Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab
|
|
- Shanna Lane
- 5 years ago
- Views:
Transcription
1 Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts 1 Objectes The objectes of ths laboratory experment are: To demonstrate the nput-output relatonshps of the ntegratng and dfferentatng amplfer confguratons usng operatonal amplfers. To smulate a frst-order lnear dfferental equaton usng an ntegratng op-amp crcut. Theory The dynamc characterstcs of capactors and nductors produce sgnal processng functons that cannot be obtaned usng resstors. The op-amp crcut of Fgure 1(a) s smlar to the nertng amplfer except for the capactor n the feedback path. To determne the nput-output relatonshp of ths crcut, we use the deal op-amp equatons as well as Krchhoff s oltage and current laws. Begn by wrtng Krchhoff s current law (KL) at the nertng node, (t) (t) = (t) (1) and substtute the - characterstcs of the resstor and capactor, (t) (t) Then use the deal op-amp equatons = (t) () (t) = (3) (t) = P (t) = (4) together wth the fact that (t) = o (t) (t) = o (t) P (t) = o (t) (5) and rewrte KL as (t) o = (6) To sole for the output oltage o (t), multply ths equaton by, sole for the dfferental o, and ntegrate to get o = 1 (t) (7) Assumng the output oltage s known at tme t =, the ntegraton lmts are o(t) o() o = 1 t (t) (8) 1
2 P P o o (a) (b) whch yelds o (t) = 1 Fgure 1: Op-Amp (a) Integrator and (b) Dfferentator rcuts t (t) o () (9) From Equaton (5), the ntal conon o () s actually the oltage on the capactor at tme t =. When ths oltage s ntally zero at tme t =, the crcut nput-output relatonshp reduces to o (t) = 1 t (t) (1) The output oltage s proportonal to the ntegral of the nput oltage when the ntal capactor oltage s dscharged. Ths crcut s an nertng ntegrator snce the proportonalty constant (1/) s negate. Ths constant has the unts of sec 1 so that both sdes of Equaton (1) hae unts of olts. Interchangng the resstor and the capactor n Fgure 1(a) produces the op-amp dfferentator n Fgure 1(b). To dere the nput-output characterstc of ths crcut, wrte KL as before at the nertng node : (t) (t) = (t) (11) Then, use the deal op-amp equatons (t) = (1) (t) = P (t) = (13) together wth the fact that (t) = (t) (t) = (t) P (t) = (t) (14) and rewrte KL as o(t) = (15) Solng ths equaton for o (t) produces the crcut nput-output relatonshp o (t) = (16)
3 The output oltage s proportonal to the derate of the nput oltage. Ths crcut s called an nertng dfferentator snce the proportonalty constant () s negate. Ths constant has unts of sec so that both sdes of the equaton hae unts of olts. 1% 63.% (t)/ ss τ τ 3τ 4τ t Fgure : Tme esponse of a Frst-Order Lnear Dfferental Equaton The soluton of the followng lnear frst-order equaton n a arable (t), s gen by = a(t) b, () = (17) (t) = b a ( 1 e at) = ss (1 e t/τ ) (18) where ss = b/a s the fnal steady state of the quantty (t) and τ = 1/a s the tme constant. The soluton x(t) gen by Equaton (18) can be erfed by drect substtuton nto Equaton (17). As shown n Fgure, the tme constant τ s the tme that t takes the arable x(t) to reach approxmately 63.% of ts fnal steady state alue ss. ote also that the ntal slope at tme t = s equal to t= = b so that a new arable followng ths tangent lne would reach the fnal steady state ss n a tme ss = bt 1 = b a = t 1 = 1 a = τ () It can easly be erfed that the crcut n Fgure 3 yelds the followng nput-output relatonshp: (t) = 1 t [ ( V dc 1 ) ( ) ] 4 (t), () = (1) Dfferentatng ths ntegral equaton wth respect to tme yelds = 1 [ ( V dc 1 ) ( ) ] 4 (t), () = () (19) 3
4 1 5 V dc 3 4 (t) Fgure 3: Integratng Op-Amp rcut = 1 ( 1 ) ( ) (t) 1 5 ( 1 ) V dc, () = (3) Identfyng ths last equaton wth Equaton (17), we get ( 1 a = 1 ) ( ) ( ) 4 1 b = V dc 5 1 (4) (5) 3 Equpment Aglent DSO514A Dgtal Storage Osclloscope Aglent 33A Functon/Arbtrary Waeform Generator Fluke 115 True MS Multmeter Assorted resstors and capactors. 4
5 4 Procedure 1k 1n 1k 1k 1 Vdc 1k 1k (t) Fgure 4: Integratng Op-Amp Test rcut Smulaton of a Frst-Order Lnear Dfferental Equaton 1. Buld the crcut of Fgure 4 on your protoboard. (Assume that the large resstor 6 s nfnte.) Use precson resstors and try to match the capactor as close to 1 nf as possble by measurement.. Apply a 1-Hz, 1-V peak-to-peak square wae wth.5-v offset and 5% duty cycle to the nput of the ntegratng op-amp. Make sure the functon generator s set on HIGH Z. Obsere the nput square waeform 1 (t) on hannel 1 and the output waeform (t) on hannel of the scope. Does the output resemble the theoretcal soluton gen by Equaton (18)? 3. Usng the cursors, measure the response alues of the output waeform at tme alues of τ, τ, 3τ, and 4τ. 5 Data Analyss and Interpretaton 1. ompare the measured tme constant τ wth the predcted alue of τ = 5 and calculate the relate error between the two alues.. Gen that (t) = 1 e (t/τ), calculate the theoretcal alues of (t) at t = τ, τ, 3τ, 4τ. ompare these alues to the ones measured n the lab. 3. Draw a tangent lne to the output waeform at tme t = and erfy that ts crosses the steady state output at tme t = τ. 5
6 Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts Date: Data Sheet ecorded by: Equpment Lst Equpment Descrpton Aglent DSO514A Dgtal Storage Osclloscope Aglent 33A Functon/Arbtrary Waeform Generator HP/Aglent E3631A Trple Output Power Supply BSU Tag umber or Seral umber Smulaton of a Frst-Order Lnear Dfferental Equaton: τ τ 3τ 4τ t (ms) (t) (V).63 apactance Measurement: = nf.
Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab
Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts 1 Objectes The objectes of ths laboratory experment
More informationEE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING
EE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING TaChang Chen Unersty of Washngton, Bothell Sprng 2010 EE215 1 WEEK 8 FIRST ORDER CIRCUIT RESPONSE May 21 st, 2010 EE215 2 1 QUESTIONS TO ANSWER Frst order crcuts
More informationEnergy Storage Elements: Capacitors and Inductors
CHAPTER 6 Energy Storage Elements: Capactors and Inductors To ths pont n our study of electronc crcuts, tme has not been mportant. The analyss and desgns we hae performed so far hae been statc, and all
More informationCHAPTER 13. Exercises. E13.1 The emitter current is given by the Shockley equation:
HPT 3 xercses 3. The emtter current s gen by the Shockley equaton: S exp VT For operaton wth, we hae exp >> S >>, and we can wrte VT S exp VT Solng for, we hae 3. 0 6ln 78.4 mv 0 0.784 5 4.86 V VT ln 4
More informationElectrical Engineering Department Network Lab.
Electrcal Engneerng Department Network Lab. Objecte: - Experment on -port Network: Negate Impedance Conerter To fnd the frequency response of a smple Negate Impedance Conerter Theory: Negate Impedance
More informationELG 2135 ELECTRONICS I SECOND CHAPTER: OPERATIONAL AMPLIFIERS
ELG 35 ELECTONICS I SECOND CHAPTE: OPEATIONAL AMPLIFIES Sesson Wnter 003 Dr. M. YAGOUB Second Chapter: Operatonal amplfers II - _ After reewng the basc aspects of amplfers, we wll ntroduce a crcut representng
More informationCopyright 2004 by Oxford University Press, Inc.
JT as an Amplfer &a Swtch, Large Sgnal Operaton, Graphcal Analyss, JT at D, asng JT, Small Sgnal Operaton Model, Hybrd P-Model, TModel. Lecture # 7 1 Drecton of urrent Flow & Operaton for Amplfer Applcaton
More informationCOLLEGE OF ENGINEERING PUTRAJAYA CAMPUS FINAL EXAMINATION SPECIAL SEMESTER 2013 / 2014
OLLEGE OF ENGNEENG PUTAJAYA AMPUS FNAL EXAMNATON SPEAL SEMESTE 03 / 04 POGAMME SUBJET ODE SUBJET : Bachelor of Electrcal & Electroncs Engneerng (Honours) Bachelor of Electrcal Power Engneerng (Honours)
More informationWeek 11: Differential Amplifiers
ELE 0A Electronc rcuts Week : Dfferental Amplfers Lecture - Large sgnal analyss Topcs to coer A analyss Half-crcut analyss eadng Assgnment: hap 5.-5.8 of Jaeger and Blalock or hap 7. - 7.3, of Sedra and
More informationElectrical Circuits II (ECE233b)
Electrcal Crcuts (ECE33b SteadyState Power Analyss Anests Dounas The Unersty of Western Ontaro Faculty of Engneerng Scence SteadyState Power Analyss (t AC crcut: The steady state oltage and current can
More informationI. INTRODUCTION. There are two other circuit elements that we will use and are special cases of the above elements. They are:
I. INTRODUCTION 1.1 Crcut Theory Fundamentals In ths course we study crcuts wth non-lnear elements or deces (dodes and transstors). We wll use crcut theory tools to analyze these crcuts. Snce some of tools
More informationMAE140 - Linear Circuits - Winter 16 Final, March 16, 2016
ME140 - Lnear rcuts - Wnter 16 Fnal, March 16, 2016 Instructons () The exam s open book. You may use your class notes and textbook. You may use a hand calculator wth no communcaton capabltes. () You have
More informationV V. This calculation is repeated now for each current I.
Page1 Page2 The power supply oltage V = +5 olts and the load resstor R = 1 k. For the range of collector bas currents, I = 0.5 ma, 1 ma, 2.5 ma, 4 ma and 4.5 ma, determne the correspondng collector-to-emtter
More informationChapter 9 Complete Response of Circuits with Two Storage Elements
hapter 9 omplete Response of rcuts wth Two Storage Elements In hapter 8, we had rreducble storage element and a frst order crcut. In hapter 9, we wll hae rreducble storage elements and therefore, a second
More informationLinearity. If kx is applied to the element, the output must be ky. kx ky. 2. additivity property. x 1 y 1, x 2 y 2
Lnearty An element s sad to be lnear f t satsfes homogenety (scalng) property and addte (superposton) property. 1. homogenety property Let x be the nput and y be the output of an element. x y If kx s appled
More informationI. INTRODUCTION. 1.1 Circuit Theory Fundamentals
I. INTRODUCTION 1.1 Crcut Theory Fundamentals Crcut theory s an approxmaton to Maxwell s electromagnetc equatons n order to smplfy analyss of complcated crcuts. A crcut s made of seeral elements (boxes
More informationEE C245 ME C218 Introduction to MEMS Design
EE C45 ME C8 Introducton to MEM Desgn Fall 7 Prof. Clark T.C. Nguyen Dept. of Electrcal Engneerng & Computer cences Unersty of Calforna at Berkeley Berkeley, C 947 Dscusson: eew of Op mps EE C45: Introducton
More informationComplex Numbers, Signals, and Circuits
Complex Numbers, Sgnals, and Crcuts 3 August, 009 Complex Numbers: a Revew Suppose we have a complex number z = x jy. To convert to polar form, we need to know the magntude of z and the phase of z. z =
More informationFE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)( ) 8/25/2010
FE REVEW OPERATONAL AMPLFERS (OP-AMPS)( ) 1 The Op-amp 2 An op-amp has two nputs and one output. Note the op-amp below. The termnal labeled l wth the (-) sgn s the nvertng nput and the nput labeled wth
More informationDiode. Current HmAL Voltage HVL Simplified equivalent circuit. V γ. Reverse bias. Forward bias. Designation: Symbol:
Dode Materal: Desgnaton: Symbol: Poste Current flow: ptype ntype Anode Cathode Smplfed equalent crcut Ideal dode Current HmAL 0 8 6 4 2 Smplfed model 0.5.5 2 V γ eal dode Voltage HVL V γ closed open V
More informationLecture 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 informationSelected Student Solutions for Chapter 2
/3/003 Assessment Prolems Selected Student Solutons for Chapter. Frst note that we know the current through all elements n the crcut except the 6 kw resstor (the current n the three elements to the left
More information( ) ( ) ( ) ( ) ( ) 1 2. ELEC 201 Electric Circuit Analysis I Lecture 8(a) RL and RC Circuits: Single Switch 11/9/2017. Driven RL Circuit: Equation
/9/7 Dren rcut: Equaton EE Electrc rcut Analyss I ecture 8(a) an rcuts: Sngle Swtch THE ITADE, THE MIITAY OEGE OF SOUTH AOINA All sles an content 7 Moultre courtesy Street, of harleston, Dr. Gregory S
More informationTUTORIAL PROBLEMS. E.1 KCL, KVL, Power and Energy. Q.1 Determine the current i in the following circuit. All units in VAΩ,,
196 E TUTORIAL PROBLEMS E.1 KCL, KVL, Power and Energy Q.1 Determne the current n the followng crcut. 3 5 3 8 9 6 5 Appendx E Tutoral Problems 197 Q. Determne the current and the oltage n the followng
More information(b) i(t) for t 0. (c) υ 1 (t) and υ 2 (t) for t 0. Solution: υ 2 (0 ) = I 0 R 1 = = 10 V. υ 1 (0 ) = 0. (Given).
Problem 5.37 Pror to t =, capactor C 1 n the crcut of Fg. P5.37 was uncharged. For I = 5 ma, R 1 = 2 kω, = 5 kω, C 1 = 3 µf, and C 2 = 6 µf, determne: (a) The equvalent crcut nvolvng the capactors for
More informationEE 2006 Electric Circuit Analysis Spring January 23, 2015 Lecture 02
EE 2006 Electrc Crcut Analyss Sprng 2015 January 23, 2015 Lecture 02 1 Lab 1 Dgtal Multmeter Lab nstructons Aalable onlne Prnt out and read before Lab MWAH 391, 4:00 7:00 pm, next Monday or Wednesday (January
More informationNote 10. Modeling and Simulation of Dynamic Systems
Lecture Notes of ME 475: Introducton to Mechatroncs Note 0 Modelng and Smulaton of Dynamc Systems Department of Mechancal Engneerng, Unversty Of Saskatchewan, 57 Campus Drve, Saskatoon, SK S7N 5A9, Canada
More informationElectrical Circuits 2.1 INTRODUCTION CHAPTER
CHAPTE Electrcal Crcuts. INTODUCTION In ths chapter, we brefly revew the three types of basc passve electrcal elements: resstor, nductor and capactor. esstance Elements: Ohm s Law: The voltage drop across
More informationGraphical Analysis of a BJT Amplifier
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 1/18 Graphcal Analyss of a BJT Amplfer onsder agan ths smple BJT amplfer: ( t) = + ( t) O O o B + We note that for ths amplfer, the output oltage s
More informationG = G 1 + G 2 + G 3 G 2 +G 3 G1 G2 G3. Network (a) Network (b) Network (c) Network (d)
Massachusetts Insttute of Technology Department of Electrcal Engneerng and Computer Scence 6.002 í Electronc Crcuts Homework 2 Soluton Handout F98023 Exercse 21: Determne the conductance of each network
More information( ) = ( ) + ( 0) ) ( )
EETOMAGNETI OMPATIBIITY HANDBOOK 1 hapter 9: Transent Behavor n the Tme Doman 9.1 Desgn a crcut usng reasonable values for the components that s capable of provdng a tme delay of 100 ms to a dgtal sgnal.
More informationEE 2006 Electric Circuit Analysis Fall September 04, 2014 Lecture 02
EE 2006 Electrc Crcut Analyss Fall 2014 September 04, 2014 Lecture 02 1 For Your Informaton Course Webpage http://www.d.umn.edu/~jngba/electrc_crcut_analyss_(ee_2006).html You can fnd on the webpage: Lecture:
More information6.01: Introduction to EECS I Lecture 7 March 15, 2011
6.0: Introducton to EECS I Lecture 7 March 5, 20 6.0: Introducton to EECS I Crcuts The Crcut Abstracton Crcuts represent systems as connectons of elements through whch currents (through arables) flow and
More informationECE 320 Energy Conversion and Power Electronics Dr. Tim Hogan. Chapter 1: Introduction and Three Phase Power
ECE 3 Energy Conerson and Power Electroncs Dr. Tm Hogan Chapter : ntroducton and Three Phase Power. eew of Basc Crcut Analyss Defntons: Node - Electrcal juncton between two or more deces. Loop - Closed
More informationDriving your LED s. LED Driver. The question then is: how do we use this square wave to turn on and turn off the LED?
0//00 rng your LE.doc / rng your LE s As we hae preously learned, n optcal communcaton crcuts, a dgtal sgnal wth a frequency n the tens or hundreds of khz s used to ampltude modulate (on and off) the emssons
More information55:041 Electronic Circuits
55:04 Electronc Crcuts Feedback & Stablty Sectons of Chapter 2. Kruger Feedback & Stablty Confguraton of Feedback mplfer Negate feedback β s the feedback transfer functon S o S S o o S S o f S S S S fb
More informationLecture #4 Capacitors and Inductors Energy Stored in C and L Equivalent Circuits Thevenin Norton
EES ntro. electroncs for S Sprng 003 Lecture : 0/03/03 A.R. Neureuther Verson Date 0/0/03 EES ntroducton to Electroncs for omputer Scence Andrew R. Neureuther Lecture # apactors and nductors Energy Stored
More informationCHAPTER 8 COMPLETE RESPONSE OF RC & RL CIRCUITS
HAPTER 8 OMPETE RESPONSE OF R & R IRUITS The order of the crcut s defned by the number of rreducble storage elements n the crcut. In ths chapter, we wll fnd the complete response of a frst-order crcut;
More informationI = α I I. Bipolar Junction Transistors (BJTs) 2.15 The Emitter-Coupled Pair. By using KVL: V
Bpolar Juncton ransstors (BJs).5 he Emtter-oupled Par By usng KL: + + 0 Wth the transstors based n the forward-acte mode, the reerse saturaton current of the collector-base juncton s neglgble. / α F ES
More information6.01: Introduction to EECS 1 Week 6 October 15, 2009
6.0: ntroducton to EECS Week 6 October 5, 2009 6.0: ntroducton to EECS Crcuts The Crcut Abstracton Crcuts represent systems as connectons of component through whch currents (through arables) flow and across
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erckson Department of Electrcal, Computer, and Energy Engneerng Unersty of Colorado, Boulder 3.5. Example: ncluson of semconductor conducton losses n the boost conerter model Boost conerter example
More informationELCT 503: Semiconductors. Fall 2014
EL503 Semconductors Fall 2014 Lecture 09: BJ rcut Analyss Dr. Hassan Mostafa د. حسن مصطفى hmostafa@aucegypt.edu EL 503: Semconductors ntroducton npn transstor pnp transstor EL 503: Semconductors ntroducton
More informationChapter 6 Electrical Systems and Electromechanical Systems
ME 43 Systems Dynamcs & Control Chapter 6: Electrcal Systems and Electromechancal Systems Chapter 6 Electrcal Systems and Electromechancal Systems 6. INTODUCTION A. Bazoune The majorty of engneerng systems
More informationAdvanced Circuits Topics - Part 1 by Dr. Colton (Fall 2017)
Advanced rcuts Topcs - Part by Dr. olton (Fall 07) Part : Some thngs you should already know from Physcs 0 and 45 These are all thngs that you should have learned n Physcs 0 and/or 45. Ths secton s organzed
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationPHYSICS - CLUTCH CH 28: INDUCTION AND INDUCTANCE.
!! www.clutchprep.com CONCEPT: ELECTROMAGNETIC INDUCTION A col of wre wth a VOLTAGE across each end wll have a current n t - Wre doesn t HAVE to have voltage source, voltage can be INDUCED V Common ways
More informationbetween standard Gibbs free energies of formation for products and reactants, ΔG! R = ν i ΔG f,i, we
hermodynamcs, Statstcal hermodynamcs, and Knetcs 4 th Edton,. Engel & P. ed Ch. 6 Part Answers to Selected Problems Q6.. Q6.4. If ξ =0. mole at equlbrum, the reacton s not ery far along. hus, there would
More informationCoupling Element and Coupled circuits. Coupled inductor Ideal transformer Controlled sources
Couplng Element and Coupled crcuts Coupled nductor Ideal transformer Controlled sources Couplng Element and Coupled crcuts Coupled elements hae more that one branch and branch oltages or branch currents
More information55:041 Electronic Circuits
55:04 Electronc Crcuts Feedback & Stablty Sectons of Chapter 2. Kruger Feedback & Stablty Confguraton of Feedback mplfer S o S ε S o ( S β S ) o Negate feedback S S o + β β s the feedback transfer functon
More informationINDUCTANCE. RC Cicuits vs LR Circuits
INDUTANE R cuts vs LR rcuts R rcut hargng (battery s connected): (1/ )q + (R)dq/ dt LR rcut = (R) + (L)d/ dt q = e -t/ R ) = / R(1 - e -(R/ L)t ) q ncreases from 0 to = dq/ dt decreases from / R to 0 Dschargng
More informationThe Decibel and its Usage
The Decbel and ts Usage Consder a two-stage amlfer system, as shown n Fg.. Each amlfer rodes an ncrease of the sgnal ower. Ths effect s referred to as the ower gan,, of the amlfer. Ths means that the sgnal
More informationFormulation of Circuit Equations
ECE 570 Sesson 2 IC 752E Computer Aded Engneerng for Integrated Crcuts Formulaton of Crcut Equatons Bascs of crcut modelng 1. Notaton 2. Crcut elements 3. Krchoff laws 4. ableau formulaton 5. Modfed nodal
More informationPHYSICS - CLUTCH 1E CH 28: INDUCTION AND INDUCTANCE.
!! www.clutchprep.com CONCEPT: ELECTROMAGNETIC INDUCTION A col of wre wth a VOLTAGE across each end wll have a current n t - Wre doesn t HAVE to have voltage source, voltage can be INDUCED V Common ways
More informationAnnouncements. Lecture #2
Announcements Lectures wll be n 4 LeConte begnnng Frday 8/29 Addtonal dscusson TA Denns Chang (Sectons 101, 105) Offce hours: Mo 2-3 PM; Th 5-6 PM Lab sectons begn Tuesday 9/2 Read Experment #1 onlne Download
More informationTransfer Characteristic
Eeld-Effect Transstors (FETs 3.3 The CMS Common-Source Amplfer Transfer Characterstc Electronc Crcuts, Dept. of Elec. Eng., The Chnese Unersty of Hong Kong, Prof. K.-L. Wu Lesson 8&9 Eeld-Effect Transstors
More information55:141 Advanced Circuit Techniques Two-Port Theory
55:4 Adanced Crcut Technques Two-Port Theory Materal: Lecture Notes A. Kruger 55:4: Adanced Crcut Technques The Unersty of Iowa, 03 Two-Port Theory, Slde What Are Two-Ports? Basc dea: replace a complex
More informationHow Differential Equations Arise. Newton s Second Law of Motion
page 1 CHAPTER 1 Frst-Order Dfferental Equatons Among all of the mathematcal dscplnes the theory of dfferental equatons s the most mportant. It furnshes the explanaton of all those elementary manfestatons
More informationCollege of Engineering Department of Electronics and Communication Engineering. Test 1 With Model Answer
Name: Student D Number: Secton Number: 01/0/03/04 A/B Lecturer: Dr Jamaludn/ Dr Jehana Ermy/ Dr Azn Wat Table Number: College of Engneerng Department of Electroncs and Communcaton Engneerng Test 1 Wth
More informationS-Domain Analysis. s-domain Circuit Analysis. EE695K VLSI Interconnect. Time domain (t domain) Complex frequency domain (s domain) Laplace Transform L
EE695K S nterconnect S-Doman naly -Doman rcut naly Tme doman t doman near rcut aplace Tranform omplex frequency doman doman Tranformed rcut Dfferental equaton lacal technque epone waveform aplace Tranform
More informationVI. Transistor Amplifiers
VI. Transstor Amplfers 6. Introducton In ths secton we wll use the transstor small-sgnal model to analyze and desgn transstor amplfers. There are two ssues that we need to dscuss frst: ) What are the mportant
More informationComputer-Aided Circuit Simulation and Verification. CSE245 Fall 2004 Professor:Chung-Kuan Cheng
Computer-Aded Crcut Smulaton and Verfcaton CSE245 Fall 24 Professor:Chung-Kuan Cheng Admnstraton Lectures: 5:pm ~ 6:2pm TTH HSS 252 Offce Hours: 4:pm ~ 4:45pm TTH APM 4256 Textbook Electronc Crcut and
More informationKIRCHHOFF CURRENT LAW
KRCHHOFF CURRENT LAW ONE OF THE FUNDAMENTAL CONSERATON PRNCPLES N ELECTRCAL ENGNEERNG CHARGE CANNOT BE CREATED NOR DESTROYED NODES, BRANCHES, LOOPS A NODE CONNECTS SEERAL COMPONENTS. BUT T DOES NOT HOLD
More informationDO NOT DO HOMEWORK UNTIL IT IS ASSIGNED. THE ASSIGNMENTS MAY CHANGE UNTIL ANNOUNCED.
EE 539 Homeworks Sprng 08 Updated: Tuesday, Aprl 7, 08 DO NOT DO HOMEWORK UNTIL IT IS ASSIGNED. THE ASSIGNMENTS MAY CHANGE UNTIL ANNOUNCED. For full credt, show all work. Some problems requre hand calculatons.
More informationMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science Circuits and Electronics Spring 2001
Massachusetts Insttute of Technology Department of Electrcal Engneerng and Computer Scence Read Chapters 11 through 12. 6.002 Crcuts and Electroncs Sprng 2001 Homework #5 Handout S01031 Issued: 3/8/2001
More informationCollege of Engineering Department of Electronics and Communication Engineering. Test 2
Name: Student D Number: Secton Number: 01/0/03/04 A/B Lecturer: Dr Jamaludn/ Dr Azn Wat/ Dr Jehana Ermy/ Prof Md Zan Table Number: ollege of Engneerng Department of Electroncs and ommuncaton Engneerng
More informationSection 8.3 Polar Form of Complex Numbers
80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the
More informationMAE140 - Linear Circuits - Fall 13 Midterm, October 31
Instructons ME140 - Lnear Crcuts - Fall 13 Mdterm, October 31 () Ths exam s open book. You may use whatever wrtten materals you choose, ncludng your class notes and textbook. You may use a hand calculator
More informationNumerical Transient Heat Conduction Experiment
Numercal ransent Heat Conducton Experment OBJECIVE 1. o demonstrate the basc prncples of conducton heat transfer.. o show how the thermal conductvty of a sold can be measured. 3. o demonstrate the use
More information55:141 Advanced Circuit Techniques Two-Port Theory
55:4 Adanced Crcut Technques Two-Port Theory Materal: Lecture Notes A. Kruger 55:4: Adanced Crcut Technques The Unersty of Iowa, 205 Two-Port Theory, Slde Two-Port Networks Note, the BJT s all are hghly
More informationGravitational Acceleration: A case of constant acceleration (approx. 2 hr.) (6/7/11)
Gravtatonal Acceleraton: A case of constant acceleraton (approx. hr.) (6/7/11) Introducton The gravtatonal force s one of the fundamental forces of nature. Under the nfluence of ths force all objects havng
More informationUNIVERSITY OF UTAH ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT. 10k. 3mH. 10k. Only one current in the branch:
UNIERSITY OF UTH ELECTRICL & COMPUTER ENGINEERING DEPRTMENT ECE 70 HOMEWORK #6 Soluton Summer 009. fter beng closed a long tme, the swtch opens at t = 0. Fnd (t) for t > 0. t = 0 0kΩ 0kΩ 3mH Step : (Redraw
More informationSemistate Theory and Design of Analog VLSI Circuits
Semstate Theory and Desgn of Analog VLSI Crcuts Roert W. Newcom Electrcal and Computer Engneerng Department Unersty of Maryland, College Park, MD 74 USA URL: http://www.ece.umd.edu/~newcom/msla.html emal:
More informationDC Circuits. Crossing the emf in this direction +ΔV
DC Crcuts Delverng a steady flow of electrc charge to a crcut requres an emf devce such as a battery, solar cell or electrc generator for example. mf stands for electromotve force, but an emf devce transforms
More informationChapter 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 informationPhysics 1202: Lecture 11 Today s Agenda
Physcs 122: Lecture 11 Today s Agenda Announcements: Team problems start ths Thursday Team 1: Hend Ouda, Mke Glnsk, Stephane Auger Team 2: Analese Bruder, Krsten Dean, Alson Smth Offce hours: Monday 2:3-3:3
More informationLesson 16: Basic Control Modes
0/8/05 Lesson 6: Basc Control Modes ET 438a Automatc Control Systems Technology lesson6et438a.tx Learnng Objectves Ater ths resentaton you wll be able to: Descrbe the common control modes used n analog
More informationLab 2e Thermal System Response and Effective Heat Transfer Coefficient
58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),
More information4.1 The Ideal Diode. Reading Assignment: pp Before we get started with ideal diodes, let s first recall linear device behavior!
1/25/2012 secton3_1the_ideal_ode 1/2 4.1 The Ideal ode Readng Assgnment: pp.165-172 Before we get started wth deal dodes, let s frst recall lnear dece behaor! HO: LINEAR EVICE BEHAVIOR Now, the deal dode
More informationCircuit Variables. Unit: volt (V = J/C)
Crcut Varables Scentfc nestgaton of statc electrcty was done n late 700 s and Coulomb s credted wth most of the dscoeres. He found that electrc charges hae two attrbutes: amount and polarty. There are
More information3.2 Terminal Characteristics of Junction Diodes (pp )
/9/008 secton3_termnal_characterstcs_of_juncton_odes.doc /6 3. Termnal Characterstcs of Juncton odes (pp.47-53) A Juncton ode I.E., A real dode! Smlar to an deal dode, ts crcut symbol s: HO: The Juncton
More informationPhysics 4B. Question and 3 tie (clockwise), then 2 and 5 tie (zero), then 4 and 6 tie (counterclockwise) B i. ( T / s) = 1.74 V.
Physcs 4 Solutons to Chapter 3 HW Chapter 3: Questons:, 4, 1 Problems:, 15, 19, 7, 33, 41, 45, 54, 65 Queston 3-1 and 3 te (clockwse), then and 5 te (zero), then 4 and 6 te (counterclockwse) Queston 3-4
More informationi I (I + i) 3/27/2006 Circuits ( F.Robilliard) 1
4V I 2V (I + ) 0 0 --- 3V 1 2 4Ω 6Ω 3Ω 3/27/2006 Crcuts ( F.obllard) 1 Introducton: Electrcal crcuts are ubqutous n the modern world, and t s dffcult to oerstate ther mportance. They range from smple drect
More informationMAE140 - Linear Circuits - Winter 16 Midterm, February 5
Instructons ME140 - Lnear Crcuts - Wnter 16 Mdterm, February 5 () Ths exam s open book. You may use whatever wrtten materals you choose, ncludng your class notes and textbook. You may use a hand calculator
More informationRevision: December 13, E Main Suite D Pullman, WA (509) Voice and Fax
.9.1: AC power analyss Reson: Deceber 13, 010 15 E Man Sute D Pullan, WA 99163 (509 334 6306 Voce and Fax Oerew n chapter.9.0, we ntroduced soe basc quanttes relate to delery of power usng snusodal sgnals.
More informationMAE140 Linear Circuits (for non-electrical engs)
MAE4 Lnear Crcuts (for non-electrcal engs) Topcs coered Crcut analyss technques Krchoff s Laws KVL, KCL Nodal and Mesh Analyss Théenn and Norton Equalent Crcuts Resste crcuts, RLC crcuts Steady-state and
More informationModule B3 3.1 Sinusoidal steady-state analysis (single-phase), a review 3.2 Three-phase analysis. Kirtley
Module B3 3.1 Snusodal steady-state analyss (sngle-phase), a reew 3. hree-phase analyss Krtley Chapter : AC oltage, Current and Power.1 Sources and Power. Resstors, Inductors, and Capactors Chapter 4:
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationCOLLEGE OF ENGINEERING PUTRAJAYA CAMPUS FINAL EXAMINATION SEMESTER / 2014
OLLEGE OF ENGNEERNG PUTRAJAYA AMPUS FNAL EXAMNATON SEMESTER 013 / 014 PROGRAMME SUBJET ODE SUBJET : Bachelor of Electrcal & Electrocs Egeerg (Hoours) Bachelor of Electrcal Power Egeerg (Hoours) : EEEB73
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationCircuits II EE221. Instructor: Kevin D. Donohue. Instantaneous, Average, RMS, and Apparent Power, and, Maximum Power Transfer, and Power Factors
Crcuts II EE1 Unt 3 Instructor: Ken D. Donohue Instantaneous, Aerage, RMS, and Apparent Power, and, Maxmum Power pp ransfer, and Power Factors Power Defntons/Unts: Work s n unts of newton-meters or joules
More informationPhysics Courseware Electronics
Physcs ourseware Electroncs ommon emtter amplfer Problem 1.- In the followg ommon Emtter mplfer calculate: a) The Q pot, whch s the D base current (I ), the D collector current (I ) and the voltage collector
More informationMAE140 - Linear Circuits - Fall 10 Midterm, October 28
M140 - Lnear rcuts - Fall 10 Mdterm, October 28 nstructons () Ths exam s open book. You may use whatever wrtten materals you choose, ncludng your class notes and textbook. You may use a hand calculator
More informationOn the Throughput of Clustered Photolithography Tools:
On the hroughput of lustered Photolthography ools: Wafer Advancement and Intrnsc Equpment Loss Maruth Kumar Mutnur James R. Morrson, Ph.D. September 23, 2007 Presentaton Outlne Motvaton Model : Synchronous
More informationELE B7 Power Systems Engineering. Power Flow- Introduction
ELE B7 Power Systems Engneerng Power Flow- Introducton Introducton to Load Flow Analyss The power flow s the backbone of the power system operaton, analyss and desgn. It s necessary for plannng, operaton,
More informationDifference Equations
Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1
More information(8) Gain Stage and Simple Output Stage
EEEB23 Electoncs Analyss & Desgn (8) Gan Stage and Smple Output Stage Leanng Outcome Able to: Analyze an example of a gan stage and output stage of a multstage amplfe. efeence: Neamen, Chapte 11 8.0) ntoducton
More informationDigital Signal Processing
Dgtal Sgnal Processng Dscrete-tme System Analyss Manar Mohasen Offce: F8 Emal: manar.subh@ut.ac.r School of IT Engneerng Revew of Precedent Class Contnuous Sgnal The value of the sgnal s avalable over
More informationScroll Generation with Inductorless Chua s Circuit and Wien Bridge Oscillator
Latest Trends on Crcuts, Systems and Sgnals Scroll Generaton wth Inductorless Chua s Crcut and Wen Brdge Oscllator Watcharn Jantanate, Peter A. Chayasena, and Sarawut Sutorn * Abstract An nductorless Chua
More informationFEEDBACK 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 informationPressure Measurements Laboratory
Lab # Pressure Measurements Laboratory Objectves:. To get hands-on experences on how to make pressure (surface pressure, statc pressure and total pressure nsde flow) measurements usng conventonal pressuremeasurng
More information