Study of substrate energy dissipation mechanism in in-phase and anti-phase micromachined vibratory gyroscopes

This paper analyzes energy dissipation mechanisms in in-phase and anti-phase actuated micromachined z-axis vibratory gyroscopes. The type of actuation is experimentally identified as the key factor to energy dissipation. For in-phase devices, dissipation through the die substrate is the dominant energy loss mechanism. This damping mechanism depends strongly on the die attachment method; rigid attachment increases Q-factor at the cost of reduced isolation of the MEMS device from package stresses and vibrations. In contrast, anti-phase operation suppresses dissipation through the die substrate while providing immunity to external vibrations. Higher Q-factors in anti-phase devices are explained by effective subtraction of stresses applied to the substrate during vibrations. Based on the experimental investigation and the developed analytical model for energy dissipation through the die substrate, the limiting Q-factor for in-phase devices is generally below 20 thousand, while Q-factors much higher than 100 thousand can be achieved with balanced anti-phase actuated gyroscopes.