Abstract
In this work, the electrostatic spring-softening effect is used to achieve matched resonant frequencies between two MEMS resonators. Matched-mode operation is important for a MEMS vibratory gyroscope to achieve high sensitivity. Both the capacitive micro-resonators and the phase-locked-loop (PLL) driving circuit are monolithically integrated on the same CMOS chip. In the oscillator loop, PLL provides a driving signal to the target resonator with a 90-degree phase compensation at the resonant frequency. Based on this frequency, the resonant frequency of the second micro-resonator is adjusted for mode-matching by the spring-softening electrode, whose input is provided by a PLL-based control loop. The chip containing MEMS structures, sensing circuit and PLL is fabricated by using the TSMC two-polysilicon four-metal 0.35-μm standard CMOS process. This chip area size is 2.8x2.8 mm2. The analog PLL contains a phase detector (PD), a voltage-controlled oscillator (VCO) and a loop filter. The chip contains six MEMS structures whose resonant frequencies vary due to manufacturing tolerance. Experimental results show that the frequency difference of the two MEMS resonators can be reduced from the original 250 Hz to 40 Hz with the proposed control method. The measured Allan variance provides as an efficient method to quantify frequency stability. We found the best frequency resolution was 0.62 Hz over an average time of 1 second.