Frequency Stability of a Closed-Loop Oscillator Using Micro-Electro-Mechanical Cantilever Resonator Against Temperature Fluctuation

The frequency stability of a silicon cantilever resonator against temperature was investigated under open-loop and closed-loop conditions. The authors found that the adjustment of the circuit phase in the closed-loop condition induced a significant change in temperature coefficient. The observed temperature coefficient dependence on the circuit phase was analyzed with the temperature dependence of elasticity in silicon and the phase shift originated from the oscillation circuit. The existence of a phase shift of 1.37 \circ /°C was evaluated from the measured results. The phase effect was comparable to the elasticity effect on the temperature coefficient.