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
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1 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, Ayaz, e al, MEMS 06] Osllaon Susanng Amlfer Dfferenal TransR Amlfer Osllaon Susanng Amlfer Axs Equalen Cru 180 o C o1 1:η e 180 o x Generaes re slaemen eloy x o whh he Corols fore s rooronal Volage EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 19 C o To Amlfer (for synhronzaon) x& x& s o Transfer Funon Moe Ω Moe x& x& s x n Veloy x s Veloy s Amlue / Resonse Sera: Resonse Resonse f o (@ T 1 ) EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 0 1
2 F Gyro Reaou Equalen Cru (for a sngle ne) Soures x 0 a Gyro Elemen Cru EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 1 a f Cononng Cru (Transressane Amlfer) Eases o analyze f all nose soures are summe a a ommon noe Mnmum Deeable (MDS) Mnmum Deeable (MDS): Inu sgnal leel when he sgnalonose rao (SNR) s equal o uny Sale Faor Cru Gan Cru Cononng Cru The sensor sale faor s goerne by he sensor ye The effe of nose s bes eermne a analyss of he equalen ru for he sysem Inlues esre ouu lus nose EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 Moe Soures o a Common Pon Moe nose soures so ha all sum a he nu o he amlfer ru (.e., a he ouu of he sense elemen) Then, an omare he ouu of he sense sgnal rely o he nose a hs noe o ge he MDS Sale Faor Cru Gan Cru Inu Referre Cononng Cru Inlues esre ouu lus nose EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 3 F Gyro Reaou Equalen Cru (for a sngle ne) Soures a x 0 a Gyro Elemen Cru EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 4 f Cononng Cru (Transressane Amlfer) Eases o analyze f all nose soures are summe a a ommon noe
3 Gyro Reaou Equalen Cru (for a sngle ne) Soures less F x 0 eq C eq + Gyro Elemen Cru Cononng Cru (Transressane Amlfer) Here, eq an eq are equalen nureferre olage an urren nose soures EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 5 EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 6 : Ranom fluuaon of a gen arameer I() In aon, a nose waeform has a zero aerage alue Ag. alue (e.g. oul be DC urren) EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 7 I D I() We an hanle nose a nsananeous mes Bu we an hanle some of he aerage effes of ranom fluuaons by gng nose a ower seral ensy reresenaon Thus, reresen nose by s meansquare alue: Le ( ) I( ) I D Then T ( I I ) lm I 1 D T T 0 I D Seral Densy We an lo he seral ensy of hs meansquare alue: Twose seral ensy (1/ he onese) Ofen use n sysems ourses Δf [uns /Hz] Onese seral ensy use n rus measure by serum analyzers negrae meansquare nose seral ensy oer all frequenes (area uner he ure) EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 8 3
4 Inus Ranom Deermns: o j) Ranom: Cru Calulaons Deermns s ( j) o ( j) H ( j) S () S o () Lnear TmeInaran Sysem o () S o () ( H ( j) ( j) EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 9 π o o ( j) ο S o ( j) ο Mean square seral ensy * [ H ( j) H ( j) ] S ( ) H ( j) S ( ) S ( ) o S ( ) H ( j) S ( ) o Roo mean square amlues How s we an o hs? Hanlng Deermnsally Can o hs for nose n a ny banwh (e.g., 1 Hz) 1 S1 ( f n Δf ο S n ( j) ο B ) n 1 S f ) B S S [Ths s aually he rnle by whh osllaors work osllaors are jus nose gong hrough a ny banwh fler] o 1 ( o () A oso EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 30 o B Can aroxmae hs by a snusoal olage generaor (eseally for small B, say 1 Hz) 1 τ ~ B Why? Neher he amlue nor he hase of a sgnal an hange areably whn a me ero 1/B. Sysema Calulaon Proeure Sysema Calulaon Proeure General Cru Wh Seeral Soures n n1 n3 H( j) n5 n4 n6 H5( j) on H1( j). Calulae on 1( ) n1( ) H ( j) (reang lke a eermns sgnal) 3. Deermne on1 n1 H ( j) 4. Reea for eah nose soure: n1, n, n3 5. A nose ower (mean square alues) ontot on1 + on + on3 + on4 +L Assume nose soures are unorrelae 1. For n1, relae w/ a eermns soure of alue ontot on1 + on + on3 + on4 +L n1 n1 Δf (1Hz) Toal rms alue EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 31 EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 3 4
5 Deermnng Resoluon Examle: Gyro MDS Calulaon eq F x& 0 s eq less The gyro sense resens a large effee soure meane Currens are he moran arable; olages are oene ou Mus omare wh he oal urren nose eqtot gong no he amlfer ru EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 33 EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 34 Examle: Gyro MDS Calulaon (on) eq F x& 0 s eq less Examle: Gyro MDS Calulaon (on) Frs, fn he roaon o ransfer funon: EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 35 EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/
6 Examle: Gyro MDS Calulaon (on) eq F x& 0 s eq less Examle: Gyro MDS Calulaon (on) Now, fn he eqtot enerng he amlfer nu: EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 37 EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 38 LF356 O Am Daa Shee Examle ARW Calulaon EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 39 Examle Desgn: Elemen: 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 Crury: 100kΩ a 0.01 A/ Hz a 1 nv/ Hz z Eleroe EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 40 Ω r 6
7 Examle ARW Calulaon (on) Examle ARW Calulaon (on) EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 41 EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/08 4 Wha f s? EE C45: Inrouon o MEMS Desgn LeM 15 C. Nguyen 11/18/
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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