Nonlinearity and hysteresis of resonant strain gauges

The nonlinearity and hysteresis effects of the electrostatically activated voltage-driven resonant microbridges have been studied theoretically and experimentally. It is shown that in order to avoid vibration instability and hysteresis to occur, the choices of the ac and dc driving voltages and of the quality factor of a resonator, with a given geometry and choice of materials, are limited by a hysteresis criterion. The limiting conditions are also formulated as the hysteresis-free design rules. Expressions for the maximum allowable quality factor and maximum attainable figure of merit are given. Experimental results, as obtained from electrostatically driven vacuum-encapsulated low-pressure chemical-vapor deposition (LPCVD) polysilicon microbridges, are presented and show good agreement with the theory.