For higher resolution, can try to match drive and sense axis another to avoid output drift. Drive Electrode. Tuning. Electrodes. Response Amplitude

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EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 MEMSBase Fork Gyrosoe Moe Mathng for Hgher Resoluton an sense axes must be stable or at least trak one For hgheesoluton, an try to math re

1 EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 MEMSBase Fork Gyrosoe Moe Mathng for Hgher Resoluton an sense axes must be stable or at least trak one For hgheesoluton, an try to math re an sense axs another to ao outut rft resonane frequenes an beneft from Q amlfaton Problem: Problem: ff re re frequeny frequeny hanges hanges relate relate to to sense sense frequeny, frequeny, outut outut hanges bas hanges bas rft rft Eletroe Nee: Nee: small small or or mathe mathe re re an an sense sense axs axs temerature temerature oeffents oeffents to to suress suress rft rft EE C45: Introuton to MEMS Desgn Quarature Canellaton T1 fo (@ C. Nguyen LeM 15 T1) fo (@ T) 11/18/08 1 Nee: Nee: small small or or mathe mathe re re an an sense sense axs axs temerature temerature oeffents oeffents to to make make ths ths work work EE C45: Introuton to MEMS Desgn Imbalanes n the system an lea to zero rate bas error Quarature Canellaton mbalane mbalane offaxs offaxsmoton moton of ofthe theroof roofmass mass EE C45: Introuton to MEMS Desgn 0º 0º Eletroe Mass Massmbalane mbalane offaxs offaxsmoton moton of the roof of the roofmass mass sgnal sgnaln n hase hasewth wththe the Corols Corolsaeleraton aeleraton LeM 15 11/18/08 T1) fo (@ T) 11/18/08 13 Better Betterffths thsssaanoble noblegas gasnuleus nuleus (rather (ratherthan thane), e),sne snenule nuleare are heaer less susetble to heaer less susetble tobbfel fel 19 Soln: Soln:Sn Snolarze olarzexe Xe19nule nuleby by 87 frst frstolarzng olarzngeeof ofrb Rb87(a (ala la CSAC), CSAC),then thenallowng allowngsn snexhange exhange Laser Polarzer 0º Rb/Xe Cell 0º Quarature Quaratureoutut outut sgnal sgnalthat thatan anbe be onfuse onfusewth wththe the Corols Corolsaeleraton aeleraton C. Nguyen fo (@ C. Nguyen LeM 15 ª from CSAC, we may now hae the tehnology to o ths 0º T The ultmate n mnaturze snnng gyrosoes? Quarature Canellaton Eletroe Nulear Magnet Res. Gyrosoe Issue: Zero Rate Bas Error T1 T Problem: Problem: msmath msmath between between re re an an sense sense frequenes frequenes een een larger largeft! rft! Eletroe Amltue Eletroe Quarature Canellaton Amltue Eletroe 14 Coyrght 009 Regents of the Unersty of Calforna Photooe 0º Atoms Algne Nulear Sns EE C45: Introuton to MEMS Desgn θ&t 3. mm Challenge: Challenge:suressng suressng the theeffets effetsof ofbbfel fel LeM 15 C. Nguyen 1 mm 1 mm 11/18/08 15

EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 MEMSBase Fork Gyrosoe Ω r

C. Nguyen 11/18/08 16 [Zaman, Ayaz, et al, MEMS 06] Osllaton Sustanng Amlfer

Nguyen 11/18/08 17 MEMSBase Fork Gyrosoe Axs Equalent Crut Ω r z Voltage Sgnal 180 o

Nguyen 11/18/08 18 [Zaman, Ayaz, et al, MEMS 06] Osllaton Sustanng Amlfer Dfferental

to whh the Corols fore s roortonal Voltage Sgnal EE C45: Introuton to MEMS Desgn LeM

2 EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 MEMSBase Fork Gyrosoe Ω r z Voltage Sgnal () Current (+) Current Eletroe EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 16 [Zaman, Ayaz, et al, MEMS 06] Osllaton Sustanng Amlfer Dfferental TransR Amlfer Determnng Resoluton EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 17 MEMSBase Fork Gyrosoe Axs Equalent Crut Ω r z Voltage Sgnal 180 o 1:η e x () Current (+) Current Eletroe EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 18 [Zaman, Ayaz, et al, MEMS 06] Osllaton Sustanng Amlfer Dfferental TransR Amlfer o Osllaton Sustanng Amlfer C o1 180 o x Generates re slaement eloty x to whh the Corols fore s roortonal Voltage Sgnal EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 19 C o To Amlfer (for synhronzaton) Coyrght 009 Regents of the Unersty of Calforna

EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 x& to Transfer Funton Moe Ω x& = x n Veloty Amltue / Setra: f o (@ T 1 ) F = ma F x Gyro Reaout Equalent Crut (for a sngle tne) Soures = m (

Nguyen 11/18/08 0 Gyro Element Crut Sgnal Contonng Crut (Transresstane Amlfer) Easest to analyze f all nose soures are summe at a ommon noe EE C45: Introuton to MEMS Desgn LeM 15 C.

sensor sale fator s goerne by the sensor tye The effet of nose s best etermne a analyss of the equalent rut for the system Inlues esre outut lus nose EE C45: Introuton to MEMS Desgn LeM 15 C.

3 EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 x& to Transfer Funton Moe Ω x& = x n Veloty Amltue / Setra: f o (@ T 1 ) F = ma F x Gyro Reaout Equalent Crut (for a sngle tne) Soures = m ( x o a x 0 a f x& s Moe x& s = x s Veloty s EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 0 Gyro Element Crut Sgnal Contonng Crut (Transresstane Amlfer) Easest to analyze f all nose soures are summe at a ommon noe EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 1 Mnmum Detetable Sgnal (MDS) Mnmum Detetable Sgnal (MDS): Inut sgnal leel when the sgnaltonose rato (SNR) s equal to unty Sgnal Sale Fator Crut Gan Crut Sgnal Contonng Crut The sensor sale fator s goerne by the sensor tye The effet of nose s best etermne a analyss of the equalent rut for the system Inlues esre outut lus nose EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 Moe Soures to a Common Pont Moe nose soures so that all sum at the nut to the amlfer rut (.e., at the outut of the sense element) Then, an omare the outut of the sense sgnal retly to the nose at ths noe to get the MDS Sgnal Sale Fator Crut Gan Crut Inut Referre Sgnal Contonng Crut Inlues esre outut lus nose EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 3 Coyrght 009 Regents of the Unersty of Calforna

4 EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 F = ma Gyro Reaout Equalent Crut (for a sngle tne) Soures = m ( x f F = ma Gyro Reaout Equalent Crut (for a sngle tne) = m ( x Soures less F x o a x 0 a x o F x 0 eq C eq + Gyro Element Crut Sgnal Contonng Crut (Transresstane Amlfer) Easest to analyze f all nose soures are summe at a ommon noe EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 4 Gyro Element Crut Sgnal Contonng Crut (Transresstane Amlfer) Here, eq an eq are equalent nutreferre oltage an urrent nose soures EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 5 : Ranom flutuaton of a gen arameter I(t) In aton, a nose waeform has a zero aerage alue Ag. alue (e.g. oul be DC urrent) I D I(t) t EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 6 We an t hanle nose at nstantaneous tmes But we an hanle some of the aerage effets of ranom flutuatons by gng nose a ower setral ensty reresentaton Thus, reresent nose by ts meansquare alue: Let ( t) = I( t) I D Then T ( I I ) = lm I 1 = D T D EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 7 T 0 I t Coyrght 009 Regents of the Unersty of Calforna

5 EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 Setral Densty We an lot the setral ensty of ths meansquare alue: Twose setral ensty (1/ the onese) Often use n systems ourses Δf [unts /Hz] Onese setral ensty use n ruts measure by setrum analyzers = ntegrate meansquare nose setral ensty oer all frequenes (area uner the ure) EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 8 Inuts Ranom Determnst: o j) = Ranom: o( ) = H ( j Crut Calulatons Determnst s ( j) o ( j) H ( j) S () S o () Lnear TmeInarant System o (t) S o (t) ( H ( j) ( j) EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 9 π o t t o ( j) ο S o ( j) ο Mean square setral ensty * [ ) H ( j) ] S ( ) H ( j) S ( ) S = S ( ) = H ( j) S ( ) o Root mean square amltues How s t we an o ths? Hanlng Determnstally Can o ths for nose n a tny banwth (e.g., 1 Hz) 1 S1 ( f n = Δf ο S n ( j) ο B ) n 1 = S f ) B S S [Ths s atually the rnle by whh osllators work osllators are just nose gong through a tny banwth flter] o 1 ( o (t) A oso t EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 30 o B Can aroxmate ths by a snusoal oltage generator (eseally for small B, say 1 Hz) 1 τ ~ B Why? Nether the amltue nor the hase of a sgnal an hange areably wthn a tme ero 1/B. t Systemat Calulaton Proeure General Crut Wth Seeral Soures n n1 n3 H( j) n5 n4 n6 Assume nose soures are unorrelate 1. For n1, relae w/ a etermnst soure of alue n1 n1 = Δf (1Hz) H5( j) on H1( j) EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 31 Coyrght 009 Regents of the Unersty of Calforna

6 EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 Systemat Calulaton Proeure. Calulate on 1( ) = n1( ) H ( j) (treatng t lke a etermnst sgnal) 3. Determne on1 = n1 H ( j) 4. Reeat for eah nose soure: n1, n, n3 5. A nose ower (mean square alues) ontot = on1 + on + on3 + on4 +L Determnng Resoluton ontot = on1 + on + on3 + on4 +L Total rms alue EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 3 EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 33 F = ma Examle: Gyro MDS Calulaton = m ( x x o eq F x& 0 s eq less Examle: Gyro MDS Calulaton (ont) F = ma = m ( x x o eq F x& 0 s eq less The gyro sense resents a large effete soure meane Currents are the mortant arable; oltages are oene out Must omare o wth the total urrent nose eqtot gong nto the amlfer rut Frst, fn the rotaton to o transfer funton: EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 34 EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 35 Coyrght 009 Regents of the Unersty of Calforna

EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 Examle: Gyro MDS Calulaton (ont) Examle: Gyro MDS Calulaton (ont) F = ma = m ( x x o eq F x& 0 s eq less Now, fn the eqtot enterng the

7 EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 Examle: Gyro MDS Calulaton (ont) Examle: Gyro MDS Calulaton (ont) F = ma = m ( x x o eq F x& 0 s eq less Now, fn the eqtot enterng the amlfer nut: EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 36 EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 37 Examle: Gyro MDS Calulaton (ont) LF356 O Am Data Sheet EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 38 EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 39 Coyrght 009 Regents of the Unersty of Calforna

EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 Examle ARW Calulaton Examle ARW Calulaton (ont) Examle Desgn: Element: m = (100μm)(100μm)(0μm)(300kg/m 3 ) = 4.

8 EE 45: Introuton to MEMS Leture 7: Gyros, & MDS CTN 1/3/09 Examle ARW Calulaton Examle ARW Calulaton (ont) Examle Desgn: Element: m = (100μm)(100μm)(0μm)(300kg/m 3 ) = 4.6x10 10 kg s = π(15khz) = π(10khz) k s = s m = 4.09 N/m x = 0 μm Q s = 50,000 V P = 5V h = 0 μm = 1 μm Sensng Crutry: = 100kΩ a = 0.01 A/ Hz a = 1 nv/ Hz z Eletroe EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 40 Ω r EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 41 Examle ARW Calulaton (ont) What f = s? EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 4 EE C45: Introuton to MEMS Desgn LeM 15 C. Nguyen 11/18/08 43 Coyrght 009 Regents of the Unersty of Calforna

EE 247B/ME 218: Introduction to MEMS Design Lecture 27m2: Gyros, Noise & MDS CTN 5/1/14. Copyright 2014 Regents of the University of California

EE 247B/ME 218: Introduction to MEMS Design Lecture 27m2: Gyros, Noise & MDS CTN 5/1/14. Copyright 2014 Regents of the University of California MEMSBase Fork Gyrosoe Ω r z Volage Deermnng Resoluon EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 17 () Curren (+) Curren Eleroe EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 18 [Zaman,