Lecture 9. MEMS Inertial Sensors. Inertial Sensors. Inertial Sensors. Agenda: MEMS Inertial Sensors. Coriolis Force Principle of Vibratory Gyroscope

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1 EEL6935 Advancd MEMS (Spring 5) Intructor: Dr. Huikai i MEMS Inrtial Snor Lctur 9 Agnda: MEMS Inrtial Snor Corioli Forc Principl of Vibrator Grocop Emrging application Low cot Automobil, computr gam, motion dtction Small i -- Camcordr, nano-atllit, halth monitoring Intgratd Inrtial Maurmnt Unit (IMU) tm MEMS inrtial nor Traditional application of inrtial nor EEL6935 Advancd MEMS 5 H. i /4/5 EEL6935 Advancd MEMS 5 H. i Inrtial Snor Inrtial Snor Acclromtr Singl-ai, dual-ai, 3-ai Tp Capacitiv Pioritiv Piolctric Tunnling Optical Grocop -- Angular rat nor Optical grocop Fibr-optic grocop Ring lar grocop Mchanical grocop Spinning whl Vibrating fork, hll, plat Commrcial Product: ADI, Motorola, Boch, Honwll, ST Microlctronic, -> Micromachind vibrator grocop Corioli Acclration EEL6935 Advancd MEMS 5 H. i EEL6935 Advancd MEMS 5 H. i 4

2 Corioli Forc Corioli Acclration A moving ball on a tationar tabl A ma-pring tm on a rotating tabl Anchor A moving ball on a rotating tabl a c = V v : Corioli acclration Corioli forc i a fictitiou forc rtd on a bod whn it mov in a rotating rfrnc fram A particl in a rotating fram r Y r = Y f Rotation Vibration Corioli acclration V p,r r f a p, f = ap, r ar, f a c = V p, r r-yr: Rotating fram f-yf: Fid fram a a p, f -- Acclration of th particl w.r.t th fid fram a -- Acclration of th particl w.r.t th p, r rotating fram a -- Acclration of th rotating fram r, f w.r.t. th fid fram at P a -- Corioli acclration c V -- Vlocit of th particl w.r.t th p, r rotating fram c EEL6935 Advancd MEMS 5 H. i 5 EEL6935 Advancd MEMS 5 H. i 6 Innr fram Rollr Vibrator Grocop - modl Gimbald Smmtric Dign k Ma Sn mod Capacitiv Pioritiv Piolctric. k Anchor Driv mod EEL6935 Advancd MEMS 5 H. i 7 _ = V Elctrotatic, piolctric, lctromagntic, thrmal Ocillating acclromtr q k k m m (P,q ) (,) (P,q ) (p,q ) p-q: fid fram -: rotating fram Vibrator Grocop - EOM p U Lagrang quation, T = mp mq I whr V = k k p() t = co in p qt () = in co q L = T V d L L dt = d L L F dt = EEL6935 Advancd MEMS 5 H. i 8

3 Vibrator Grocop - EOM Vibrator Grocop - EOM q k m D m k m p in q co = Corioli acclration q k m D m k m p in q co = Corioli acclration k m (P,q ) (,) (P,q ) (p,q ) D k m m m m p co q in = F m m k m (P,q ) (,) (P,q ) (p,q ) D k m m m m p co q in = F m m p-q: fid fram -: rotating fram p Whr D -- Damping cofficint = p-q: fid fram -: rotating fram p Whr D -- Damping cofficint = EEL6935 Advancd MEMS 5 H. i 9 EEL6935 Advancd MEMS 5 H. i Vibrator Grocop Quadratur Th ning diplacmnt ac v ϕ = K ϕ = K ωr, ωr, whr ω rd, ω rd, K = ω r, Qω r, / ϕ ϕ ω ω rd, rd, = tan Q ω r, ω r, Quadratur i th coupld motion du to aniolaticit of microtructur. Driv in, but motion ma it. 9 o pha diffrnc Mchanical Snitivit m dm ωr, d m = K ωr, q c Brownian Noi m BW = kbtωr, mqωr, d dm q c Pha (dgr) EEL6935 Advancd MEMS 5 H. i EEL6935 Advancd MEMS 5 H. i

4 MATLAB-Aitd Dign Grocop Structural Dign Stm dign Singl Ma Nw ida Mchanical modl Equation of motion Phical Proprti (k, m, Q) Simulink Singl-ai tranlational Singl-ai Torional Dual-ai No Satif? Driv Laout dign & vrification Don Optimid paramtr Y No Comparabl? Mchanical dign Laout Y Driv Mchanical Proprti (k, m) FEM anali (Abaqu) EEL6935 Advancd MEMS 5 H. i 3 EEL6935 Advancd MEMS 5 H. i 4 Grocop Structural Dign Diffrntial (Dual-Ma) Eampl: Latral-Ai Grocop Chooing latral-ai grocop to ci vrtical ning or actuation Tranlational Torional Driv Spring Driv Driv Comb Cancl linar acclration Cancl tmpratur variation Driv Sn Comb = V _ Proof ma Anchor or = V _ Sn Spring Eithr vrtical actuation or vrtical ning EEL6935 Advancd MEMS 5 H. i 5 EEL6935 Advancd MEMS 5 H. i 6

5 Elctrotatic Forc in a Comb Driv Elctrotatic Forc in a Comb Driv C(,,) C(,, ) = ε ( h )( ) g g Elctrotatic forc it in all dirction: h V dc V in N dc f = V d N dc f = V d - g- g : ovrlap of comb fingr : latral offt du to procing : vrtical offt du to procing N dc f = V d V = V dc V ac N: numbr of comb fingr EEL6935 Advancd MEMS 5 H. i EEL6935 Advancd MEMS 5 H. i Dnamic Anali Dnamic Anali Equation of Motion: Matlab/Simulink Modl: w/q '.m at To Fil dc F = V d '' w^ '' quation Sum '' Contant p/g p/g dc/d = ( ω Q ) ω N F / m '' w/q ' w ^ 4*p/g^3 Contant4 Sin Wav Contant ( ω Q ) ω ω = '' quation Sum '' f Product w/q ' V i th vctor of,, and diplacmnt of th proof ma i th vctor of diplacmnt of th driv fram. Q, Q, Q : mchanical Q-factor in,, dirction, rpctivl. ω, ω, ω : ronant frqunci in,, dirction, rpctivl. '' w^ '' quation h- Contant Sum '' Contant3 p/g f dc/d p/g Product *N/m Contant5 EEL6935 Advancd MEMS 5 H. i 9 EEL6935 Advancd MEMS 5 H. i f

6 Simulatd Sn Signal Simulation Rult Et. rotation rat(rad/) Driv mod(m) (µm) (nm) mall vibration amplitud larg vibration amplitud ~ 9 ~ 4 Sn mod(m) Tim (cond) Z (nm) fram proof ma Vdc = V, Vac =.5V Vdc = 8V, Vac = 5V EEL6935 Advancd MEMS 5 H. i EEL6935 Advancd MEMS 5 H. i Simulation Rult Homwork#3 (µm) mall comb fingr ovrlap larg comb fingr ovrlap L. Mirovitch, Analtical Mthod in Vibration, Chaptr, p5-53: (nm) Du: Monda, /4 Z (nm) fram proof ma EEL6935 Advancd MEMS 5 H. i = 5 µm = 5 µm EEL6935 Advancd MEMS 5 H. i