Technote 6. Op Amp Definitions. April 1990 Revised 11/22/02. Tim J. Sobering SDE Consulting

Size: px
Start display at page:

Download "Technote 6. Op Amp Definitions. April 1990 Revised 11/22/02. Tim J. Sobering SDE Consulting"

Transcription

1 Technte 6 prl 990 Resed /22/02 Op mp Dentns Tm J. Sberng SDE Cnsultng sdecnsultng@pbx.cm 990 Tm J. Sberng. ll rghts resered.

2 Op mp Dentns Pge 2 Op mp Dentns Ths Technte summrzes the bsc pertnl mpler dentns nd cmpres the del Op mp ssumptns wth the perrmnce rel mplers. Open Lp Gn: () Fgure. Op mp n pen-lp cngurtn Clsed Lp Gn (nertng): r: cl cl ( n) ( n) α (2) (3) Fgure 2. Inertng Op mp cngurtn Inertng mpler blck dgrm: α Σ Fgure 3. Inertng Op mp blck dgrm Clsed Lp Gn (nn-nertng): r: cl cl ( nn) ( nn) (4) (5) Fgure 4. Nn-Inertng Op mp cngurtn Cpyrght 990 Tm J. Sberng. ll rghts resered.

3 Op mp Dentns Pge 3 Nn-nertng mpler blck dgrm: Σ Lp Gn: Fgure 5. Nn-nertng Op mp blck dgrm l (6) Fgure 6. Dentn lp gn Feedbck Fctr: 2 (7) 2 ( ) α (8) Fgure 7. Dentn eedbck ctr Dertn cl, Inertng mpler Reerrng t Fgure 2 be nd pplyng KCL t the nertng nde: 0 (9) 0 (0) () cl ( n) (2) Cpyrght 990 Tm J. Sberng. ll rghts resered.

4 Resed /9/02 Pge 4 Cpyrght 990 Tm J. Sberng. ll rghts resered. cl n (3) cl n (4) Recgnzng tht nd α (5) α cl n (6) s cl n α (7) Nte tht Equtn (6) cn ls be expressed s: cl n (8) Dertn cl, Nn-nertng mpler 0 (9) 0 (20) (2) cl nn (22) cl nn (23)

5 Resed /9/02 Pge 5 Recgnzng tht (24) cl ( nn) (25) s ( nn) cl Equtn (25) cn ls be expressed s: cl ( nn) (27) Equtns (8) nd (27) re ery useul n exmnng the gn errr s unctn requency s the errr term ppers n the sme rm n bth equtns. Ths shws why hgh pen lp gn s mprtnt nd ls why t s ten necessry t select n Op mp wth hgh pen-lp gn nd/r hgher then expected bndwdth. Gn _ Errr (28) Settlng tme s relted, but seprte, prmeter. Due t the delys n prpgtn sgnl thrugh the nternl pmp crcutry, the utput tkes tme t rech t s nl lue. Ths s prtculr cncern r step nputs when slew rte, ersht nd rngng my dmnte the utput respnse. Gn (db) OPEN LOOP GIN (26) CL CLOSED-LOOP BNDWIDTH CLOSED LOOP GIN CL LOG Fgure 8. Open Lp nd Clsed Lp Mgntude Respnses. Cpyrght 990 Tm J. Sberng. ll rghts resered.

6 Resed /9/02 Pge 6 Idel Op mp ssumptns: R R Fgure 9. Op mp Equlent Crcut Idel Chrcterstc Crcut Eect N current lws n the nputs Ibs(,) 0 r n ltge gn s nnte, 0 N utput ltge r zer nput s 0 Output mpednce s zer ut 0 Frequency respnse s lt nd nnte BW r Dely 0 nd GBW Slew Rte s nnte BW r Dely 0 nd GBW CMRR s nnte Unlmted nput ltge rnge PSRR s nnte Immune t PS set nd rtns Nse ree Output due t sgnl nly Tble. Idel Op mp Chrcterstcs Reltes:. Bs currents cuse sets nd drt. 2. Fnte pen lp gn nd nte bndwdth result n gn errrs exmne lp gn term,, n Equtns (6) nd (25). 3. Input resstnce (mpednce) ntrduces errrs ppers n prllel wth. 4. Output resstnce (mpednce) ntrduces errrs ppers s ltge dder wth nd the ld. 5. Oset ltge ppers t the utput multpled by the nse gn. Oset ltge ls drts er tme due t temperture chnges. 6. Bs currents cuse sets nd re nt mtched between the nputs. They ls drt er tme due t temperture chnges. 7. Pwer supply msmtch cuses sets ppers s cmmn mde ltge t the nput. 8. CMRR s nt nnte s the nput ltge rnge s lmted nd nnlnertes pper n the putput s result cmmn mde ltges, prtuculrly n the nn-nertng cngurtn. 9. Rel Op mps he nse. 0. Op mps he grup dely,.e. nt ll requences experence the sme tme dely thrugh the crcut. Ths results n dstrtn.. Fnte slew rte cn result n utput dstrtn. Cpyrght 990 Tm J. Sberng. ll rghts resered.

55:041 Electronic Circuits

55:041 Electronic Circuits 55:04 Electrnc Crcuts Feedback & Stablty Sectns f Chapter 2. Kruger Feedback & Stablty Cnfguratn f Feedback mplfer S S S S fb Negate feedback S S S fb S S S S S β s the feedback transfer functn Implct

More information

Design of Analog Integrated Circuits

Design of Analog Integrated Circuits Desgn f Analg Integrated Crcuts I. Amplfers Desgn f Analg Integrated Crcuts Fall 2012, Dr. Guxng Wang 1 Oerew Basc MOS amplfer structures Cmmn-Surce Amplfer Surce Fllwer Cmmn-Gate Amplfer Desgn f Analg

More information

Lecture 5: Operational Amplifiers and Op Amp Circuits

Lecture 5: Operational Amplifiers and Op Amp Circuits Lecture 5: peratonal mplers and p mp Crcuts Gu-Yeon We Dson o Engneerng and ppled Scences Harard Unersty guyeon@eecs.harard.edu We erew eadng S&S: Chapter Supplemental eadng Background rmed wth our crcut

More information

The three major operations done on biological signals using Op-Amp:

The three major operations done on biological signals using Op-Amp: The three majr peratns dne n blgcal sgnals usng Op-Amp: ) Amplcatns and Attenuatns 2) DC settng: add r subtract a DC 3) Shape ts requency cntent: Flterng Ideal Op-Amp Mst belectrc sgnals are small and

More information

ME2142/ME2142E Feedback Control Systems. Modelling of Physical Systems The Transfer Function

ME2142/ME2142E Feedback Control Systems. Modelling of Physical Systems The Transfer Function Mdellng Physcal Systems The Transer Functn Derental Equatns U Plant Y In the plant shwn, the nput u aects the respnse the utput y. In general, the dynamcs ths respnse can be descrbed by a derental equatn

More information

Chapter 6. Operational Amplifier. inputs can be defined as the average of the sum of the two signals.

Chapter 6. Operational Amplifier.  inputs can be defined as the average of the sum of the two signals. 6 Operatonal mpler Chapter 6 Operatonal mpler CC Symbol: nput nput Output EE () Non-nvertng termnal, () nvertng termnal nput mpedance : Few mega (ery hgh), Output mpedance : Less than (ery low) Derental

More information

ELG3150 DGD 6 P9.5; P9.7; P9.13; P9.18; AP9.5; DP9.2

ELG3150 DGD 6 P9.5; P9.7; P9.13; P9.18; AP9.5; DP9.2 ELG3150 DGD 6 P9.5; P9.7; P9.13; P9.18; AP9.5; DP9.2 P9.5 A speed cntrl fr gsline engine is shwn in Figure P9.5 in the textbk. () Determine the necessry gin if the stedy-stte speed errr is required t be

More information

Physics 102. Final Examination. Spring Semester ( ) P M. Fundamental constants. n = 10P

Physics 102. Final Examination. Spring Semester ( ) P M. Fundamental constants. n = 10P ε µ0 N mp M G T Kuwit University hysics Deprtment hysics 0 Finl Exmintin Spring Semester (0-0) My, 0 Time: 5:00 M :00 M Nme.Student N Sectin N nstructrs: Drs. bdelkrim, frsheh, Dvis, Kkj, Ljk, Mrfi, ichler,

More information

Limitations for Op Amps due to input signal

Limitations for Op Amps due to input signal ECEN 607 (ESS) Liittin fr Op Ap due t input ignl TANSIENT ESPONSE.- Let u cnider vltge fllwer nd deterine it tep repne Then v in 0 v Thu fr i v (t) i u t r i t Tking the invere Lplce it yield t / v t e

More information

Objective of curve fitting is to represent a set of discrete data by a function (curve). Consider a set of discrete data as given in table.

Objective of curve fitting is to represent a set of discrete data by a function (curve). Consider a set of discrete data as given in table. CURVE FITTING Obectve curve ttg s t represet set dscrete dt b uct curve. Csder set dscrete dt s gve tble. 3 3 = T use the dt eectvel, curve epress s tted t the gve dt set, s = + = + + = e b ler uct plml

More information

Section I5: Feedback in Operational Amplifiers

Section I5: Feedback in Operational Amplifiers Sectin I5: eedback in Operatinal mplifiers s discussed earlier, practical p-amps hae a high gain under dc (zer frequency) cnditins and the gain decreases as frequency increases. This frequency dependence

More information

Exercises for Frequency Response. ECE 102, Winter 2011, F. Najmabadi

Exercises for Frequency Response. ECE 102, Winter 2011, F. Najmabadi Eercses r Frequency espnse EE 0, Wnter 0, F. Najabad Eercse : A Mdy the crcut belw t nclude a dnant ple at 00 Mz ( 00 Ω, k, k, / 00 Ω, λ 0, and nre nternal capactances the MOS. pute the dnant ple n the

More information

Solution of Tutorial 5 Drive dynamics & control

Solution of Tutorial 5 Drive dynamics & control ELEC463 Unversty of New South Wles School of Electrcl Engneerng & elecommunctons ELEC463 Electrc Drve Systems Queston Motor Soluton of utorl 5 Drve dynmcs & control 500 rev/mn = 5.3 rd/s 750 rted 4.3 Nm

More information

Faculty of Engineering

Faculty of Engineering Faculty f Engneerng DEPARTMENT f ELECTRICAL AND ELECTRONIC ENGINEERING EEE 223 Crcut Thery I Instructrs: M. K. Uygurğlu E. Erdl Fnal EXAMINATION June 20, 2003 Duratn : 120 mnutes Number f Prblems: 6 Gd

More information

Waveshapping Circuits and Data Converters. Lesson #17 Comparators and Schmitt Triggers Section BME 373 Electronics II J.

Waveshapping Circuits and Data Converters. Lesson #17 Comparators and Schmitt Triggers Section BME 373 Electronics II J. Waeshappg Crcuts and Data Cnerters Lessn #7 Cmparatrs and Schmtt Trggers Sectn. BME 7 Electrncs II 0 Waeshappg Crcuts and Data Cnerters Cmparatrs and Schmtt Trggers Astable Multbratrs and Tmers ectfers,

More information

CHAPTER 3: FEEDBACK. Dr. Wan Mahani Hafizah binti Wan Mahmud

CHAPTER 3: FEEDBACK. Dr. Wan Mahani Hafizah binti Wan Mahmud CHPTER 3: FEEDBCK Dr. Wan Mahan Hafzah bnt Wan Mahmud Feedback ntrductn Types f Feedback dvantages, Characterstcs and effect f Negatve Feedback mplfers Crcuts wth negatve feedback Pstve feedback and Oscllatr

More information

Introduction to Electronic circuits.

Introduction to Electronic circuits. Intrductn t Electrnc crcuts. Passve and Actve crcut elements. Capactrs, esstrs and Inductrs n AC crcuts. Vltage and current dvders. Vltage and current surces. Amplfers, and ther transfer characterstc.

More information

OVERVIEW Using Similarity and Proving Triangle Theorems G.SRT.4

OVERVIEW Using Similarity and Proving Triangle Theorems G.SRT.4 OVRVIW Using Similrity nd Prving Tringle Therems G.SRT.4 G.SRT.4 Prve therems ut tringles. Therems include: line prllel t ne side f tringle divides the ther tw prprtinlly, nd cnversely; the Pythgren Therem

More information

PHYSICS 536 Experiment 12: Applications of the Golden Rules for Negative Feedback

PHYSICS 536 Experiment 12: Applications of the Golden Rules for Negative Feedback PHYSICS 536 Experment : Applcatns f the Glden Rules fr Negatve Feedback The purpse f ths experment s t llustrate the glden rules f negatve feedback fr a varety f crcuts. These cncepts permt yu t create

More information

332:221 Principles of Electrical Engineering I Fall Hourly Exam 2 November 6, 2006

332:221 Principles of Electrical Engineering I Fall Hourly Exam 2 November 6, 2006 2:221 Principles of Electricl Engineering I Fll 2006 Nme of the student nd ID numer: Hourly Exm 2 Novemer 6, 2006 This is closed-ook closed-notes exm. Do ll your work on these sheets. If more spce is required,

More information

Performance Evaluation of Cross-Flow Heat Exchanger in Coal-Fired Power Plant under Particulate Condition

Performance Evaluation of Cross-Flow Heat Exchanger in Coal-Fired Power Plant under Particulate Condition การประช มว ชาการเคร อข ายว ศวกรรมเคร องกลแห งประเทศไทย 18-20 ต ลาคม 2547 จ งหว ด-ขอนแก น Perfrmnce Evlutn f Crss-Flw Het Exchnger n Cl-Fred Pwer Plnt under Prtculte Cndtn Ppt Jungjndee Me Mh Pwer Plnt

More information

Schedule. ECEN 301 Discussion #17 Operational Amplifiers 1. Date Day Class No. Lab Due date. Exam

Schedule. ECEN 301 Discussion #17 Operational Amplifiers 1. Date Day Class No. Lab Due date. Exam chedule Date Day Class N. Title Chapters HW Due date 29 Oct Wed 17 Operatinal mplifiers 8.1 8.2 Lab Due date Exam 30 Oct Thu 31 Oct ri ecitatin HW 7 1 N at 2 N un 3 N Mn 18 Operatinal mplifiers 8.3 8.4

More information

Lecture 20a. Circuit Topologies and Techniques: Opamps

Lecture 20a. Circuit Topologies and Techniques: Opamps Lecture a Circuit Tplgies and Techniques: Opamps In this lecture yu will learn: Sme circuit tplgies and techniques Intrductin t peratinal amplifiers Differential mplifier IBIS1 I BIS M VI1 vi1 Vi vi I

More information

Circuits Op-Amp. Interaction of Circuit Elements. Quick Check How does closing the switch affect V o and I o?

Circuits Op-Amp. Interaction of Circuit Elements. Quick Check How does closing the switch affect V o and I o? Crcuts Op-Amp ENGG1015 1 st Semester, 01 Interactn f Crcut Elements Crcut desgn s cmplcated by nteractns amng the elements. Addng an element changes vltages & currents thrughut crcut. Example: clsng a

More information

OP AMP CHARACTERISTICS

OP AMP CHARACTERISTICS O AM CHAACTESTCS Static p amp limitatins EFEENCE: Chapter 5 textbk (ESS) EOS CAUSED BY THE NUT BAS CUENT AND THE NUT OFFSET CUENT Op Amp t functin shuld have fr the input terminals a DC path thrugh which

More information

Position and Speed Control. Industrial Electrical Engineering and Automation Lund University, Sweden

Position and Speed Control. Industrial Electrical Engineering and Automation Lund University, Sweden Poton nd Speed Control Lund Unverty, Seden Generc Structure R poer Reference Sh tte Voltge Current Control ytem M Speed Poton Ccde Control * θ Poton * Speed * control control - - he ytem contn to ntegrton.

More information

EE 215A Fundamentals of Electrical Engineering Lecture Notes Operational Amplifiers (Op Amps) 8/6/01 Reviewed 10/04

EE 215A Fundamentals of Electrical Engineering Lecture Notes Operational Amplifiers (Op Amps) 8/6/01 Reviewed 10/04 EE 5 Fundamental Electrcal Engneerng Lecture Nte Operatnal mpler (Op mp) 8/6/ eewed /4 ch Chrte Oerew: The peratnal ampler, r p amp r hrt, a undamental buldng blck n crcut degn. Stued nde a chp are a bunch

More information

WYSE Academic Challenge Regional Physics 2008 SOLUTION SET

WYSE Academic Challenge Regional Physics 2008 SOLUTION SET WYSE cdemic Chllenge eginl 008 SOLUTION SET. Crrect nswer: E. Since the blck is mving lng circulr rc when it is t pint Y, it hs centripetl ccelertin which is in the directin lbeled c. Hwever, the blck

More information

Diodes Waveform shaping Circuits. Sedra & Smith (6 th Ed): Sec. 4.5 & 4.6 Sedra & Smith (5 th Ed): Sec. 3.5 & 3.6

Diodes Waveform shaping Circuits. Sedra & Smith (6 th Ed): Sec. 4.5 & 4.6 Sedra & Smith (5 th Ed): Sec. 3.5 & 3.6 des Waefrm shapng Cruts Sedra & Smth (6 th Ed): Se. 4.5 & 4.6 Sedra & Smth (5 th Ed): Se. 3.5 & 3.6 Tw-prt netwrks as buldng blks Reall: Transfer funtn f a tw-prt netwrk an be fund by slng ths rut ne.

More information

Diodes Waveform shaping Circuits

Diodes Waveform shaping Circuits des Waefrm shapng Cruts Leture ntes: page 2-2 t 2-31 Sedra & Smth (6 th Ed): Se. 4.5 & 4.6 Sedra & Smth (5 th Ed): Se. 3.5 & 3.6 F. Najmabad, ECE65, Wnter 212 Tw-prt netwrks as buldng blks Reall: Transfer

More information

Introduction of Two Port Network Negative Feedback (Uni lateral Case) Feedback Topology Analysis of feedback applications

Introduction of Two Port Network Negative Feedback (Uni lateral Case) Feedback Topology Analysis of feedback applications Lectue Feedback mple ntductn w Pt Netwk Negatve Feedback Un lateal Case Feedback plg nalss eedback applcatns Clse Lp Gan nput/output esstances e:83h 3 Feedback w-pt Netwk z-paametes Open-Ccut mpedance

More information

CHAPTER 11. Solutions for Exercises. (b) An inverting amplifier has negative gain. Thus L

CHAPTER 11. Solutions for Exercises. (b) An inverting amplifier has negative gain. Thus L CHPTE Slutn fr Exerce E. (a nnnertng amplfer ha pte gan. Thu ( t ( t 50 ( t 5.0 n(000πt (b n nertng amplfer ha negate gan. Thu ( t ( t 50 ( t 5.0 n(000πt E. V V 75 500 + 5+ 75 c 75 V 000 75 500 V + + 500

More information

EE C245 ME C218 Introduction to MEMS Design

EE C245 ME C218 Introduction to MEMS Design EE C45 ME C8 Introducton to MEM Desgn Fall 7 Prof. Clark T.C. Nguyen Dept. of Electrcal Engneerng & Computer cences Unersty of Calforna at Berkeley Berkeley, C 947 Dscusson: eew of Op mps EE C45: Introducton

More information

Physics 121 Sample Common Exam 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7. Instructions:

Physics 121 Sample Common Exam 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7. Instructions: Physcs 121 Smple Common Exm 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7 Nme (Prnt): 4 Dgt ID: Secton: Instructons: Answer ll 27 multple choce questons. You my need to do some clculton. Answer ech queston on the

More information

BRIEF NOTES ADDITIONAL MATHEMATICS FORM

BRIEF NOTES ADDITIONAL MATHEMATICS FORM BRIEF NOTES ADDITIONAL MATHEMATICS FORM CHAPTER : FUNCTION. : + is the object, + is the imge : + cn be written s () = +. To ind the imge or mens () = + = Imge or is. Find the object or 8 mens () = 8 wht

More information

EE 221 Practice Problems for the Final Exam

EE 221 Practice Problems for the Final Exam EE 1 Practce Prblems fr the Fnal Exam 1. The netwrk functn f a crcut s 1.5 H. ω 1+ j 500 Ths table recrds frequency respnse data fr ths crcut. Fll n the blanks n the table:. The netwrk functn f a crcut

More information

Lesson 5. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)

Lesson 5. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER) Lessn 5 Thermmechancal Measurements r Energy Systems (MEN) Measurements r Mechancal Systems and Prductn (MME) A.Y. 205-6 Zaccara (n ) Del Prete We wll nw analyze mre n depth each ne the unctnal blcks the

More information

SMARANDACHE GROUPOIDS

SMARANDACHE GROUPOIDS SMARANDACHE GROUPOIDS W. B. Vsnth Kndsmy Deprtment f Mthemtics Indin Institute f Technlgy Mdrs Chenni - 6 6 Indi. E-mil: vsntk@md.vsnl.net.in Astrct: In this pper we study the cncept f Smrndche Grupids

More information

Lecture 2 Feedback Amplifier

Lecture 2 Feedback Amplifier Lectue Feedback mple ntductn w-pt Netwk Negatve Feedback Un-lateal Case Feedback plg nalss eedback applcatns Clse-Lp Gan nput/output esstances e:83hkn 3 Feedback mples w-pt Netwk z-paametes Open-Ccut mpedance

More information

CURRENT FEEDBACK AMPLIFIERs

CURRENT FEEDBACK AMPLIFIERs Abstract-The need r hgh speed, wdeband amplers s the drng rce behnd the deelpment the Current Feedback Ampler (CFA). The CFA has sgncant adantages er cnentnal amplers n terms slew rate perrmance and nherently

More information

Designing Information Devices and Systems I Discussion 8B

Designing Information Devices and Systems I Discussion 8B Lst Updted: 2018-10-17 19:40 1 EECS 16A Fll 2018 Designing Informtion Devices nd Systems I Discussion 8B 1. Why Bother With Thévenin Anywy? () Find Thévenin eqiuvlent for the circuit shown elow. 2kΩ 5V

More information

CHAPTER 20: Second Law of Thermodynamics

CHAPTER 20: Second Law of Thermodynamics CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het

More information

ragsdale (zdr82) HW6 ditmire (58335) 1 the direction of the current in the figure. Using the lower circuit in the figure, we get

ragsdale (zdr82) HW6 ditmire (58335) 1 the direction of the current in the figure. Using the lower circuit in the figure, we get rgsdle (zdr8) HW6 dtmre (58335) Ths prnt-out should hve 5 questons Multple-choce questons my contnue on the next column or pge fnd ll choces efore nswerng 00 (prt of ) 00 ponts The currents re flowng n

More information

Common Gate Amplifier

Common Gate Amplifier mmn Gate Ampler Fure (a) shs a cmmn ate ampler th deal current surce lad. Fure (b) shs the deal current surce mplemented by PMOS th cnstant ate t surce vltae. DD DD G M G M G M (a) (b) Fure. mmn ate ampler.

More information

Dead-beat controller design

Dead-beat controller design J. Hetthéssy, A. Barta, R. Bars: Dead beat cntrller design Nvember, 4 Dead-beat cntrller design In sampled data cntrl systems the cntrller is realised by an intelligent device, typically by a PLC (Prgrammable

More information

Mathematics Extension 1

Mathematics Extension 1 04 Bored of Studies Tril Emintions Mthemtics Etension Written by Crrotsticks & Trebl. Generl Instructions Totl Mrks 70 Reding time 5 minutes. Working time hours. Write using blck or blue pen. Blck pen

More information

Feedback Principle :-

Feedback Principle :- Feedback Prncple : Feedback amplfer s that n whch a part f the utput f the basc amplfer s returned back t the nput termnal and mxed up wth the nternal nput sgnal. The sub netwrks f feedback amplfer are:

More information

Linear Amplifiers and OpAmps

Linear Amplifiers and OpAmps Lnear Amplfers and OpAmps eferences: Barbw (pp 7-80), Hayes & Hrwtz (pp 63-40), zzn (Chapter ) Amplfers are tw-prt netwrks n whch the utput ltage r current s drectly prprtnal t ether nput ltage r current.

More information

ANALOG ELECTRONICS 1 DR NORLAILI MOHD NOH

ANALOG ELECTRONICS 1 DR NORLAILI MOHD NOH 24 ANALOG LTRONIS TUTORIAL DR NORLAILI MOHD NOH . 0 8kΩ Gen, Y β β 00 T F 26, 00 0.7 (a)deterne the dc ltages at the 3 X ternals f the JT (,, ). 0kΩ Z (b) Deterne g,r π and r? (c) Deterne the ltage gan

More information

fiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics

fiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics Solid Stte Physics JEST-0 Q. bem of X-rys is incident on BCC crystl. If the difference between the incident nd scttered wvevectors is K nxˆkyˆlzˆ where xˆ, yˆ, zˆ re the unit vectors of the ssocited cubic

More information

ECEN 4872/5827 Lecture Notes

ECEN 4872/5827 Lecture Notes ECEN 4872/5827 Lecture Ntes Lecture #5 Objectives fr lecture #5: 1. Analysis f precisin current reference 2. Appraches fr evaluating tlerances 3. Temperature Cefficients evaluatin technique 4. Fundamentals

More information

Part a: Writing the nodal equations and solving for v o gives the magnitude and phase response: tan ( 0.25 )

Part a: Writing the nodal equations and solving for v o gives the magnitude and phase response: tan ( 0.25 ) + - Hmewrk 0 Slutin ) In the circuit belw: a. Find the magnitude and phase respnse. b. What kind f filter is it? c. At what frequency is the respnse 0.707 if the generatr has a ltage f? d. What is the

More information

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax .7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical

More information

4. Eccentric axial loading, cross-section core

4. Eccentric axial loading, cross-section core . Eccentrc xl lodng, cross-secton core Introducton We re strtng to consder more generl cse when the xl force nd bxl bendng ct smultneousl n the cross-secton of the br. B vrtue of Snt-Vennt s prncple we

More information

ME306 Dynamics, Spring HW1 Solution Key. AB, where θ is the angle between the vectors A and B, the proof

ME306 Dynamics, Spring HW1 Solution Key. AB, where θ is the angle between the vectors A and B, the proof ME6 Dnms, Spng HW Slutn Ke - Pve, gemetll.e. usng wngs sethes n nltll.e. usng equtns n nequltes, tht V then V. Nte: qunttes n l tpee e vets n n egul tpee e sls. Slutn: Let, Then V V V We wnt t pve tht:

More information

ELG4139: Op Amp-based Active Filters

ELG4139: Op Amp-based Active Filters ELG439: Op Amp-baed Actve Flter Advantage: educed ze and weght, and therere paratc. Increaed relablty and mprved perrmance. Smpler degn than r pave lter and can realze a wder range unctn a well a prvdng

More information

FEEDBACK AMPLIFIERS. v i or v s v 0

FEEDBACK AMPLIFIERS. v i or v s v 0 FEEDBCK MPLIFIERS Feedback n mplers FEEDBCK IS THE PROCESS OF FEEDING FRCTION OF OUTPUT ENERGY (VOLTGE OR CURRENT) BCK TO THE INPUT CIRCUIT. THE CIRCUIT EMPLOYED FOR THIS PURPOSE IS CLLED FEEDBCK NETWORK.

More information

GUC (Dr. Hany Hammad) 9/19/2016

GUC (Dr. Hany Hammad) 9/19/2016 UC (Dr. Hny Hmmd) 9/9/6 ecture # ignl flw grph: Defitin. Rule f Reductin. Mn Rule. ignl-flw grph repreenttin f : ltge urce. ive gle-prt device. ignl Flw rph A ignl-flw grph i grphicl men f prtryg the reltinhip

More information

GAUSS ELIMINATION. Consider the following system of algebraic linear equations

GAUSS ELIMINATION. Consider the following system of algebraic linear equations Numercl Anlyss for Engneers Germn Jordnn Unversty GAUSS ELIMINATION Consder the followng system of lgebrc lner equtons To solve the bove system usng clsscl methods, equton () s subtrcted from equton ()

More information

Fast Feedback Strategies for Longitudinal Beam Stabilization

Fast Feedback Strategies for Longitudinal Beam Stabilization 1 / 12 Fst Feedbck Strtegies for Longitudinl Bem Stbiliztion IPAC 2012, New Orlens, USA S. Pfeiffer 1, C. Schmidt 1, M.K. Bock 1, H. Schlrb 1, W. Jlmuzn 2, G. Lichtenberg 3, H. Werner 3 1 DESY Hmburg 2

More information

2. VECTORS AND MATRICES IN 3 DIMENSIONS

2. VECTORS AND MATRICES IN 3 DIMENSIONS 2 VECTORS AND MATRICES IN 3 DIMENSIONS 21 Extending the Theory of 2-dimensionl Vectors x A point in 3-dimensionl spce cn e represented y column vector of the form y z z-xis y-xis z x y x-xis Most of the

More information

Applied Statistics Qualifier Examination

Applied Statistics Qualifier Examination Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng

More information

3.1 Exponential Functions and Their Graphs

3.1 Exponential Functions and Their Graphs . Eponentil Functions nd Their Grphs Sllbus Objective: 9. The student will sketch the grph of eponentil, logistic, or logrithmic function. 9. The student will evlute eponentil or logrithmic epressions.

More information

Institute for Competitive Examinations

Institute for Competitive Examinations hysics, Chemistry & Mthemtics (per-) Cde-5 AR : HYSCS -JEE-01 SECN- : Single Crrect Answer ype his sectin cntins 10 multiple chice questins. Ech questin hs fur chices,, nd (D) ut f which NLY NE is crrect:

More information

Applying Kirchoff s law on the primary circuit. V = - e1 V+ e1 = 0 V.D. e.m.f. From the secondary circuit e2 = v2. K e. Equivalent circuit :

Applying Kirchoff s law on the primary circuit. V = - e1 V+ e1 = 0 V.D. e.m.f. From the secondary circuit e2 = v2. K e. Equivalent circuit : TRANSFORMERS Definitin : Transfrmers can be defined as a static electric machine which cnverts electric energy frm ne ptential t anther at the same frequency. It can als be defined as cnsists f tw electric

More information

Part I: Basic Concepts of Thermodynamics

Part I: Basic Concepts of Thermodynamics Prt I: Bsic Concepts o Thermodynmics Lecture 4: Kinetic Theory o Gses Kinetic Theory or rel gses 4-1 Kinetic Theory or rel gses Recll tht or rel gses: (i The volume occupied by the molecules under ordinry

More information

3.2.2 Kinetics. Maxwell Boltzmann distribution. 128 minutes. 128 marks. Page 1 of 12

3.2.2 Kinetics. Maxwell Boltzmann distribution. 128 minutes. 128 marks. Page 1 of 12 3.. Kinetics Mxwell Boltzmnn distribution 8 minutes 8 mrks Pge of M. () M On the energy xis E mp t the mximum of the originl pek M The limits for the horizontl position of E mp re defined s bove the word

More information

, where. This is a highpass filter. The frequency response is the same as that for P.P.14.1 RC. Thus, the sketches of H and φ are shown below.

, where. This is a highpass filter. The frequency response is the same as that for P.P.14.1 RC. Thus, the sketches of H and φ are shown below. hapter 4, Slutn. H ( H(, where H π H ( φ H ( tan - ( Th a hghpa lter. The requency repne the ame a that r P.P.4. except that. Thu, the ketche H and φ are hwn belw. H.77 / φ 9 45 / hapter 4, Slutn. H(,

More information

Microelectronics Circuit Analysis and Design. NMOS Common-Source Circuit. NMOS Common-Source Circuit 10/15/2013. In this chapter, we will:

Microelectronics Circuit Analysis and Design. NMOS Common-Source Circuit. NMOS Common-Source Circuit 10/15/2013. In this chapter, we will: Mcrelectrncs Crcut Analyss and Desn Dnald A. Neaen Chapter 4 Basc FET Aplfers In ths chapter, we wll: Inestate a snle-transstr crcut that can aplfy a sall, te-aryn nput snal Deelp sall-snal dels that are

More information

Rank One Update And the Google Matrix by Al Bernstein Signal Science, LLC

Rank One Update And the Google Matrix by Al Bernstein Signal Science, LLC Introducton Rnk One Updte And the Google Mtrx y Al Bernsten Sgnl Scence, LLC www.sgnlscence.net here re two dfferent wys to perform mtrx multplctons. he frst uses dot product formulton nd the second uses

More information

ME 3600 Control Systems Frequency Domain Analysis

ME 3600 Control Systems Frequency Domain Analysis ME 3600 Cntl Systems Fequency Dmain Analysis The fequency espnse f a system is defined as the steady-state espnse f the system t a sinusidal (hamnic) input. F linea systems, the esulting utput is itself

More information

Consequently, the temperature must be the same at each point in the cross section at x. Let:

Consequently, the temperature must be the same at each point in the cross section at x. Let: HW 2 Comments: L1-3. Derive the het eqution for n inhomogeneous rod where the therml coefficients used in the derivtion of the het eqution for homogeneous rod now become functions of position x in the

More information

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write

More information

Topics Covered AP Calculus AB

Topics Covered AP Calculus AB Topics Covered AP Clculus AB ) Elementry Functions ) Properties of Functions i) A function f is defined s set of ll ordered pirs (, y), such tht for ech element, there corresponds ectly one element y.

More information

Lecture 7 Circuits Ch. 27

Lecture 7 Circuits Ch. 27 Leture 7 Cruts Ch. 7 Crtoon -Krhhoff's Lws Tops Dret Current Cruts Krhhoff's Two ules Anlyss of Cruts Exmples Ammeter nd voltmeter C ruts Demos Three uls n rut Power loss n trnsmsson lnes esstvty of penl

More information

EEO 401 Digital Signal Processing Prof. Mark Fowler

EEO 401 Digital Signal Processing Prof. Mark Fowler EEO 4 Digital Signal Prcessing Pr. ar Fwler DT Filters te Set #2 Reading Assignment: Sect. 5.4 Prais & anlais /29 Ideal LP Filter Put in the signal we want passed. Suppse that ( ) [, ] X π xn [ ] y[ n]

More information

Chapter 4 Homework solution: P4.2-2, 7 P4.3-2, 3, 6, 9 P4.4-2, 5, 8, 18 P4.5-2, 4, 5 P4.6-2, 4, 8 P4.7-2, 4, 9, 15 P4.8-2

Chapter 4 Homework solution: P4.2-2, 7 P4.3-2, 3, 6, 9 P4.4-2, 5, 8, 18 P4.5-2, 4, 5 P4.6-2, 4, 8 P4.7-2, 4, 9, 15 P4.8-2 Chpter 4 Homework solution: P4.2-2, 7 P4.3-2, 3, 6, 9 P4.4-2, 5, 8, 18 P4.5-2, 4, 5 P4.6-2, 4, 8 P4.7-2, 4, 9, 15 P4.8-2 P 4.2-2 P 4.2-2. Determine the node voltges for the circuit of Figure Answer: v

More information

Strong Bisimulation. Overview. References. Actions Labeled transition system Transition semantics Simulation Bisimulation

Strong Bisimulation. Overview. References. Actions Labeled transition system Transition semantics Simulation Bisimulation Strong Bisimultion Overview Actions Lbeled trnsition system Trnsition semntics Simultion Bisimultion References Robin Milner, Communiction nd Concurrency Robin Milner, Communicting nd Mobil Systems 32

More information

Fast Feedback Reactivity Effects

Fast Feedback Reactivity Effects SUPPLEMENT TO CHAPTER 12 OF REACTOR PHYSICS FUNDAMENTALS This supplement summrizes some key physics principles in the text nd expnds on the mthemticl tretment. You should be milir with the text mteril

More information

CTN 2/23/16. EE 247B/ME 218: Introduction to MEMS Design Lecture 11m2: Mechanics of Materials. Copyright 2016 Regents of the University of California

CTN 2/23/16. EE 247B/ME 218: Introduction to MEMS Design Lecture 11m2: Mechanics of Materials. Copyright 2016 Regents of the University of California Vlume Change fr a Unaxal Stress Istrpc lastcty n 3D Istrpc = same n all drectns The cmplete stress-stran relatns fr an strpc elastc Stresses actng n a dfferental vlume element sld n 3D: (.e., a generalzed

More information

1. Ideal OP Amps. +V cc. R o. v 1 v 2. v o. R d 2 1. V cc. Ideal Characteristics A = (gain is infinite) (no offset voltage) R

1. Ideal OP Amps. +V cc. R o. v 1 v 2. v o. R d 2 1. V cc. Ideal Characteristics A = (gain is infinite) (no offset voltage) R . Ideal OP Amps Op amp Hgh-gan d dfferental amplfer ( ) D pwer supples are requred Usually used wth external negate feedbak Assume deal p amp desgn rut hek nn-deal haratersts are mprtant mdfy f neessary

More information

CYLINDER MADE FROM BRITTLE MATERIAL AND SUBJECT TO INTERNAL PRESSURE ONLY

CYLINDER MADE FROM BRITTLE MATERIAL AND SUBJECT TO INTERNAL PRESSURE ONLY CYLINDER MADE FROM BRITTLE MATERIAL AND SUBJECT TO INTERNAL PRESSURE ONLY STRESS DISTRIBUTION ACROSS THE CYLINDER WALL The stresses n cyner suject t ntern ressure ny cn e etermne t tw ctns n the cyner

More information

Solutions to Problems. Then, using the formula for the speed in a parabolic orbit (equation ), we have

Solutions to Problems. Then, using the formula for the speed in a parabolic orbit (equation ), we have Slutins t Prblems. Nttin: V speed f cmet immeditely befre cllisin. V speed f cmbined bject immeditely fter cllisin, mmentum is cnserved. V, becuse liner + k q perihelin distnce f riginl prblic rbit, s

More information

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response

More information

ARITHMETIC OPERATIONS. The real numbers have the following properties: a b c ab ac

ARITHMETIC OPERATIONS. The real numbers have the following properties: a b c ab ac REVIEW OF ALGEBRA Here we review the bsic rules nd procedures of lgebr tht you need to know in order to be successful in clculus. ARITHMETIC OPERATIONS The rel numbers hve the following properties: b b

More information

Network Analysis and Synthesis. Chapter 5 Two port networks

Network Analysis and Synthesis. Chapter 5 Two port networks Network Anlsis nd Snthesis hpter 5 Two port networks . ntroduction A one port network is completel specified when the voltge current reltionship t the terminls of the port is given. A generl two port on

More information

Torsion, Thermal Effects and Indeterminacy

Torsion, Thermal Effects and Indeterminacy ENDS Note Set 7 F007bn orson, herml Effects nd Indetermncy Deformton n orsonlly Loded Members Ax-symmetrc cross sectons subjected to xl moment or torque wll remn plne nd undstorted. At secton, nternl torque

More information

R(3, 8) P( 3, 0) Q( 2, 2) S(5, 3) Q(2, 32) P(0, 8) Higher Mathematics Objective Test Practice Book. 1 The diagram shows a sketch of part of

R(3, 8) P( 3, 0) Q( 2, 2) S(5, 3) Q(2, 32) P(0, 8) Higher Mathematics Objective Test Practice Book. 1 The diagram shows a sketch of part of Higher Mthemtics Ojective Test Prctice ook The digrm shows sketch of prt of the grph of f ( ). The digrm shows sketch of the cuic f ( ). R(, 8) f ( ) f ( ) P(, ) Q(, ) S(, ) Wht re the domin nd rnge of

More information

Lesson 2. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)

Lesson 2. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER) Lesson 2 Thermomechncl Mesurements for Energy Systems (MEN) Mesurements for Mechncl Systems nd Producton (MME) 1 A.Y. 2015-16 Zccr (no ) Del Prete A U The property A s clled: «mesurnd» the reference property

More information

4. Introduction and Chapter Objectives

4. Introduction and Chapter Objectives Rel Anlog Crcuts 1 Chpter 4: Systems nd Network Theorems 4. Introducton nd Chpter Ojectes In preous chpters, numer of pproches he een presented for nlyzng electrcl crcuts. In these nlyss pproches, we he

More information

Why symmetry? Symmetry is often argued from the requirement that the strain energy must be positive. (e.g. Generalized 3-D Hooke s law)

Why symmetry? Symmetry is often argued from the requirement that the strain energy must be positive. (e.g. Generalized 3-D Hooke s law) Why symmetry? Symmetry is oten rgued rom the requirement tht the strin energy must be positie. (e.g. Generlized -D Hooke s lw) One o the derities o energy principles is the Betti- Mxwell reciprocity theorem.

More information

Let s start from a first-order low pass filter we already discussed.

Let s start from a first-order low pass filter we already discussed. EEE0 Netrk Analy II Dr. harle Km Nte09: Actve Flter ---Part. gher-order Actve Flter The rt-rder lter d nt harply dvde the pa band and the tp band. One apprach t btan a harper trantn beteen the pa band

More information

4.4 Areas, Integrals and Antiderivatives

4.4 Areas, Integrals and Antiderivatives . res, integrls nd ntiderivtives 333. Ares, Integrls nd Antiderivtives This section explores properties of functions defined s res nd exmines some connections mong res, integrls nd ntiderivtives. In order

More information

The Operational Amplifier and Application

The Operational Amplifier and Application Intrductn t Electrnc Crcuts: A Desgn Apprach Jse Sla-Martnez and Marn Onabaj The Operatnal Amplfer and Applcatn The peratnal ltage amplfer (mre cmmnly referred t as peratnal amplfer) s ne f the mst useful

More information

Mathematics Extension 2

Mathematics Extension 2 S Y D N E Y B O Y S H I G H S C H O O L M O O R E P A R K, S U R R Y H I L L S 005 HIGHER SCHOOL CERTIFICATE TRIAL PAPER Mthemtics Extension Generl Instructions Totl Mrks 0 Reding Time 5 Minutes Attempt

More information

5.1 Properties of Inverse Trigonometric Functions.

5.1 Properties of Inverse Trigonometric Functions. Inverse Trignmetricl Functins The inverse f functin f( ) f ( ) f : A B eists if f is ne-ne nt ie, ijectin nd is given Cnsider the e functin with dmin R nd rnge [, ] Clerl this functin is nt ijectin nd

More information

LINKÖPINGS TEKNISKA HÖGSKOLA. Fluid and Mechanical Engineering Systems

LINKÖPINGS TEKNISKA HÖGSKOLA. Fluid and Mechanical Engineering Systems (6) Fluid nd Mechnicl Engineering Sytem 008086. ) Cvittion in orifice In hydrulic ytem cvittion occur downtrem orifice with high preure drop. For n orifice with contnt inlet preure of p = 00 br cvittion

More information

Use 10 m/s 2 for the acceleration due to gravity.

Use 10 m/s 2 for the acceleration due to gravity. ANSWERS Prjecle mn s he ecrl sum w ndependen elces, hrznl cmpnen nd ercl cmpnen. The hrznl cmpnen elcy s cnsn hrughu he mn whle he ercl cmpnen elcy s dencl ree ll. The cul r nsnneus elcy ny pn lng he prblc

More information

PH2200 Practice Exam I Summer 2003

PH2200 Practice Exam I Summer 2003 PH00 Prctice Exm I Summer 003 INSTRUCTIONS. Write yur nme nd student identifictin number n the nswer sheet.. Plese cver yur nswer sheet t ll times. 3. This is clsed bk exm. Yu my use the PH00 frmul sheet

More information