EE 245: Introduction to MEMSModule 12: Capacitive TransducersCTN 11/4/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 1EE C245 – ME C218Introduction to MEMS DesignFall 2009Prof. Clark T.-C. NguyenDept. of Electrical Engineering & Computer SciencesUniversity of California at BerkeleyBerkeley, CA 94720Lecture Module 12: Capacitive TransducersEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 2Lecture Outline• Reading: Senturia, Chpt. 5, Chpt. 6• Lecture Topics:ª Energy Conserving Transducers( Charge Control( Voltage Controlª Parallel-Plate Capacitive Transducers( Linearizing Capacitive Actuators( Electrical Stiffnessª Electrostatic Comb-Drive( 1stOrder Analysis( 2ndOrder AnalysisEE 245: Introduction to MEMSModule 12: Capacitive TransducersCTN 11/4/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 3Basic Physics of Electrostatic Actuation• Goal: Determine gap spacing g as a function of input variables• First, need to determine the energy of the system• Two ways to change the energy:ª Change the charge qª Change the separation gΔW(q,g) = VΔq+ FeΔgdW = Vdq + Fedg• Note: We assume that the plates are supported elastically, so they don’t collapseEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 4Stored Energy• Here, the stored energy is the work done in increasing the gap after charging capacitor at zero gapEE 245: Introduction to MEMSModule 12: Capacitive TransducersCTN 11/4/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 5Charge-Control Case• Having found stored energy, we can now find the force acting on the plates and the voltage across them:+-VEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 6Voltage-Control Case• Practical situation: We control Vª Charge control on the typical sub-pF MEMS actuation capacitor is difficultª Need to find Feas a partial derivative of the stored energy W = W(V,g) with respect to g with V held constant? But can’t do this with present W(q,g) formulaª Solution: Apply Legendre transformation and define the co-energy W′(V,g)EE 245: Introduction to MEMSModule 12: Capacitive TransducersCTN 11/4/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 7Co-Energy Formulation• For our present problem (i.e., movable capacitive plates), the co-energy formulation becomesEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 8Electrostatic Force (Voltage Control)• Find co-energy in terms of voltage• Variation of co-energy with respect to gap yields electrostatic force:• Variation of co-energy with respect to voltage yields charge:EE 245: Introduction to MEMSModule 12: Capacitive TransducersCTN 11/4/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 9Spring-Suspended Capacitive PlateEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 10Charge Control of a Spring-Suspended CIEE 245: Introduction to MEMSModule 12: Capacitive TransducersCTN 11/4/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 11Voltage Control of a Spring-Suspended CEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 12Stability Analysis• Net attractive force on the plate:• An increment in gap dg leads to an increment in net attractive force dFnetEE 245: Introduction to MEMSModule 12: Capacitive TransducersCTN 11/4/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 13Pull-In Voltage VPI• VPI= voltage at which the plates collapse• The plate goes unstable when• Substituting (1) into (2):and(1) (2)When a gap is driven by a voltage to (2/3) its original spacing, collapse will occur!When a gap is driven by a voltage to (2/3) its original spacing, collapse will occur!EE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 14Voltage-Controlled Plate Stability Graph• Below: Plot of normalized electrostatic and spring forces vs. normalized displacement 1-(g/go)Normalized DisplacementForcesSpring ForceElectrical ForcesIncreasing VStable Equilibrium PointsEE 245: Introduction to MEMSModule 12: Capacitive TransducersCTN 11/4/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 15Advantages of Electrostatic Actuators• Easy to manufacture in micromachining processes, since conductors and air gaps are all that’s needed → low cost!• Energy conserving → only parasitic energy loss through I2R losses in conductors and interconnects• Variety of geometries available that allow tailoring of the relationships between voltage, force, and displacement• Electrostatic forces can become very large when dimensions shrink → electrostatics scales well!• Same capacitive structures can be used for both drive and sense of velocity or displacement• Simplicity of transducer greatly reduces mechanical energy losses, allowing the highest Q’s for resonant structuresEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 16Problems With Electrostatic Actuators• Nonlinear voltage-to-force transfer function• Relatively weak compared with other transducers (e.g., piezoelectric), but things get better as dimensions scaleEE 245: Introduction to MEMSModule 12: Capacitive TransducersCTN 11/4/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 17Linearizing the Voltage-to-Force Transfer FunctionEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 18Linearizing the Voltage-to-Force T.F.• Apply a DC bias (or polarization) voltage VPtogether with the intended input (or drive) voltage vi(t), where VP>> vi(t)v(t) = VP+ vi(t)EE 245: Introduction to MEMSModule 12: Capacitive TransducersCTN 11/4/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 12 C. Nguyen 11/18/08 19Differential Capacitive Transducer• The net force on the suspended center electrode isEE C245: Introduction to MEMS Design
View Full Document
Unlocking...