Research Of Equivalent Circuit For A MEMS Capacitive Square Resonator

Radio-frequency Micro-electrical-mechanical systems(RF-MEMS) can achieve multiple functions of traditional RF electrical devices through mechanical vibrating. MEMS devices are excellent on their high Q, small size, low insertion loss, low power consumption and good compatibility with traditional CMOS process. Thus they can be potential solutions to overcome the shortcomings of traditional frequency-selecting devices. However, their large motional resistance, low reliability, together with the lack of effective circuit models has long limited the application.This thesis proposes a novel equivalent circuit through the analyzing of mechanical structure and electrical property of an RF-MEMS capacitive square plate resonator. This model is then verified by experiments. What’s more, a movable electrode structure used to lower the motional resistance is also analyzed with its optimizing method presented in this thesis. The main contents of the thesis is:(1)Two methods---theoretical analyze and finite element simulation, are used in this thesis to calculate mode shape of the resonator. The results are the same. The direct separation of variables is used during the analyzing process and can be further used for calculating mechanical and electrical parameters. Another result of this theoretical analyze is the wildly used frequency calculating formula for square plate resonator.(2)By analyzing the advantages and disadvantages of traditional lumped RLC model and three different circuit models for MEMS resonator, this thesis proposes a novel voltage-controlled-current-source(VCCS) model. A voltage-controlled tuning capacitor is also added in the circuit to express the frequency nonlinearity of the device. This capacitor can be calculated and extracted from measurement data.(3)Mechanical and electrical parameters of the resonator is deduced using mechanical-electrical analogy. Results of theoretical analyze are in good agreement with references and simulation and are verified through experiments, the maximum relative error of motional parameters is 18%. The tuning capacitor is deduced using nonlinear spring constant and connected with frequency, stiffness, equivalent capacitor and inductor and vibrating amplitude. It can be seen from the results that capacitance of the tuning capacitor is negatively correlated with nonlinear frequency drifting.(4)A movable electrode structure for reducing motional resistance is analyzed in mechanics. The minimum bias voltage is calculated by comparing the electrostatic force(generated by the capacitor between electrodes and resonator body) and restrain force of the movable beam. A figure of merit, which is deduced through bias voltage, manufacturing tolerance and reliability, is proposed to optimize design of the movable beam.