CMOS. Dynamic Logic Circuits. Chapter 9. Digital Integrated Circuits Analysis and Design

Size: px
Start display at page:

Download "CMOS. Dynamic Logic Circuits. Chapter 9. Digital Integrated Circuits Analysis and Design"

Transcription

1 MOS Digital Itegrated ircuits Aalysis ad Desig hapter 9 Dyamic Logic ircuits 1

2 Itroductio Static logic circuit Output correspodig to the iput voltage after a certai time delay Preservig its output level as log as the power supply is provided Large area time delay Dyamic logic circuit he operatio of all dyamic logic gates depeds o temporary (trasiet) storage of charge i parasitic ode capacitaces Need periodic clock sigals charge refreshig Smaller silico area osume less power

3 Eample 9.1 K1 MP o chargig or dischargig QD K0 MP off isolated from D Q (deped o the charge store i ) d iverter remove rasistor couts Q-D Assumig OL0 IL.1 IH.9 OH K1 MP o ioh higher tha IH so Q K0 M off 4. if charge leakage <.9 ca t be iterpreted as a logic 1 3

4 Basic priciples of pass trasistor circuits he fudametal buildig block of MOS dyamic logic circuits MP A MOS pass trasistor drivig the gate of aother MOS trasistor Drivig by the periodic clock sigal Acts as access switch If K1 Logic 1 trasfer Logic 0 trasfer If K0 ease to coduct ad the charge store I the parasitic capacitace 4

5 5 Logic 1 trasfer ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) F F t t t k t k t k t k d k dt k φ φ γ 1 ) ( dt d to charge up the MP o i saturatio regio starts 1 0 K : 0 0) (t Itially ma 0 ma OH i + + he ode has a upper limit of ma ( - )

6 6 Logic 1 trasfer ( ) ( ).... ma 0 ma1 0 1 F F F F φ φ γ φ φ γ + +

7 7 Logic 0 trasfer ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ] ( ) fall t k k t t k t k k t k t k t d k dt d k dt k dt d 90% 10% 10% 90% 0.74 l(1.) l(19) l l ) 0.9( ) 0.9)( ( l l l τ he pass trasistor operates i the liear regio throughout this cycle sice DS < GS -

8 harge storage ad charge leakage I leakage I subthreshold(mp) +I reverse(mp) 8

9 Equivalet circuit used for aalyzig the charge leakage process Q Q ( i dq dq j( ) dqi Ileakage + dt dt dt dq j( ) A j0 where j ( ) d 1+ φ k N D N φ l 0 q i + t mi hold j gb ΔQ I ) + Q + gb i poly criticalmi leakagema + poly where Q + A metal j0 metal i + where ΔQ i 0 qε SiN A ( N + N ) A dbmi criticalmi A N D D mi qε SiN 0 ( φ + ) 0 ma A qε SiN φ i : these costat capacitace compoets : due to reverse biased drai-substrate juctio mi : the miimum combied soft-ode capacitace db.mim : the miimum juctio capacitace obtaied uder the bias coditio ma t hold : worst-case holdig time the shortest time required for the soft-ode voltage to drop from the iitial logic high value to the logic threshold voltage due to leakage φ 0 A 9

10 Eample 10

11 Eample (cot.) 11

12 oltage bootstrappig o overcome threshold voltage drops i digital circuits Figure 9.11 osiderig M i saturatio out(ma) - (out) o obtai a full logic-high level the voltage must be icreased Figure 9.1 A third trasistor has bee added to the circuit s : dyamic couple to the groud boot : dyamic couple to his circuit produce a high durig switchig + ( out ) 1

13 oltage bootstrappig i s ( + ) s if 3 (mi) ( + ) s i boot s boot boot boot boot d boot 3 d dt ( ) s ( + ) out 3 ( + ) OL ( + ) + s OL d dt boot OU OU ( OU boot boot boot d dt OU out OL is much larger tha + + ( ( )) 3 3 d( out ) dt d dt ) d s ( ma ) 3 3 s ( boot + boot - ( + ) *s: the sum of the parasitic source-to-substrate cap. ofm3 ad the gate-to substrate cap of M *o obtai a sufficietly large bootstrap cap. boot i compariso to s a etra dummy trasistor is added *he dummy trasistor acts as a MOS capacitor betwee ad out s 3 d dt boot - out ) + OL boot s ( boot boot OL ( ) OL ) 13

14 Eample

15 Sychroous dyamic circuit techiques Previous sectio Basic cocepts associated with temporary storage of logic levels i capacitive circuit odes his sectio Pay attetio to digital circuit desig Differet eamples of sychroous dyamic circuit Depletio-load MOS Ehacemet-load MOS MOS buildig block 15

16 Dyamic pass trasistor circuits ascaded combiatioal logic stage Itercoected through MOS trasistor All iput of each combiatioal logic block are drive by a sigle clock sigal wo phase clockig 16

17 Depletio-load MOS dyamic shift register circuit Φ1 active i is trasferred to i1 out1 is determied Φ active out1 is trasferred to i out is determied i1 retai its previous level via charge storage Φ1 active agai he origial data bit writte ito the register (3rd)!st stage accept ew data 17

18 Depletio-load MOS dyamic shift register circuit Maimum clock frequecy Beig determied by the sigal propagatio delay through oe iverter stage Oe half period of the clock sigal must be log eough to allow i to charge up or dow ad the logic level to propagate to the output by chargig out Logic-high iput level of each iverter stage is oe threshold voltage lower tha the power supply level 18

19 A two-stage sychroous comple logic circuit he same operatio priciple eteded to sychroous comple logic I order to guaratee correct logic levels are propagated durig each active clock cycle he half period legth of the clock sigal must be loger tha the largest sigal-stage sigal propagatio delay foud i the cirucit 19

20 Ehacemet-load dyamic shift register (ratioed logic)(1) Oe importat differece Applyig the clock sigal to the gate of the load trasistor Power dissipatio ad the silico area ca be reduced sigificatly he iput pass trasistor ad load trasistor are drive by opposite clock phase 0

21 Ehacemet-load dyamic shift register (ratioed logic)() Φ1 active i i1 MOS load off Φ active MOS load o the output of 1st iverter attais its valid logic (i1 preserved) Pass trasistor of d stage o out1 i Φ1 active out is determied ad trasferred ito i3 Also a ew iput level ca be accepted ito i1 OL of each stage is strictly determied by the driver to load ratio (ratioeddyamic logic) 1

22 Geeral circuit structure of ratioed sychroous dyamic logic Eteded to arbitrary comple logic

23 Ehacemet-load dyamic shift register (ratioless logic)(1) I each stage the iput pass trasistor ad the load trasistor are drive by the same clock phase Φ1 active i trasfer to i 1st iverter is active out1 attais its valid logic level Φ active d pass trasistor o the logic level is trasferred oto the et stage 3

24 Ehacemet-load dyamic shift register (ratioless logic)() osiderig two cases ase 1 If out1 high at the ed of the active Φ1 phase By mea of i1 low iput MOS driver off out1- Φ active he voltage level is trasfer to i via charge sharig over the pass trasistor out/i to correctly trasfer a logic-high level 4

25 Ehacemet-load dyamic shift register (ratioless logic)(3) osiderig two cases ase If out1 is logic-low at the ed of the active Φ1 phase i1 high MOS driver o out10 As Φ active rasfer by pass trasistor Ratioless dyamic logic OL 0 idepedet of driver-to-load ratio 5

26 Geeral circuit structure of ratioless sychroous dyamic logic 6

27 Dyamic MOS trasmissio gate logic otally require four clock sigals 7

28 MOS trasmissio gate dyamic shift register Low o-resistace of trasmissio gate (ref.p310) Smaller trasfer time (R ) No threshold voltage drop 8

29 Sigle-phase MOS trasmissio gate dyamic shift register Ideally K1 Odd o eve off isolated I practical do ot truly ooverlappig LK have fiite t r ad t f So prefer Φ1 Φ 9

30 Dyamic MOS logic gate implemetig a comple Boolea fuctio(1) ( A A A B ) F B Sigificatly reduce the umber of trasistors used to implemet ay logic fuctio Operatio First prechargig the output ode capacitace Evaluatig the output level accordig to the applied iputs Both of theses of operatios are scheduled by a sigle clock sigal Which drives oe MOS ad oe pmos trasistor i each dyamic stage 30

31 Dyamic MOS logic gate implemetig a comple Boolea fuctio() Φ0 (precharge phase) Mp o Me off the parasitic capacitace of the circuit is charged up to out he iput voltages are also applied durig this phase o ifluece o the output Φ1 (evaluate phase) Mp off Me o the output voltage deped o the iput voltage levels OL or he practical multi-stage applicatios however the dyamic MOS gate presets a sigificat problem 31

32 Illustratio of the cascadig problem i dyamic MOS logic(1) Assume Durig the precharge phase Both output voltages out1 ad out are pulled up Durig evaluatio phase he iput variables of 1st stage assume to be such that Output out1 drop to logic 0 he eteral iput of d stage assume to be logic 1 As evaluatio Begiig Both out1 a d out are logic-high he out1 drops to its correct logic after a certai time delay out Startig with the high value of out1 at the begiig of the evaluatio phase the output voltage out at the ed of the evaluatio phase will be erroeously low 3

33 Illustratio of the cascadig problem i dyamic MOS logic(1) his eample illustrates that Dyamic MOS logic gates drive by the same clock sigal caot be cascade directly his limitatio udermie some advatages such as Low power dissipatio Large oise margis Low trasistor cout 33

34 High-performace dyamic MOS circuits Base o the basic dyamic MOS logic gate structure Desig to take full advatage of the obvious beefits of dyamic operatio o all urestricted cascadig of multiple stages he ultimate goal is to achieve usig the least complicated clockig scheme possible Reliable High-speed ompact circuit 34

35 35

36 36

37 37

38 38

39 39

40 40

41 41

42 4

43 43

44 44

45 45

46 46

47 47

48 48

Minimum Source/Drain Area AS,AD = (0.48µm)(0.60µm) - (0.12µm)(0.12µm) = µm 2

Minimum Source/Drain Area AS,AD = (0.48µm)(0.60µm) - (0.12µm)(0.12µm) = µm 2 UNIERSITY OF CALIFORNIA College of Egieerig Departmet of Electrical Egieerig ad Computer Scieces Last modified o February 1 st, 005 by Chris Baer (crbaer@eecs Adrei ladimirescu Homewor #3 EECS141 Due Friday,

More information

Digital Integrated Circuits. Inverter. YuZhuo Fu. Digital IC. Introduction

Digital Integrated Circuits. Inverter. YuZhuo Fu. Digital IC. Introduction Digital Itegrated Circuits Iverter YuZhuo Fu Itroductio outlie CMOS at a glace CMOS static behavior CMOS dyamic behavior Power, Eergy, ad Eergy Delay Persective tech. /48 outlie CMOS at a glace CMOS static

More information

YuZhuo Fu Office location:417 room WeiDianZi building,no 800 DongChuan road,minhang Campus

YuZhuo Fu Office location:417 room WeiDianZi building,no 800 DongChuan road,minhang Campus Digital Itegrated Circuits YuZhuo Fu cotact:fuyuzhuo@ic.sjtu.edu.c Office locatio:417 room WeiDiaZi buildig,no 800 DogChua road,mihag Camus Itroductio Digital IC outlie CMOS at a glace CMOS static behavior

More information

Digital Integrated Circuits

Digital Integrated Circuits Digital Itegrated Circuits YuZhuo Fu cotact:fuyuzhuo@ic.sjtu.edu.c Office locatio:417 room WeiDiaZi buildig,no 800 DogChua road,mihag Camus Itroductio outlie CMOS at a glace CMOS static behavior CMOS dyamic

More information

Time-Domain Representations of LTI Systems

Time-Domain Representations of LTI Systems 2.1 Itroductio Objectives: 1. Impulse resposes of LTI systems 2. Liear costat-coefficiets differetial or differece equatios of LTI systems 3. Bloc diagram represetatios of LTI systems 4. State-variable

More information

Regenerative Property

Regenerative Property DESIGN OF LOGIC FAMILIES Some desirable characteristics to have: 1. Low ower dissiatio. High oise margi (Equal high ad low margis) 3. High seed 4. Low area 5. Low outut resistace 6. High iut resistace

More information

EEC 118 Lecture #4: CMOS Inverters. Rajeevan Amirtharajah University of California, Davis Jeff Parkhurst Intel Corporation

EEC 118 Lecture #4: CMOS Inverters. Rajeevan Amirtharajah University of California, Davis Jeff Parkhurst Intel Corporation EEC 118 Lecture #4: CMOS Iverters ajeeva Amirtharajah Uiversity of Califoria, Davis Jeff Parhurst Itel Cororatio Outlie eview: Iverter Trasfer Characteristics Lecture 3: Noise Margis, ise & Fall Times,

More information

OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES

OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES Peter M. Maurer Why Hashig is θ(). As i biary search, hashig assumes that keys are stored i a array which is idexed by a iteger. However, hashig attempts to bypass

More information

LECTURE 5 PART 2 MOS INVERTERS STATIC DESIGN CMOS. CMOS STATIC PARAMETERS The Inverter Circuit and Operating Regions

LECTURE 5 PART 2 MOS INVERTERS STATIC DESIGN CMOS. CMOS STATIC PARAMETERS The Inverter Circuit and Operating Regions LECTURE 5 PART 2 MOS INVERTERS STATIC ESIGN CMOS Objectives for Lecture 5 - Part 2* Uderstad the VTC of a CMOS iverter. Uderstad static aalysis of the CMOS iverter icludig breakpoits, VOL, V OH,, V IH,

More information

EE 505. Lecture 28. ADC Design SAR

EE 505. Lecture 28. ADC Design SAR EE 505 Lecture 28 ADC Desig SAR Review from Last Lecture Elimiatio of Iput S/H C LK X IN S/H Stage 1 r 1 Stage 2 r 2 Stage k r k Stage m r m 1 2 k m Pipelied Assembler (Shift Register

More information

Mechatronics. Time Response & Frequency Response 2 nd -Order Dynamic System 2-Pole, Low-Pass, Active Filter

Mechatronics. Time Response & Frequency Response 2 nd -Order Dynamic System 2-Pole, Low-Pass, Active Filter Time Respose & Frequecy Respose d -Order Dyamic System -Pole, Low-Pass, Active Filter R 4 R 7 C 5 e i R 1 C R 3 - + R 6 - + e out Assigmet: Perform a Complete Dyamic System Ivestigatio of the Two-Pole,

More information

2.CMOS Transistor Theory

2.CMOS Transistor Theory CMOS LSI esig.cmos rasistor heory Fu yuzhuo School of microelectroics,sju Itroductio omar fadhil,baghdad outlie PN juctio priciple CMOS trasistor itroductio Ideal I- characteristics uder static coditios

More information

Chapter 9 - CD companion 1. A Generic Implementation; The Common-Merge Amplifier. 1 τ is. ω ch. τ io

Chapter 9 - CD companion 1. A Generic Implementation; The Common-Merge Amplifier. 1 τ is. ω ch. τ io Chapter 9 - CD compaio CHAPTER NINE CD-9.2 CD-9.2. Stages With Voltage ad Curret Gai A Geeric Implemetatio; The Commo-Merge Amplifier The advaced method preseted i the text for approximatig cutoff frequecies

More information

Chapter 9 Computer Design Basics

Chapter 9 Computer Design Basics Logic ad Computer Desig Fudametals Chapter 9 Computer Desig Basics Part 1 Datapaths Overview Part 1 Datapaths Itroductio Datapath Example Arithmetic Logic Uit (ALU) Shifter Datapath Represetatio Cotrol

More information

Bipolar Junction Transistors

Bipolar Junction Transistors ipolar Juctio Trasistors ipolar juctio trasistor (JT) was iveted i 948 at ell Telephoe Laboratories Sice 97, the high desity ad low power advatage of the MOS techology steadily eroded the JT s early domiace.

More information

EE260: Digital Design, Spring n Binary Addition. n Complement forms. n Subtraction. n Multiplication. n Inputs: A 0, B 0. n Boolean equations:

EE260: Digital Design, Spring n Binary Addition. n Complement forms. n Subtraction. n Multiplication. n Inputs: A 0, B 0. n Boolean equations: EE260: Digital Desig, Sprig 2018 EE 260: Itroductio to Digital Desig Arithmetic Biary Additio Complemet forms Subtractio Multiplicatio Overview Yao Zheg Departmet of Electrical Egieerig Uiversity of Hawaiʻi

More information

EE 505. Lecture 29. ADC Design. Oversampled

EE 505. Lecture 29. ADC Design. Oversampled EE 505 Lecture 29 ADC Desig Oversampled Review from Last Lecture SAR ADC V IN Sample Hold C LK V REF DAC DAC Cotroller DAC Cotroller stores estimates of iput i Successive Approximatio Register (SAR) At

More information

Filter banks. Separately, the lowpass and highpass filters are not invertible. removes the highest frequency 1/ 2and

Filter banks. Separately, the lowpass and highpass filters are not invertible. removes the highest frequency 1/ 2and Filter bas Separately, the lowpass ad highpass filters are ot ivertible T removes the highest frequecy / ad removes the lowest frequecy Together these filters separate the sigal ito low-frequecy ad high-frequecy

More information

Summary of pn-junction (Lec )

Summary of pn-junction (Lec ) Lecture #12 OUTLNE Diode aalysis ad applicatios cotiued The MOFET The MOFET as a cotrolled resistor Pich-off ad curret saturatio Chael-legth modulatio Velocity saturatio i a short-chael MOFET Readig Howe

More information

DESCRIPTION OF THE SYSTEM

DESCRIPTION OF THE SYSTEM Sychroous-Serial Iterface for absolute Ecoders SSI 1060 BE 10 / 01 DESCRIPTION OF THE SYSTEM TWK-ELEKTRONIK GmbH D-001 Düsseldorf PB 1006 Heirichstr. Tel +9/11/6067 Fax +9/11/6770 e-mail: ifo@twk.de Page

More information

Design and Analysis of ALGORITHM (Topic 2)

Design and Analysis of ALGORITHM (Topic 2) DR. Gatot F. Hertoo, MSc. Desig ad Aalysis of ALGORITHM (Topic 2) Algorithms + Data Structures = Programs Lessos Leared 1 Our Machie Model: Assumptios Geeric Radom Access Machie (RAM) Executes operatios

More information

Principle Of Superposition

Principle Of Superposition ecture 5: PREIMINRY CONCEP O RUCUR NYI Priciple Of uperpositio Mathematically, the priciple of superpositio is stated as ( a ) G( a ) G( ) G a a or for a liear structural system, the respose at a give

More information

Digital Integrated Circuits

Digital Integrated Circuits Digital Itegrated Circuits YuZhuo Fu cotact:fuyuzhuo@ic.sjtu.edu.c Office locatio:417 room WeiDiaZi buildig,no 800 DogChua road,mihag Camus Itroductio Review cotet Tye Cocet 15, Comutig 10 hours Fri. 6

More information

Run-length & Entropy Coding. Redundancy Removal. Sampling. Quantization. Perform inverse operations at the receiver EEE

Run-length & Entropy Coding. Redundancy Removal. Sampling. Quantization. Perform inverse operations at the receiver EEE Geeral e Image Coder Structure Motio Video (s 1,s 2,t) or (s 1,s 2 ) Natural Image Samplig A form of data compressio; usually lossless, but ca be lossy Redudacy Removal Lossless compressio: predictive

More information

TECHNIQUES OF INTEGRATION

TECHNIQUES OF INTEGRATION 7 TECHNIQUES OF INTEGRATION Simpso s Rule estimates itegrals b approimatig graphs with parabolas. Because of the Fudametal Theorem of Calculus, we ca itegrate a fuctio if we kow a atiderivative, that is,

More information

Chapter 4 : Laplace Transform

Chapter 4 : Laplace Transform 4. Itroductio Laplace trasform is a alterative to solve the differetial equatio by the complex frequecy domai ( s = σ + jω), istead of the usual time domai. The DE ca be easily trasformed ito a algebraic

More information

Olli Simula T / Chapter 1 3. Olli Simula T / Chapter 1 5

Olli Simula T / Chapter 1 3. Olli Simula T / Chapter 1 5 Sigals ad Systems Sigals ad Systems Sigals are variables that carry iformatio Systemstake sigals as iputs ad produce sigals as outputs The course deals with the passage of sigals through systems T-6.4

More information

Discrete-Time Systems, LTI Systems, and Discrete-Time Convolution

Discrete-Time Systems, LTI Systems, and Discrete-Time Convolution EEL5: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we begi our mathematical treatmet of discrete-time s. As show i Figure, a discrete-time operates or trasforms some iput sequece x [

More information

ECE 308 Discrete-Time Signals and Systems

ECE 308 Discrete-Time Signals and Systems ECE 38-5 ECE 38 Discrete-Time Sigals ad Systems Z. Aliyazicioglu Electrical ad Computer Egieerig Departmet Cal Poly Pomoa ECE 38-5 1 Additio, Multiplicatio, ad Scalig of Sequeces Amplitude Scalig: (A Costat

More information

Sequences A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence

Sequences A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence Sequeces A sequece of umbers is a fuctio whose domai is the positive itegers. We ca see that the sequece 1, 1, 2, 2, 3, 3,... is a fuctio from the positive itegers whe we write the first sequece elemet

More information

EE 505. Lecture 13. String DACs

EE 505. Lecture 13. String DACs EE 505 Lecture 13 Strig DACs -Strig DAC V FF S 1 S 2 Simple structure Iheretly mootoe Very low DNL Challeges: S N-2 S N-1 S N S k d k Maagig INL Large umber of devices for large outig thermometer/bubble

More information

EE260: Digital Design, Spring n MUX Gate n Rudimentary functions n Binary Decoders. n Binary Encoders n Priority Encoders

EE260: Digital Design, Spring n MUX Gate n Rudimentary functions n Binary Decoders. n Binary Encoders n Priority Encoders EE260: Digital Desig, Sprig 2018 EE 260: Itroductio to Digital Desig MUXs, Ecoders, Decoders Yao Zheg Departmet of Electrical Egieerig Uiversity of Hawaiʻi at Māoa Overview of Ecoder ad Decoder MUX Gate

More information

Quantum Annealing for Heisenberg Spin Chains

Quantum Annealing for Heisenberg Spin Chains LA-UR # - Quatum Aealig for Heiseberg Spi Chais G.P. Berma, V.N. Gorshkov,, ad V.I.Tsifriovich Theoretical Divisio, Los Alamos Natioal Laboratory, Los Alamos, NM Istitute of Physics, Natioal Academy of

More information

Numerical Methods for Ordinary Differential Equations

Numerical Methods for Ordinary Differential Equations Numerical Methods for Ordiary Differetial Equatios Braislav K. Nikolić Departmet of Physics ad Astroomy, Uiversity of Delaware, U.S.A. PHYS 460/660: Computatioal Methods of Physics http://www.physics.udel.edu/~bikolic/teachig/phys660/phys660.html

More information

C/CS/Phys C191 Deutsch and Deutsch-Josza algorithms 10/20/07 Fall 2007 Lecture 17

C/CS/Phys C191 Deutsch and Deutsch-Josza algorithms 10/20/07 Fall 2007 Lecture 17 C/CS/Phs C9 Deutsch ad Deutsch-Josza algorithms 0/0/07 Fall 007 Lecture 7 Readigs Beeti et al., Ch. 3.9-3.9. Stolze ad Suter, Quatum Computig, Ch. 8. - 8..5) Nielse ad Chuag, Quatum Computatio ad Quatum

More information

ECE606: Solid State Devices Lecture 19 Bipolar Transistors Design

ECE606: Solid State Devices Lecture 19 Bipolar Transistors Design 606: Solid State Devices Lecture 9 ipolar Trasistors Desig Gerhard Klimeck gekco@purdue.edu Outlie ) urret gai i JTs ) osideratios for base dopig 3) osideratios for collector dopig 4) termediate Summary

More information

Infinite Sequences and Series

Infinite Sequences and Series Chapter 6 Ifiite Sequeces ad Series 6.1 Ifiite Sequeces 6.1.1 Elemetary Cocepts Simply speakig, a sequece is a ordered list of umbers writte: {a 1, a 2, a 3,...a, a +1,...} where the elemets a i represet

More information

ANALYSIS OF EXPERIMENTAL ERRORS

ANALYSIS OF EXPERIMENTAL ERRORS ANALYSIS OF EXPERIMENTAL ERRORS All physical measuremets ecoutered i the verificatio of physics theories ad cocepts are subject to ucertaities that deped o the measurig istrumets used ad the coditios uder

More information

Markov Decision Processes

Markov Decision Processes Markov Decisio Processes Defiitios; Statioary policies; Value improvemet algorithm, Policy improvemet algorithm, ad liear programmig for discouted cost ad average cost criteria. Markov Decisio Processes

More information

Chapter 11 Output Analysis for a Single Model. Banks, Carson, Nelson & Nicol Discrete-Event System Simulation

Chapter 11 Output Analysis for a Single Model. Banks, Carson, Nelson & Nicol Discrete-Event System Simulation Chapter Output Aalysis for a Sigle Model Baks, Carso, Nelso & Nicol Discrete-Evet System Simulatio Error Estimatio If {,, } are ot statistically idepedet, the S / is a biased estimator of the true variace.

More information

mx bx kx F t. dt IR I LI V t, Q LQ RQ V t,

mx bx kx F t. dt IR I LI V t, Q LQ RQ V t, Lecture 5 omplex Variables II (Applicatios i Physics) (See hapter i Boas) To see why complex variables are so useful cosider first the (liear) mechaics of a sigle particle described by Newto s equatio

More information

7. Modern Techniques. Data Encryption Standard (DES)

7. Modern Techniques. Data Encryption Standard (DES) 7. Moder Techiques. Data Ecryptio Stadard (DES) The objective of this chapter is to illustrate the priciples of moder covetioal ecryptio. For this purpose, we focus o the most widely used covetioal ecryptio

More information

3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,

3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense, 3. Z Trasform Referece: Etire Chapter 3 of text. Recall that the Fourier trasform (FT) of a DT sigal x [ ] is ω ( ) [ ] X e = j jω k = xe I order for the FT to exist i the fiite magitude sese, S = x [

More information

Reliability and Queueing

Reliability and Queueing Copyright 999 Uiversity of Califoria Reliability ad Queueig by David G. Messerschmitt Supplemetary sectio for Uderstadig Networked Applicatios: A First Course, Morga Kaufma, 999. Copyright otice: Permissio

More information

The target reliability and design working life

The target reliability and design working life Safety ad Security Egieerig IV 161 The target reliability ad desig workig life M. Holický Kloker Istitute, CTU i Prague, Czech Republic Abstract Desig workig life ad target reliability levels recommeded

More information

Notes on iteration and Newton s method. Iteration

Notes on iteration and Newton s method. Iteration Notes o iteratio ad Newto s method Iteratio Iteratio meas doig somethig over ad over. I our cotet, a iteratio is a sequece of umbers, vectors, fuctios, etc. geerated by a iteratio rule of the type 1 f

More information

Exponents. Learning Objectives. Pre-Activity

Exponents. Learning Objectives. Pre-Activity Sectio. Pre-Activity Preparatio Epoets A Chai Letter Chai letters are geerated every day. If you sed a chai letter to three frieds ad they each sed it o to three frieds, who each sed it o to three frieds,

More information

ECE-S352 Introduction to Digital Signal Processing Lecture 3A Direct Solution of Difference Equations

ECE-S352 Introduction to Digital Signal Processing Lecture 3A Direct Solution of Difference Equations ECE-S352 Itroductio to Digital Sigal Processig Lecture 3A Direct Solutio of Differece Equatios Discrete Time Systems Described by Differece Equatios Uit impulse (sample) respose h() of a DT system allows

More information

1 Hash tables. 1.1 Implementation

1 Hash tables. 1.1 Implementation Lecture 8 Hash Tables, Uiversal Hash Fuctios, Balls ad Bis Scribes: Luke Johsto, Moses Charikar, G. Valiat Date: Oct 18, 2017 Adapted From Virgiia Williams lecture otes 1 Hash tables A hash table is a

More information

(b) What is the probability that a particle reaches the upper boundary n before the lower boundary m?

(b) What is the probability that a particle reaches the upper boundary n before the lower boundary m? MATH 529 The Boudary Problem The drukard s walk (or boudary problem) is oe of the most famous problems i the theory of radom walks. Oe versio of the problem is described as follows: Suppose a particle

More information

Voltage controlled oscillator (VCO)

Voltage controlled oscillator (VCO) Voltage cotrolled oscillator (VO) Oscillatio frequecy jl Z L(V) jl[ L(V)] [L L (V)] L L (V) T VO gai / Logf Log 4 L (V) f f 4 L(V) Logf / L(V) f 4 L (V) f (V) 3 Lf 3 VO gai / (V) j V / V Bi (V) / V Bi

More information

8. Applications To Linear Differential Equations

8. Applications To Linear Differential Equations 8. Applicatios To Liear Differetial Equatios 8.. Itroductio 8.. Review Of Results Cocerig Liear Differetial Equatios Of First Ad Secod Orders 8.3. Eercises 8.4. Liear Differetial Equatios Of Order N 8.5.

More information

Discrete-Time Signals and Systems. Discrete-Time Signals and Systems. Signal Symmetry. Elementary Discrete-Time Signals.

Discrete-Time Signals and Systems. Discrete-Time Signals and Systems. Signal Symmetry. Elementary Discrete-Time Signals. Discrete-ime Sigals ad Systems Discrete-ime Sigals ad Systems Dr. Deepa Kudur Uiversity of oroto Referece: Sectios. -.5 of Joh G. Proakis ad Dimitris G. Maolakis, Digital Sigal Processig: Priciples, Algorithms,

More information

Lecture 9: Hierarchy Theorems

Lecture 9: Hierarchy Theorems IAS/PCMI Summer Sessio 2000 Clay Mathematics Udergraduate Program Basic Course o Computatioal Complexity Lecture 9: Hierarchy Theorems David Mix Barrigto ad Alexis Maciel July 27, 2000 Most of this lecture

More information

Chapter 9: Numerical Differentiation

Chapter 9: Numerical Differentiation 178 Chapter 9: Numerical Differetiatio Numerical Differetiatio Formulatio of equatios for physical problems ofte ivolve derivatives (rate-of-chage quatities, such as velocity ad acceleratio). Numerical

More information

Diversity Combining Techniques

Diversity Combining Techniques Diversity Combiig Techiques Whe the required sigal is a combiatio of several waves (i.e, multipath), the total sigal amplitude may experiece deep fades (i.e, Rayleigh fadig), over time or space. The major

More information

Measurement uncertainty of the sound absorption

Measurement uncertainty of the sound absorption Measuremet ucertaity of the soud absorptio coefficiet Aa Izewska Buildig Research Istitute, Filtrowa Str., 00-6 Warsaw, Polad a.izewska@itb.pl 6887 The stadard ISO/IEC 705:005 o the competece of testig

More information

6.111 Lecture 6 Today: 1.Blocking vs. non-blocking assignments 2.Single clock synchronous circuits 3.Finite State Machines

6.111 Lecture 6 Today: 1.Blocking vs. non-blocking assignments 2.Single clock synchronous circuits 3.Finite State Machines 6. Lecture 6 Today:.Blockig vs. o-blockig assigmets 2.Sigle clock sychroous circuits 3.Fiite State Machies 6. Fall 25 Lecture 6, Slide I. Blockig vs. Noblockig Assigmets Coceptual eed for two kids of assigmet

More information

Chapter 9 Computer Design Basics

Chapter 9 Computer Design Basics Logic ad Computer Desig Fudametals Chapter 9 Computer Desig asics Part Datapaths Charles Kime & Thomas Kamiski 008 Pearso Educatio, Ic. (Hyperliks are active i View Show mode) Overview Part Datapaths Itroductio

More information

Classification of problem & problem solving strategies. classification of time complexities (linear, logarithmic etc)

Classification of problem & problem solving strategies. classification of time complexities (linear, logarithmic etc) Classificatio of problem & problem solvig strategies classificatio of time complexities (liear, arithmic etc) Problem subdivisio Divide ad Coquer strategy. Asymptotic otatios, lower boud ad upper boud:

More information

MORE TUTORIALS FOR VERILOG DIGITAL ELECTRONICS SYSTEM DESIGN HOMEWORK ASSIGNMENTS DATASHEETS FOR PARTS 10/3/2018

MORE TUTORIALS FOR VERILOG DIGITAL ELECTRONICS SYSTEM DESIGN HOMEWORK ASSIGNMENTS DATASHEETS FOR PARTS 10/3/2018 //8 DIGITA EECTRONICS SYSTEM DESIGN FA 8 PROFS. IRIS BAHAR & ROD BERESFORD OCTOBER, 8 ECTURE 9: CMOS TRANSIENT BEHAIOR MORE TUTORIAS FOR ERIOG O the course website you ca fid some useful liks to additioal

More information

Last time: Moments of the Poisson distribution from its generating function. Example: Using telescope to measure intensity of an object

Last time: Moments of the Poisson distribution from its generating function. Example: Using telescope to measure intensity of an object 6.3 Stochastic Estimatio ad Cotrol, Fall 004 Lecture 7 Last time: Momets of the Poisso distributio from its geeratig fuctio. Gs () e dg µ e ds dg µ ( s) µ ( s) µ ( s) µ e ds dg X µ ds X s dg dg + ds ds

More information

POWER SERIES SOLUTION OF FIRST ORDER MATRIX DIFFERENTIAL EQUATIONS

POWER SERIES SOLUTION OF FIRST ORDER MATRIX DIFFERENTIAL EQUATIONS Joural of Applied Mathematics ad Computatioal Mechaics 4 3(3) 3-8 POWER SERIES SOLUION OF FIRS ORDER MARIX DIFFERENIAL EQUAIONS Staisław Kukla Izabela Zamorska Istitute of Mathematics Czestochowa Uiversity

More information

The z-transform. 7.1 Introduction. 7.2 The z-transform Derivation of the z-transform: x[n] = z n LTI system, h[n] z = re j

The z-transform. 7.1 Introduction. 7.2 The z-transform Derivation of the z-transform: x[n] = z n LTI system, h[n] z = re j The -Trasform 7. Itroductio Geeralie the complex siusoidal represetatio offered by DTFT to a represetatio of complex expoetial sigals. Obtai more geeral characteristics for discrete-time LTI systems. 7.

More information

Charge Recycling in MTCMOS Circuits: Concept and Analysis Ehsan Pakbaznia University of Southern California

Charge Recycling in MTCMOS Circuits: Concept and Analysis Ehsan Pakbaznia University of Southern California Charge Recyclig i MTCMOS Circuits: Cocept ad Aalysis hsa akbazia Uiversity of Souther Califoria pakbazi@usc.edu Farza Fallah Fujitsu Labs of America farza@us.fujitsu.com Massoud edram Uiversity of Souther

More information

Analysis of Algorithms. Introduction. Contents

Analysis of Algorithms. Introduction. Contents Itroductio The focus of this module is mathematical aspects of algorithms. Our mai focus is aalysis of algorithms, which meas evaluatig efficiecy of algorithms by aalytical ad mathematical methods. We

More information

A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence

A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence Sequeces A sequece of umbers is a fuctio whose domai is the positive itegers. We ca see that the sequece,, 2, 2, 3, 3,... is a fuctio from the positive itegers whe we write the first sequece elemet as

More information

Parasitic Resistance L R W. Polysilicon gate. Drain. contact L D. V GS,eff R S R D. Drain

Parasitic Resistance L R W. Polysilicon gate. Drain. contact L D. V GS,eff R S R D. Drain Parasitic Resistace G Polysilico gate rai cotact V GS,eff S R S R S, R S, R + R C rai Short Chael Effects Chael-egth Modulatio Equatio k ( V V ) GS T suggests that the trasistor i the saturatio mode acts

More information

CS 270 Algorithms. Oliver Kullmann. Growth of Functions. Divide-and- Conquer Min-Max- Problem. Tutorial. Reading from CLRS for week 2

CS 270 Algorithms. Oliver Kullmann. Growth of Functions. Divide-and- Conquer Min-Max- Problem. Tutorial. Reading from CLRS for week 2 Geeral remarks Week 2 1 Divide ad First we cosider a importat tool for the aalysis of algorithms: Big-Oh. The we itroduce a importat algorithmic paradigm:. We coclude by presetig ad aalysig two examples.

More information

Probability, Expectation Value and Uncertainty

Probability, Expectation Value and Uncertainty Chapter 1 Probability, Expectatio Value ad Ucertaity We have see that the physically observable properties of a quatum system are represeted by Hermitea operators (also referred to as observables ) such

More information

Oblivious Gradient Clock Synchronization

Oblivious Gradient Clock Synchronization Motivatio: Clock Sychroizatio Oblivious Gradiet Clock Sychroizatio Thomas Locher, ETH Zurich Roger Wattehofer, ETH Zurich Clock sychroizatio is a classic, importat problem! May results have bee published

More information

1 Review of Probability & Statistics

1 Review of Probability & Statistics 1 Review of Probability & Statistics a. I a group of 000 people, it has bee reported that there are: 61 smokers 670 over 5 960 people who imbibe (drik alcohol) 86 smokers who imbibe 90 imbibers over 5

More information

Statistical Analysis on Uncertainty for Autocorrelated Measurements and its Applications to Key Comparisons

Statistical Analysis on Uncertainty for Autocorrelated Measurements and its Applications to Key Comparisons Statistical Aalysis o Ucertaity for Autocorrelated Measuremets ad its Applicatios to Key Comparisos Nie Fa Zhag Natioal Istitute of Stadards ad Techology Gaithersburg, MD 0899, USA Outlies. Itroductio.

More information

Statistical Pattern Recognition

Statistical Pattern Recognition Statistical Patter Recogitio Classificatio: No-Parametric Modelig Hamid R. Rabiee Jafar Muhammadi Sprig 2014 http://ce.sharif.edu/courses/92-93/2/ce725-2/ Ageda Parametric Modelig No-Parametric Modelig

More information

PC5215 Numerical Recipes with Applications - Review Problems

PC5215 Numerical Recipes with Applications - Review Problems PC55 Numerical Recipes with Applicatios - Review Problems Give the IEEE 754 sigle precisio bit patter (biary or he format) of the followig umbers: 0 0 05 00 0 00 Note that it has 8 bits for the epoet,

More information

Castiel, Supernatural, Season 6, Episode 18

Castiel, Supernatural, Season 6, Episode 18 13 Differetial Equatios the aswer to your questio ca best be epressed as a series of partial differetial equatios... Castiel, Superatural, Seaso 6, Episode 18 A differetial equatio is a mathematical equatio

More information

Ch3. Asymptotic Notation

Ch3. Asymptotic Notation Ch. Asymptotic Notatio copyright 006 Preview of Chapters Chapter How to aalyze the space ad time complexities of program Chapter Review asymptotic otatios such as O, Ω, Θ, o for simplifyig the aalysis

More information

THE ASYMPTOTIC COMPLEXITY OF MATRIX REDUCTION OVER FINITE FIELDS

THE ASYMPTOTIC COMPLEXITY OF MATRIX REDUCTION OVER FINITE FIELDS THE ASYMPTOTIC COMPLEXITY OF MATRIX REDUCTION OVER FINITE FIELDS DEMETRES CHRISTOFIDES Abstract. Cosider a ivertible matrix over some field. The Gauss-Jorda elimiatio reduces this matrix to the idetity

More information

CS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 5

CS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 5 CS434a/54a: Patter Recogitio Prof. Olga Veksler Lecture 5 Today Itroductio to parameter estimatio Two methods for parameter estimatio Maimum Likelihood Estimatio Bayesia Estimatio Itroducto Bayesia Decisio

More information

NUMERICAL METHODS FOR SOLVING EQUATIONS

NUMERICAL METHODS FOR SOLVING EQUATIONS Mathematics Revisio Guides Numerical Methods for Solvig Equatios Page 1 of 11 M.K. HOME TUITION Mathematics Revisio Guides Level: GCSE Higher Tier NUMERICAL METHODS FOR SOLVING EQUATIONS Versio:. Date:

More information

OBJECTIVES. Chapter 1 INTRODUCTION TO INSTRUMENTATION FUNCTION AND ADVANTAGES INTRODUCTION. At the end of this chapter, students should be able to:

OBJECTIVES. Chapter 1 INTRODUCTION TO INSTRUMENTATION FUNCTION AND ADVANTAGES INTRODUCTION. At the end of this chapter, students should be able to: OBJECTIVES Chapter 1 INTRODUCTION TO INSTRUMENTATION At the ed of this chapter, studets should be able to: 1. Explai the static ad dyamic characteristics of a istrumet. 2. Calculate ad aalyze the measuremet

More information

ELEC1200: A System View of Communications: from Signals to Packets Lecture 3

ELEC1200: A System View of Communications: from Signals to Packets Lecture 3 ELEC2: A System View of Commuicatios: from Sigals to Packets Lecture 3 Commuicatio chaels Discrete time Chael Modelig the chael Liear Time Ivariat Systems Step Respose Respose to sigle bit Respose to geeral

More information

Introduction to Microelectronics

Introduction to Microelectronics The iolar Juctio Trasistor Physical Structure of the iolar Trasistor Oeratio of the NPN Trasistor i the Active Mode Trasit Time ad Diffusio aacitace Ijectio fficiecy ad ase Trasort Factor The bers-moll

More information

ADVANCED DIGITAL SIGNAL PROCESSING

ADVANCED DIGITAL SIGNAL PROCESSING ADVANCED DIGITAL SIGNAL PROCESSING PROF. S. C. CHAN (email : sccha@eee.hku.hk, Rm. CYC-702) DISCRETE-TIME SIGNALS AND SYSTEMS MULTI-DIMENSIONAL SIGNALS AND SYSTEMS RANDOM PROCESSES AND APPLICATIONS ADAPTIVE

More information

( ) = p and P( i = b) = q.

( ) = p and P( i = b) = q. MATH 540 Radom Walks Part 1 A radom walk X is special stochastic process that measures the height (or value) of a particle that radomly moves upward or dowward certai fixed amouts o each uit icremet of

More information

Section 13.3 Area and the Definite Integral

Section 13.3 Area and the Definite Integral Sectio 3.3 Area ad the Defiite Itegral We ca easily fid areas of certai geometric figures usig well-kow formulas: However, it is t easy to fid the area of a regio with curved sides: METHOD: To evaluate

More information

Introduction to Signals and Systems, Part V: Lecture Summary

Introduction to Signals and Systems, Part V: Lecture Summary EEL33: Discrete-Time Sigals ad Systems Itroductio to Sigals ad Systems, Part V: Lecture Summary Itroductio to Sigals ad Systems, Part V: Lecture Summary So far we have oly looked at examples of o-recursive

More information

Machine Learning Regression I Hamid R. Rabiee [Slides are based on Bishop Book] Spring

Machine Learning Regression I Hamid R. Rabiee [Slides are based on Bishop Book] Spring Machie Learig Regressio I Hamid R. Rabiee [Slides are based o Bishop Book] Sprig 015 http://ce.sharif.edu/courses/93-94//ce717-1 Liear Regressio Liear regressio: ivolves a respose variable ad a sigle predictor

More information

Application of Single Electron Threshold Logic based Device: - A case study

Application of Single Electron Threshold Logic based Device: - A case study Applicatio of Sigle Electro Threshold Logic based Device: - A case study N. Basata Sigh Associate Professor, Departmet of ECE, Maipur Istitute of Techology, Imphal, Maipur, Idia ABSTRACT: The very high

More information

Chapter 7 z-transform

Chapter 7 z-transform Chapter 7 -Trasform Itroductio Trasform Uilateral Trasform Properties Uilateral Trasform Iversio of Uilateral Trasform Determiig the Frequecy Respose from Poles ad Zeros Itroductio Role i Discrete-Time

More information

10. Comparative Tests among Spatial Regression Models. Here we revisit the example in Section 8.1 of estimating the mean of a normal random

10. Comparative Tests among Spatial Regression Models. Here we revisit the example in Section 8.1 of estimating the mean of a normal random Part III. Areal Data Aalysis 0. Comparative Tests amog Spatial Regressio Models While the otio of relative likelihood values for differet models is somewhat difficult to iterpret directly (as metioed above),

More information

4.3 Growth Rates of Solutions to Recurrences

4.3 Growth Rates of Solutions to Recurrences 4.3. GROWTH RATES OF SOLUTIONS TO RECURRENCES 81 4.3 Growth Rates of Solutios to Recurreces 4.3.1 Divide ad Coquer Algorithms Oe of the most basic ad powerful algorithmic techiques is divide ad coquer.

More information

A statistical method to determine sample size to estimate characteristic value of soil parameters

A statistical method to determine sample size to estimate characteristic value of soil parameters A statistical method to determie sample size to estimate characteristic value of soil parameters Y. Hojo, B. Setiawa 2 ad M. Suzuki 3 Abstract Sample size is a importat factor to be cosidered i determiig

More information

Appendix: The Laplace Transform

Appendix: The Laplace Transform Appedix: The Laplace Trasform The Laplace trasform is a powerful method that ca be used to solve differetial equatio, ad other mathematical problems. Its stregth lies i the fact that it allows the trasformatio

More information

FIR Filter Design: Part II

FIR Filter Design: Part II EEL335: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we cosider how we might go about desigig FIR filters with arbitrary frequecy resposes, through compositio of multiple sigle-peak

More information

Polynomial Functions and Their Graphs

Polynomial Functions and Their Graphs Polyomial Fuctios ad Their Graphs I this sectio we begi the study of fuctios defied by polyomial expressios. Polyomial ad ratioal fuctios are the most commo fuctios used to model data, ad are used extesively

More information

Lecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting

Lecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would

More information

Ch3 Discrete Time Fourier Transform

Ch3 Discrete Time Fourier Transform Ch3 Discrete Time Fourier Trasform 3. Show that the DTFT of [] is give by ( k). e k 3. Determie the DTFT of the two sided sigal y [ ],. 3.3 Determie the DTFT of the causal sequece x[ ] A cos( 0 ) [ ],

More information

Review of Discrete-time Signals. ELEC 635 Prof. Siripong Potisuk

Review of Discrete-time Signals. ELEC 635 Prof. Siripong Potisuk Review of Discrete-time Sigals ELEC 635 Prof. Siripog Potisuk 1 Discrete-time Sigals Discrete-time, cotiuous-valued amplitude (sampled-data sigal) Discrete-time, discrete-valued amplitude (digital sigal)

More information

Analysis of MOS Capacitor Loaded Annular Ring MICROSTRIP Antenna

Analysis of MOS Capacitor Loaded Annular Ring MICROSTRIP Antenna Iteratioal OPEN AESS Joural Of Moder Egieerig Research (IJMER Aalysis of MOS apacitor Loaded Aular Rig MIROSTRIP Atea Mohit Kumar, Suredra Kumar, Devedra Kumar 3, Ravi Kumar 4,, 3, 4 (Assistat Professor,

More information