Non-linear modeling of MEMS-based oscillators using an analog hardware description language

This paper presents a Verilog-A model of a microelectromechanical systems (MEMS) clamped-clamped beam resonator. The model captures the electrical and mechanical non-linear effects, and accounts for the spring softening and Duffing behavior present in resonators at high drive levels. A transimpedance amplifier is designed in 0.13μm CMOS to implement and simulate a MEMS-based oscillator incorporating the Verilog-A model. The phase noise performance dependance on the resonator non-linear effects and its bias voltage are illustrated through simulations. Simulation results confirm that careful design must be applied when MEMS resonators are utilised in order to ensure that non-linearities and biasing do not significantly deteriorate oscillator performance.