroscope in order to improve its rate resolution performance. A multiple scales perturbation method is used to propose a methodology and this demonstrates the significance of the parametric instability boundary in facilitating the design of the required control strategies. The analysis shows that the ‘effective’ quality factor of any mode of vibration of the resonator may be increased arbitrarily through parametric excitation. This scheme, when applied to the primary motion of the gyroscope, allows forcing levels to be reduced by several orders of magnitude whilst sustaining the response amplitude. As the parametric excitation and forcing are at different frequencies the excitation scheme proposed minimizes the unwanted effect of electrical ‘feedthrough’ at the forcing frequency, resulting from parasitic capacitances. Simulation of the oscillator scheme, which is highly nonlinear, is achieved using MATLAB-Simulink and this validates the perturbation analysis. Agreement between the models within 8% is demonstrated. The excitation scheme proposed may be readily applied to many resonant MEMS/NEMS sensors.

In this paper an excitation method employing both harmonic forcing and parametric excitation is applied to a resonant MEMS sensor in order to investigate and characterize the phenomena of parametric resonance and parametric amplification. The motivation for this research is that parametric excitation may be used to significantly reduce the total damping in MEMS sensors in a controllable manner. This is extremely pertinent to devices where the Q-factor is a principal factor in determining sensor performance. In this paper it is shown that, by adjusting the parametric excitation parameters (frequency, amplitude and phase) of an electrostatically actuated and sensed device, the gain of the frequency response function of a mode of vibration may be amplified. The amplification is quantified by the gain factor which is characterized experimentally. The instability regions defining the regions for parametric resonance are also characterized experimentally and compared to theoretical predictions. The boundaries of these instability regions define the thresholds for parametric resonance and play a crucial role in the design of the parametric amplifier.

One of the major issues facing electrostatically actuated and sensed microelectromechanical systems (MEMS) sensors is electrical feed-through between the drive and the sense electrodes due to parasitic capacitances. This feed-through, in the case of a 'tuned' MEMS gyroscope, limits the sensor sensitivity. In the current paper, the first practical step towards demonstrating reduced feed-through using a combined harmonic forcing and parametric excitation scheme is demonstrated. The equation of motion for the primary mode of vibration of the electrostatically actuated MEMS ring gyroscope is shown to contain a stiffness modulating term which, when modulated at a frequency near twice the natural frequency of the mode, results in parametric resonance. A solution for the equation of motion is assumed, based on Floquet theory, and the method of harmonic balance is employed for analysis. Regions of stability and instability and the stability boundary demarcating the stable and unstable regions are determined. Frequency sweeps, centred on twice the measured resonant frequency of the primary mode, were performed at various values of voltage amplitudes of the parametric excitation and the parametric resonance was observed electrically at half the excitation frequency. This data were used to map the stability boundary of the parametric resonance. The theoretical and experimental stability boundaries are shown to demonstrate significant similarity.

No abstract

No abstract