EECE 301 Signals & Systems Prof. Mark Fowler

Size: px
Start display at page:

Download "EECE 301 Signals & Systems Prof. Mark Fowler"

Transcription

1 -T Sytem: Ung Bode Plot EEE 30 Sgnal & Sytem Pro. Mark Fowler Note Set #37 /3

2 Bode Plot Idea an Help Vualze What rcut Do Lowpa Flter Break Pont = / H ( ) j /3

3 Hghpa Flter c = / L Bandpa Flter n nn ( a) n n ( a)( b) (db) j j T Frequency (rad/ec) All lope are 0 db/decade! /3

4 A Better Bandpa Flter? Suppoe you want a BPF. wth ater rollo! Need an term n the numerator! At we need to change lope by 40 db/dec So need double At we need to change lope by 40 db/dec So need double K ( ) ( ) There are (at leat) three way to get th! K K ( )( ) ( )( ) K K ( ) ( ) K K ( ) ( ) BPF L w/ dtnct pole BPF L w/ repeated pole HPF L w/ ep. pole LPF L w/ ep. pole Same exact crcut jut derent choce o L!!! 4/3

5 Look lke we could jut cacade two o our L crcut Here we cacade BPF. Our cacade theory only hold when attachng the nd ytem doe not change how the rt one behave! Although TF Theory ay th wll work the problem that the econd crcut Load the rt one!!! So one approach would be to re-analyze th cacade and ee t wll tll work but wth ome tweek on the component choce. Another approach to ue an op amp a a buer between the tage! Bandpa L Bandpa L VEY large nput retance o op amp prevent loadng o rt tage! VEY mall output retance o op amp mnmze mpact on nd tage! emember there are two way to chooe the component here:. Each tage ha repeated pole. Each tage ha dtnct pole It may be derable to add another buer here 5/3

6 Another way to make a better BPF: Here we mut chooe the component o that each tage ha repeated pole. nd Ord Hghpa L nd Ord Lowpa L Although thee dea lead to workable crcut they are not necearly the bet For one thng they need nductor (whch are bg and can t be made n an I!) There are other orm See th lnk or the orm ued below. nd Ord Hghpa nd Ord Lowpa + + 6/3

7 Degn Example ung Bode Plot Inght Suppoe you want to buld a treble booter or an electrc gutar. You decde that omethng lke th mght work: 0dB H ( ) 00Hz 68 rad/ = 0dB (Hz) 000Hz 683 rad/ = Notce that we are dong our rough degn thnkng n term o Bode Plot approxmaton!!! The A trng on a gutar ha a undamental requency o 0 Hz The A note on 7 th ret o the hgh-e trng ha a undamental requency o 880 Hz From our Bode Plot Inght we know we can get th rom a ngle real pole, ngle real zero ytem wth the zero rt, then the pole : H ( ) ( ( / ) / ) H ( ) ( ( j / ) j / ) wth: = 68 rad/ = 680 rad/ 7/3

8 8/3 A ere combnaton ha mpedance Z() = + / Note: we could get + L wth an nductor but nductor are generally avoded when poble So what do we get we could ome how orm a rato o uch mpedance? / / ) ( ) ( Z Z / / : Let Aha!!! What we want! Now, how do we get a crcut to do th? Let explore! / / ) ( ) ( j j Z Z

9 Okay how do we buld a crcut that ha a traner uncton that a rato o mpedance?! ecall the op-amp nvertng ampler! v n v o Gan ato o retance Extendng the analy to nclude mpedance we can how that: Z () Z () v n v o H ( ) Z Z ( ) ( ) Won t aect our magntude: 9/3

10 v n v o Now, you can chooe the & to gve the dered requency pont p. 98, The Art o Electronc, Horowtz & Hll, ambrdge Pre, 980 But wat!! You then remember that op amp mut alway have negatve eedback at D o puttng here not a good dea So we have to contnue We alo mght not lke th crcut becaue t mght not gve u a very large nput mpedance and that mght excevely load the crcut that you plug nto th (e.g., the gutar) Back to the drawng board!!! 0/3

11 Okay, then you remember there alo Non-Invertng Op-Amp crcut Innte nput mpedance v n v o Gan We avod the no D eedback ue but we re not yet ure we ll get what we want! Applyng th gan ormula we get: ( / ) ( ) / / / / H ( ) Oh ool!! We Get What We want! ( ) Set: 683 rad/ 68 rad/ hooe: 5k 0.F.5k Ung tandard value /3

12 H( ) (db) omputed Frequency epone ung Matlab Dcrepancy due to ue o tandard value (Hz) /3

13 Summary o Bode-Plot-Drven Degn Example. Through nght ganed rom knowng how to do Bode plot by hand we recognzed the knd o traner uncton we needed. Through nght ganed n crcut cla about mpedance we recognzed a key buldng block needed: Sere - 3. Through nght ganed n electronc cla about op-amp we ound a poble oluton the nvertng op-amp approach 4. We then crutnzed our degn or any overlooked ue a. We dcovered two problem that we needed to x 5. We ued urther nght nto op-amp to realze that we could x the nput mpedance ue ung a non-nvertng orm o the op-amp crcut 6. We ddn t gve up at rt gn that the nvertng orm mght not gve u the orm we want a. Through mathematcal analy we howed that we dd n act get what we wanted!!!!!! 3/3

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

Prof. Paolo Colantonio a.a

Prof. Paolo Colantonio a.a Pro. Paolo olantono a.a. 3 4 Let s consder a two ports network o Two ports Network o L For passve network (.e. wthout nternal sources or actve devces), a general representaton can be made by a sutable

More information

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS) FE EIEW OPEATIONAL AMPLIFIES (OPAMPS) 1 The Opamp An opamp has two nputs and one output. Note the opamp below. The termnal labeled wth the () sgn s the nvertng nput and the nput labeled wth the () sgn

More information

MAE140 - Linear Circuits - Winter 16 Final, March 16, 2016

MAE140 - 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 information

ELG3336: Op Amp-based Active Filters

ELG3336: Op Amp-based Active Filters ELG6: Op Amp-baed Actve Flter Advantage: educed ze and weght, and thereore paratc. Increaed relablty and mproved perormance. Smpler degn than or pave lter and can realze a wder range o uncton a well a

More information

( ) 2. 1) Bode plots/transfer functions. a. Draw magnitude and phase bode plots for the transfer function

( ) 2. 1) Bode plots/transfer functions. a. Draw magnitude and phase bode plots for the transfer function ECSE CP7 olution Spring 5 ) Bode plot/tranfer function a. Draw magnitude and phae bode plot for the tranfer function H( ). ( ) ( E4) In your magnitude plot, indicate correction at the pole and zero. Step

More information

Lesson 16: Basic Control Modes

Lesson 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 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

, 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

Department of Mechanical Engineering Massachusetts Institute of Technology Modeling, Dynamics and Control III Spring 2002

Department of Mechanical Engineering Massachusetts Institute of Technology Modeling, Dynamics and Control III Spring 2002 Department of Mechanical Engineering Maachuett Intitute of Technology 2.010 Modeling, Dynamic and Control III Spring 2002 SOLUTIONS: Problem Set # 10 Problem 1 Etimating tranfer function from Bode Plot.

More information

Root Locus Techniques

Root Locus Techniques Root Locu Technque ELEC 32 Cloed-Loop Control The control nput u t ynthezed baed on the a pror knowledge of the ytem plant, the reference nput r t, and the error gnal, e t The control ytem meaure the output,

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

Department of Electrical and Computer Engineering FEEDBACK AMPLIFIERS

Department of Electrical and Computer Engineering FEEDBACK AMPLIFIERS Department o Electrcal and Computer Engneerng UNIT I EII FEEDBCK MPLIFIES porton the output sgnal s ed back to the nput o the ampler s called Feedback mpler. Feedback Concept: block dagram o an ampler

More information

Why working at higher frequencies?

Why working at higher frequencies? Advanced course on ELECTRICAL CHARACTERISATION OF NANOSCALE SAMPLES & BIOCHEMICAL INTERFACES: methods and electronc nstrumentaton. MEASURING SMALL CURRENTS When speed comes nto play Why workng at hgher

More information

Physics 111. CQ1: springs. con t. Aristocrat at a fixed angle. Wednesday, 8-9 pm in NSC 118/119 Sunday, 6:30-8 pm in CCLIR 468.

Physics 111. CQ1: springs. con t. Aristocrat at a fixed angle. Wednesday, 8-9 pm in NSC 118/119 Sunday, 6:30-8 pm in CCLIR 468. c Announcement day, ober 8, 004 Ch 8: Ch 10: Work done by orce at an angle Power Rotatonal Knematc angular dplacement angular velocty angular acceleraton Wedneday, 8-9 pm n NSC 118/119 Sunday, 6:30-8 pm

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

5.5 Sampling. The Connection Between: Continuous Time & Discrete Time

5.5 Sampling. The Connection Between: Continuous Time & Discrete Time 5.5 Sampling he Connection Between: Continuou ime & Dicrete ime Warning: I don t really like how the book cover thi! It i not that it i wrong it jut ail to make the correct connection between the mathematic

More information

s 0.068μ s Rearrange the function into a more convenient form and verify that it is still equal to the original.

s 0.068μ s Rearrange the function into a more convenient form and verify that it is still equal to the original. Title: TCS Traner Function Author: Eric Warmbier Decription: Thi document derive the variou traner unction or the TCS ytem on the IRTF. The ytem i broken down into block in a Viio document. A traner unction

More information

ENGR-4300 Electronic Instrumentation Quiz 4 Fall 2010 Name Section. Question Value Grade I 20 II 20 III 20 IV 20 V 20. Total (100 points)

ENGR-4300 Electronic Instrumentation Quiz 4 Fall 2010 Name Section. Question Value Grade I 20 II 20 III 20 IV 20 V 20. Total (100 points) ENGR-43 Electronc Instrumentaton Quz 4 Fall 21 Name Secton Queston Value Grade I 2 II 2 III 2 IV 2 V 2 Total (1 ponts) On all questons: SHOW LL WORK. EGIN WITH FORMULS, THEN SUSTITUTE VLUES ND UNITS. No

More information

Problem Free Expansion of Ideal Gas

Problem Free Expansion of Ideal Gas Problem 4.3 Free Expanon o Ideal Ga In general: ds ds du P dv P dv NR V dn Snce U o deal ga ndependent on olume (du=), and N = cont n the proce: dv In a ere o nntemal ree expanon, entropy change by: S

More information

55:041 Electronic Circuits

55:041 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 information

Chapter 11. Supplemental Text Material. The method of steepest ascent can be derived as follows. Suppose that we have fit a firstorder

Chapter 11. Supplemental Text Material. The method of steepest ascent can be derived as follows. Suppose that we have fit a firstorder S-. The Method of Steepet cent Chapter. Supplemental Text Materal The method of teepet acent can be derved a follow. Suppoe that we have ft a frtorder model y = β + β x and we wh to ue th model to determne

More information

Chapter 9: Controller design. Controller design. Controller design

Chapter 9: Controller design. Controller design. Controller design Chapter 9. Controller Deign 9.. Introduction 9.2. Eect o negative eedback on the network traner unction 9.2.. Feedback reduce the traner unction rom diturbance to the output 9.2.2. Feedback caue the traner

More information

Lecture 4. Chapter 11 Nise. Controller Design via Frequency Response. G. Hovland 2004

Lecture 4. Chapter 11 Nise. Controller Design via Frequency Response. G. Hovland 2004 METR4200 Advanced Control Lecture 4 Chapter Nie Controller Deign via Frequency Repone G. Hovland 2004 Deign Goal Tranient repone via imple gain adjutment Cacade compenator to improve teady-tate error Cacade

More information

EE 330 Lecture 24. Small Signal Analysis Small Signal Analysis of BJT Amplifier

EE 330 Lecture 24. Small Signal Analysis Small Signal Analysis of BJT Amplifier EE 0 Lecture 4 Small Sgnal Analss Small Sgnal Analss o BJT Ampler Eam Frda March 9 Eam Frda Aprl Revew Sesson or Eam : 6:00 p.m. on Thursda March 8 n Room Sweene 6 Revew rom Last Lecture Comparson o Gans

More information

II. PASSIVE FILTERS. H(j ω) Pass. Stop

II. PASSIVE FILTERS. H(j ω) Pass. Stop II. PASSIE FILTES Frequency-selectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called pass band). The ampltude of sgnals outsde ths range of frequences

More information

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)( ) 8/25/2010

FE 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 information

Electrical Engineering Department Network Lab.

Electrical 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 information

55:041 Electronic Circuits

55:041 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 information

Design of Recursive Digital Filters IIR

Design of Recursive Digital Filters IIR Degn of Recurve Dgtal Flter IIR The outut from a recurve dgtal flter deend on one or more revou outut value, a well a on nut t nvolve feedbac. A recurve flter ha an nfnte mule reone (IIR). The mulve reone

More information

Two Approaches to Proving. Goldbach s Conjecture

Two Approaches to Proving. Goldbach s Conjecture Two Approache to Provng Goldbach Conecture By Bernard Farley Adved By Charle Parry May 3 rd 5 A Bref Introducton to Goldbach Conecture In 74 Goldbach made h mot famou contrbuton n mathematc wth the conecture

More information

SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. Solutions to Assignment 3 February 2005.

SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. Solutions to Assignment 3 February 2005. SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuit II Solution to Aignment 3 February 2005. Initial Condition Source 0 V battery witch flip at t 0 find i 3 (t) Component value:

More information

Improvements on Waring s Problem

Improvements on Waring s Problem Improvement on Warng Problem L An-Png Bejng, PR Chna apl@nacom Abtract By a new recurve algorthm for the auxlary equaton, n th paper, we wll gve ome mprovement for Warng problem Keyword: Warng Problem,

More information

Root Locus Contents. Root locus, sketching algorithm. Root locus, examples. Root locus, proofs. Root locus, control examples

Root Locus Contents. Root locus, sketching algorithm. Root locus, examples. Root locus, proofs. Root locus, control examples Root Locu Content Root locu, ketching algorithm Root locu, example Root locu, proof Root locu, control example Root locu, influence of zero and pole Root locu, lead lag controller deign 9 Spring ME45 -

More information

General Tips on How to Do Well in Physics Exams. 1. Establish a good habit in keeping track of your steps. For example, when you use the equation

General Tips on How to Do Well in Physics Exams. 1. Establish a good habit in keeping track of your steps. For example, when you use the equation General Tps on How to Do Well n Physcs Exams 1. Establsh a good habt n keepng track o your steps. For example when you use the equaton 1 1 1 + = d d to solve or d o you should rst rewrte t as 1 1 1 = d

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

ELECTRONICS. EE 42/100 Lecture 4: Resistive Networks and Nodal Analysis. Rev B 1/25/2012 (9:49PM) Prof. Ali M. Niknejad

ELECTRONICS. EE 42/100 Lecture 4: Resistive Networks and Nodal Analysis. Rev B 1/25/2012 (9:49PM) Prof. Ali M. Niknejad A. M. Nknejad Unversty of Calforna, Berkeley EE 100 / 42 Lecture 4 p. 1/14 EE 42/100 Lecture 4: Resstve Networks and Nodal Analyss ELECTRONICS Rev B 1/25/2012 (9:49PM) Prof. Al M. Nknejad Unversty of Calforna,

More information

EE40 Lec 13. Prof. Nathan Cheung 10/13/2009. Reading: Hambley Chapter Chapter 14.10,14.5

EE40 Lec 13. Prof. Nathan Cheung 10/13/2009. Reading: Hambley Chapter Chapter 14.10,14.5 EE4 Lec 13 Filter and eonance Pro. Nathan Cheung 1/13/9 eading: Hambley Chapter 6.6-6.8 Chapter 14.1,14.5 Slide 1 Common Filter Traner Function v. Freq H ( ) H( ) Low Pa High Pa Frequency H ( ) H ( ) Frequency

More information

S-Domain Analysis. s-domain Circuit Analysis. EE695K VLSI Interconnect. Time domain (t domain) Complex frequency domain (s domain) Laplace Transform L

S-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 information

Harmonic oscillator approximation

Harmonic oscillator approximation armonc ocllator approxmaton armonc ocllator approxmaton Euaton to be olved We are fndng a mnmum of the functon under the retrcton where W P, P,..., P, Q, Q,..., Q P, P,..., P, Q, Q,..., Q lnwgner functon

More information

CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS

CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS 103 Phy 1 9.1 Lnear Momentum The prncple o energy conervaton can be ued to olve problem that are harder to olve jut ung Newton law. It ued to decrbe moton

More information

Electric and magnetic field sensor and integrator equations

Electric and magnetic field sensor and integrator equations Techncal Note - TN12 Electrc and magnetc feld enor and ntegrator uaton Bertrand Da, montena technology, 1728 oen, Swtzerland Table of content 1. Equaton of the derate electrc feld enor... 1 2. Integraton

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

5.5 Application of Frequency Response: Signal Filters

5.5 Application of Frequency Response: Signal Filters 44 Dynamic Sytem Second order lowpa filter having tranfer function H()=H ()H () u H () H () y Firt order lowpa filter Figure 5.5: Contruction of a econd order low-pa filter by combining two firt order

More information

E-Companion: Mathematical Proofs

E-Companion: Mathematical Proofs E-omnon: Mthemtcl Poo Poo o emm : Pt DS Sytem y denton o t ey to vey tht t ncee n wth d ncee n We dene } ] : [ { M whee / We let the ttegy et o ech etle n DS e ]} [ ] [ : { M w whee M lge otve nume oth

More information

ELG 2135 ELECTRONICS I SECOND CHAPTER: OPERATIONAL AMPLIFIERS

ELG 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 information

Main Topics: The Past, H(s): Poles, zeros, s-plane, and stability; Decomposition of the complete response.

Main Topics: The Past, H(s): Poles, zeros, s-plane, and stability; Decomposition of the complete response. EE202 HOMEWORK PROBLEMS SPRING 18 TO THE STUDENT: ALWAYS CHECK THE ERRATA on the web. Quote for your Parent' Partie: 1. Only with nodal analyi i the ret of the emeter a poibility. Ray DeCarlo 2. (The need

More information

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web:     Ph: Serial :. PT_EE_A+C_Control Sytem_798 Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubanewar olkata Patna Web: E-mail: info@madeeay.in Ph: -4546 CLASS TEST 8-9 ELECTRICAL ENGINEERING Subject

More information

Physics 120. Exam #1. April 15, 2011

Physics 120. Exam #1. April 15, 2011 Phyc 120 Exam #1 Aprl 15, 2011 Name Multple Choce /16 Problem #1 /28 Problem #2 /28 Problem #3 /28 Total /100 PartI:Multple Choce:Crclethebetanwertoeachqueton.Anyothermark wllnotbegvencredt.eachmultple

More information

Problem #1. Known: All required parameters. Schematic: Find: Depth of freezing as function of time. Strategy:

Problem #1. Known: All required parameters. Schematic: Find: Depth of freezing as function of time. Strategy: BEE 3500 013 Prelm Soluton Problem #1 Known: All requred parameter. Schematc: Fnd: Depth of freezng a functon of tme. Strategy: In thee mplfed analy for freezng tme, a wa done n cla for a lab geometry,

More information

Pythagorean triples. Leen Noordzij.

Pythagorean triples. Leen Noordzij. Pythagorean trple. Leen Noordz Dr.l.noordz@leennoordz.nl www.leennoordz.me Content A Roadmap for generatng Pythagorean Trple.... Pythagorean Trple.... 3 Dcuon Concluon.... 5 A Roadmap for generatng Pythagorean

More information

AP Statistics Ch 3 Examining Relationships

AP Statistics Ch 3 Examining Relationships Introducton To tud relatonhp between varable, we mut meaure the varable on the ame group of ndvdual. If we thnk a varable ma eplan or even caue change n another varable, then the eplanator varable and

More information

Graphical Analysis of a BJT Amplifier

Graphical 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 information

March 18, 2014 Academic Year 2013/14

March 18, 2014 Academic Year 2013/14 POLITONG - SHANGHAI BASIC AUTOMATIC CONTROL Exam grade March 8, 4 Academic Year 3/4 NAME (Pinyin/Italian)... STUDENT ID Ue only thee page (including the back) for anwer. Do not ue additional heet. Ue of

More information

Additional File 1 - Detailed explanation of the expression level CPD

Additional File 1 - Detailed explanation of the expression level CPD Addtonal Fle - Detaled explanaton of the expreon level CPD A mentoned n the man text, the man CPD for the uterng model cont of two ndvdual factor: P( level gen P( level gen P ( level gen 2 (.).. CPD factor

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

Asymptote. 2 Problems 2 Methods

Asymptote. 2 Problems 2 Methods Asymptote Problems Methods Problems Assume we have the ollowing transer unction which has a zero at =, a pole at = and a pole at =. We are going to look at two problems: problem is where >> and problem

More information

SKEE 3143 CONTROL SYSTEM DESIGN. CHAPTER 3 Compensator Design Using the Bode Plot

SKEE 3143 CONTROL SYSTEM DESIGN. CHAPTER 3 Compensator Design Using the Bode Plot SKEE 3143 CONTROL SYSTEM DESIGN CHAPTER 3 Compenator Deign Uing the Bode Plot 1 Chapter Outline 3.1 Introduc4on Re- viit to Frequency Repone, ploang frequency repone, bode plot tability analyi. 3.2 Gain

More information

Advanced Circuits Topics - Part 1 by Dr. Colton (Fall 2017)

Advanced 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 information

E40M Device Models, Resistors, Voltage and Current Sources, Diodes, Solar Cells. M. Horowitz, J. Plummer, R. Howe 1

E40M Device Models, Resistors, Voltage and Current Sources, Diodes, Solar Cells. M. Horowitz, J. Plummer, R. Howe 1 E40M Devce Models, Resstors, Voltage and Current Sources, Dodes, Solar Cells M. Horowtz, J. Plummer, R. Howe 1 Understandng the Solar Charger Lab Project #1 We need to understand how: 1. Current, voltage

More information

Team. Outline. Statistics and Art: Sampling, Response Error, Mixed Models, Missing Data, and Inference

Team. Outline. Statistics and Art: Sampling, Response Error, Mixed Models, Missing Data, and Inference Team Stattc and Art: Samplng, Repone Error, Mxed Model, Mng Data, and nference Ed Stanek Unverty of Maachuett- Amhert, USA 9/5/8 9/5/8 Outlne. Example: Doe-repone Model n Toxcology. ow to Predct Realzed

More information

Reference:W:\Lib\MathCAD\Default\defaults.mcd

Reference:W:\Lib\MathCAD\Default\defaults.mcd 4/9/9 Page of 5 Reference:W:\Lib\MathCAD\Default\default.mcd. Objective a. Motivation. Finite circuit peed, e.g. amplifier - effect on ignal. E.g. how "fat" an amp do we need for audio? For video? For

More information

Improvements on Waring s Problem

Improvements on Waring s Problem Imrovement on Warng Problem L An-Png Bejng 85, PR Chna al@nacom Abtract By a new recurve algorthm for the auxlary equaton, n th aer, we wll gve ome mrovement for Warng roblem Keyword: Warng Problem, Hardy-Lttlewood

More information

Specification -- Assumptions of the Simple Classical Linear Regression Model (CLRM) 1. Introduction

Specification -- Assumptions of the Simple Classical Linear Regression Model (CLRM) 1. Introduction ECONOMICS 35* -- NOTE ECON 35* -- NOTE Specfcaton -- Aumpton of the Smple Clacal Lnear Regreon Model (CLRM). Introducton CLRM tand for the Clacal Lnear Regreon Model. The CLRM alo known a the tandard lnear

More information

DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATIONS Laplace Tranform Paul Dawkin Table of Content Preface... Laplace Tranform... Introduction... The Definition... 5 Laplace Tranform... 9 Invere Laplace Tranform... Step Function...4

More information

INDUCTANCE. RC Cicuits vs LR Circuits

INDUCTANCE. 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 information

Chapter 6 The Effect of the GPS Systematic Errors on Deformation Parameters

Chapter 6 The Effect of the GPS Systematic Errors on Deformation Parameters Chapter 6 The Effect of the GPS Sytematc Error on Deformaton Parameter 6.. General Beutler et al., (988) dd the frt comprehenve tudy on the GPS ytematc error. Baed on a geometrc approach and aumng a unform

More information

Use these variables to select a formula. x = t Average speed = 100 m/s = distance / time t = x/v = ~2 m / 100 m/s = 0.02 s or 20 milliseconds

Use these variables to select a formula. x = t Average speed = 100 m/s = distance / time t = x/v = ~2 m / 100 m/s = 0.02 s or 20 milliseconds The speed o a nere mpulse n the human body s about 100 m/s. I you accdentally stub your toe n the dark, estmatethe tme t takes the nere mpulse to trael to your bran. Tps: pcture, poste drecton, and lst

More information

Small signal analysis

Small signal analysis Small gnal analy. ntroducton Let u conder the crcut hown n Fg., where the nonlnear retor decrbed by the equaton g v havng graphcal repreentaton hown n Fg.. ( G (t G v(t v Fg. Fg. a D current ource wherea

More information

6.01: Introduction to EECS 1 Week 6 October 15, 2009

6.01: 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 information

into a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get

into a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get Lecture 25 Introduction to Some Matlab c2d Code in Relation to Sampled Sytem here are many way to convert a continuou time function, { h( t) ; t [0, )} into a dicrete time function { h ( k) ; k {0,,, }}

More information

Week 11: Differential Amplifiers

Week 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 information

Geometrical Optics Mirrors and Prisms

Geometrical Optics Mirrors and Prisms Phy 322 Lecture 4 Chapter 5 Geometrcal Optc Mrror and Prm Optcal bench http://webphyc.davdon.edu/applet/optc4/default.html Mrror Ancent bronze mrror Hubble telecope mrror Lqud mercury mrror Planar mrror

More information

Physics 6A. Angular Momentum. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Physics 6A. Angular Momentum. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Phyic 6A Angular Momentum For Campu earning Angular Momentum Thi i the rotational equivalent of linear momentum. t quantifie the momentum of a rotating object, or ytem of object. f we imply tranlate the

More information

Lecture #9 Continuous time filter

Lecture #9 Continuous time filter Lecture #9 Continuou time filter Oliver Faut December 5, 2006 Content Review. Motivation......................................... 2 2 Filter pecification 2 2. Low pa..........................................

More information

Variable Structure Control ~ Basics

Variable Structure Control ~ Basics Varable Structure Control ~ Bac Harry G. Kwatny Department of Mechancal Engneerng & Mechanc Drexel Unverty Outlne A prelmnary example VS ytem, ldng mode, reachng Bac of dcontnuou ytem Example: underea

More information

Homework 12 Solution - AME30315, Spring 2013

Homework 12 Solution - AME30315, Spring 2013 Homework 2 Solution - AME335, Spring 23 Problem :[2 pt] The Aerotech AGS 5 i a linear motor driven XY poitioning ytem (ee attached product heet). A friend of mine, through careful experimentation, identified

More information

Two Port Characterizations

Two Port Characterizations lectronc Crcuts Two Port Characterzatons Contents Input and output resstances Two port networks Models Prof. C.K. Tse: -port networks Impedances and loadng effects Voltage amplfers R s R out smaller the

More information

CONTROL SYSTEMS. Chapter 7 : Bode Plot. 40dB/dec 1.0. db/dec so resultant slope will be 20 db/dec and this is due to the factor s

CONTROL SYSTEMS. Chapter 7 : Bode Plot. 40dB/dec 1.0. db/dec so resultant slope will be 20 db/dec and this is due to the factor s CONTROL SYSTEMS Chapter 7 : Bode Plot GATE Objective & Numerical Type Solutio Quetio 6 [Practice Book] [GATE EE 999 IIT-Bombay : 5 Mark] The aymptotic Bode plot of the miimum phae ope-loop trafer fuctio

More information

Question 1 Equivalent Circuits

Question 1 Equivalent Circuits MAE 40 inear ircuit Fall 2007 Final Intruction ) Thi exam i open book You may ue whatever written material you chooe, including your cla note and textbook You may ue a hand calculator with no communication

More information

SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. R 4 := 100 kohm

SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. R 4 := 100 kohm SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuit II Solution to Aignment 3 February 2003. Cacaded Op Amp [DC&L, problem 4.29] An ideal op amp ha an output impedance of zero,

More information

Not at Steady State! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Yes! Class 15. Is the following possible?

Not at Steady State! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Yes! Class 15. Is the following possible? Chapter 5-6 (where we are gong) Ideal gae and lqud (today) Dente Partal preure Non-deal gae (next tme) Eqn. of tate Reduced preure and temperature Compreblty chart (z) Vapor-lqud ytem (Ch. 6) Vapor preure

More information

Function and Impulse Response

Function and Impulse Response Tranfer Function and Impule Repone Solution of Selected Unolved Example. Tranfer Function Q.8 Solution : The -domain network i hown in the Fig... Applying VL to the two loop, R R R I () I () L I () L V()

More information

ECSE Linearity Superposition Principle Superposition Example Dependent Sources. 10 kω. 30 V 5 ma. 6 kω. 2 kω

ECSE Linearity Superposition Principle Superposition Example Dependent Sources. 10 kω. 30 V 5 ma. 6 kω. 2 kω S-00 Lnearty Superposton Prncple Superposton xample Dependent Sources Lecture 4. sawyes@rp.edu www.rp.edu/~sawyes 0 kω 6 kω 8 V 0 V 5 ma 4 Nodes Voltage Sources Ref Unknown Node Voltage, kω If hae multple

More information

No! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Survey Results. Class 15. Is the following possible?

No! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Survey Results. Class 15. Is the following possible? Survey Reult Chapter 5-6 (where we are gong) % of Student 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Hour Spent on ChE 273 1-2 3-4 5-6 7-8 9-10 11+ Hour/Week 2008 2009 2010 2011 2012 2013 2014 2015 2017 F17

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

PHYS 100 Worked Examples Week 05: Newton s 2 nd Law

PHYS 100 Worked Examples Week 05: Newton s 2 nd Law PHYS 00 Worked Eaple Week 05: ewton nd Law Poor Man Acceleroeter A drver hang an ar frehener fro ther rearvew rror wth a trng. When acceleratng onto the hghwa, the drver notce that the ar frehener ake

More information

Laser Doppler Velocimetry (LDV) Part - 01

Laser Doppler Velocimetry (LDV) Part - 01 AerE 545 cla note #1 Laer Doppler elocimetry (LD) Part - 01 Hui Hu Department o Aeropace Engineering, Iowa State Univerity Ame, Iowa 50011, U.S.A Technique or Flow elocity Meaurement Intruive technique

More information

CHAPTER 14 SIGNAL GENERATORS AND WAVEFORM-SHAPING CIRCUITS

CHAPTER 14 SIGNAL GENERATORS AND WAVEFORM-SHAPING CIRCUITS CHAPTE 4 SIGNA GENEATS AN WAEFM-SHAPING CICUITS Chapter utline 4. Baic Principle o Sinuoidal cillator 4. p Amp-C cillator 4. C and Crytal cillator 4.4 Bitable Multiibrator 4.5 Generation o Square and Triangular

More information

The Electric Potential Energy

The Electric Potential Energy Lecture 6 Chapter 28 Phyic II The Electric Potential Energy Coure webite: http://aculty.uml.edu/andriy_danylov/teaching/phyicii New Idea So ar, we ued vector quantitie: 1. Electric Force (F) Depreed! 2.

More information

Digital Control System

Digital Control System Digital Control Sytem - A D D A Micro ADC DAC Proceor Correction Element Proce Clock Meaurement A: Analog D: Digital Continuou Controller and Digital Control Rt - c Plant yt Continuou Controller Digital

More information

MULTIPLE REGRESSION ANALYSIS For the Case of Two Regressors

MULTIPLE REGRESSION ANALYSIS For the Case of Two Regressors MULTIPLE REGRESSION ANALYSIS For the Cae of Two Regreor In the followng note, leat-quare etmaton developed for multple regreon problem wth two eplanator varable, here called regreor (uch a n the Fat Food

More information

Given the following circuit with unknown initial capacitor voltage v(0): X(s) Immediately, we know that the transfer function H(s) is

Given the following circuit with unknown initial capacitor voltage v(0): X(s) Immediately, we know that the transfer function H(s) is EE 4G Note: Chapter 6 Intructor: Cheung More about ZSR and ZIR. Finding unknown initial condition: Given the following circuit with unknown initial capacitor voltage v0: F v0/ / Input xt 0Ω Output yt -

More information

Lecture 30: Frequency Response of Second-Order Systems

Lecture 30: Frequency Response of Second-Order Systems Lecture 3: Frequecy Repoe of Secod-Order Sytem UHTXHQF\ 5HVSRQVH RI 6HFRQGUGHU 6\VWHPV A geeral ecod-order ytem ha a trafer fuctio of the form b + b + b H (. (9.4 a + a + a It ca be table, utable, caual

More information

Active Filters an Introduction

Active Filters an Introduction Active Filter an Introduction + Vin() - Filter circuit G() + Vout() - Active Filter. Continuou-time or Sampled-data. Employ active element (e.g. tranitor, amplifier, op-amp) a. inductor-le (continuou-time)

More information

55:141 Advanced Circuit Techniques Two-Port Theory

55:141 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 information

Chapter 6 Electrical Systems and Electromechanical Systems

Chapter 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 information

376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD. D(s) = we get the compensated system with :

376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD. D(s) = we get the compensated system with : 376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD Therefore by applying the lead compenator with ome gain adjutment : D() =.12 4.5 +1 9 +1 we get the compenated ytem with : PM =65, ω c = 22 rad/ec, o

More information

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab

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 information

CHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS

CHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS CHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.1 INTRODUCTION 8.2 REDUCED ORDER MODEL DESIGN FOR LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.3

More information