Adder Circuits Ivor Page 1
|
|
- Percival Chapman
- 5 years ago
- Views:
Transcription
1 Adder Circuit Adder Circuit Ivor Page 4. The Ripple Carr Adder The ripple carr adder i probabl the implet parallel binar adder. It i made up of k full-adder tage, where each full-adder can be convenientl made from two half-adder and an OR gate. The truth table of the half-adder i a follow: Input Output i i c i+ z i Figure how the blockdiagram of the adder. i i i- i- HA HA c i+ c c i c c i- HA HA c c z i z i- Figure : Ripple Carr Adder Each half-adder can be contructed from four 2-input nand gate. Univerit of Tea at Dalla
2 Adder Circuit 2 i c i Figure 2: Half-Adder in Nand Gate Figure 2 how the logic diagram. The complement of the carr ignal i produced, which i eactl what i needed if the inter-tage OR gate i replaced b a nand gate: c. c 2 = c + c 2. Figure 3 i from the tet and how one of man poible CMOS implementation of a half-adder. The dela from,, or,to comprie 2-inverter dela plu the dela due to pa-tranitor in the multipleer Figure 3: Half-Adder in Nand Gate Figure 4 i from Wete & Ehraghian 2. It how one of man poible CMOS implementation of a full-adder. Thi circuit i generall referred to a 28T ince it ha 28 tranitor, including two for each inverter. The dela through thi circuit from, to come from the two erie tranitor pull-up and pull-down in the firt tage and an inverter dela. For 2 Principle of CMOS VLSI Deign, Wete & Ehraghian, Addion Wele
3 Adder Circuit 3 the um output, there are two cacaded tage, each with 2 erie tranitor pull-up and pull-down, followed b an inverter. um Figure 4: CMOS Full-Adder Figure 5 how one poible laout uing imple tranitor equencing. It doe not include the two inverter. In thi laout, darkblue i ued for metal- line and light blue for metal- 2. P-Diffuion i ellow and N-diffuion i green. Polilicon line are pink. Each time a pol line croe P-Diff, a PMOS tranitor i formed, and each time it croe N-Diff, an NMOS tranitor i formed. It i common to modif the 28T circuit to implif the laout. To do o, diconnect the ource of the top tranitor from V in the output chain for um and connect it intead to the drain of the top three parallel tranitor in the penultimate tage. Make a correponding change at the bottom end of the final chain. Thi change enable a more compact laout which ha horter connection.
4 Adder Circuit 4 V Vdd um Figure 5: CMOS Laout of Full-Adder Figure 6 how the circuit of the adder arranged according to the laout of Figure 5. A an eercie, make the circuit change dicued above and devie a new laout. You hould be able to reduce the length of the metal- trackfor the um ignal. um Figure 6: CMOS Scematic of Laout of Full-Adder
5 Adder Circuit 5 Wang and Jiang 3 introduced new laout for the CMOS full-adder. The objective of optimizing the laout i to reduce capacitance throughout the circuit, epeciall at internal ignal point. In HSPICE imulation, their laout had 6% maller dela time and % lower power conumption than thoe of Wete. Wang and Jiang alo eperimented with 4 new circuit for the full-adder, compriing mainl pa-tranitor. Some of their circuit had onl - tranitor and were hown to have 9% maller dela time and % lower power conumption than previou T circuit. Figure 7 how one of their circuit. Note that buffer gate would be needed between uch tage ince there are two pa tranitor in erie in between the and ignal in each tage. V DD V DD MID um MID Figure 7: Jiang & Wang Full Adder Circuit 3 Yingtao Jiang, Ph.D Diertation, Department of Electrical Engineering, UT Dalla 2
6 Adder Circuit Dela Through Ripple Carr Adder The dela through a k tage ripple-carr adder, from input, to output c k, uing nand-baed circuit i (2k +)D, whered i the normalized gate dela. We conider the average dela ince the probabilit of the wort cae i ver mall and, auming that it i poible to detect that carr propagation ha terminated, the computer tem need not wait for the wort cae dela time on ever addition. Unfortunatel, taking advantage of a variable time adder would erioul complicate the deign of a clocked tem. It i more practical to bae the deign on wort cae dela aumption. Firt we conider the mean carr-chain length, auming that the two value being added have random bit-pattern. Thi aumption i clearl not true of mot computer program. Mot integer calculation involve the addition or ubtraction of mall contant. Conider a imple eample, where the tranpoe of a matri i being calculated: // Matri Tranpoe Eample int in_matri[4][4], out_matri[4][4];... for(int i=;i<4;i++) for(int j=;j<4;j++) out_matri[j][i] = in_matri[i][j]; Although contrived, the eample doe reflect what take place in real program: much of the arithmetic activit i devoted to loop-counting and computing addree. Thee operation require the addition and ubtraction of mall integer contant. The Burrough B7 computer wa baed on thi premie. It enabled torage of, and arithmetic on, variable-length integer, reflecting the propenit of operation with mall integer contant. Let continue with the aumption that the two operand have random bit pattern. For each operand, ever poible value within the range of the number tem i equall likel. The following tatement are then true for an arbitrar tage: Probabilit of carr generation = /4
7 Adder Circuit 7 Probabilit of carr annihilation = /4 Probabilit of carr propagation = /2 The firt cae correpond to i. i =. The econd require i + i =,and the third require i i =. For a carr chain to begin at tage i and end at tage j, j>i,itmutbe generated b tage i, propagated b tage i+,i+2, j, and topped at tage j. To top the carr chain, tage j mut either annihilate the incoming carr, or generate a carr, thereb beginning new chain. The probabilit that a carr generated at poition i end at poition j, for j>ii: P carr chain (j, i) =2 (j i ) /2 =2 (j i) j>i The equation doe not include the probabilit that tage i generate a carr. The term /2 come from the combined probabilitie that tage j generate a carr or annihilate the incoming carr. To obtain the mean length of a carr chain beginning at tage i we um the length of all poible chain time their probabilitie. = = k j=i+ k j l= [ (j i)2 (j i) ] +(k i)2 (k i ) [ l2 l ] +(k i)2 (k i ) = 2 (k i )2 (k i ) +(k i)2 (k i ) = 2 2 (k i ) The ummation include all chain that top before or at tage k. The term (k i)2 (k i ) i for a carr chain of length k i, that mut end ince there i no tage k. The change of variable, l = j i, in the econd line facilitate the ue of the theorem: p l= l (p +2) =2 2l 2 p For k>>i, the mean carr-chain length i 2, quite hort. Now we conider the mean of the longet carr-chain length when adding pair of arbitrar
8 Adder Circuit 8 integer. That i, if we add one million pair of randoml generated integer and tabulate the length of the longet carr-chain in each of thee um, what will be the mean of thoe tabulated value? Let η k (h) be the probabilit that the longet carr-chain in a k bit addition i of length h or more. The probabilit that the longet carr chain i eactl of length h i η k (h) η k (h + ). We can form a recurrence relation b uing the following condition that enable a carr chain of length h or more: c: The leat ignificant k bit have a carr length of h or more. c2: The leat ignificant k bit do not have uch a carr chain, but the mot ignificant h bit have a carr chain of length eactl h. Condition c and c2 are mutuall ecluive. In general: η k (h) =η k (h)+2 (h+) P (condition 2) The term 2 (h+) repreent the probabilit of a carr being generated at tage k h, time the probabilit of that carr being propagated over (the mot ignificant) h 2 tage. Since we cannot know the probabilit that the econd condition will occur, we et it probabilit to, change the equal ign to le-than-or-equal, and unwind the recurrence: η k (h) η k (h)+2 (h+)... η k 2 (h)+2 2 (h+) η k 3 (h)+3 2 (h+) η k 4 (h)+4 2 (h+) Then, ince η i (h) =fori<h, η k (h) (k h +)2 (h+) k2 (h+) Note that η k (h) i a probabilit, η k (h), but the RHS of the above inequalit i forh log 2 k.
9 Adder Circuit 9 To compute the mean of the longet carr-chain, λ, we um the length time their probabilitie: λ = k h [η k (h) η k (h +)] h= = [η k () η k (2)] + 2[η k (2) η k (3)] + + k[η k (k) ] = k η k (h) h= Net we partition the um into two part. The firt γ = log 2 k term and the remaining k γ term. We et the value of the firt γ term to, the larget the can be ince the are probabilitie. Each of the remaining term i bounded above b k2 (h+). k γ k λ = η k (h) + k2 (h+) <γ+ k2 (γ+) h= h= h=γ+ Now let ɛ = log 2 k log 2 k or γ = log 2 k ɛ, where ɛ<, then, noting 2 log 2 k = k and 2 ɛ < +ɛ, λ<log 2 k ɛ +2 ɛ <log 2 k Thi conclude the proof that the mean dela through a ripple-carr adder i O(log k). To make ue of thi information, it would be necear to add logic to the adder to detect when the output wa table, i.e. when all the carr propagation had been completed. Carr-Completion Logic provide thi facilit. Stud it deign from the tet. 4.3 Mancheter Carr Chain A we aw in the above proof, each tage can generate, propagate, or annihilate a carr: g i = i i p i = i i a i = i + i t i = a i = i + i
10 Adder Circuit We have added a tranfer ignal t i that can be ued in preference to p i ince it i eaier and quicker to generate. From thee equation a imple recurrence reult: c i+ = g i + c i p i = g i + c i t i In the carr-lookahead adder, the recurrence i unwound m time to form a blockcarr tem. In the Mancheter carr chain, the equation i implemented b three witche per tage: c i+ t i c i a i g i logic logic Figure 8: Mancheter Carr Chain If thi circuit i implemented with pa tranitor and a buffer gate i ued after ever m tage, the dela would be proportional to (k/m)m 2.
Moment of Inertia of an Equilateral Triangle with Pivot at one Vertex
oment of nertia of an Equilateral Triangle with Pivot at one Vertex There are two wa (at leat) to derive the expreion f an equilateral triangle that i rotated about one vertex, and ll how ou both here.
More informationPIPELINING AND PARALLEL PROCESSING. UNIT 4 Real time Signal Processing
PIPELINING AND PARALLEL PROCESSING UNIT 4 Real time Signal Proceing Content Introduction Pipeling of FIR Digital Filter Parallel proceing Low power Deign FIR Digital Filter A FIR Filter i defined a follow:
More informationLTV System Modelling
Helinki Univerit of Technolog S-72.333 Potgraduate Coure in Radiocommunication Fall 2000 LTV Stem Modelling Heikki Lorentz Sonera Entrum O heikki.lorentz@onera.fi Januar 23 rd 200 Content. Introduction
More informationWeek 3 Statistics for bioinformatics and escience
Week 3 Statitic for bioinformatic and escience Line Skotte 28. november 2008 2.9.3-4) In thi eercie we conider microrna data from Human and Moue. The data et repreent 685 independent realiation of the
More informationLogic Design. CS 270: Mathematical Foundations of Computer Science Jeremy Johnson
Logic Deign CS 270: Mathematical Foundation of Computer Science Jeremy Johnon Logic Deign Objective: To provide an important application of propoitional logic to the deign and implification of logic circuit.
More informationLecture 18: Datapath Functional Units
Lecture 8: Datapath Functional Unit Outline Comparator Shifter Multi-input Adder Multiplier 8: Datapath Functional Unit CMOS VLSI Deign 4th Ed. 2 Comparator 0 detector: A = 00 000 detector: A = Equality
More informationLecture 12: Datapath Functional Units
Lecture 2: Datapath Functional Unit Slide courtey of Deming Chen Slide baed on the initial et from David Harri CMOS VLSI Deign Outline Comparator Shifter Multi-input Adder Multiplier Reading:.3-4;.8-9
More informationSIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. Solutions to Assignment 3 February 2005.
SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuit II Solution to Aignment 3 February 2005. Initial Condition Source 0 V battery witch flip at t 0 find i 3 (t) Component value:
More informationPosition. If the particle is at point (x, y, z) on the curved path s shown in Fig a,then its location is defined by the position vector
34 C HAPTER 1 KINEMATICS OF A PARTICLE 1 1.5 Curvilinear Motion: Rectangular Component Occaionall the motion of a particle can bet be decribed along a path that can be epreed in term of it,, coordinate.
More informationPIPELINED DIVISION OF SIGNED NUMBERS WITH THE USE OF RESIDUE ARITHMETIC FOR SMALL NUMBER RANGE WITH THE PROGRAMMABLE GATE ARRAY
POZNAN UNIVE RSITY OF TE CHNOLOGY ACADE MIC JOURNALS No 76 Electrical Engineering 03 Robert SMYK* Zenon ULMAN* Maciej CZYŻAK* PIPELINED DIVISION OF SIGNED NUMBERS WITH THE USE OF RESIDUE ARITHMETIC FOR
More information2.7.2 Limits to Parallelism
Chapter 2 Exercie 53 The 1990 will find a broader ue of multiproceor a the peed of individual proceor reache the limit of metal interconnection. The highet utainable clock rate for metal interconnection
More informationECEN620: Network Theory Broadband Circuit Design Fall 2018
ECEN60: Network Theory Broadband Circuit Deign Fall 08 Lecture 6: Loop Filter Circuit Sam Palermo Analog & Mixed-Signal Center Texa A&M Univerity Announcement HW i due Oct Require tranitor-level deign
More informationLecture 12: Datapath Functional Units
Introduction to CMOS VLSI Deign Lecture 2: Datapath Functional Unit David Harri Harvey Mudd College Spring 2004 Outline Comparator Shifter Multi-input Adder Multiplier 2: Datapath Functional Unit CMOS
More informationJul 4, 2005 turbo_code_primer Revision 0.0. Turbo Code Primer
Jul 4, 5 turbo_code_primer Reviion. Turbo Code Primer. Introduction Thi document give a quick tutorial on MAP baed turbo coder. Section develop the background theory. Section work through a imple numerical
More informationSIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. R 4 := 100 kohm
SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuit II Solution to Aignment 3 February 2003. Cacaded Op Amp [DC&L, problem 4.29] An ideal op amp ha an output impedance of zero,
More informationQuestion 1 Equivalent Circuits
MAE 40 inear ircuit Fall 2007 Final Intruction ) Thi exam i open book You may ue whatever written material you chooe, including your cla note and textbook You may ue a hand calculator with no communication
More informationA Study on Simulating Convolutional Codes and Turbo Codes
A Study on Simulating Convolutional Code and Turbo Code Final Report By Daniel Chang July 27, 2001 Advior: Dr. P. Kinman Executive Summary Thi project include the deign of imulation of everal convolutional
More informationCodes Correcting Two Deletions
1 Code Correcting Two Deletion Ryan Gabry and Frederic Sala Spawar Sytem Center Univerity of California, Lo Angele ryan.gabry@navy.mil fredala@ucla.edu Abtract In thi work, we invetigate the problem of
More informationinto a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get
Lecture 25 Introduction to Some Matlab c2d Code in Relation to Sampled Sytem here are many way to convert a continuou time function, { h( t) ; t [0, )} into a dicrete time function { h ( k) ; k {0,,, }}
More informationComparing Means: t-tests for Two Independent Samples
Comparing ean: t-tet for Two Independent Sample Independent-eaure Deign t-tet for Two Independent Sample Allow reearcher to evaluate the mean difference between two population uing data from two eparate
More informationCorrection for Simple System Example and Notes on Laplace Transforms / Deviation Variables ECHE 550 Fall 2002
Correction for Simple Sytem Example and Note on Laplace Tranform / Deviation Variable ECHE 55 Fall 22 Conider a tank draining from an initial height of h o at time t =. With no flow into the tank (F in
More informationSERIES COMPENSATION: VOLTAGE COMPENSATION USING DVR (Lectures 41-48)
Chapter 5 SERIES COMPENSATION: VOLTAGE COMPENSATION USING DVR (Lecture 41-48) 5.1 Introduction Power ytem hould enure good quality of electric power upply, which mean voltage and current waveform hould
More informationISSN: ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 5, Issue 5, November 2015
Optimum Deign of Charge Pump Circuit Uing Genetic Algorithm Dr. Ahmad T. Youni, Shamil H. Huein, and Ahmad A. Imail Abtract Integrated charge pump circuit are power converter ued to obtain a different
More informationSource slideplayer.com/fundamentals of Analytical Chemistry, F.J. Holler, S.R.Crouch. Chapter 6: Random Errors in Chemical Analysis
Source lideplayer.com/fundamental of Analytical Chemitry, F.J. Holler, S.R.Crouch Chapter 6: Random Error in Chemical Analyi Random error are preent in every meaurement no matter how careful the experimenter.
More informationDesign spacecraft external surfaces to ensure 95 percent probability of no mission-critical failures from particle impact.
PREFERRED RELIABILITY PAGE 1 OF 6 PRACTICES METEOROIDS & SPACE DEBRIS Practice: Deign pacecraft external urface to enure 95 percent probability of no miion-critical failure from particle impact. Benefit:
More informationDigital Control System
Digital Control Sytem Summary # he -tranform play an important role in digital control and dicrete ignal proceing. he -tranform i defined a F () f(k) k () A. Example Conider the following equence: f(k)
More informationLecture 7: Testing Distributions
CSE 5: Sublinear (and Streaming) Algorithm Spring 014 Lecture 7: Teting Ditribution April 1, 014 Lecturer: Paul Beame Scribe: Paul Beame 1 Teting Uniformity of Ditribution We return today to property teting
More informationChapter 13. Root Locus Introduction
Chapter 13 Root Locu 13.1 Introduction In the previou chapter we had a glimpe of controller deign iue through ome imple example. Obviouly when we have higher order ytem, uch imple deign technique will
More information3. In an interaction between two objects, each object exerts a force on the other. These forces are equal in magnitude and opposite in direction.
Lecture quiz toda. Small change to webite. Problem 4.30 the peed o the elevator i poitive even though it i decending. The WebAign anwer i wrong. ewton Law o Motion (page 9-99) 1. An object velocit vector
More informationChapter 2 Sampling and Quantization. In order to investigate sampling and quantization, the difference between analog
Chapter Sampling and Quantization.1 Analog and Digital Signal In order to invetigate ampling and quantization, the difference between analog and digital ignal mut be undertood. Analog ignal conit of continuou
More informationHIGHER-ORDER FILTERS. Cascade of Biquad Filters. Follow the Leader Feedback Filters (FLF) ELEN 622 (ESS)
HIGHER-ORDER FILTERS Cacade of Biquad Filter Follow the Leader Feedbac Filter (FLF) ELEN 6 (ESS) Than for ome of the material to David Hernandez Garduño CASCADE FILTER DESIGN N H ( ) Π H ( ) H ( ) H (
More informationf max = GHz I ave PartAData 2 :=
NTU 6342 / EE 24 Homework #3 SOLUTIONS Problem #: Delay time: t p_fo4_2 :=.424n t p_fo4_ := 2.2n Simulation value: T min := 2 t p_fo4_2 T max := 2 t p_fo4_ T min =.848 n T max = 4.24 n f max := T min Part
More informationSocial Studies 201 Notes for March 18, 2005
1 Social Studie 201 Note for March 18, 2005 Etimation of a mean, mall ample ize Section 8.4, p. 501. When a reearcher ha only a mall ample ize available, the central limit theorem doe not apply to the
More informationDesign By Emulation (Indirect Method)
Deign By Emulation (Indirect Method he baic trategy here i, that Given a continuou tranfer function, it i required to find the bet dicrete equivalent uch that the ignal produced by paing an input ignal
More informationUNIT 15 RELIABILITY EVALUATION OF k-out-of-n AND STANDBY SYSTEMS
UNIT 1 RELIABILITY EVALUATION OF k-out-of-n AND STANDBY SYSTEMS Structure 1.1 Introduction Objective 1.2 Redundancy 1.3 Reliability of k-out-of-n Sytem 1.4 Reliability of Standby Sytem 1. Summary 1.6 Solution/Anwer
More informationAt the end of this lesson, the students should be able to understand:
Intructional Objective: At the end of thi leon, the tudent hould be able to undertand: Baic failure mechanim of riveted joint. Concept of deign of a riveted joint. 1. Strength of riveted joint: Strength
More informationLecture 21. The Lovasz splitting-off lemma Topics in Combinatorial Optimization April 29th, 2004
18.997 Topic in Combinatorial Optimization April 29th, 2004 Lecture 21 Lecturer: Michel X. Goeman Scribe: Mohammad Mahdian 1 The Lovaz plitting-off lemma Lovaz plitting-off lemma tate the following. Theorem
More informationCHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS
CHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.1 INTRODUCTION 8.2 REDUCED ORDER MODEL DESIGN FOR LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.3
More informationExample: Amplifier Distortion
4/6/2011 Example Amplifier Ditortion 1/9 Example: Amplifier Ditortion Recall thi circuit from a previou handout: 15.0 R C =5 K v ( t) = v ( t) o R B =5 K β = 100 _ vi( t ) 58. R E =5 K CUS We found that
More informationGNSS Solutions: What is the carrier phase measurement? How is it generated in GNSS receivers? Simply put, the carrier phase
GNSS Solution: Carrier phae and it meaurement for GNSS GNSS Solution i a regular column featuring quetion and anwer about technical apect of GNSS. Reader are invited to end their quetion to the columnit,
More informationSuggestions - Problem Set (a) Show the discriminant condition (1) takes the form. ln ln, # # R R
Suggetion - Problem Set 3 4.2 (a) Show the dicriminant condition (1) take the form x D Ð.. Ñ. D.. D. ln ln, a deired. We then replace the quantitie. 3ß D3 by their etimate to get the proper form for thi
More informationChapter 5 Consistency, Zero Stability, and the Dahlquist Equivalence Theorem
Chapter 5 Conitency, Zero Stability, and the Dahlquit Equivalence Theorem In Chapter 2 we dicued convergence of numerical method and gave an experimental method for finding the rate of convergence (aka,
More informationCumulative Review of Calculus
Cumulative Review of Calculu. Uing the limit definition of the lope of a tangent, determine the lope of the tangent to each curve at the given point. a. f 5,, 5 f,, f, f 5,,,. The poition, in metre, of
More information1. The F-test for Equality of Two Variances
. The F-tet for Equality of Two Variance Previouly we've learned how to tet whether two population mean are equal, uing data from two independent ample. We can alo tet whether two population variance are
More informationNOTE: The items d) and e) of Question 4 gave you bonus marks.
MAE 40 Linear ircuit Summer 2007 Final Solution NOTE: The item d) and e) of Quetion 4 gave you bonu mark. Quetion [Equivalent irciut] [4 mark] Find the equivalent impedance between terminal A and B in
More informationECE 3510 Root Locus Design Examples. PI To eliminate steady-state error (for constant inputs) & perfect rejection of constant disturbances
ECE 350 Root Locu Deign Example Recall the imple crude ervo from lab G( ) 0 6.64 53.78 σ = = 3 23.473 PI To eliminate teady-tate error (for contant input) & perfect reection of contant diturbance Note:
More informationLecture 2: Computer Arithmetic: Adders
CMU 8-447 S 9 L2-29 8-447 Leture 2: Computer Arithmeti: Adder Jame C. Hoe Dept of ECE, CMU January 4, 29 Announement: No la on Monday Verilog Refreher next Wedneday Review P&H Ch 3 Handout: Lab and HW
More informationChapter 17 Amplifier Frequency Response
hapter 7 Amplifier Frequency epone Microelectronic ircuit Deign ichard. Jaeger Travi N. Blalock 8/0/0 hap 7- hapter Goal eview tranfer function analyi and dominant-pole approximation of amplifier tranfer
More information5. NON-LINER BLOCKS Non-linear standard blocks
5. NON-LINER BLOCKS In previou chapter continuou tem or tem where to the change of the input a change of the output correponded, which in the whole range of the ignal value could be expreed b one equation,
More informationSocial Studies 201 Notes for November 14, 2003
1 Social Studie 201 Note for November 14, 2003 Etimation of a mean, mall ample ize Section 8.4, p. 501. When a reearcher ha only a mall ample ize available, the central limit theorem doe not apply to the
More informationHybrid Control and Switched Systems. Lecture #6 Reachability
Hbrid Control and Switched Stem Lecture #6 Reachabilit João P. Hepanha Univerit of California at Santa Barbara Summar Review of previou lecture Reachabilit tranition tem reachabilit algorithm backward
More informationFollow The Leader Architecture
ECE 6(ESS) Follow The Leader Architecture 6 th Order Elliptic andpa Filter A numerical example Objective To deign a 6th order bandpa elliptic filter uing the Follow-the-Leader (FLF) architecture. The pecification
More informationDYNAMIC MODELS FOR CONTROLLER DESIGN
DYNAMIC MODELS FOR CONTROLLER DESIGN M.T. Tham (996,999) Dept. of Chemical and Proce Engineering Newcatle upon Tyne, NE 7RU, UK.. INTRODUCTION The problem of deigning a good control ytem i baically that
More informationLecture 6: Resonance II. Announcements
EES 5 Spring 4, Lecture 6 Lecture 6: Reonance II EES 5 Spring 4, Lecture 6 Announcement The lab tart thi week You mut how up for lab to tay enrolled in the coure. The firt lab i available on the web ite,
More informationNonlinear Single-Particle Dynamics in High Energy Accelerators
Nonlinear Single-Particle Dynamic in High Energy Accelerator Part 6: Canonical Perturbation Theory Nonlinear Single-Particle Dynamic in High Energy Accelerator Thi coure conit of eight lecture: 1. Introduction
More informationElectronic Theses and Dissertations
Eat Tenneee State Univerity Digital Common @ Eat Tenneee State Univerity Electronic Thee and Diertation Student Work 5-208 Vector Partition Jennifer French Eat Tenneee State Univerity Follow thi and additional
More informationLinearteam tech paper. The analysis of fourth-order state variable filter and it s application to Linkwitz- Riley filters
Linearteam tech paper The analyi of fourth-order tate variable filter and it application to Linkwitz- iley filter Janne honen 5.. TBLE OF CONTENTS. NTOCTON.... FOTH-OE LNWTZ-LEY (L TNSFE FNCTON.... TNSFE
More informationPreemptive scheduling on a small number of hierarchical machines
Available online at www.ciencedirect.com Information and Computation 06 (008) 60 619 www.elevier.com/locate/ic Preemptive cheduling on a mall number of hierarchical machine György Dóa a, Leah Eptein b,
More informationIntroduction to Laplace Transform Techniques in Circuit Analysis
Unit 6 Introduction to Laplace Tranform Technique in Circuit Analyi In thi unit we conider the application of Laplace Tranform to circuit analyi. A relevant dicuion of the one-ided Laplace tranform i found
More informationECE Linear Circuit Analysis II
ECE 202 - Linear Circuit Analyi II Final Exam Solution December 9, 2008 Solution Breaking F into partial fraction, F 2 9 9 + + 35 9 ft δt + [ + 35e 9t ]ut A 9 Hence 3 i the correct anwer. Solution 2 ft
More informationClustering Methods without Given Number of Clusters
Clutering Method without Given Number of Cluter Peng Xu, Fei Liu Introduction A we now, mean method i a very effective algorithm of clutering. It mot powerful feature i the calability and implicity. However,
More informationLecture 12 - Non-isolated DC-DC Buck Converter
ecture 12 - Non-iolated DC-DC Buck Converter Step-Down or Buck converter deliver DC power from a higher voltage DC level ( d ) to a lower load voltage o. d o ene ref + o v c Controller Figure 12.1 The
More informationMenu. Binary Adder EEL3701 EEL3701. Add, Subtract, Compare, ALU
Other MSI Circuit: Adders >Binar, Half & Full Canonical forms Binar Subtraction Full-Subtractor Magnitude Comparators >See Lam: Fig 4.8 ALU Menu Look into m... 1 Binar Adder Suppose we want to add two
More informationLecture 10 Filtering: Applied Concepts
Lecture Filtering: Applied Concept In the previou two lecture, you have learned about finite-impule-repone (FIR) and infinite-impule-repone (IIR) filter. In thee lecture, we introduced the concept of filtering
More informationLiquid cooling
SKiiPPACK no. 3 4 [ 1- exp (-t/ τ )] + [( P + P )/P ] R [ 1- exp (-t/ τ )] Z tha tot3 = R ν ν tot1 tot tot3 thaa-3 aa 3 ν= 1 3.3.6. Liquid cooling The following table contain the characteritic R ν and
More informationDIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS Laplace Tranform Paul Dawkin Table of Content Preface... Laplace Tranform... Introduction... The Definition... 5 Laplace Tranform... 9 Invere Laplace Tranform... Step Function...4
More informationAn Efficient Coefficient-Partitioning Algorithm for Realizing Low Complexity Digital Filters
Paper No. 03 An Efficient CoefficientPartitioning Algorithm for Realizing Low Complexity Digital Filter A. P. Vinod, Member, IEEE and Edmund MK.Lai, Senior Member, IEEE Abtract The algorithm that minimize
More informationMAE140 Linear Circuits Fall 2012 Final, December 13th
MAE40 Linear Circuit Fall 202 Final, December 3th Intruction. Thi exam i open book. You may ue whatever written material you chooe, including your cla note and textbook. You may ue a hand calculator with
More informationThe Operational Amplifier
The Operational Amplifier The operational amplifier i a building block of modern electronic intrumentation. Therefore, matery of operational amplifier fundamental i paramount to any practical application
More informationList coloring hypergraphs
Lit coloring hypergraph Penny Haxell Jacque Vertraete Department of Combinatoric and Optimization Univerity of Waterloo Waterloo, Ontario, Canada pehaxell@uwaterloo.ca Department of Mathematic Univerity
More informationSolving Differential Equations by the Laplace Transform and by Numerical Methods
36CH_PHCalter_TechMath_95099 3//007 :8 PM Page Solving Differential Equation by the Laplace Tranform and by Numerical Method OBJECTIVES When you have completed thi chapter, you hould be able to: Find the
More informationBASIC INDUCTION MOTOR CONCEPTS
INDUCTION MOTOS An induction motor ha the ame phyical tator a a ynchronou machine, with a different rotor contruction. There are two different type of induction motor rotor which can be placed inide the
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erickon Department of Electrical, Computer, and Energy Engineering Univerity of Colorado, Boulder Cloed-loop buck converter example: Section 9.5.4 In ECEN 5797, we ued the CCM mall ignal model to
More information55:041 Electronic Circuits
55:04 Electronic ircuit Frequency epone hapter 7 A. Kruger Frequency epone- ee page 4-5 of the Prologue in the text Important eview co Thi lead to the concept of phaor we encountered in ircuit In Linear
More information11.2 Stability. A gain element is an active device. One potential problem with every active circuit is its stability
5/7/2007 11_2 tability 1/2 112 tability eading Aignment: pp 542-548 A gain element i an active device One potential problem with every active circuit i it tability HO: TABIITY Jim tile The Univ of Kana
More informationControl Systems Analysis and Design by the Root-Locus Method
6 Control Sytem Analyi and Deign by the Root-Locu Method 6 1 INTRODUCTION The baic characteritic of the tranient repone of a cloed-loop ytem i cloely related to the location of the cloed-loop pole. If
More informationUnavoidable Cycles in Polynomial-Based Time-Invariant LDPC Convolutional Codes
European Wirele, April 7-9,, Vienna, Autria ISBN 978--87-4-9 VE VERLAG GMBH Unavoidable Cycle in Polynomial-Baed Time-Invariant LPC Convolutional Code Hua Zhou and Norbert Goertz Intitute of Telecommunication
More informationThe machines in the exercise work as follows:
Tik-79.148 Spring 2001 Introduction to Theoretical Computer Science Tutorial 9 Solution to Demontration Exercie 4. Contructing a complex Turing machine can be very laboriou. With the help of machine chema
More informationECE382/ME482 Spring 2004 Homework 4 Solution November 14,
ECE382/ME482 Spring 2004 Homework 4 Solution November 14, 2005 1 Solution to HW4 AP4.3 Intead of a contant or tep reference input, we are given, in thi problem, a more complicated reference path, r(t)
More informationAnnex-A: RTTOV9 Cloud validation
RTTOV-91 Science and Validation Plan Annex-A: RTTOV9 Cloud validation Author O Embury C J Merchant The Univerity of Edinburgh Intitute for Atmo. & Environ. Science Crew Building King Building Edinburgh
More informationHardware Implementation of Canonic Signed Digit Recoding
IOSR Journal of VLSI and Signal Proceing (IOSR-JVSP) Volume 6, Iue 2, Ver. I (Mar. -Apr. 2016), PP 11-15 e-issn: 2319 4200, p-issn No. : 2319 4197 www.iorjournal.org Hardware Implementation of Canonic
More informationVector-Space Methods and Kirchhoff Graphs for Reaction Networks
Vector-Space Method and Kirchhoff Graph for Reaction Network Joeph D. Fehribach Fuel Cell Center WPI Mathematical Science and Chemical Engineering 00 Intitute Rd. Worceter, MA 0609-2247 Thi article preent
More informationMassachusetts Institute of Technology Dynamics and Control II
I E Maachuett Intitute of Technology Department of Mechanical Engineering 2.004 Dynamic and Control II Laboratory Seion 5: Elimination of Steady-State Error Uing Integral Control Action 1 Laboratory Objective:
More informationSAT Math Notes. By Steve Baba, Ph.D FREE for individual or classroom use. Not free for commercial or online use.
SAT Math Note B Steve Baba, Ph.D. 2008. FREE for individual or claroom ue. Not free for commercial or online ue. For SAT reading ee m ite: www.freevocabular.com for a free lit of 5000 SAT word with brief
More informationLecture 8: Period Finding: Simon s Problem over Z N
Quantum Computation (CMU 8-859BB, Fall 205) Lecture 8: Period Finding: Simon Problem over Z October 5, 205 Lecturer: John Wright Scribe: icola Rech Problem A mentioned previouly, period finding i a rephraing
More informationNumerical algorithm for the analysis of linear and nonlinear microstructure fibres
Numerical algorithm for the anali of linear and nonlinear microtructure fibre Mariuz Zdanowicz *, Marian Marciniak, Marek Jaworki, Igor A. Goncharenko National Intitute of Telecommunication, Department
More informationLearning Objectives 10/7/2010. CE 411 Digital System Design. Fundamental of Logic Design. Review the basic concepts of logic circuits. Dr.
/7/ CE 4 Digital ystem Design Dr. Arshad Aziz Fundamental of ogic Design earning Objectives Review the basic concepts of logic circuits Variables and functions Boolean algebra Minterms and materms ogic
More informationECE-202 FINAL December 13, 2016 CIRCLE YOUR DIVISION
ECE-202 Final, Fall 16 1 ECE-202 FINAL December 13, 2016 Name: (Pleae print clearly.) Student Email: CIRCLE YOUR DIVISION DeCarlo- 8:30-9:30 Talavage-9:30-10:30 2021 2022 INSTRUCTIONS There are 35 multiple
More informationSampling and the Discrete Fourier Transform
Sampling and the Dicrete Fourier Tranform Sampling Method Sampling i mot commonly done with two device, the ample-and-hold (S/H) and the analog-to-digital-converter (ADC) The S/H acquire a CT ignal at
More informationIII.9. THE HYSTERESIS CYCLE OF FERROELECTRIC SUBSTANCES
III.9. THE HYSTERESIS CYCLE OF FERROELECTRIC SBSTANCES. Work purpoe The analyi of the behaviour of a ferroelectric ubtance placed in an eternal electric field; the dependence of the electrical polariation
More informationApproximate Analytical Solution for Quadratic Riccati Differential Equation
Iranian J. of Numerical Analyi and Optimization Vol 3, No. 2, 2013), pp 21-31 Approximate Analytical Solution for Quadratic Riccati Differential Equation H. Aminikhah Abtract In thi paper, we introduce
More information1 Basic Equations of the PLLs
1 Baic Equation of the PLL 1.1 INTRODUCTION Phae lock loop (PLL) belong to a larger et of regulation ytem. A an independent reearch and deign field it tarted in the 1950 [1] and gained major practical
More information(b) Is the game below solvable by iterated strict dominance? Does it have a unique Nash equilibrium?
14.1 Final Exam Anwer all quetion. You have 3 hour in which to complete the exam. 1. (60 Minute 40 Point) Anwer each of the following ubquetion briefly. Pleae how your calculation and provide rough explanation
More informationTheoretical Computer Science. Optimal algorithms for online scheduling with bounded rearrangement at the end
Theoretical Computer Science 4 (0) 669 678 Content lit available at SciVere ScienceDirect Theoretical Computer Science journal homepage: www.elevier.com/locate/tc Optimal algorithm for online cheduling
More informationChapter 4 Interconnection of LTI Systems
Chapter 4 Interconnection of LTI Sytem 4. INTRODUCTION Block diagram and ignal flow graph are commonly ued to decribe a large feedback control ytem. Each block in the ytem i repreented by a tranfer function,
More informationCompact finite-difference approximations for anisotropic image smoothing and painting
CWP-593 Compact finite-difference approximation for aniotropic image moothing and painting Dave Hale Center for Wave Phenomena, Colorado School of Mine, Golden CO 80401, USA ABSTRACT Finite-difference
More informationHOMEWORK ASSIGNMENT #2
Texa A&M Univerity Electrical Engineering Department ELEN Integrated Active Filter Deign Methodologie Alberto Valde-Garcia TAMU ID# 000 17 September 0, 001 HOMEWORK ASSIGNMENT # PROBLEM 1 Obtain at leat
More informationSingular perturbation theory
Singular perturbation theory Marc R. Rouel June 21, 2004 1 Introduction When we apply the teady-tate approximation (SSA) in chemical kinetic, we typically argue that ome of the intermediate are highly
More informationFloating Point Representation and Digital Logic. Lecture 11 CS301
Floating Point Representation and Digital Logic Lecture 11 CS301 Administrative Daily Review of today s lecture w Due tomorrow (10/4) at 8am Lab #3 due Friday (9/7) 1:29pm HW #5 assigned w Due Monday 10/8
More informationPublication V by authors
Publication Kontantin S. Kotov and Jorma J. Kyyrä. 008. nertion lo and network parameter in the analyi of power filter. n: Proceeding of the 008 Nordic Workhop on Power and ndutrial Electronic (NORPE 008).
More information