Answer Happy

Q4. A capacitor can also be used for electrostatic actuation in MEMS devices. Look at the bottom of the diagram, please use the following notations to explain: Applied voltage: Charge on the capacitor: Capacitance: Spring constant: Position of the movable plate: OON V Q с k Initial gap: go Real-time gap when applying V: g Permittivity: E If other notations are used, make sure they are well defined. (1) What is pull-in instability and pull-in voltage? You can draw diagram if there is a need. [5 marks] (2) Where is the boundary of the instability? (Hint: the boundary is at z=go/3, where go is the initial gap when applied voltage is 0.) You need to provide detailed steps to shown how to derive your answer. [10 marks] (3) How to calculate the pull-in voltage at the boundary of the pull-in instability. In applications, the applied voltage can't be larger than this pull-in voltage. [5 marks] The voltage on the capacitor is controlled directly by the external voltage source k E Vin V g E z