Three degrees of freedom weakly coupled resonators used for mass measurement.

Abstract

Objectives : A three degrees of freedom (DOF) resonator was designed to measure stiffness perturbation. The task assigned to this master thesis was to study the existing chips and to create models in order to represent their response to tiny mass perturbation (virus, bacteria, ...). Based on those models, techniques to quantify mass perturbation will be proposed.

Modelization and measurement strategy : Four modelized systems were characterized using the eigenvalue method. Those four systems are 2DOF and 3DOF, each of them with and without damping. The types of information obtained with those models are the resonant frequencies and the amplitude of mass movement in function of frequency. In order to simulate the behavior of the MEMS (frequency response and time domain simulations), an electrical model was derived from the mechanical model. Since the values of the components are not common values that can be bought, it was necessary to adapt them to build the circuit by a scaling process. A huge drawback of RLC circuits is that they cannot have as high a quality factor as MEMS. That is why quartz crystals were used instead of RLC components. Based on modelization process results, three main strategies to measure mass variation were investigated : frequency shifting, amplitude variation and amplitude ratio variation.

Conclusion : Based on the different models, it is clear that MEMS are used for their very high Q factor. The quartz model has shown that complex coupled mechanical systems can be realized by using smaller systems electrically coupled. It was also proved that 3DOF systems have a better sensitivity than 2DOF but still have low sensitivity around no perturbation. At the end of the project, the MEMS was turned into a sensor by adding a feedback loop.