Lecture 13 RC/RL Circuits, Time Dependent Op Amp Circuits
|
|
- Roxanne Dennis
- 6 years ago
- Views:
Transcription
1 Lecure 13 RC/RL Circuis, Time Dependen Op Amp Circuis
2 RL Circuis The seps involved in solving simple circuis conaining dc sources, resisances, and one energy-sorage elemen (inducance or capaciance) are:
3 1. Apply Kirchhoff s curren and volage laws o wrie he circui equaion.. If he equaion conains inegrals, differeniae each erm in he equaion o produce a pure differenial equaion. 3. Assume a soluion of he form K 1 K e s.
4 4. Subsiue he soluion ino he differenial equaion o deermine he values of K 1 and s. (Alernaively, we can deermine K 1 by solving he circui in seady sae) 5. Use he iniial condiions o deermine he value of K. 6. Wrie he final soluion.
5 RL Transien Analysis Find i( and he volage v( i( 0 for < 0 since he swich is open prior o 0 Apply KVL around he loop: V S i( R v( 0
6 RL Transien Analysis V S i( R v( 0 di( i( R L d V S
7 RL Transien Analysis di( i ( R L d V S Try i( K1 Ke s di( i ( R L d V S Try i( K1 Ke s RK 1 ( RK slk ) e V S s RK V K VS R 100V 50Ω 1 S 1 A RK slk 0 s L R
8 RL Transien Analysis L R e K i / ) ( 0 ) 0 ( 0 K K e K i L R e i / ) (
9 RL Transien Analysis Define τ L R i( e /τ
10 RL Transien Analysis v( V S i( R i( ( e ) 100e /τ /τ
11 RL Transien Analysis Transien sars by opening swich Prior o 0 inducor acs as a shor circui so ha: v( 0 for < 0 i( V S /R 1 for < 0
12 RL Transien Analysis Afer 0 curren circulaes hrough L and R, dissipaing energy in he resisance R / / / / 0 ) ( 0 ) ( 0 ) ( ) ( R L Ke L R RKe Ke L for Ke i R i d di L > τ τ τ τ τ τ τ
13 1 0 1 ) (0 R V K Ke R V i S S 0 ) ( / 1 > for e R V i S τ RL Transien Analysis
14 RL Transien Analysis 0 0 ) ( 0 ) ( ) ( / 1 / 1 < > for v for e R LV e R V d d L d di L v s S τ τ τ
15 RL Transien Analysis wih a Curren Source Afer he swich is opened, i R (0 ) A, I L (0 ) 0 Find v(, i R (, i L (
16 RL Transien Analysis wih a Curren Source Afer he swich is closed, i R (0 ) A, I L (0 ) 0 di ( v( L L 10iR ( and i R( il ( A d di ( L 10 i L d ( ( ))
17 RL Transien Analysis wih a Curren Source di ( L 10 i L d ( ( )) di L d ( 5i ( L 10 Try i L ( K K e 1 s
18 RL Transien Analysis wih a Curren Source dil ( d Try i L 5i ( 10 ( i L (0 ) 0 K 1 -K L K1 Ke s ske ( s s 5) Ke 5( K Ke s s ) 10 5K 10 s 5
19 RL Transien Analysis wih a Curren Source A i L ( K Ke 5 In seady sae he inducor becomes a shor circui i L ( ) K A i L ( e 5
20 RL Transien Analysis wih a Curren Source L e e d d d di L v ) ( ) ( ) ( L R e e i i 5 5 ) ( ) ( ) (
21 RL Transien Analysis Prior o 0 i(0) 100V/100Ω 1A Find i(, v(
22 RL Transien Analysis Prior o 0 i(0) 100V/100Ω 1A di( Afer 0: L i( R 100V d di( 00i( 100 d
23 RL Transien Analysis di( d 00i( 100 ry i( K 1 K e s sk e s 00( K 1 K e s ) 100 (00 s) K e s 00K s 00, τ 1/ 00 5ms
24 RL Transien Analysis i(0) 1 K K 100V i( ) K1 00Ω i( e A K 0.5A
25 RL Transien Analysis v( L di( d d d ( e 00 ) 100e 00
26 RC and RL Circuis wih General Sources Firs order differenial equaion wih consan coefficiens di( L Ri( v ( d L di( v ( i( R d R dx( τ x( f ( d Forcing funcion
27 RC and RL Circuis wih General Sources The general soluion consiss of wo pars.
28 The paricular soluion (also called he forced response) is any expression ha saisfies he equaion. dx( τ d x( f ( In order o have a soluion ha saisfies he iniial condiions, we mus add he complemenary soluion o he paricular soluion.
29 The homogeneous equaion is obained by seing he forcing funcion o zero. dx( τ x( 0 d The complemenary soluion (also called he naural response) is obained by solving he homogeneous equaion.
30 Sep-by-Sep Soluion Circuis conaining a resisance, a source, and an inducance (or a capaciance) 1. Wrie he circui equaion and reduce i o a firs-order differenial equaion.
31 . Find a paricular soluion. The deails of his sep depend on he form of he forcing funcion. 3. Obain he complee soluion by adding he paricular soluion o he complemenary soluion x c Ke -/τ which conains he arbirary consan K. 4. Use iniial condiions o find he value of K.
32 Transien Analysis of an RC Circui wih a Sinusoidal Source Ri( Ri( q( sin(00 C 1 C i( vc (0) sin(00 0
33 Transien Analysis of an RC Circui wih a Sinusoidal Source Take he derivaive: di( 1 R i( 400 cos(00 d C di( RC i( 400C cos(00 d Try a paricular soluion : i ( Acos(00 p Bsin(00
34 Transien Analysis of an RC Circui wih a Sinusoidal Source 5x10 3 di( d i( 400x10 6 cos(00 Asin(00 B cos(00 Acos(00 Bsin(00 400x10 6 cos(00 equaing he coefficiens for sin erms : A B 0 A B equaing he coefficiens for cos erms : B A Solving 400x10 : 6 A 00x μA B 00x μA i p ( 00 cos(00 00sin(00
35 Transien Analysis of an RC Circui wih a Sinusoidal Source The complemenary soluion is given by: i c ( Ke / τ τ RC (5kΩ)(1μ F) 5ms The complee soluion is given by he sum of he paricular soluion and he complemenary soluion: i( 00 cos(00 00sin(00 Ke / τ μa
36 Transien Analysis of an RC Circui wih a Sinusoidal Source Iniial condiions: sin(0 ) 0 v C (0 ) 1V v R (0 ) v C (0) 0 v R (0 ) -1V i(0 ) v R /R -1V/5000Ω -00μA 00cos(0)00sin(0)Ke 0 00 K K -400μA
37 Transien Analysis of an RC Circui wih a Sinusoidal Source i( 00 cos(00 00sin(00 400e /τ μa
38 Transien Analysis of an RC Circui wih a Sinusoidal Source Wha happens if we replace he source wih cos(00 and he capacior iniially uncharged v c (0)0?
39 Transien Analysis of an RC Circui wih a Sinusoidal Source Wha happens if we replace he source wih cos(00 and he capacior iniially uncharged v c (0)0? q( Ri( cos(00 C 1 Ri( C i( vc (0) cos(00 0
40 Transien Analysis of an RC Circui wih a Sinusoidal Source Take he derivaive: di( 1 R i( 400sin(00 d C di( RC i( 400C sin(00 d Try a paricular soluion : i ( Acos(00 p Bsin(00
41 Transien Analysis of an RC Circui wih a Sinusoidal Source 5x10 3 di( d i( 400x10 6 sin(00 Asin(00 B cos(00 Acos(00 Bsin(00 400x10 6 sin(00 equaing he coefficiens for sin erms : A B 400x10 6 equaing he coefficiens for cos erms : B A 0 Solving : A 00x μA B 00x10 i p 6 00μA ( 00 cos(00 00sin(00
42 Transien Analysis of an RC Circui wih a Sinusoidal Source The complemenary soluion is given by: i c ( Ke / τ τ RC (5kΩ)(1μ F) 5ms The complee soluion is given by he sum of he paricular soluion and he complemenary soluion: i( 00 cos(00 00sin(00 Ke / τ μa
43 Transien Analysis of an RC Circui wih a Sinusoidal Source Iniial condiions: cos(0 ) v C (0 ) 0V v R (0 ) v C (0) v R (0 ) i(0 ) v R /R V/5000Ω 400μA 00cos(0)-00sin(0)Ke 0 00 K K 00μA
44 Transien Analysis of an RC Circui wih a Sinusoidal Source i( 00 cos(00 00sin(00 00e /τ μa
45 Transien Analysis of an RC Circui wih an Exponenial Source Wha happens if we replace he source wih 10e - and he capacior is iniially charged o v c (0)5? q( Ri( 10e C Ri( 1 C i( vc (0) 0 10e
46 Transien Analysis of an RC Circui wih an Exponenial Source Take he derivaive: di( 1 R i( 10e d C di( RC i( 10Ce d Try a paricular soluion : i p ( Ae
47 Transien Analysis of an RC Circui wih an Exponenial Source RCAe Ae A RCA 10C A(1 RC) 10C 10Ce A 10C RC 1 (10)(x ) 0μA
48 Transien Analysis of an RC Circui wih an Exponenial Source The complemenary soluion is given by: i c ( Ke / τ τ RC (1M Ω)(μF) s The complee soluion is given by he sum of he paricular soluion and he complemenary soluion: i( 0e Ke / μa
49 Transien Analysis of an RC Circui wih an Exponenial Source Iniial condiions: 10e 0 10 v C (0 ) 5V v R (0 ) v C (0) 10 v R (0 ) 5 i(0 ) v R /R 5V/1MΩ 5μA 0e 0 Ke 0 0 K K -15μA
50 Transien Analysis of an RC Circui wih an Exponenial Source i( 0e 15e / μ A
51 Inegraors and Differeniaors Inegraors produce oupu volages ha are proporional o he running ime inegral of he inpu volages. In a running ime inegral, he upper limi of inegraion is.
52 i in v o v in R v c v c 0 q C 1 C v v 1 RC 1 RC o 0 i in d c 0 0 v v in in d d
53 v o () 1 v ()d in RC 0
54 If R 10 kω, C 0.1μF RC 0.1 ms v o () 1000 v () d 0 in
55 v o () 1000 v in() 0 d d 5000 for 0 < < 1ms ms 5d 0 1ms 5d for 1ms < < 3ms
56 Differeniaor Circui i in dq d C dv d in 0 R v o v o RC dv d in
57 Differeniaor Circui v o () RC dv d in
8. Basic RL and RC Circuits
8. Basic L and C Circuis This chaper deals wih he soluions of he responses of L and C circuis The analysis of C and L circuis leads o a linear differenial equaion This chaper covers he following opics
More informationVoltage/current relationship Stored Energy. RL / RC circuits Steady State / Transient response Natural / Step response
Review Capaciors/Inducors Volage/curren relaionship Sored Energy s Order Circuis RL / RC circuis Seady Sae / Transien response Naural / Sep response EE4 Summer 5: Lecure 5 Insrucor: Ocavian Florescu Lecure
More informationChapter 7 Response of First-order RL and RC Circuits
Chaper 7 Response of Firs-order RL and RC Circuis 7.- The Naural Response of RL and RC Circuis 7.3 The Sep Response of RL and RC Circuis 7.4 A General Soluion for Sep and Naural Responses 7.5 Sequenial
More informationChapter 8 The Complete Response of RL and RC Circuits
Chaper 8 The Complee Response of RL and RC Circuis Seoul Naional Universiy Deparmen of Elecrical and Compuer Engineering Wha is Firs Order Circuis? Circuis ha conain only one inducor or only one capacior
More informationFirst Order RC and RL Transient Circuits
Firs Order R and RL Transien ircuis Objecives To inroduce he ransiens phenomena. To analyze sep and naural responses of firs order R circuis. To analyze sep and naural responses of firs order RL circuis.
More informationECE 2100 Circuit Analysis
ECE 1 Circui Analysis Lesson 35 Chaper 8: Second Order Circuis Daniel M. Liynski, Ph.D. ECE 1 Circui Analysis Lesson 3-34 Chaper 7: Firs Order Circuis (Naural response RC & RL circuis, Singulariy funcions,
More information(b) (a) (d) (c) (e) Figure 10-N1. (f) Solution:
Example: The inpu o each of he circuis shown in Figure 10-N1 is he volage source volage. The oupu of each circui is he curren i( ). Deermine he oupu of each of he circuis. (a) (b) (c) (d) (e) Figure 10-N1
More informationES 250 Practice Final Exam
ES 50 Pracice Final Exam. Given ha v 8 V, a Deermine he values of v o : 0 Ω, v o. V 0 Firs, v o 8. V 0 + 0 Nex, 8 40 40 0 40 0 400 400 ib i 0 40 + 40 + 40 40 40 + + ( ) 480 + 5 + 40 + 8 400 400( 0) 000
More informationDirect Current Circuits. February 19, 2014 Physics for Scientists & Engineers 2, Chapter 26 1
Direc Curren Circuis February 19, 2014 Physics for Scieniss & Engineers 2, Chaper 26 1 Ammeers and Volmeers! A device used o measure curren is called an ammeer! A device used o measure poenial difference
More informationHomework-8(1) P8.3-1, 3, 8, 10, 17, 21, 24, 28,29 P8.4-1, 2, 5
Homework-8() P8.3-, 3, 8, 0, 7, 2, 24, 28,29 P8.4-, 2, 5 Secion 8.3: The Response of a Firs Order Circui o a Consan Inpu P 8.3- The circui shown in Figure P 8.3- is a seady sae before he swich closes a
More informationECE 2100 Circuit Analysis
ECE 1 Circui Analysis Lesson 37 Chaper 8: Second Order Circuis Discuss Exam Daniel M. Liynski, Ph.D. Exam CH 1-4: On Exam 1; Basis for work CH 5: Operaional Amplifiers CH 6: Capaciors and Inducor CH 7-8:
More informationINDEX. Transient analysis 1 Initial Conditions 1
INDEX Secion Page Transien analysis 1 Iniial Condiions 1 Please inform me of your opinion of he relaive emphasis of he review maerial by simply making commens on his page and sending i o me a: Frank Mera
More information( ) = Q 0. ( ) R = R dq. ( t) = I t
ircuis onceps The addiion of a simple capacior o a circui of resisors allows wo relaed phenomena o occur The observaion ha he ime-dependence of a complex waveform is alered by he circui is referred o as
More information7. Capacitors and Inductors
7. Capaciors and Inducors 7. The Capacior The ideal capacior is a passive elemen wih circui symbol The curren-volage relaion is i=c dv where v and i saisfy he convenions for a passive elemen The capacior
More informationEEEB113 CIRCUIT ANALYSIS I
9/14/29 1 EEEB113 CICUIT ANALYSIS I Chaper 7 Firs-Order Circuis Maerials from Fundamenals of Elecric Circuis 4e, Alexander Sadiku, McGraw-Hill Companies, Inc. 2 Firs-Order Circuis -Chaper 7 7.2 The Source-Free
More informationCHAPTER 6: FIRST-ORDER CIRCUITS
EEE5: CI CUI T THEOY CHAPTE 6: FIST-ODE CICUITS 6. Inroducion This chaper considers L and C circuis. Applying he Kirshoff s law o C and L circuis produces differenial equaions. The differenial equaions
More informationSection 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
Secion 3.5 Nonhomogeneous Equaions; Mehod of Undeermined Coefficiens Key Terms/Ideas: Linear Differenial operaor Nonlinear operaor Second order homogeneous DE Second order nonhomogeneous DE Soluion o homogeneous
More informationEE202 Circuit Theory II , Spring. Dr. Yılmaz KALKAN & Dr. Atilla DÖNÜK
EE202 Circui Theory II 2018 2019, Spring Dr. Yılmaz KALKAN & Dr. Ailla DÖNÜK 1. Basic Conceps (Chaper 1 of Nilsson - 3 Hrs.) Inroducion, Curren and Volage, Power and Energy 2. Basic Laws (Chaper 2&3 of
More informationR.#W.#Erickson# Department#of#Electrical,#Computer,#and#Energy#Engineering# University#of#Colorado,#Boulder#
.#W.#Erickson# Deparmen#of#Elecrical,#Compuer,#and#Energy#Engineering# Universiy#of#Colorado,#Boulder# Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance,
More information( ) ( ) ( ) () () Signals And Systems Exam#1. 1. Given x(t) and y(t) below: x(t) y(t) (A) Give the expression of x(t) in terms of step functions.
Signals And Sysems Exam#. Given x() and y() below: x() y() 4 4 (A) Give he expression of x() in erms of sep funcions. (%) x () = q() q( ) + q( 4) (B) Plo x(.5). (%) x() g() = x( ) h() = g(. 5) = x(. 5)
More informationCHAPTER 12 DIRECT CURRENT CIRCUITS
CHAPTER 12 DIRECT CURRENT CIUITS DIRECT CURRENT CIUITS 257 12.1 RESISTORS IN SERIES AND IN PARALLEL When wo resisors are conneced ogeher as shown in Figure 12.1 we said ha hey are conneced in series. As
More informationBasic Circuit Elements Professor J R Lucas November 2001
Basic Circui Elemens - J ucas An elecrical circui is an inerconnecion of circui elemens. These circui elemens can be caegorised ino wo ypes, namely acive and passive elemens. Some Definiions/explanaions
More informationEECE251. Circuit Analysis I. Set 4: Capacitors, Inductors, and First-Order Linear Circuits
EEE25 ircui Analysis I Se 4: apaciors, Inducors, and Firs-Order inear ircuis Shahriar Mirabbasi Deparmen of Elecrical and ompuer Engineering Universiy of Briish olumbia shahriar@ece.ubc.ca Overview Passive
More informationInductor Energy Storage
School of Compuer Science and Elecrical Engineering 5/5/ nducor Energy Sorage Boh capaciors and inducors are energy sorage devices They do no dissipae energy like a resisor, bu sore and reurn i o he circui
More informationElectrical Circuits. 1. Circuit Laws. Tools Used in Lab 13 Series Circuits Damped Vibrations: Energy Van der Pol Circuit
V() R L C 513 Elecrical Circuis Tools Used in Lab 13 Series Circuis Damped Vibraions: Energy Van der Pol Circui A series circui wih an inducor, resisor, and capacior can be represened by Lq + Rq + 1, a
More informationUniversity of Cyprus Biomedical Imaging and Applied Optics. Appendix. DC Circuits Capacitors and Inductors AC Circuits Operational Amplifiers
Universiy of Cyprus Biomedical Imaging and Applied Opics Appendix DC Circuis Capaciors and Inducors AC Circuis Operaional Amplifiers Circui Elemens An elecrical circui consiss of circui elemens such as
More information2.9 Modeling: Electric Circuits
SE. 2.9 Modeling: Elecric ircuis 93 2.9 Modeling: Elecric ircuis Designing good models is a ask he compuer canno do. Hence seing up models has become an imporan ask in modern applied mahemaics. The bes
More information2.4 Cuk converter example
2.4 Cuk converer example C 1 Cuk converer, wih ideal swich i 1 i v 1 2 1 2 C 2 v 2 Cuk converer: pracical realizaion using MOSFET and diode C 1 i 1 i v 1 2 Q 1 D 1 C 2 v 2 28 Analysis sraegy This converer
More informationLab 10: RC, RL, and RLC Circuits
Lab 10: RC, RL, and RLC Circuis In his experimen, we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors. We will sudy he way volages and currens change in
More information( ) ( ) if t = t. It must satisfy the identity. So, bulkiness of the unit impulse (hyper)function is equal to 1. The defining characteristic is
UNIT IMPULSE RESPONSE, UNIT STEP RESPONSE, STABILITY. Uni impulse funcion (Dirac dela funcion, dela funcion) rigorously defined is no sricly a funcion, bu disribuion (or measure), precise reamen requires
More informationEE100 Lab 3 Experiment Guide: RC Circuits
I. Inroducion EE100 Lab 3 Experimen Guide: A. apaciors A capacior is a passive elecronic componen ha sores energy in he form of an elecrosaic field. The uni of capaciance is he farad (coulomb/vol). Pracical
More informationSignal and System (Chapter 3. Continuous-Time Systems)
Signal and Sysem (Chaper 3. Coninuous-Time Sysems) Prof. Kwang-Chun Ho kwangho@hansung.ac.kr Tel: 0-760-453 Fax:0-760-4435 1 Dep. Elecronics and Informaion Eng. 1 Nodes, Branches, Loops A nework wih b
More informationReading from Young & Freedman: For this topic, read sections 25.4 & 25.5, the introduction to chapter 26 and sections 26.1 to 26.2 & 26.4.
PHY1 Elecriciy Topic 7 (Lecures 1 & 11) Elecric Circuis n his opic, we will cover: 1) Elecromoive Force (EMF) ) Series and parallel resisor combinaions 3) Kirchhoff s rules for circuis 4) Time dependence
More informationChapter 2: Principles of steady-state converter analysis
Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer
More informationENGI 9420 Engineering Analysis Assignment 2 Solutions
ENGI 940 Engineering Analysis Assignmen Soluions 0 Fall [Second order ODEs, Laplace ransforms; Secions.0-.09]. Use Laplace ransforms o solve he iniial value problem [0] dy y, y( 0) 4 d + [This was Quesion
More informationPhysics 1502: Lecture 20 Today s Agenda
Physics 152: Lecure 2 Today s Agenda Announcemens: Chap.27 & 28 Homework 6: Friday nducion Faraday's Law ds N S v S N v 1 A Loop Moving Through a Magneic Field ε() =? F() =? Φ() =? Schemaic Diagram of
More information8.022 (E&M) Lecture 16
8. (E&M) ecure 16 Topics: Inducors in circuis circuis circuis circuis as ime Our second lecure on elecromagneic inducance 3 ways of creaing emf using Faraday s law: hange area of circui S() hange angle
More informationEE202 Circuit Theory II
EE202 Circui Theory II 2017-2018, Spring Dr. Yılmaz KALKAN I. Inroducion & eview of Fir Order Circui (Chaper 7 of Nilon - 3 Hr. Inroducion, C and L Circui, Naural and Sep epone of Serie and Parallel L/C
More informationdv 7. Voltage-current relationship can be obtained by integrating both sides of i = C :
EECE202 NETWORK ANALYSIS I Dr. Charles J. Kim Class Noe 22: Capaciors, Inducors, and Op Amp Circuis A. Capaciors. A capacior is a passive elemen designed o sored energy in is elecric field. 2. A capacior
More informationln 2 1 ln y x c y C x
Lecure 14 Appendi B: Some sample problems from Boas Here are some soluions o he sample problems assigned for Chaper 8 8: 6 Soluion: We wan o find he soluion o he following firs order equaion using separaion
More informationMath 333 Problem Set #2 Solution 14 February 2003
Mah 333 Problem Se #2 Soluion 14 February 2003 A1. Solve he iniial value problem dy dx = x2 + e 3x ; 2y 4 y(0) = 1. Soluion: This is separable; we wrie 2y 4 dy = x 2 + e x dx and inegrae o ge The iniial
More information8.022 (E&M) Lecture 9
8.0 (E&M) Lecure 9 Topics: circuis Thevenin s heorem Las ime Elecromoive force: How does a baery work and is inernal resisance How o solve simple circuis: Kirchhoff s firs rule: a any node, sum of he currens
More informationSome Basic Information about M-S-D Systems
Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,
More informationComplete solutions to Exercise 14(b) 1. Very similar to EXAMPLE 4. We have same characteristic equation:
Soluions 4(b) Complee soluions o Exercise 4(b). Very similar o EXAMPE 4. We have same characerisic equaion: 5 i Ae = + Be By using he given iniial condiions we obain he simulaneous equaions A+ B= 0 5A
More informationChapter 10 INDUCTANCE Recommended Problems:
Chaper 0 NDUCTANCE Recommended Problems: 3,5,7,9,5,6,7,8,9,,,3,6,7,9,3,35,47,48,5,5,69, 7,7. Self nducance Consider he circui shown in he Figure. When he swich is closed, he curren, and so he magneic field,
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
More informationME 391 Mechanical Engineering Analysis
Fall 04 ME 39 Mechanical Engineering Analsis Eam # Soluions Direcions: Open noes (including course web posings). No books, compuers, or phones. An calculaor is fair game. Problem Deermine he posiion of
More informationECE-205 Dynamical Systems
ECE-5 Dynamical Sysems Course Noes Spring Bob Throne Copyrigh Rober D. Throne Copyrigh Rober D. Throne . Elecrical Sysems The ypes of dynamical sysems we will be sudying can be modeled in erms of algebraic
More informationMEI STRUCTURED MATHEMATICS 4758
OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Cerificae of Educaion Advanced General Cerificae of Educaion MEI STRUCTURED MATHEMATICS 4758 Differenial Equaions Thursday 5 JUNE 006 Afernoon
More informationChallenge Problems. DIS 203 and 210. March 6, (e 2) k. k(k + 2). k=1. f(x) = k(k + 2) = 1 x k
Challenge Problems DIS 03 and 0 March 6, 05 Choose one of he following problems, and work on i in your group. Your goal is o convince me ha your answer is correc. Even if your answer isn compleely correc,
More informationPhys1112: DC and RC circuits
Name: Group Members: Dae: TA s Name: Phys1112: DC and RC circuis Objecives: 1. To undersand curren and volage characerisics of a DC RC discharging circui. 2. To undersand he effec of he RC ime consan.
More informationLabQuest 24. Capacitors
Capaciors LabQues 24 The charge q on a capacior s plae is proporional o he poenial difference V across he capacior. We express his wih q V = C where C is a proporionaliy consan known as he capaciance.
More informationi L = VT L (16.34) 918a i D v OUT i L v C V - S 1 FIGURE A switched power supply circuit with diode and a switch.
16.4.3 A SWITHED POWER SUPPY USINGA DIODE In his example, we will analyze he behavior of he diodebased swiched power supply circui shown in Figure 16.15. Noice ha his circui is similar o ha in Figure 12.41,
More informationMorning Time: 1 hour 30 minutes Additional materials (enclosed):
ADVANCED GCE 78/0 MATHEMATICS (MEI) Differenial Equaions THURSDAY JANUARY 008 Morning Time: hour 30 minues Addiional maerials (enclosed): None Addiional maerials (required): Answer Bookle (8 pages) Graph
More informationChapter 8 The Complete Response of RL and RC Circuits
Chaper 8 he Complee Response of R and RC Ciruis Exerises Ex 8.3-1 Before he swih loses: Afer he swih loses: 2 = = 8 Ω so = 8 0.05 = 0.4 s. 0.25 herefore R ( ) Finally, 2.5 ( ) = o + ( (0) o ) = 2 + V for
More informationLectures 29 and 30 BIQUADRATICS AND STATE SPACE OP AMP REALIZATIONS. I. Introduction
EE-202/445, 3/18/18 9-1 R. A. DeCarlo Lecures 29 and 30 BIQUADRATICS AND STATE SPACE OP AMP REALIZATIONS I. Inroducion 1. The biquadraic ransfer funcion has boh a 2nd order numeraor and a 2nd order denominaor:
More informationdv i= C. dt 1. Assuming the passive sign convention, (a) i = 0 (dc) (b) (220)( 9)(16.2) t t Engineering Circuit Analysis 8 th Edition
. Assuming he passive sign convenion, dv i= C. d (a) i = (dc) 9 9 (b) (22)( 9)(6.2) i= e = 32.8e A 9 3 (c) i (22 = )(8 )(.) sin. = 7.6sin. pa 9 (d) i= (22 )(9)(.8) cos.8 = 58.4 cos.8 na 2. (a) C = 3 pf,
More informationExperimental Buck Converter
Experimenal Buck Converer Inpu Filer Cap MOSFET Schoky Diode Inducor Conroller Block Proecion Conroller ASIC Experimenal Synchronous Buck Converer SoC Buck Converer Basic Sysem S 1 u D 1 r r C C R R X
More informationChapter 9 Sinusoidal Steady State Analysis
Chaper 9 Sinusoidal Seady Sae Analysis 9.-9. The Sinusoidal Source and Response 9.3 The Phasor 9.4 pedances of Passive Eleens 9.5-9.9 Circui Analysis Techniques in he Frequency Doain 9.0-9. The Transforer
More informationAC Circuits AC Circuit with only R AC circuit with only L AC circuit with only C AC circuit with LRC phasors Resonance Transformers
A ircuis A ircui wih only A circui wih only A circui wih only A circui wih phasors esonance Transformers Phys 435: hap 31, Pg 1 A ircuis New Topic Phys : hap. 6, Pg Physics Moivaion as ime we discovered
More informationDifferential Equations
Mah 21 (Fall 29) Differenial Equaions Soluion #3 1. Find he paricular soluion of he following differenial equaion by variaion of parameer (a) y + y = csc (b) 2 y + y y = ln, > Soluion: (a) The corresponding
More informationELEG 205 Fall Lecture #13. Mark Mirotznik, Ph.D. Professor The University of Delaware Tel: (302)
ELEG 205 Fall 2017 Leure #13 Mark Miroznik, Ph.D. Professor The Universiy of Delaware Tel: (302831-4221 Email: mirozni@ee.udel.edu Chaper 8: RL and RC Ciruis 1. Soure-free RL iruis (naural response 2.
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signals & Sysems Prof. Mar Fowler Noe Se #1 C-T Signals: Circuis wih Periodic Sources 1/1 Solving Circuis wih Periodic Sources FS maes i easy o find he response of an RLC circui o a periodic source!
More informationDesigning Information Devices and Systems I Spring 2019 Lecture Notes Note 17
EES 16A Designing Informaion Devices and Sysems I Spring 019 Lecure Noes Noe 17 17.1 apaciive ouchscreen In he las noe, we saw ha a capacior consiss of wo pieces on conducive maerial separaed by a nonconducive
More informationSystem of Linear Differential Equations
Sysem of Linear Differenial Equaions In "Ordinary Differenial Equaions" we've learned how o solve a differenial equaion for a variable, such as: y'k5$e K2$x =0 solve DE yx = K 5 2 ek2 x C_C1 2$y''C7$y
More informationMA 214 Calculus IV (Spring 2016) Section 2. Homework Assignment 1 Solutions
MA 14 Calculus IV (Spring 016) Secion Homework Assignmen 1 Soluions 1 Boyce and DiPrima, p 40, Problem 10 (c) Soluion: In sandard form he given firs-order linear ODE is: An inegraing facor is given by
More informationSolutions to Assignment 1
MA 2326 Differenial Equaions Insrucor: Peronela Radu Friday, February 8, 203 Soluions o Assignmen. Find he general soluions of he following ODEs: (a) 2 x = an x Soluion: I is a separable equaion as we
More informationLaplace Transforms. Examples. Is this equation differential? y 2 2y + 1 = 0, y 2 2y + 1 = 0, (y ) 2 2y + 1 = cos x,
Laplace Transforms Definiion. An ordinary differenial equaion is an equaion ha conains one or several derivaives of an unknown funcion which we call y and which we wan o deermine from he equaion. The equaion
More informationEE 301 Lab 2 Convolution
EE 301 Lab 2 Convoluion 1 Inroducion In his lab we will gain some more experience wih he convoluion inegral and creae a scrip ha shows he graphical mehod of convoluion. 2 Wha you will learn This lab will
More informationLAPLACE TRANSFORM AND TRANSFER FUNCTION
CHBE320 LECTURE V LAPLACE TRANSFORM AND TRANSFER FUNCTION Professor Dae Ryook Yang Spring 2018 Dep. of Chemical and Biological Engineering 5-1 Road Map of he Lecure V Laplace Transform and Transfer funcions
More informationUNIVERSITY OF CALIFORNIA AT BERKELEY
Homework #10 Soluions EECS 40, Fall 2006 Prof. Chang-Hasnain Due a 6 pm in 240 Cory on Wednesday, 04/18/07 oal Poins: 100 Pu (1) your name and (2) discussion secion number on your homework. You need o
More informationChapter 5-4 Operational amplifier Department of Mechanical Engineering
MEMS08 Chaper 5-4 Operaional amplifier Deparmen of Mechanical Engineering Insrumenaion amplifier Very high inpu impedance Large common mode rejecion raio (CMRR) Capabiliy o amplify low leel signals Consisen
More informationSection 2.2 Charge and Current 2.6 b) The current direction is designated as the direction of the movement of positive charges.
Chaper Soluions Secion. Inroducion. Curren source. Volage source. esisor.4 Capacior.5 Inducor Secion. Charge and Curren.6 b) The curren direcion is designaed as he direcion of he movemen of posiive charges..7
More informationWall. x(t) f(t) x(t = 0) = x 0, t=0. which describes the motion of the mass in absence of any external forcing.
MECHANICS APPLICATIONS OF SECOND-ORDER ODES 7 Mechanics applicaions of second-order ODEs Second-order linear ODEs wih consan coefficiens arise in many physical applicaions. One physical sysems whose behaviour
More informationSection 3.8, Mechanical and Electrical Vibrations
Secion 3.8, Mechanical and Elecrical Vibraions Mechanical Unis in he U.S. Cusomary and Meric Sysems Disance Mass Time Force g (Earh) Uni U.S. Cusomary MKS Sysem CGS Sysem fee f slugs seconds sec pounds
More informationContinuous Time. Time-Domain System Analysis. Impulse Response. Impulse Response. Impulse Response. Impulse Response. ( t) + b 0.
Time-Domain Sysem Analysis Coninuous Time. J. Robers - All Righs Reserved. Edied by Dr. Rober Akl 1. J. Robers - All Righs Reserved. Edied by Dr. Rober Akl 2 Le a sysem be described by a 2 y ( ) + a 1
More informationdt = C exp (3 ln t 4 ). t 4 W = C exp ( ln(4 t) 3) = C(4 t) 3.
Mah Rahman Exam Review Soluions () Consider he IVP: ( 4)y 3y + 4y = ; y(3) = 0, y (3) =. (a) Please deermine he longes inerval for which he IVP is guaraneed o have a unique soluion. Soluion: The disconinuiies
More informationTHE BERNOULLI NUMBERS. t k. = lim. = lim = 1, d t B 1 = lim. 1+e t te t = lim t 0 (e t 1) 2. = lim = 1 2.
THE BERNOULLI NUMBERS The Bernoulli numbers are defined here by he exponenial generaing funcion ( e The firs one is easy o compue: (2 and (3 B 0 lim 0 e lim, 0 e ( d B lim 0 d e +e e lim 0 (e 2 lim 0 2(e
More information6.2 Transforms of Derivatives and Integrals.
SEC. 6.2 Transforms of Derivaives and Inegrals. ODEs 2 3 33 39 23. Change of scale. If l( f ()) F(s) and c is any 33 45 APPLICATION OF s-shifting posiive consan, show ha l( f (c)) F(s>c)>c (Hin: In Probs.
More information3. Alternating Current
3. Alernaing Curren TOPCS Definiion and nroducion AC Generaor Componens of AC Circuis Series LRC Circuis Power in AC Circuis Transformers & AC Transmission nroducion o AC The elecric power ou of a home
More informationUniversità degli Studi di Roma Tor Vergata Dipartimento di Ingegneria Elettronica. Analogue Electronics. Paolo Colantonio A.A.
Universià degli Sudi di Roma Tor Vergaa Diparimeno di Ingegneria Eleronica Analogue Elecronics Paolo Colanonio A.A. 2015-16 Diode circui analysis The non linearbehaviorofdiodesmakesanalysisdifficul consider
More informationPulse Generators. Any of the following calculations may be asked in the midterms/exam.
ulse Generaors ny of he following calculaions may be asked in he miderms/exam.. a) capacior of wha capaciance forms an RC circui of s ime consan wih a 0 MΩ resisor? b) Wha percenage of he iniial volage
More informationThe problem with linear regulators
he problem wih linear regulaors i in P in = i in V REF R a i ref i q i C v CE P o = i o i B ie P = v i o o in R 1 R 2 i o i f η = P o P in iref is small ( 0). iq (quiescen curren) is small (probably).
More information6.01: Introduction to EECS I Lecture 8 March 29, 2011
6.01: Inroducion o EES I Lecure 8 March 29, 2011 6.01: Inroducion o EES I Op-Amps Las Time: The ircui Absracion ircuis represen sysems as connecions of elemens hrough which currens (hrough variables) flow
More informationd 1 = c 1 b 2 - b 1 c 2 d 2 = c 1 b 3 - b 1 c 3
and d = c b - b c c d = c b - b c c This process is coninued unil he nh row has been compleed. The complee array of coefficiens is riangular. Noe ha in developing he array an enire row may be divided or
More informationAnalytic Model and Bilateral Approximation for Clocked Comparator
Analyic Model and Bilaeral Approximaion for Clocked Comparaor M. Greians, E. Hermanis, G.Supols Insiue of, Riga, Lavia, e-mail: gais.supols@edi.lv Research is suppored by: 1) ESF projec Nr.1DP/1.1.1.2.0/09/APIA/VIAA/020,
More informationnon-linear oscillators
non-linear oscillaors The invering comparaor operaion can be summarized as When he inpu is low, he oupu is high. When he inpu is high, he oupu is low. R b V REF R a and are given by he expressions derived
More information10. State Space Methods
. Sae Space Mehods. Inroducion Sae space modelling was briefly inroduced in chaper. Here more coverage is provided of sae space mehods before some of heir uses in conrol sysem design are covered in he
More informationChapter 1 Fundamental Concepts
Chaper 1 Fundamenal Conceps 1 Signals A signal is a paern of variaion of a physical quaniy, ofen as a funcion of ime (bu also space, disance, posiion, ec). These quaniies are usually he independen variables
More informationMEMS 0031 Electric Circuits
MEMS 0031 Elecric Circuis Chaper 1 Circui variables Chaper/Lecure Learning Objecives A he end of his lecure and chaper, you should able o: Represen he curren and volage of an elecric circui elemen, paying
More informationV(z, t) t < L v. z = 0 z = vt z = L. I(z, t) z = L
W.C.Chew ECE 35 Lecure Noes 12. Transiens on a Transmission Line. When we do no have a ime harmonic signal on a ransmission line, we have o use ransien analysis o undersand he waves on a ransmission line.
More informationHomework: See website. Table of Contents
Dr. Friz Wilhelm page of 4 C:\physics\3 lecure\ch3 Inducance C circuis.docx; P /5/8 S: 5/4/9 9:39: AM Homework: See websie. Table of Conens: 3. Self-inducance in a circui, 3. -Circuis, 4 3.a Charging he
More informationProblem Set #1. i z. the complex propagation constant. For the characteristic impedance:
Problem Se # Problem : a) Using phasor noaion, calculae he volage and curren waves on a ransmission line by solving he wave equaion Assume ha R, L,, G are all non-zero and independen of frequency From
More informationDEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATIONS 2008
[E5] IMPERIAL COLLEGE LONDON DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATIONS 008 EEE/ISE PART II MEng BEng and ACGI SIGNALS AND LINEAR SYSTEMS Time allowed: :00 hours There are FOUR quesions
More informationSilicon Controlled Rectifiers UNIT-1
Silicon Conrolled Recifiers UNIT-1 Silicon Conrolled Recifier A Silicon Conrolled Recifier (or Semiconducor Conrolled Recifier) is a four layer solid sae device ha conrols curren flow The name silicon
More informationMath Final Exam Solutions
Mah 246 - Final Exam Soluions Friday, July h, 204 () Find explici soluions and give he inerval of definiion o he following iniial value problems (a) ( + 2 )y + 2y = e, y(0) = 0 Soluion: In normal form,
More information555 Timer. Digital Electronics
555 Timer Digial Elecronics This presenaion will Inroduce he 555 Timer. 555 Timer Derive he characerisic equaions for he charging and discharging of a capacior. Presen he equaions for period, frequency,
More informationfirst-order circuit Complete response can be regarded as the superposition of zero-input response and zero-state response.
Experimen 4:he Sdies of ransiional processes of 1. Prpose firs-order circi a) Use he oscilloscope o observe he ransiional processes of firs-order circi. b) Use he oscilloscope o measre he ime consan of
More informationL1, L2, N1 N2. + Vout. C out. Figure 2.1.1: Flyback converter
page 11 Flyback converer The Flyback converer belongs o he primary swiched converer family, which means here is isolaion beween in and oupu. Flyback converers are used in nearly all mains supplied elecronic
More informationStructural Dynamics and Earthquake Engineering
Srucural Dynamics and Earhquae Engineering Course 1 Inroducion. Single degree of freedom sysems: Equaions of moion, problem saemen, soluion mehods. Course noes are available for download a hp://www.c.up.ro/users/aurelsraan/
More information