Effects of Operational Frequency Scaling in Multi-Degree of Freedom MEMS Gyroscopes

This paper analyzes the design tradeoffs associated with increasing the operational frequency of single-axis microelectromechanical systems (MEMS) gyroscopes with multi-degree of freedom (DOF) sense modes. Previously, a z-axis multi-DOF gyroscope (1-DOF drive, 2-DOF sense) was shown to be robust to thermal variations using a prototype with a subkilohertz operational frequency; automotive applications, however, require higher frequencies of operation to suppress the effect of ambient vibrations. To study scaling effects on the multi-DOF concept, design equations were obtained in terms of operational frequency. These revealed a constraint on system parameters that introduces two scaling methods that dictate a tradeoff between gain, die size, and sense capacitance. Second generation multi-DOF gyroscopes were designed and fabricated resulting in 0.7-, 3.1-, and 5.1-kHz devices with smaller sense mode resonant frequency spacings than previously achievable. Experimental rate characterization resulted in scale factors of 14.2, 5.08, and 2.34 mu V/deg /s, respectively, confirming the predicted scaling effects while also demonstrating the feasibility of increased frequency multi-DOF gyroscopes.