# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

3 Pages

### Slds Chap 7

Course: ECE 602, Fall 2011
School: Purdue
Rating:

Word Count: 1572

#### Document Preview

Quiz EE-602 Fall Discussion 09 1. Using a forward Euler approximation with h = 0.1, ! x (t k ) = to the differential equation, x (t k + h ) ! x (t k ) h dx !1 = ,!!! x (0 ) = 0.1, compute an dt 2 x estimate for x(0.1). 2. Using separation of variables, solve the diff. equation, dx !1 = ,!!! x (0 ) = 0.1, to compute an exact expression for x(t) and dt 2 x evaluate it at t = 0.1. Compare with your answer to...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Indiana >> Purdue >> ECE 602

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Quiz EE-602 Fall Discussion 09 1. Using a forward Euler approximation with h = 0.1, ! x (t k ) = to the differential equation, x (t k + h ) ! x (t k ) h dx !1 = ,!!! x (0 ) = 0.1, compute an dt 2 x estimate for x(0.1). 2. Using separation of variables, solve the diff. equation, dx !1 = ,!!! x (0 ) = 0.1, to compute an exact expression for x(t) and dt 2 x evaluate it at t = 0.1. Compare with your answer to the Euler approximation of part 1. EE-602,Chap 7, Fall 08 7- 2 R. A. DeCarlo CHAPTER 7: EXISTENCE AND UNIQUENESS OF STATE TRAJECTORIES I. INTRODUCTION: 1. QUESTION 7.1: Precisely, what is meant by a solution to ! x = f ( x, t ), x (t 0 ) = x0 ? ANSWER: ! (", t 0 ; x0 ) denotes a solution if and only if i. ! (t 0 , t 0 ; x0 ) = x0 (satisfies IC), and ! ii. ! (t , t 0 ; x0 ) = f (! (t , t 0 ; x0 ), t ) (satisfies DE) 2. QUESTION 7.2: What does uniqueness of a solution mean? ANSWER: A UNIQUE ! (t , t 0 ; x0 ) means that if !1 and !2 both satisfy the differential equation: ! !i = f (!i , t ) and the same IC !1 (t 0 , t 0 ; x0 ) = !2 (t 0 , t 0 ; x0 ) THEN for all t in R + = {t !|! t ! 0} . !1 (t , t 0 ; x0 ) = !2 (t , t 0 ; x0 ) EE-602,Chap 7, Fall 08 7- 3 R. A. DeCarlo 3. QUESTION 7.3: When does there exist a solution to the nonlinear state dynamics: ! x (t ) = f [ x (t ), t ], x (t 0 ) = x0 where x (t ) ! R n and f (!, !) : R n " R # R n . ANSWER: Momentarily postponed. 3. QUESTION 7.4: Why is EXISTENCE and UNIQUENESS of a solution important? ANSWER VIA MOTIVATIONAL EXAMPLE: OBJECTIVE: Numerically, using forward Euler, and analytically compute solution to ! x= !1 2x x (0 ) = x0 = 0.1 at t = 0.1. Part 1: Numerical solution via Euler at t = 0.1: See Quiz Part 2: Analytic solution via separation of variables: EE-602,Chap 7, Fall 08 7- 4 R. A. DeCarlo II. MATHEMATICAL PRELIMINARIES PART I: NORMS AND NORM PROPERTIES 1. Vector Norms (a) EUCLIDEAN VECTOR NORM: v = ! v1 v2 ! vn # " \$ T has 2-norm (Euclidean) 2 2 2 = v1 + v2 + ! + vn v (b) -norm: 2. Proposition: v v ! 2 ! = max vi "v i 2 " nv ! Why are NORMS important? ANSWER: They measure different properties of a function or matrix, like the color of eyes, the color of hair, the height, the weight, the shoe size of the matrix or function. EE-602,Chap 7, Fall 08 7- 5 R. A. DeCarlo 3. THE FUNCTION L OR SUP-NORM (a) Let a(!) : R " R . The L! or sup-norm is a(.) ! = sup a(t ) t (b) Restricted to a domain, D: a(.) !, D = sup a(t ) t "D (c) The vector L! -norm: Let a(!) : R " R n , then a(.) !, D = max ai (t ) i !, D QUESTION: Why is this norm important? ANSWER: It measures the "highest absolute value" a function can achieve over R or over some domain D. EE-602,Chap 7, Fall 08 7- 6 R. A. DeCarlo 4. MATRIX NORMS: (a) Matrix spectral or 2-norm: for a constant matrix A A 2 = max x!0 Ax x 2 = max Ax 2 x =1 2 = "1 where ! 1 is the largest singular value of A. (b) Matrix L-norm of constant A A ! #n = max % " aij i % j =1 \$ & ( ( ' (c) Matrix L-norm of A(!) = " aij (!) \$ : R & R n' n restricted to # % a domain D is: A(.) !, D = max i " aij (.) j !, D EE-602,Chap 7, Fall 08 7- 7 R. A. DeCarlo EXAMPLE 7.1. Compute the L! -norm of # e! t ! e! t A(t ) = % % ! cos(t ) 2 sin("t ) \$ Step 1: Compute L! -norm of row 1: Step 2: Compute L! -norm of row 2: Step 3: Choose largest: & (1+ (t ) ( ' EE-602,Chap 7, Fall 08 7- 8 R. A. DeCarlo 5. MATRIX NORM PROPERTIES: (a) 1 A n ! "A 2 " nA ! (b) Ax 2 ! A 2 x 2 (c) A USEFUL LEMMA: A(!) x 2, D j " A(!) 2, D x j 2 " n A(!) #, D x j 2 EE-602,Chap 7, Fall 08 7- 9 R. A. DeCarlo PART 2. CONTINUITY 1. CONTINUITY IN A DOMAIN: f (!, !) : R n " R # R n is continuous on some domain D ! R n " R if it is continuous at each point of D. Pictorially, 2. LEFT AND RIGHT HAND LIMITS: EE-602,Chap 7, Fall 08 7-10 3. PIECEWISE CONTINUOUS R. A. DeCarlo EE-602,Chap 7, Fall 08 7-11 R. A. DeCarlo III. GLOBAL EXISTENCE AND UNIQUENESS 1. PROBLEM STATEMENT: Determine sufficient conditions for the existence of a unique solution to ! x = f ( x, t ), x (0 ) = x0 where x (t ) ! R n and t ! R + = [ 0,! " ) REMARK: A simple change of variable makes the forthcoming conditions valid over an arbitrary interval [t 0 ,! ! ) . 2. What ASSUMPTIONS are pertinent? i. There is a set S contained in R + containing at most a finite number of points per unit interval. S will depend on f ( x, t ) and will denote possible discontinuity points. ! 1\$ REMARK: The points, t, 0 ! t ! 1, for which sin # & = 0 could not "t% be in S. EE-602,Chap 7, Fall 08 7-12 R. A. DeCarlo ii. for each x ! R n , f ( x, t ) is continuous for t ! S . iii. for each x ! R n and for each ti ! S , f ( x, t ) has finite left and right hand limits at t = ti . iv. (!, f !) : R n " R # R n satisfies a global Lipschitz condition-i.e. there exists a piecewise continuous function k (!) : R + " R + such that f ( x1, t ) ! f ( x 2 , t ) 2 " k (t ) x1 ! x 2 for all t ! R + and all points x1, x 2 ! R n . 2 EE-602,Chap 7, Fall 08 7-13 R. A. DeCarlo 3. WHY ARE THESE ASSUMPTIONS PERTINENT? i. For each fixed t , f ( x, t ) is continuous at x ; ii. For each x , the points of discontinuity of f ( x, t ) lie in S; iii. If x (t ) is continuous, f ( x (t ), t ) is piecewise continuous in t . iv. From (i) - (iii), f ( x (t ), t ) is integrable with respect to t and the derivative of its integral equals f ( x (t ), t ) except possibly at t ! S by the fundamental theorem of calculus. v. They allow us to state and prove an existence and uniqueness theorem. EE-602,Chap 7, Fall 08 7-14 R. A. DeCarlo 4. EXISTENCE AND UNIQUENESS THEOREM: Given assumptions (i) through (iv), for each x0 ! R n and t 0 ! R + , there exists a unique continuous function ! (., t 0 ; x0 ) :R+ ---> Rn such that ! i. ! (t , t 0 ; x0 ) = f [! (t , t 0 ; x0 ), t ] , and ii. ! (t 0 , t 0 ; x0 ) = x0 for all t ! R + and t S. 5. EXAMPLE 7.2. Determine if the state equations for the inverted pendulum have a unique solution. The state equations are ! x1 ! # ! # x2 " \$! x2 &=# & # q sin( x1 ) %" \$ & ' f ( x, t ) = f ( x ) & % The only essential part of the proof is to show that f ( x, t ) is Lipschitz. EE-602,Chap 7, Fall 08 7-15 R. A. DeCarlo EE-602,Chap 7, Fall 08 7-16 R. A. DeCarlo IV. EXISTENCE AND UNIQUENESS OF LINEAR STATE DYNAMICS 1. Linear State Dynamics ! x (t ) = f ( x (t ), t ) = A(t ) x (t ) where A(!) = " aij (!) \$ has piecewise continuous entries over the # % interval [t 0 , ! ] . 2. PROPOSITION: If A(!) has piecewise continuous entries on R + then f ( x, t ) = A(t ) x satisfies a global Lipschitz condition on R n ! R + . PROOF: Step 1: Define D j = [ j ! 1, j ) for j = 1,2,3,.... ! Step 2. Observe that ! D j = R+ j =1 EE-602,Chap 7, Fall 08 7-17 R. A. DeCarlo Step 3. For each t ! D j and all points x1, x 2 ! R n . it follows that f ( x1, t ) ! f ( x 2 , t ) 2 = A(t ) " x1 ! x 2 \$ # % 2 & A(t ) 2 x1 ! x 2 2 It follows that A(t ) " x1 ! x 2 \$ # % 2, D j & n A(t ) ', D x1 ! x 2 j 2 Step 4. Define # % k (t ) = \$ % & n A(t ) !, D 0 j t "Dj otherwise Thus A(t ) " x1 ! x 2 \$ # % 2 & k (t ) x1 ! x 2 2 means that the right side of our differential equation satisfies a global Lipschitz condition. EE-602,Chap 7, Fall 08 7-18 R. A. DeCarlo 3. THEOREM: A solution ! (", t 0 , x0 , u ) to ! x (t ) = A(t ) x (t ) + B(t ) u (t ) , x (t 0 ) = x0 exists and is unique over [t 0 , ! ) provided A(!) and B(!)u (!) are piecewise continuous over [t 0 , ! ) 1. Corollary: If A(!) is piecewise continuous, a solution, designated ! ! (", t 0 , x0 ) , to x (t ) = A(t ) x (t ) , exists and is unique for each initial conditon x0 . 1 For our work, the solution will be unique even when B(.)u(.) is not piecewise continuous for example when u(t) = (t). EE-602,Chap 7, Fall 08 7-19 R. A. DeCarlo Quiz Questions: Part 1. True-false. Question 1: The differential equation ! x = f ( x, u ) = sin(t )(1 ! 2 x )u (t ) has a unique solution solvable by separation of variables for each initial condition x(0) 0.5 and t 0. Question 2: Consider the state dynamics, ! x (t ) = A(t ) x (t ) + B(t ) u (t ) ! f ( x, t ) . If there exists a unique solution, then f ( x, t ) satisfies a Lipschitz condition. _______________ Question 2: If A(t ) and B(t ) have piecewise continuous entries, then there exists a unique solution. _______________ EE-602,Chap 7, Fall 08 7-20 R. A. DeCarlo Question 3: The state dynamics " 1 1 + cos(t ) ! sin(t ) ! x (t ) = \$ \$0 exp(! t )1+ (t ) # % ' x (t ) ' & has a unique solution. _______________ ! Problem 1. (a) Suppose x = f(x,t). Precisely state the definition of a Lipschitz condition for f(x,t). (b) Prove or disprove: the state dynamics ! x1 ! # ! # x2 " \$ ! t cos(t ) sin( x2 ) &=# & # q cos( x1 ) sin( x1 ) %" \$ ! cos(t ) &+# &# 1 %" has a unique solution where q is a non-zero constant. \$ & u (t ) & % EE-602,Chap 7, Fall 08 7-21 R. A. DeCarlo Problem 2. Consider the state dynamics ! x = A(t ) f ( x ) + B( x, t )u (t ) (a) State the Lipschitz condition, precisely. (b) Develop conditions on A(t ) , f ( x ) , B( x, t ) , and u (t ) which are sufficient for the existence of a unique solution. Explain your reasoning. EE-602,Chap 7, Fall 08 7-22 OTHER MATHEMATICAL PROPERTIES 1. OTHER VECTOR NORMS n (a) 1-norm: (b) p-norm: v v 1 p = ! vi i =1 "n = \$ ! vi \$ i =1 # p %1/ p ' ' & 2. VECTOR NORM PROPERTIES (a) v (b) v 2 !v 1 ! nv ! "v 1 "n v 2 ! R. A. DeCarlo
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Purdue - ECE - 602
Chap 7 Sols, EE-602, Fall 11EE 602 Homework #7SolutionsFall 2011/Stu*3. (a) Similar as that described in class.&quot;!1x2 + ! 2t1+ (t )\$(b) Let f ( x, t ) =\$ ! 3t sin(w1t ) sin (! 4 x1 )#()()12f x ,t ! f x ,t2=!!!=%' . Then for any x1 and
Purdue - ECE - 602
2. MATHEMATICAL UNDERPINNINGSThe characterizing equations 5.3 and 5.5 of the two problems given in the introductory sectionalways have the form Rx = b or Q! = b . Generally, R has more rows than columns meaning that the set ofequations 5.3 is over spec
DeVry Sandy - PSYCH - 101
Classical Conditioning1. Learning1. Learning-performance distinction2. Basics of Classical Conditioning1. Pavlov &amp; psychic secretions2. CS, UCS, CR, UCR3. Factors in Classical Conditioning1. Contiguity; amplitude2. Spontaneous recovery &amp; savings3
DeVry Sandy - PSYCH - 101
Operant Conditioning1. Elements of Conditioning1. Skinner box2. shaping; chaining2. Reinforcers1. positive vs negative (vs punishment)2. cues, extinction, spontaneous recovery3. four training schedules4. superstition5. secondary; partial6. four
DeVry Sandy - PSYCH - 101
Visual Perception1. Figure &amp; Ground2. Gestalt Laws of Grouping3. Pattern Perception1. templates vs prototypes2. bottom-up vs top-down processing4. Depth1. Monocular and binocular cues5. Constancy &amp; Context6. Motion1. Saccades &amp; fixationsPET Sca
DeVry Sandy - PSYCH - 101
Sensation &amp; Perception1. Sensation vs Perception2. Psychophysics1. Thresholds2. Just Noticeable Difference (jnd)3. Signal Detection Theory3. Subliminal Perception4. Attention1. Alerting, vigilance, selective, dividedDefinitionsSensation: the det
DeVry Sandy - PSYCH - 101
Vision1. Light1. Wave characteristics2. The Eye1. Structure of the eye2. Problems with vision3. Colour1. Rods and cones2. Colour blindnessLightPhysical Characteristicstransduction: conversion of externalstimulus energy into internal neural ene
DeVry Sandy - PSYCH - 101
Neural Systems 11. A Single Neuron1. Cell body, dendrite, and axon2. Sensory, motor, and interneurons3. Afferent vs efferent4. Glial cells2. Neuronal transmission1. Action potential and resting potential2. Synapse and neurotransmitters3. Excitati
DeVry Sandy - PSYCH - 101
Research Methods I1. The Correlational Methods1. Survey2. Case Study3. Longitudinal Study4. Cross-Sectional Study5. Naturalistic Observation6. Psychological Testing (Psychometrics)Research Methods II1. Correlations vs Experiments1. Causation2.
DeVry Sandy - PSYCH - 101
UNIVERSITYOFWATERLOODepartmentofEconomicsEconomics101(02)IntroductiontoMicroeconomicsAngelaTrimarchiInstructor:Office:Fall2010AngelaE.TrimarchiHH130Phone(519)8884567Ext.36006Email:atrimarchi@uwaterloo.caOfficeHours: TTh:10:0011:30a.m.ClassMeet
DeVry Sandy - PSYCH - 101
DeVry Sandy - PSYCH - 101
U niversity of W aterloo - School of Accounting &amp; FinanceA FM 101Introduction to Financial AccountingFall 2010Course OutlineContact InformationInstructors:Name:Office:Phone:Shari MannHH 383JN/ADonna PsutkaHH 3162519-888-4567 ext. 36914Mind
DeVry Sandy - PSYCH - 101
EntrepreneurshipMultiple Choice Question Themes1. From Careers: be your own boss, risk takers are not taking risks (slide 10)a. Managing risks2. From Careers: be your own boss, reasonable sales forecast and expensesestimate (slide 11)3. Why take the
DeVry Sandy - PSYCH - 101
Ethical Problems in ArchaeologyDigging up the Dead-absences of living descendants-religious beliefs-no personal connection-easier to understand people from the past by digging up the graves-much of our knowledge comes from burials/graves-tombstones
DeVry Sandy - PSYCH - 101
F ormativePeerEvaluationFormEvaluator: Praveen YogendranReceiver: Camille TanTeam: iBikeThis form is used to give performance feedback to each team member, so you will needto complete as many forms as there are other team members. The assessment isg
DeVry Sandy - PSYCH - 101
F ormativePeerEvaluationFormEvaluator: Miranda McKie Receiver: Camille Tan Team: iBikeThis form is used to give performance feedback to each team member, so you will needto complete as many forms as there are other team members. The assessment isgroup
DeVry Sandy - PSYCH - 101
INDIVIDUAL SKILLS WORKSHEETPlease indicate the extent to which you agree or disagree with each of the followingstatements about your team related skills. Rate the items using the following scale:1 = Strongly Disagree 4 = Strongly AgreeI need to improv
DeVry Sandy - PSYCH - 101
Team Mid-Point ReflectionCamille Tan 20383581How have the discussion topics and the rollovers for Mikes Bikes gone?Originally, we were unaware that we had to post on the discussion board, so ourdiscussions were not very efficient. After we learned how
DeVry Sandy - PSYCH - 101
F ormativePeerEvaluationFormEvaluator: Natalie WongReceiver: Camille TanTeam: iBike (A1G-04)This form is used to give performance feedback to each team member, so you will needto complete as many forms as there are other team members. The assessment
DeVry Sandy - PSYCH - 101
TEAM SUMMARY FORMCamille Tan; 20383581I.Identify two things you considered positive about the experience.Two things I found positive about this experience was I was able to meet newpeople in this class and how it helped me understand how to manage a
DeVry Sandy - PSYCH - 101
S ummativePeerEvaluationFormThis form is used to evaluate each team member and to do a self assessment, so youwill need to complete up to 3 sections for each of your teammates and the final sectionfor the self evaluation. The assessment is grouped into
DeVry Sandy - PSYCH - 101
AppendixAppendix ContentsAppendix A: Multifirm Shareholder ValuesAppendix B: Multifirm ProfitAppendix C: Multifirm Product AwarenessAppendix D: Multifirm Production CapacityAppendix E: Multifirm Market Share-Appendix E (1): Multifirm Market Share 2
DeVry Sandy - PSYCH - 101
Rollover 4: Year 2012Basic StrategiesOur firm discontinued the strategy in which was previously used in 2011. iBike decidedto take a new approach, which involved the increase of price of the mountain bike and a decreaseof production.For this year, iB
DeVry Sandy - PSYCH - 101
Chapters2&amp;3TheBalanceSheet&amp;theIncomeStatementNeed for Conceptual FrameworkTo apply GAAP to the preparation of financialstatementsTo solve new and emerging problems( preparers and standard setters)To interpret financial statements( preparers )( u
DeVry Sandy - PSYCH - 101
basic strategies identified and then revisitedreview of the prior year results including comparison ofexpected performance with actual results for your firm and comparison of yourfirms performance with your competitionspecific decisions with regards
DeVry Sandy - PSYCH - 101
Mikes BikesOctober 14: Rollover 1 Marketing-advertise more, market is sensitive-forecast low, sell more so that shareholders value increases-selling/focusing on mountain bikes first-raising price to \$15, to be in the middle-so price is not too high
DeVry Sandy - PSYCH - 101
S mall Business ~ WorksheetIntroduction to Forms of Business OrganizationsQA-What three choices does a business owner have when forming a small business?Q-If you were to consider becoming an owner of a business, in what ways does personal financial r
DeVry Sandy - PSYCH - 101
G lobalization ~ WorksheetIntroduction to GlobalizationRead Chapter 3 of the text book.Using the space provided below, respond to the following questions.QA-How does globalization affect you as a: consumer, employee, business owner, and student?-Con
DeVry Sandy - PSYCH - 101
I mpactofGovernmentonBusiness ~WorksheetIntroduction to Forms of Business OrganizationsRead page 102 in the text book.Using the space provided below,respond to the following questions.Q-How can we use / or how doesgovernment involvement in business
DeVry Sandy - PSYCH - 101
Dec. 1st, 2010How Hoplites Died in Battle: The Battle of Chaironeia (338 BC)Occurred August 338 BCOccurred in Macedonia w/ Phillip and Alexander (18 at the time)Went down to Boeotia and easily defeated themWas the beginning of the end for the Greeks
DeVry Sandy - PSYCH - 101
ReviewSignificance of Greece and Rome Today-the legacy of the ancient world in the modern world (historical, artistic, cultural)-the foundations of language-the bases of political thought-slaves, males have controletc.-the bases of philosophical inq
Arizona - ECE - 369
ECE 369 Fundamentals of Computer ArchitectureMidterm Exam 2Limit your answers to the space provided. Unnecessarily long answers will be penalized. If youuse more space than is provided, you are probably doing something wrong. Use the back of eachpage
Arizona - ECE - 369
ECE 369Homework 3Due: December 7, 2009In Class, Hard Copy1) Consider a 64-byte cache with 8 byte blocks, an associativity of 2 and LRU block replacement.Virtual addresses are 16 bits. The cache is physically tagged. The processor has 16KB of physical
Arizona - ECE - 369
Page 1 of 12ECE 369Homework 2, total: 200ptsIn Class, Hard CopyProblem 1 (26pts)This is a three-part question about critical path calculation. Consider a simple singlecycle implementation ofMIPS ISA. The operation times for the major functional comp
Arizona - ECE - 369
I1I(D3s.83@as-3c.-E=02X\=6Y &quot;;)nga?zw3- &quot;0Iv6ea3Y,30II30PltXrU30IIVr,IHn-+&quot;r,X 2.11u-&quot;-.P+\=-r;--92&lt;0as--hTJhd34543/O2-CI,)dI34IQ ?!Y0,rc,I49LJ5-+AJt4'a)awXe
Arizona - ECE - 369
ECE 320aHomework #9Spring 2012Due Date: April 26, 2012.All problems are from Electric Circuits, Ninth Edition by James W. Nilsson and SusanA. Riedel.1. Sketch the straight-line approximation Bode plot diagrams (magnitude and phase). You might want
Arizona - ECE - 369
hapter 5Problems 331MOS F ield-Effect T ransistors ( MOSFETs) , -channel device has k~ = 50 ~AIV', V, = 0.8 V,20. The device is to operate as a switch for smallng a control voltage vGS in the range 0 V to 5 V.witch closure resistance, r DS&gt; and clo
Arizona - ECE - 369
NCSU Department of MathematicsEngineering OnlineMA 501 (651) Advanced Mathematics for Engineers and Scientists IFall 2011Instructor: Dr. Alina DucaOfce: 3232 SAS HallEmail: anduca@ncsu.eduPhone: (919) 515-1875Personal Webpage: http:/www4.ncsu.edu/
Arizona - ECE - 369
Arizona - ECE - 369
Spring 2012 - ECE 372(25 pts)Homework #21.Due _Feb 28, 2012(10 points) The following C code is intended to toggle the output RB15 precisely every 100 ms starting with an initialoutput of 0. Describe and correct at least three functional errors (i.e.
Arizona - ECE - 369
ECE-372 Lecture 1IndustrialDr. DonControllersCoxSpring2012Things toWire Wrap &amp; Solder Class Must Do!DoOffice hours: 0800 0915 Tu &amp; Thdcox@email.arizona.edu(Dr. Cox)luding@email.arizona.edu(Lu)mosfet@email.arizona.edu (Matt)No Web page Use
Arizona - ECE - 369
TRIGONOMETRYRight Triangle Definitions opp adj sin = cos = hyp hyp opp adj cot = tan = adj opp hyp hyp sec = csc = adj opp Circular Definitionssin = tan = sec = y r y x r x cos = cot = csc = x r x y r y tan x = sec x = sin x cos x 1 cos x cot x = csc x
Arizona - ECE - 369
Spring 12 ECE 372Quiz 3 (10 pts)Instructions: Answer each question listed on this composite quiz. The material covered is fromthe lectures presented in class. (Including all comments, etc. presented by the instructor). Thisis an open book/notes quiz.
Arizona - ECE - 369
Spring 12 ECE 372Quiz 5 &amp; 6 (20 pts)Instructions: Answer each question listed on this composite quiz. The material coveredis from the lectures presented in class. (Including all comments, etc. presented by theinstructor). This is an open book/notes qu
Arizona - ECE - 369
Spring 12 ECE 372Quiz 7 (10 pts)Instructions: Answer each question listed on this quiz in class. The material covered isfrom the lecture. (Including all comments, etc. presented by the instructor). This is anopen book/notes quiz.Grade value is 10 poi
Arizona - ECE - 369
ECE 369, Fall 2011Semester Project, Assignment 1The diagram above shows a simple datapath. In this assignment, you will build and test the registerfile,the memory modules, the multiplexors and the sign extension unit. Please check the TAs office hours
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-1: IntroductionFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Course orientation Objective, textbook, and grading VLSI design evolutiondesign History, today, and tomorrow Integration and
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-2: Logic Gate BasicsFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight MOSFET basics The structure and operation First-order model: a switch + a resistor Logic gates Logic construction Dynam
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-3: CMOS TechnologyFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Lecture 03-1-Highlight Front end process MOSFET transistors Process definitionProcess definition Backend process On-chip intercon
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-4: Circuit Layout andDesign RulesFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Layout rules and optimization Layout: mapping between circuits and fabrication Robust under fabrication Com
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-5: CMOS ModelingFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Threshold voltage (Vth) Body effect Extraction of Vth Current-voltage relations (IV) Linear and saturation regions Channel
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-7: Inverter DesignFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Static behavior Voltage Transfer Curve (VTC) Sizing of NMOS and PMOSNMOSPMOS Static noise margin Dynamic analysis The R
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-10: Technology ScalingFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Technology scaling: why and how? Scaling models Trend and challenges Review for Midterm I Questions? Sample test Rea
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-11: CombinationalStatic Logic DesignFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Combinational static logic Definition Implementation in CMOSCMOS Logic gate construction Stick diagram
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-12: Delay MinimizationFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Delay minimization for a logic gate Elmore delay Worst-case switching pattern Transistor sizing Fan-In, Fan-Out, and l
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-13: Logical EffortsFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Delay optimization for a data path Critical path in a complex circuit Design example of an inverter chain Logical efforts
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-16: Pass Gate LogicFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Pass gate logic design (PL) General structure and comparisons Design considerations of PLPL NMOS only and transmission ga
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-17: Dynamic LogicFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Dynamic logic gate design Precharge and evaluate Data storage Main design issues and solutions Dynamic logic path construct
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-19: Adder DesignFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Lab 4/5: A Mini Design Projecta0 b0a1 b1a2 b2a3 b3FCFCFCFCCc0=0c1c2c3RegisterRegistersCL =50fF Design target: a 4-bit bin
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-20: Sequential CircuitsFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Sequential logic Data storage mechanisms Basic latch design Circuit structure Design issues Design of a flip-flop D
ASU - EEE - 591
EEE 425/591: Digital Systems and CircuitsL-23: Timing IssuesFall 2011, ASUYu (Kevin) Cao, yu.cao@asu.edu, GWC 336Highlight Timing definitions Delay, setup (tsu) and hold (thold) time Flip-Flop Latch Sequential logic construction Register (flip-f