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
|
|
- Marjorie Collins
- 5 years ago
- Views:
Transcription
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
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
More informationEE C245 ME C218 Introduction to MEMS Design
EE C45 ME C18 Introduction to MEMS Design Fall 008 Prof. Clark T.-C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 9470 Lecture 6: Output
More information2/20/2013. EE 101 Midterm 2 Review
//3 EE Mderm eew //3 Volage-mplfer Model The npu ressance s he equalen ressance see when lookng no he npu ermnals of he amplfer. o s he oupu ressance. I causes he oupu olage o decrease as he load ressance
More informationEE C245 ME C218 Introduction to MEMS Design Fall 2007
EE C45 ME C18 Introducton to MEMS Desgn Fall 007 Prof. Clark T.C. Nguyen Dept. of Electrcal Engneerng & Computer Scences Unversty of Calforna at Berkeley Berkeley, CA 9470 Lecture 8: Mnmum Detectable Sgnal
More informationDirect Current Circuits
Eler urren (hrges n Moon) Eler urren () The ne moun of hrge h psses hrough onduor per un me ny pon. urren s defned s: Dre urren rus = dq d Eler urren s mesured n oulom s per seond or mperes. ( = /s) n
More informationEnergy Storage Devices
Energy Sorage Deces Objece of Lecure Descrbe he consrucon of a capacor and how charge s sored. Inroduce seeral ypes of capacors Dscuss he elecrcal properes of a capacor The relaonshp beween charge, olage,
More informationCHAPTER II AC POWER CALCULATIONS
CHAE AC OWE CACUAON Conens nroducon nsananeous and Aerage ower Effece or M alue Apparen ower Coplex ower Conseraon of AC ower ower Facor and ower Facor Correcon Maxu Aerage ower ransfer Applcaons 3 nroducon
More informationEP2200 Queuing theory and teletraffic systems. 3rd lecture Markov chains Birth-death process - Poisson process. Viktoria Fodor KTH EES
EP Queung heory and eleraffc sysems 3rd lecure Marov chans Brh-deah rocess - Posson rocess Vora Fodor KTH EES Oulne for oday Marov rocesses Connuous-me Marov-chans Grah and marx reresenaon Transen and
More informationChapter 5. Circuit Theorems
Chaper 5 Crcu Theorems Source Transformaons eplace a olage source and seres ressor by a curren and parallel ressor Fgure 5.-1 (a) A nondeal olage source. (b) A nondeal curren source. (c) Crcu B-conneced
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon If we say wh one bass se, properes vary only because of changes n he coeffcens weghng each bass se funcon x = h< Ix > - hs s how we calculae
More informationChapters 2 Kinematics. Position, Distance, Displacement
Chapers Knemacs Poson, Dsance, Dsplacemen Mechancs: Knemacs and Dynamcs. Knemacs deals wh moon, bu s no concerned wh he cause o moon. Dynamcs deals wh he relaonshp beween orce and moon. The word dsplacemen
More informationLecture 11 Inductance and Capacitance
ecure Inducance and apacance EETRIA ENGINEERING: PRINIPES AND APPIATIONS, Fourh Edon, by Allan R. Hambley, 8 Pearson Educaon, Inc. Goals. Fnd he curren olage for a capacance or nducance gen he olage curren
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon Alernae approach o second order specra: ask abou x magnezaon nsead of energes and ranson probables. If we say wh one bass se, properes vary
More informationChapter Lagrangian Interpolation
Chaper 5.4 agrangan Inerpolaon Afer readng hs chaper you should be able o:. dere agrangan mehod of nerpolaon. sole problems usng agrangan mehod of nerpolaon and. use agrangan nerpolans o fnd deraes and
More informationCapacitance and Inductance. The Capacitor
apaiane and Induane OUTINE apaiors apaior volage, urren, power, energy Induors eure 9, 9/9/5 Reading Hambley haper 3 (A) EE4 Fall 5 eure 9, Slide The apaior Two onduors (a,b) separaed by an insulaor: differene
More informationTUTORIAL SOLUTIONS. F.1 KCL, KVL, Power and Energy Q.1. i All units in VAΩ,,
F TUTOIAL SOLUTIONS F. KCL, KVL, Power and Energy Q. 8 9 6 All uns n VAΩ,, Appendx F Tuoral Soluons Applyng KCL o he doed surface: + + Q. All uns n V, A, Ω Nework A Nework B Applyng KCL o he doed surface:
More informationLecture 18: The Laplace Transform (See Sections and 14.7 in Boas)
Lecure 8: The Lalace Transform (See Secons 88- and 47 n Boas) Recall ha our bg-cure goal s he analyss of he dfferenal equaon, ax bx cx F, where we emloy varous exansons for he drvng funcon F deendng on
More informationChapter 7 AC Power and Three-Phase Circuits
Chaper 7 AC ower and Three-hae Crcu Chaper 7: Oulne eance eacance eal power eacve power ower n AC Crcu ower and Energy Gven nananeou power p, he oal energy w ranferred o a load beween and : w p d The average
More informationLinear Circuit Elements
1/25/2011 inear ircui Elemens.doc 1/6 inear ircui Elemens Mos microwave devices can be described or modeled in erms of he hree sandard circui elemens: 1. ESISTANE () 2. INDUTANE () 3. APAITANE () For he
More informationChapter 6: AC Circuits
Chaper 6: AC Crcus Chaper 6: Oulne Phasors and he AC Seady Sae AC Crcus A sable, lnear crcu operang n he seady sae wh snusodal excaon (.e., snusodal seady sae. Complee response forced response naural response.
More informationA capacitor consists of two conducting plates, separated by an insulator. Conduction plates: e.g., Aluminum foil Insulator: air, mica, ceramic, etc
3//7 haper 6 apacors and Inducors Makng preparaon for dynamc crcus, whch hae far more applcaons han he sac crcus we hae learned so far. 6. apacors Sore energy n elecrc feld nsulaor onducng plaes A capacor
More informationIntroduction to AC Power, RMS RMS. ECE 2210 AC Power p1. Use RMS in power calculations. AC Power P =? DC Power P =. V I = R =. I 2 R. V p.
ECE MS I DC Power P I = Inroducion o AC Power, MS I AC Power P =? A Solp //9, // // correced p4 '4 v( ) = p cos( ω ) v( ) p( ) Couldn' we define an "effecive" volage ha would allow us o use he same relaionships
More informationSolution in semi infinite diffusion couples (error function analysis)
Soluon n sem nfne dffuson couples (error funcon analyss) Le us consder now he sem nfne dffuson couple of wo blocks wh concenraon of and I means ha, n a A- bnary sysem, s bondng beween wo blocks made of
More informationMotion in Two Dimensions
Phys 1 Chaper 4 Moon n Two Dmensons adzyubenko@csub.edu hp://www.csub.edu/~adzyubenko 005, 014 A. Dzyubenko 004 Brooks/Cole 1 Dsplacemen as a Vecor The poson of an objec s descrbed by s poson ecor, r The
More informationLaser Interferometer Space Antenna (LISA)
aser nerferomeer Sace Anenna SA Tme-elay nerferomery wh Movng Sacecraf Arrays Massmo Tno Je Proulson aboraory, Calforna nsue of Technology GSFC JP 8 h GWAW, ec 7-0, 00, Mlwaukee, Wsconsn WM Folkner e al,
More informationLecture 2: Telegrapher Equations For Transmission Lines. Power Flow.
Whies, EE 481/581 Lecure 2 Page 1 of 13 Lecure 2: Telegraher Equaions For Transmission Lines. Power Flow. Microsri is one mehod for making elecrical connecions in a microwae circui. I is consruced wih
More informationR th is the Thevenin equivalent at the capacitor terminals.
Chaper 7, Slun. Applyng KV Fg. 7.. d 0 C - Takng he derae f each erm, d 0 C d d d r C Inegrang, () ln I 0 - () I 0 e - C C () () r - I 0 e - () V 0 e C C Chaper 7, Slun. h C where h s he Theenn equalen
More information3. Alternating Current
3. Alernaing Curren TOPCS Definiion and nroducion AC Generaor Componens of AC Circuis Series LRC Circuis Power in AC Circuis Transformers & AC Transmission nroducion o AC The elecric power ou of a home
More informationLesson 2 Transmission Lines Fundamentals
Lesson Transmsson Lnes Funamenals 楊尚達 Shang-Da Yang Insue of Phooncs Technologes Deparmen of Elecrcal Engneerng Naonal Tsng Hua Unersy Tawan Sec. -1 Inroucon 1. Why o scuss TX lnes srbue crcus?. Crera
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 3 Signals & Sysems Prof. Mark Fowler Noe Se # Wha are Coninuous-Time Signals??? /6 Coninuous-Time Signal Coninuous Time (C-T) Signal: A C-T signal is defined on he coninuum of ime values. Tha is:
More informationExample: MOSFET Amplifier Distortion
4/25/2011 Example MSFET Amplfer Dsoron 1/9 Example: MSFET Amplfer Dsoron Recall hs crcu from a prevous handou: ( ) = I ( ) D D d 15.0 V RD = 5K v ( ) = V v ( ) D o v( ) - K = 2 0.25 ma/v V = 2.0 V 40V.
More informationElectromagnetic waves in vacuum.
leromagne waves n vauum. The dsovery of dsplaemen urrens enals a peular lass of soluons of Maxwell equaons: ravellng waves of eler and magne felds n vauum. In he absene of urrens and harges, he equaons
More informationFirst-order piecewise-linear dynamic circuits
Frs-order pecewse-lnear dynamc crcus. Fndng he soluon We wll sudy rs-order dynamc crcus composed o a nonlnear resse one-por, ermnaed eher by a lnear capacor or a lnear nducor (see Fg.. Nonlnear resse one-por
More informationAC Circuits AC Circuit with only R AC circuit with only L AC circuit with only C AC circuit with LRC phasors Resonance Transformers
A ircuis A ircui wih only A circui wih only A circui wih only A circui wih phasors esonance Transformers Phys 435: hap 31, Pg 1 A ircuis New Topic Phys : hap. 6, Pg Physics Moivaion as ime we discovered
More informationCHAPTER 6: FIRST-ORDER CIRCUITS
EEE5: CI CUI T THEOY CHAPTE 6: FIST-ODE CICUITS 6. Inroducion This chaper considers L and C circuis. Applying he Kirshoff s law o C and L circuis produces differenial equaions. The differenial equaions
More informationChapter 5-4 Operational amplifier Department of Mechanical Engineering
MEMS08 Chaper 5-4 Operaional amplifier Deparmen of Mechanical Engineering Insrumenaion amplifier Very high inpu impedance Large common mode rejecion raio (CMRR) Capabiliy o amplify low leel signals Consisen
More informationApplication Notes for AP3772 System Solution
lcaon oe 08 lcaon oes for 377 ysem oluon reared by Zhao Jng Jng ysem Engneerng De.. nroducon The 377 uses ulse Frequency Modulaon (FM) mehod o realze Dsconnuous Conducon Mode (DCM) oeraon for Flyback ower
More informationChapter 7 Stead St y- ate Errors
Char 7 Say-Sa rror Inroucon Conrol ym analy an gn cfcaon a. rann ron b. Sably c. Say-a rror fnon of ay-a rror : u c a whr u : nu, c: ouu Val only for abl ym chck ym ably fr! nu for ay-a a nu analy U o
More informationComputational results on new staff scheduling benchmark instances
TECHNICAL REPORT Compuaonal resuls on new saff shedulng enhmark nsanes Tm Curos Rong Qu ASAP Researh Group Shool of Compuer Sene Unersy of Nongham NG8 1BB Nongham UK Frs pulshed onlne: 19-Sep-2014 las
More informationELEG 205 Fall Lecture #13. Mark Mirotznik, Ph.D. Professor The University of Delaware Tel: (302)
ELEG 205 Fall 2017 Leure #13 Mark Miroznik, Ph.D. Professor The Universiy of Delaware Tel: (302831-4221 Email: mirozni@ee.udel.edu Chaper 8: RL and RC Ciruis 1. Soure-free RL iruis (naural response 2.
More information3. MODELING OF PARALLEL THREE-PHASE CURRENT-UNIDIRECTIONAL CONVERTERS 3. MODELING OF PARALLEL THREE-PHASE CURRENT-
3. MOEING OF PARAE THREE-PHASE URRENT-UNIIRETIONA ONERTERS 3. MOEING OF PARAE THREE-PHASE URRENT- UNIIRETIONA ONERTERS Ths chater eelos the moels of the arallel three-hase current-unrectonal swtch base
More informationChapter 4 AC Network Analysis
haper 4 A Nework Analysis Jaesung Jang apaciance Inducance and Inducion Time-Varying Signals Sinusoidal Signals Reference: David K. heng, Field and Wave Elecromagneics. Energy Sorage ircui Elemens Energy
More informationPhys1112: DC and RC circuits
Name: Group Members: Dae: TA s Name: Phys1112: DC and RC circuis Objecives: 1. To undersand curren and volage characerisics of a DC RC discharging circui. 2. To undersand he effec of he RC ime consan.
More informationApplication Notes for AP3770 System Solution
lcaon oe 1067 lcaon oes for 3770 ysem oluon reared by u Qg Hua ysem Engeerg De. 1. nroducon The 3770 uses ulse Frequency Modulaon (FM) mehod o realze Dsconuous Conducon Mode (DCM) oeraon for FYBCK ower
More informationEE 435 Lecture 42. Phased Locked Loops and VCOs
EE 435 Lecure 42 d Locked Loops and VCOs Basis PLL Archiecure Loop Filer (LF) Volage Conrolled Oscillaor (VCO) Frequency Divider N Applicaions include: Frequency Demodulaion Frequency Synhesis Clock Synchronizaion
More informationVoltage/current relationship Stored Energy. RL / RC circuits Steady State / Transient response Natural / Step response
Review Capaciors/Inducors Volage/curren relaionship Sored Energy s Order Circuis RL / RC circuis Seady Sae / Transien response Naural / Sep response EE4 Summer 5: Lecure 5 Insrucor: Ocavian Florescu Lecure
More informationNotes on the stability of dynamic systems and the use of Eigen Values.
Noes on he sabl of dnamc ssems and he use of Egen Values. Source: Macro II course noes, Dr. Davd Bessler s Tme Seres course noes, zarads (999) Ineremporal Macroeconomcs chaper 4 & Techncal ppend, and Hamlon
More informationEE 247B/ME 218: Introduction to MEMS Design Lecture 26m1: Noise & MDS CTN 4/25/17. Copyright 2017 Regents of the University of California
EE 47B/ME 18: Introduction to MEMS Design Lecture 6m1: & MDS CTN 4/5/17 Thermal Sources Thermal in Electronics: (Johnson noise, Nyquist noise) Produced as a result of the thermally excited random motion
More informationEE 301 Lab 2 Convolution
EE 301 Lab 2 Convoluion 1 Inroducion In his lab we will gain some more experience wih he convoluion inegral and creae a scrip ha shows he graphical mehod of convoluion. 2 Wha you will learn This lab will
More informationNPTEL Project. Econometric Modelling. Module23: Granger Causality Test. Lecture35: Granger Causality Test. Vinod Gupta School of Management
P age NPTEL Proec Economerc Modellng Vnod Gua School of Managemen Module23: Granger Causaly Tes Lecure35: Granger Causaly Tes Rudra P. Pradhan Vnod Gua School of Managemen Indan Insue of Technology Kharagur,
More informationCS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 4
CS434a/54a: Paern Recognon Prof. Olga Veksler Lecure 4 Oulne Normal Random Varable Properes Dscrmnan funcons Why Normal Random Varables? Analycally racable Works well when observaon comes form a corruped
More informationWeek 11: Differential Amplifiers
ELE 0A Electronc rcuts Week : Dfferental Amplfers Lecture - Large sgnal analyss Topcs to coer A analyss Half-crcut analyss eadng Assgnment: hap 5.-5.8 of Jaeger and Blalock or hap 7. - 7.3, of Sedra and
More informationA. Inventory model. Why are we interested in it? What do we really study in such cases.
Some general yem model.. Inenory model. Why are we nereed n? Wha do we really udy n uch cae. General raegy of machng wo dmlar procee, ay, machng a fa proce wh a low one. We need an nenory or a buffer or
More informationPHYS-3301 Lecture 5. Chapter 2. Announcement. Sep. 12, Special Relativity. What about y and z coordinates? (x - direction of motion)
Announemen Course webpage hp://www.phys.u.edu/~slee/33/ Tebook PHYS-33 Leure 5 HW (due 9/4) Chaper, 6, 36, 4, 45, 5, 5, 55, 58 Sep., 7 Chaper Speial Relaiiy. Basi Ideas. Consequenes of Einsein s Posulaes
More informationIntroduction to Digital Circuits
The NMOS nerer The NMOS Depleion oad 50 [ D ] µ A GS.0 + 40 30 0 0 Resisance characerisic of Q 3 4 5 6 GS 0.5 GS 0 GS 0.5 GS.0 GS.5 [ ] DS GS i 0 Q Q Depleion load Enhancemen drier Drain characerisic of
More informationLinear Response Theory: The connection between QFT and experiments
Phys540.nb 39 3 Lnear Response Theory: The connecon beween QFT and expermens 3.1. Basc conceps and deas Q: ow do we measure he conducvy of a meal? A: we frs nroduce a weak elecrc feld E, and hen measure
More informationLab 10: RC, RL, and RLC Circuits
Lab 10: RC, RL, and RLC Circuis In his experimen, we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors. We will sudy he way volages and currens change in
More information8.022 (E&M) Lecture 9
8.0 (E&M) Lecure 9 Topics: circuis Thevenin s heorem Las ime Elecromoive force: How does a baery work and is inernal resisance How o solve simple circuis: Kirchhoff s firs rule: a any node, sum of he currens
More informationChapter 8 The Complete Response of RL and RC Circuits
Chaper 8 he Complee Response of R and RC Ciruis Exerises Ex 8.3-1 Before he swih loses: Afer he swih loses: 2 = = 8 Ω so = 8 0.05 = 0.4 s. 0.25 herefore R ( ) Finally, 2.5 ( ) = o + ( (0) o ) = 2 + V for
More informationCapacitors. C d. An electrical component which stores charge. parallel plate capacitor. Scale in cm
apaciors An elecrical componen which sores charge E 2 2 d A 2 parallel plae capacior Scale in cm Leyden Jars I was invened independenly by German cleric Ewald Georg von Kleis on Ocober 745 and by Duch
More informationApplication Notes for AP3771 System Solution
lcaon oe 1074 lcaon oes for 3771 ysem oluon reared by Zhao Jg Jg ysem Engeerg De. 1. nroducon The 3771 uses ulse Frequency Modulaon (FM) mehod o realze Dsconuous Conducon Mode (DCM) oeraon for FYBCK ower
More informationTSS = SST + SSE An orthogonal partition of the total SS
ANOVA: Topc 4. Orhogonal conrass [ST&D p. 183] H 0 : µ 1 = µ =... = µ H 1 : The mean of a leas one reamen group s dfferen To es hs hypohess, a basc ANOVA allocaes he varaon among reamen means (SST) equally
More information6.01: Introduction to EECS I Lecture 8 March 29, 2011
6.01: Inroducion o EES I Lecure 8 March 29, 2011 6.01: Inroducion o EES I Op-Amps Las Time: The ircui Absracion ircuis represen sysems as connecions of elemens hrough which currens (hrough variables) flow
More informationTraffic Signal Control. Signalized Intersection Analysis and Level of Service. Traffic Signal Control. Traffic Signal Control 11/4/2009
Sgnalze Intersecton nalyss an Leel of Serce CE3 Transportaton Engneerng Dr. hme bel-rahm Traffc Sgnal Control Pretme sgnal whose tmng (cycle length, green tme, an so on) s fxe oer specfe tme peros an oes
More informationThe Decibel and its Usage
The Decbel and ts Usage Consder a two-stage amlfer system, as shown n Fg.. Each amlfer rodes an ncrease of the sgnal ower. Ths effect s referred to as the ower gan,, of the amlfer. Ths means that the sgnal
More informationLet s treat the problem of the response of a system to an applied external force. Again,
Page 33 QUANTUM LNEAR RESPONSE FUNCTON Le s rea he problem of he response of a sysem o an appled exernal force. Agan, H() H f () A H + V () Exernal agen acng on nernal varable Hamlonan for equlbrum sysem
More informationChapter 1 Relativity
Chaper Relaii - Posulaes of Speial Relaii and Loren Transformaion The s posulae: The laws of phsis ma be epressed in equaions haing he same form in all frames of referene moing a onsan eloi wih respe o
More informationfakultät für informatik informatik 12 technische universität dortmund Petri Nets Peter Marwedel TU Dortmund, Informatik /10/10
2 Peri Nes Peer Marwedel TU Dormund, Informaik 2 2008/0/0 Grahics: Alexandra Nole, Gesine Marwedel, 2003 Generalizaion of daa flow: Comuaional grahs Examle: Peri nes Inroduced in 962 by Carl Adam Peri
More information2.4 Cuk converter example
2.4 Cuk converer example C 1 Cuk converer, wih ideal swich i 1 i v 1 2 1 2 C 2 v 2 Cuk converer: pracical realizaion using MOSFET and diode C 1 i 1 i v 1 2 Q 1 D 1 C 2 v 2 28 Analysis sraegy This converer
More informationPHYS 1443 Section 001 Lecture #4
PHYS 1443 Secon 001 Lecure #4 Monda, June 5, 006 Moon n Two Dmensons Moon under consan acceleraon Projecle Moon Mamum ranges and heghs Reerence Frames and relae moon Newon s Laws o Moon Force Newon s Law
More informationXPT IGBT Module MIXA450PF1200TSF. Phase leg + free wheeling Diodes + NTC MIXA450PF1200TSF. Part number
XPT IGBT Module CS 2x 12 I C25 1.8 C(sa) Phase leg + free wheeling Diodes + NTC Par number Backside: isolaed 5 2 1 8 7 9 3 4 /11 Feaures / dvanages: pplicaions: Package: SimBus F High level of inegraion
More informationChapter 9 Transient Response
har 9 Transn sons har 9: Ouln N F n F Frs-Ordr Transns Frs-Ordr rcus Frs ordr crcus: rcus conan onl on nducor or on caacor gornd b frs-ordr dffrnal quaons. Zro-nu rsons: h crcu has no ald sourc afr a cran
More informationPhysics 1402: Lecture 22 Today s Agenda
Physics 142: ecure 22 Today s Agenda Announcemens: R - RV - R circuis Homework 6: due nex Wednesday Inducion / A curren Inducion Self-Inducance, R ircuis X X X X X X X X X long solenoid Energy and energy
More information10. A.C CIRCUITS. Theoretically current grows to maximum value after infinite time. But practically it grows to maximum after 5τ. Decay of current :
. A. IUITS Synopss : GOWTH OF UNT IN IUIT : d. When swch S s closed a =; = d. A me, curren = e 3. The consan / has dmensons of me and s called he nducve me consan ( τ ) of he crcu. 4. = τ; =.63, n one
More informationSignalized Intersections LOS. Signalized Intersection Analysis and Level of Service. Signalized Intersections LOS. Lane Grouping 11/17/2009
Sgnalze Intersecton nalyss an Leel of Serce CE3 Transportaton Engneerng Dr. hme bel-rahm Sgnalze Intersectons LOS Recall that leel of serce (LOS) s a qualtate assessment of faclty operatons base upon a
More informationScattering at an Interface: Oblique Incidence
Course Insrucor Dr. Raymond C. Rumpf Offce: A 337 Phone: (915) 747 6958 E Mal: rcrumpf@uep.edu EE 4347 Appled Elecromagnecs Topc 3g Scaerng a an Inerface: Oblque Incdence Scaerng These Oblque noes may
More informationComputing with diode model
ECE 570 Session 5 C 752E Comuer Aided Engineering for negraed Circuis Comuing wih diode model Objecie: nroduce conces in numerical circui analsis Ouline: 1. Model of an examle circui wih a diode 2. Ouline
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
More informationOne-Dimensional Kinematics
One-Dimensional Kinemaics One dimensional kinemaics refers o moion along a sraigh line. Een hough we lie in a 3-dimension world, moion can ofen be absraced o a single dimension. We can also describe moion
More informationLecture VI Regression
Lecure VI Regresson (Lnear Mehods for Regresson) Conens: Lnear Mehods for Regresson Leas Squares, Gauss Markov heorem Recursve Leas Squares Lecure VI: MLSC - Dr. Sehu Vjayakumar Lnear Regresson Model M
More informationMEMS 0031 Electric Circuits
MEMS 0031 Elecric Circuis Chaper 1 Circui variables Chaper/Lecure Learning Objecives A he end of his lecure and chaper, you should able o: Represen he curren and volage of an elecric circui elemen, paying
More informationFuji Power MOSFET Power calculation method
Fuji Power MOSFE Power clculi mehod Design ool Cher. Overview is necessry o check wheher he ower loss hs no exceeded he Asolue Mximum Rings for using MOSFE. Since he MOSFE loss cnno e mesured using ower
More informationTopic Astable Circuits. Recall that an astable circuit has two unstable states;
Topic 2.2. Asable Circuis. Learning Objecives: A he end o his opic you will be able o; Recall ha an asable circui has wo unsable saes; Explain he operaion o a circui based on a Schmi inverer, and esimae
More informationThe ray paths and travel times for multiple layers can be computed using ray-tracing, as demonstrated in Lab 3.
C. Trael me cures for mulple reflecors The ray pahs ad rael mes for mulple layers ca be compued usg ray-racg, as demosraed Lab. MATLAB scrp reflec_layers_.m performs smple ray racg. (m) ref(ms) ref(ms)
More informationLecture 6: Learning for Control (Generalised Linear Regression)
Lecure 6: Learnng for Conrol (Generalsed Lnear Regresson) Conens: Lnear Mehods for Regresson Leas Squares, Gauss Markov heorem Recursve Leas Squares Lecure 6: RLSC - Prof. Sehu Vjayakumar Lnear Regresson
More information8. Basic RL and RC Circuits
8. Basic L and C Circuis This chaper deals wih he soluions of he responses of L and C circuis The analysis of C and L circuis leads o a linear differenial equaion This chaper covers he following opics
More informationCircuit Variables. AP 1.1 Use a product of ratios to convert two-thirds the speed of light from meters per second to miles per second: 1 ft 12 in
Circui Variables 1 Assessmen Problems AP 1.1 Use a produc of raios o conver wo-hirds he speed of ligh from meers per second o miles per second: ( ) 2 3 1 8 m 3 1 s 1 cm 1 m 1 in 2.54 cm 1 f 12 in 1 mile
More information( )a = "t = 1 E =" B E = 5016 V. E = BHv # 3. 2 %r. c.) direction of induced current in the loop for : i.) "t < 1
99 3 c dr b a µ r.? d b µ d d cdr a r & b d & µ c µ c b dr µ c µ c b & ' ln' a +*+* b ln r ln a a r a ' µ c b 'b* µ c ln' * & ln, &a a+ ncreang no he page o nduced curren wll creae a - feldou of he page
More informationMC14040B. 12-Bit Binary Counter
M4040B 2Bi Binary ouner The M4040B 2sage binary couner is coruced wih MOS Phannel and Nhannel enhancemen mode devices in a single monolihic srucure. This par is designed wih an inpu wave shaping circui
More informationRevision: June 12, E Main Suite D Pullman, WA (509) Voice and Fax
.: apacors Reson: June, 5 E Man Sue D Pullman, WA 9963 59 334 636 Voce an Fax Oerew We begn our suy of energy sorage elemens wh a scusson of capacors. apacors, lke ressors, are passe wo-ermnal crcu elemens.
More information( ) ( ) if t = t. It must satisfy the identity. So, bulkiness of the unit impulse (hyper)function is equal to 1. The defining characteristic is
UNIT IMPULSE RESPONSE, UNIT STEP RESPONSE, STABILITY. Uni impulse funcion (Dirac dela funcion, dela funcion) rigorously defined is no sricly a funcion, bu disribuion (or measure), precise reamen requires
More informationChapter 3: Vectors and Two-Dimensional Motion
Chape 3: Vecos and Two-Dmensonal Moon Vecos: magnude and decon Negae o a eco: eese s decon Mulplng o ddng a eco b a scala Vecos n he same decon (eaed lke numbes) Geneal Veco Addon: Tangle mehod o addon
More informationApplication Notes for AP3770 System Solution
lcaon oe 1068 lcaon oes for 3770 ysem oluon reared by u Qg Hua ysem Engeerg De. 1. nroducon The 3770 uses ulse Frequency Modulaon (FM) mehod o realze Dsconuous Conducon Mode (DCM) oeraon for FYBCK ower
More informationMechanics Physics 151
Mechancs Physcs 5 Lecure 0 Canoncal Transformaons (Chaper 9) Wha We Dd Las Tme Hamlon s Prncple n he Hamlonan formalsm Dervaon was smple δi δ Addonal end-pon consrans pq H( q, p, ) d 0 δ q ( ) δq ( ) δ
More informationIntermediate Macroeconomics: Mid-term exam May 30 th, 2016 Makoto Saito
1 Inermediae Macroeconomics: Mid-erm exam May 30 h, 2016 Makoo Saio Try he following hree roblems, and submi your answer in handwrien A4 aers. You are execed o dro your aers ino he mailbox assigned for
More informationCircuits II EE221. Instructor: Kevin D. Donohue. Instantaneous, Average, RMS, and Apparent Power, and, Maximum Power Transfer, and Power Factors
Crcuts II EE1 Unt 3 Instructor: Ken D. Donohue Instantaneous, Aerage, RMS, and Apparent Power, and, Maxmum Power pp ransfer, and Power Factors Power Defntons/Unts: Work s n unts of newton-meters or joules
More informationSINUSOIDAL WAVEFORMS
SINUSOIDAL WAVEFORMS The sinusoidal waveform is he only waveform whose shape is no affeced by he response characerisics of R, L, and C elemens. Enzo Paerno CIRCUIT ELEMENTS R [ Ω ] Resisance: Ω: Ohms Georg
More informationChapter 2: Principles of steady-state converter analysis
Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer
More informationJohn Geweke a and Gianni Amisano b a Departments of Economics and Statistics, University of Iowa, USA b European Central Bank, Frankfurt, Germany
Herarchcal Markov Normal Mxure models wh Applcaons o Fnancal Asse Reurns Appendx: Proofs of Theorems and Condonal Poseror Dsrbuons John Geweke a and Gann Amsano b a Deparmens of Economcs and Sascs, Unversy
More informationEE C245 ME C218 Introduction to MEMS Design
EE C45 ME C8 Introducton to MEM Desgn Fall 7 Prof. Clark T.C. Nguyen Dept. of Electrcal Engneerng & Computer cences Unersty of Calforna at Berkeley Berkeley, C 947 Dscusson: eew of Op mps EE C45: Introducton
More information