Unformatted text preview:

qEqFKG=EGParallel-plate capacitordwlArea: A=wlX0xVFWhat’s the electrostatic force on the electrodes?Fixed electrodeMovable electrodedACCVQε==222xAVxVCxVQQEFxVEε−=−=−==−=xxACε=Electrostatic ActuationWhat’s wrong here?ρ(X)E(X)-V/xXXMethod 1: Assume the charges distribute in a sheet with small but nonzero thickness.2222122)()(xAVxCVxVQdXXEXFερ−=−=−==∫GMethod 2 (energy method): 222222)(21 )( ,)(21 0VxAVdxxdCFVdxxdCdxdQVdxdEVdxxdCdxdEdxdEdxdEFdEdEFdxBCBCBCε−==⇒−=−==−−=⇒=++Assume the electrode moves by a very small distance dx. The energy conservation of the system requires:The stored energy of a capacitorVqAdQCQdqCqdqqVWQQε22)(2200====∫∫ Half of the field in a capacitor is due to the charges on a given plateÆ only one half of the field has to be taken into account to calculate the forceE0+Q-Q-QE0/2Field with two platesField with only one platesTangential force to the plateYZVybd0F0)(dbyyCε=202022022)(,21)(210VdbFVdbVdyydCdydQVdydEVdbVdyydCdydEdydEdydEFdEdEFdyBCBCBCεεε=⇒−=−=−===−−=⇒=++Parallel-Plate Actuator, Voltage-controlVFixed electrodekZd00Suppose the displacement of the top electrode is δThe force balance requires:2202( )AVkdεδδ=−δFF=kδd0Stable unstableMathematically, the condition for a stableState isElectrostatic forceSpring force2202( )AVFkdεδδ=−−23000()FAVkdεδδ∂<⇒ −<∂−(*)Balanced position:abVoltage-control, InstabilityVFixed electrodekZd00This means that the balanced displacement is stable when it is less than1/3 of d0 no matter what the spring constant is23000()FAVkdεδδ∂<⇒−<∂−2202( )AVkdεδδ=−223200()2()AV AVddεεδδδ<−−02dδδ−>03dδ<Q: does Eq.(*) necessarily have solution between 0 and d0What will happen if we increase the voltage applied between the two electrodes?δFF=kδd0The electrostatic force Feincreases as V increases. Points a and b move closer with each other. Finally, at a critical voltage VPI a and b will coincide. For any voltage larger than VPIthere will be no intersection between the two curves. The This means there is no equilibrium position between the two electrodes. The top electrode will collapse to the bottom electrode. This phenomenon is called pull-inbaTo calculate this threshold voltage, we need to use the following equations: 2202( )AVkdεδδ=−230()ekFFAVkdεδδ δ∂∂=⇒ =∂∂ −εAkdVPI27830=stableunstableVδ-1/3 d0-2/3 d00VPIPull-in Effect-d0Parallel-Plate Actuator, Charge-controlFixed electrodekZd00Suppose the displacement of the top electrode is δThe force balance requires:ZFF=kzd0Electrostatic forceSpring force00Fkz∂<⇒−<∂With Charge-Control method, all positions are stable.Why is it difficult in practice ?Balanced position:202QFkAδε=−=ITorsional Electrostatic ActuatorVϕZ0Z1Z2BCBSiO2Substrateb/2OxzMicromirrordxLow-costsubstrates(glass)ColumnaddressingRowaddressingPlanarizedinterlayerAluminummirrorElectroplatedNi postSignal, deflectedNo signal, undeflectedElectrostatic MotorCombdrive ActuatorVdFcombtx() 2AtxCx nddεε==2212combdC tVFVndx dε==(n=number of fingers)Combdrive ActuatorCombdrive ActuatorScratchdrive


View Full Document

CALTECH EE 40 - Electrostatic Actuation

Download Electrostatic Actuation
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Electrostatic Actuation and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Electrostatic Actuation 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?