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

Size: px
Start display at page:

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

Transcription

1 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 and the tp band t cacade dentcal lter t, three, r mre. The harpne the cacaded lter can be clearly een by a Bde plt. Let tart rm a rt-rder l pa lter e already dcued. The traner unctn the abve crcut : and the teady-tate traner unctn : j j The relatve db ampltude : 0 lg 0 lg[ A db ] / N let cnnect ne mre dentcal lter crcut t the abve crcut: Then the traner unctn becme:

2 The teady-tate traner unctn becme: j j The relatve db ampltude becme: 0 lg 0 lg[ A db ] / Let dra t Bde plt th 800, 000, and 0.uF r the rt-rder and the ecnd-rder t cacaded rt-rder lter. D yu ee the lpe db/octave r 0 db/decade r the cacaded-lter, ntead the rt-rder lter 6dB/Octave r 0 db/decade? an e dra a general lpe harpne r n-element cacade? 0n db/decade r 6n db/octave.

3 5. gher-order Actve Flter Butterrth Flter The ther ay t acheve hgher rder lter ther than cacadng dentcal lter.. Brth engneer S. Butterrth develped th type lter.. Th ectn may cntan me materal that g abve yur current undertandng math r math related ubject. Frtunately, yur man jb t undertand the reult nt the prce. Bttm lne: Yu may ant t kn nly the tem number 9, by the ay.. A unty-gan Butterrth LPF ha a traner unctn he magntude gven by j, nrder the lter n c. A unty-gan Butterrth LPF ha a traner unctn he magntude gven by j n n c 5.Let' cnder the LPF cae: Obervatn cut requency c all the ame r all the value n. I n large enugh, the denmnatr alay cle t hen < c The expnent / c alay even. 6. Then, the next bg quetn h t nd a traner unctn rm the magntude the traner unctn gven a abve. Th dervatn nvlve a lng prce: Let' tart rm a prttype LPF th c [rad/ec]. Then the LPF magntude traner unctn becme: j n By the ay, j the teady-tate traner unctn a traner unctn, therere, n requency dman: j and -j-. Al rm j, v Then, j j j n n n n n n v Al, [ ] [ ] [ ] vtherere, j n n n v Therere, n n 7. Fndng rm equatn the dcun anther length prce: Fnd the rt the plynmal: n n 0 Agn the let-hal plane rt t, and the rght-plane rt t -. mbne term n the denmnatr t rm rt- and ecnd-rder actr. 8. Let' have an example applyng the prce tated n 7 abve. Q: Fnd the Butterrth traner unctn r n nd rder Butterrth lter

4 The plynmal then: 0 ± j Fr j, e have the llng t lutn: j and j v Fr j, e have the llng t lutn: j and j v Therere, v Fnally, j j 9 Fr all n', e have the llng Butterrth plynmal n 5 nth rder Butterrth Plynmal [] LPF cae PF cae N let' dcu abut the mplementatn a Butterrth lter. The rt rder Butterrth Flter buldng blck very mple: and, and thee t can be acheved ealy rm the very bac actve lter crcut r LPF and PF. Therere, ur majr cncern h t mplement a ecnd rder Butterrth lter buldng blck ha the llng traner unctn r LPF and PF, repectvely: b r LPF r r PF. b Let' dcu abut rder Butterrth LPF. b mplementatn. See the llng gure r a ecnd

5 a: 0 / a a a b: 0 / a Then, I e aume a prttype lter th and c, then the traner unctn becme: Therere, b and Implementatn b. See the llng crcut r the dcun. Butterrth PF Smlar nde vltage equatn lead t: Aumng a prttype lter th, Therere, b and

6 EXAMPLE DESIGN r BUTTEWOT FILTE: Degn a th rder Butterrth LPF th cut requency 500 z and paband gan 0. Ue a many K retr a pble. SOLUTION: 6

, 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

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

Energy & Work

Energy & Work rk Dne by a Cntant Frce 6.-6.4 Energy & rk F N m jule () J rk Dne by a Cntant Frce Example Pullng a Sutcae-n-heel Fnd the wrk dne the rce 45.0-N, the angle 50.0 degree, and the dplacement 75.0 m. 3 ( F

More information

Problem 1. Refracting Surface (Modified from Pedrotti 2-2)

Problem 1. Refracting Surface (Modified from Pedrotti 2-2) .70 Optc Hmewrk # February 8, 04 Prblem. Reractng Surace (Me rm Pertt -) Part (a) Fermat prncple requre that every ray that emanate rm the bject an pae thrugh the mage pnt mut be chrnu (.e., have equal

More information

EECE 301 Signals & Systems Prof. Mark Fowler

EECE 301 Signals & Systems Prof. Mark Fowler -T Sytem: Ung Bode Plot EEE 30 Sgnal & Sytem Pro. Mark Fowler Note Set #37 /3 Bode Plot Idea an Help Vualze What rcut Do Lowpa Flter Break Pont = / H ( ) j /3 Hghpa Flter c = / L Bandpa Flter n nn ( a)

More information

Section 3: Detailed Solutions of Word Problems Unit 1: Solving Word Problems by Modeling with Formulas

Section 3: Detailed Solutions of Word Problems Unit 1: Solving Word Problems by Modeling with Formulas Sectn : Detaled Slutns f Wrd Prblems Unt : Slvng Wrd Prblems by Mdelng wth Frmulas Example : The factry nvce fr a mnvan shws that the dealer pad $,5 fr the vehcle. If the stcker prce f the van s $5,, hw

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

Part III Lectures Field-Effect Transistors (FETs) and Circuits

Part III Lectures Field-Effect Transistors (FETs) and Circuits Part III Lecture 5-8 Feld-Effect Trantr (FET) and Crcut Unverty f Technlgy Feld-Effect Trantr (FET) Electrcal and Electrnc Engneerng epartment Lecture Ffteen - Page f 8 ecnd Year, Electrnc I, 2009-200

More information

Introduction to Electronic circuits.

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

More information

University of Southern California School Of Engineering Department Of Electrical Engineering

University of Southern California School Of Engineering Department Of Electrical Engineering Unverty f Suthern afrna Sch Of Enneern Deartent Of Eectrca Enneern EE 48: ewrk nent # fa, Due 9/7/ ha Fure : The redrawn cnfuratn f "F P." t b t a Gven the fure, ne can wrte the fwn equatn: λ t t { λ }

More information

EE 221 Practice Problems for the Final Exam

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

More information

EE 204 Lecture 25 More Examples on Power Factor and the Reactive Power

EE 204 Lecture 25 More Examples on Power Factor and the Reactive Power EE 204 Lecture 25 Mre Examples n Pwer Factr and the Reactve Pwer The pwer factr has been defned n the prevus lecture wth an example n pwer factr calculatn. We present tw mre examples n ths lecture. Example

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

Solution to HW14 Fall-2002

Solution to HW14 Fall-2002 Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges

More information

A Result on a Cyclic Polynomials

A Result on a Cyclic Polynomials Gen. Math. Note, Vol. 6, No., Feruary 05, pp. 59-65 ISSN 9-78 Copyrght ICSRS Pulcaton, 05.-cr.org Avalale free onlne at http:.geman.n A Reult on a Cyclc Polynomal S.A. Wahd Department of Mathematc & Stattc

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

Experiment #3. Graphing with Excel

Experiment #3. Graphing with Excel Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-

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

Chapter 8. Root Locus Techniques

Chapter 8. Root Locus Techniques Chapter 8 Rt Lcu Technique Intrductin Sytem perfrmance and tability dt determined dby cled-lp l ple Typical cled-lp feedback cntrl ytem G Open-lp TF KG H Zer -, - Ple 0, -, -4 K 4 Lcatin f ple eaily fund

More information

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

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

More information

FYSE400 ANALOG ELECTRONICS

FYSE400 ANALOG ELECTRONICS YS400 NLOG LCONCS LCU 12 eedback plfer 1 uptn 1. he bac aplfer unlateral. 2. he gan OL f the bac aplfer deterned wthut feedback. 3. he calculated gan OL laded gan : ladng f the feedback netwrk, urce and

More information

Design of Analog Integrated Circuits

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

More information

Chapter 7. Systems 7.1 INTRODUCTION 7.2 MATHEMATICAL MODELING OF LIQUID LEVEL SYSTEMS. Steady State Flow. A. Bazoune

Chapter 7. Systems 7.1 INTRODUCTION 7.2 MATHEMATICAL MODELING OF LIQUID LEVEL SYSTEMS. Steady State Flow. A. Bazoune Chapter 7 Flud Systems and Thermal Systems 7.1 INTODUCTION A. Bazune A flud system uses ne r mre fluds t acheve ts purpse. Dampers and shck absrbers are eamples f flud systems because they depend n the

More information

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

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

More information

CHM112 Lab Graphing with Excel Grading Rubric

CHM112 Lab Graphing with Excel Grading Rubric Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline

More information

AP Physics Kinematic Wrap Up

AP Physics Kinematic Wrap Up AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x

More information

Lecture 13 - Boost DC-DC Converters. Step-Up or Boost converters deliver DC power from a lower voltage DC level (V d ) to a higher load voltage V o.

Lecture 13 - Boost DC-DC Converters. Step-Up or Boost converters deliver DC power from a lower voltage DC level (V d ) to a higher load voltage V o. ecture 13 - Bt C-C Cnverter Pwer Electrnic Step-Up r Bt cnverter eliver C pwer frm a lwer vltage C level ( ) t a higher la vltage. i i i + v i c T C (a) + R (a) v 0 0 i 0 R1 t n t ff + t T i n T t ff =

More information

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007 CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is

More information

Wp/Lmin. Wn/Lmin 2.5V

Wp/Lmin. Wn/Lmin 2.5V UNIVERITY OF CALIFORNIA Cllege f Engneerng Department f Electrcal Engneerng and Cmputer cences Andre Vladmrescu Hmewrk #7 EEC Due Frday, Aprl 8 th, pm @ 0 Cry Prblem #.5V Wp/Lmn 0.0V Wp/Lmn n ut Wn/Lmn.5V

More information

, which yields. where z1. and z2

, which yields. where z1. and z2 The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

More information

Richard s Transformations

Richard s Transformations 4/27/25 Rihard Tranfrmatin.d /7 Rihard Tranfrmatin Reall the put impedane f hrt-iruited and peniruited tranmiin le tub. j tan β, β t β, β Nte that the put impedane are purely reatie jut like lumped element!

More information

Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.

Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic. Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage

More information

Grumman F-14 Tomcat Control Design BY: Chike Uduku

Grumman F-14 Tomcat Control Design BY: Chike Uduku Grumman F-4 Tmcat Cntrl Deign BY: Chike duku I. Atract SECTIONS II. III. IV. Deign jective eaured Cntant Deign V. Reult VI. VII. Cncluin Cmplete atla Cde I. Atract Deigning cntrller fr fighter jet i a

More information

Note: Please use the actual date you accessed this material in your citation.

Note: Please use the actual date you accessed this material in your citation. MIT OpenCureWare http://w.mit.edu 6.03/ESD.03J Eletrmagneti and ppliatin, Fall 005 Pleae ue the fllwing itatin frmat: Marku Zahn, Erih Ippen, and David Staelin, 6.03/ESD.03J Eletrmagneti and ppliatin,

More information

FEEDBACK AMPLIFIERS. β f

FEEDBACK AMPLIFIERS. β f FEEDBC MPLFES X - X X X * What negatve eedback? ddng the eedback gnal t the nput a t patally cancel the nput gnal t the ample. * What eedback? Takng a ptn the gnal avng at the lad and eedng t back t the

More information

Chapter 3, Solution 1C.

Chapter 3, Solution 1C. COSMOS: Cmplete Onlne Slutns Manual Organzatn System Chapter 3, Slutn C. (a If the lateral surfaces f the rd are nsulated, the heat transfer surface area f the cylndrcal rd s the bttm r the tp surface

More information

Chapter 8 Predicting Molecular Geometries

Chapter 8 Predicting Molecular Geometries Chapter 8 Predicting Mlecular Gemetries 8-1 Mlecular shape The Lewis diagram we learned t make in the last chapter are a way t find bnds between atms and lne pais f electrns n atms, but are nt intended

More information

PHYS 219 Spring semester Lecture 02: Coulomb s Law how point charges interact. Ron Reifenberger Birck Nanotechnology Center Purdue University

PHYS 219 Spring semester Lecture 02: Coulomb s Law how point charges interact. Ron Reifenberger Birck Nanotechnology Center Purdue University PHYS 19 Spring semester 016 Lecture 0: Culmb s Law hw pint charges interact Rn Reifenberger Birck Nantechnlg Center Purdue Universit Lecture 0 1 Earl Develpments in Electrstatics Tw f the ur rces in Nature:

More information

Fourier Analysis, Low Pass Filters, Decibels

Fourier Analysis, Low Pass Filters, Decibels Lecture 8 Furier Analysis, Lw Pass Filters, Decibels ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Furth Edit, by Allan R. Hambley, 008 Pearsn Educat, Inc. Chapter 6 Frequency Respnse, Bde Plts,

More information

WYSE Academic Challenge 2004 Sectional Physics Solution Set

WYSE Academic Challenge 2004 Sectional Physics Solution Set WYSE Acadec Challenge 004 Sectnal Physcs Slutn Set. Answer: e. The axu pssble statc rctn r ths stuatn wuld be: ax µ sn µ sg (0.600)(40.0N) 4.0N. Snce yur pushng rce s less than the axu pssble rctnal rce,

More information

III. Operational Amplifiers

III. Operational Amplifiers III. Operatnal Amplfers Amplfers are tw-prt netwrks n whch the utput vltage r current s drectly prprtnal t ether nput vltage r current. Fur dfferent knds f amplfers ext: ltage amplfer: Current amplfer:

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

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

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

More information

Supplementary Course Notes Adding and Subtracting AC Voltages and Currents

Supplementary Course Notes Adding and Subtracting AC Voltages and Currents Supplementary Curse Ntes Adding and Subtracting AC Vltages and Currents As mentined previusly, when cmbining DC vltages r currents, we nly need t knw the plarity (vltage) and directin (current). In the

More information

Section 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law

Section 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law Sectin 5.8 Ntes Page 1 5.8 Expnential Grwth and Decay Mdels; Newtn s Law There are many applicatins t expnential functins that we will fcus n in this sectin. First let s lk at the expnential mdel. Expnential

More information

ECE-320: Linear Control Systems Homework 1. 1) For the following transfer functions, determine both the impulse response and the unit step response.

ECE-320: Linear Control Systems Homework 1. 1) For the following transfer functions, determine both the impulse response and the unit step response. Due: Mnday Marh 4, 6 at the beginning f la ECE-: Linear Cntrl Sytem Hmewrk ) Fr the fllwing tranfer funtin, determine bth the imule rene and the unit te rene. Srambled Anwer: H ( ) H ( ) ( )( ) ( )( )

More information

Three charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter).

Three charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter). Three charges, all with a charge f 0 are situated as shwn (each grid line is separated by meter). ) What is the net wrk needed t assemble this charge distributin? a) +0.5 J b) +0.8 J c) 0 J d) -0.8 J e)

More information

(b) Using the ideal gas equation of state, and noting that the total mass of gas occupies the same total volume at the final state as initially: where

(b) Using the ideal gas equation of state, and noting that the total mass of gas occupies the same total volume at the final state as initially: where 6.55 Given: An inulated cylinder i initially divided int halve y a itn. On either ide the itn i a ga at a knwn tate. The itn i releaed and equiliriu i attained. Find: Deterine the inal reure, inal teerature,

More information

Exercise - INSTRUCTIONS

Exercise - INSTRUCTIONS Learning mdule: Create Cmb Charts Exercise - INSTRUCTIONS Using the Example Dwnlad instructins n the right, pen the Create Cmb Chart_Exercise.qvf file. This app already cntains data, but has n sheets r

More information

Continuous-Time Filters

Continuous-Time Filters tuute Flter.0 Operatal Tracductace Aplfer (OTA Z Z ut (a (b (c (d Fgure. deal all gal equvalet crcut f Sgle eded OTA ad Fully dfferetal OTA pleetat Ug Sgle eded OTA. Fgure (a h the ybl f gle eded OTA.

More information

Functions. EXPLORE \g the Inverse of ao Exponential Function

Functions. EXPLORE \g the Inverse of ao Exponential Function ifeg Seepe3 Functins Essential questin: What are the characteristics f lgarithmic functins? Recall that if/(x) is a ne-t-ne functin, then the graphs f/(x) and its inverse,/'~\x}, are reflectins f each

More information

f = µ mg = kg 9.8m/s = 15.7N. Since this is more than the applied

f = µ mg = kg 9.8m/s = 15.7N. Since this is more than the applied Phsics 141H lutins r Hmewrk et #5 Chapter 5: Multiple chice: 8) (a) he maimum rce eerted b static rictin is µ N. ince the blck is resting n a level surace, N = mg. the maimum rictinal rce is ( ) ( ) (

More information

element k Using FEM to Solve Truss Problems

element k Using FEM to Solve Truss Problems sng EM t Slve Truss Prblems A truss s an engneerng structure cmpsed straght members, a certan materal, that are tpcall pn-ned at ther ends. Such members are als called tw-rce members snce the can nl transmt

More information

CHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review

CHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review Review Accrding t the nd law f Thermdynamics, a prcess is spntaneus if S universe = S system + S surrundings > 0 Even thugh S system

More information

In-Class Problem 5: Newton s Laws of Motion

In-Class Problem 5: Newton s Laws of Motion In-Cla Problem 5: Neton La of Motion Conider a trac ith a pulley located at the end. The force enor and cart have total ma m 1. They are connected by a inextenible rope of length l (paing over the pulley)

More information

Plan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations

Plan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations STAPLE Physics 201 Name Final Exam May 14, 2013 This is a clsed bk examinatin but during the exam yu may refer t a 5 x7 nte card with wrds f wisdm yu have written n it. There is extra scratch paper available.

More information

Chemistry 20 Lesson 11 Electronegativity, Polarity and Shapes

Chemistry 20 Lesson 11 Electronegativity, Polarity and Shapes Chemistry 20 Lessn 11 Electrnegativity, Plarity and Shapes In ur previus wrk we learned why atms frm cvalent bnds and hw t draw the resulting rganizatin f atms. In this lessn we will learn (a) hw the cmbinatin

More information

Chapter 9 Compressible Flow 667

Chapter 9 Compressible Flow 667 Chapter 9 Cmpreible Flw 667 9.57 Air flw frm a tank thrugh a nzzle int the tandard atmphere, a in Fig. P9.57. A nrmal hck tand in the exit f the nzzle, a hwn. Etimate (a) the tank preure; and (b) the ma

More information

55:041 Electronic Circuits

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

More information

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving.

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving. Sectin 3.2: Many f yu WILL need t watch the crrespnding vides fr this sectin n MyOpenMath! This sectin is primarily fcused n tls t aid us in finding rts/zers/ -intercepts f plynmials. Essentially, ur fcus

More information

Lesson #15. Section BME 373 Electronics II J.Schesser

Lesson #15. Section BME 373 Electronics II J.Schesser Feedack and Ocillatr Len # Tranient and Frequency Repne Sectin 9.6- BME 373 Electrnic II J.Scheer 78 Cled-Lp Gain in the Frequency Dmain ume that th the pen-lp gain, and the eedack, β are unctin requency

More information

Supplementary Course Notes Adding and Subtracting AC Voltages and Currents

Supplementary Course Notes Adding and Subtracting AC Voltages and Currents Supplementary Curse Ntes Adding and Subtracting AC Vltages and Currents As mentined previusly, when cmbining DC vltages r currents, we nly need t knw the plarity (vltage) and directin (current). In the

More information

Lecture 12: Chemical reaction equilibria

Lecture 12: Chemical reaction equilibria 3.012 Fundamentals f Materials Science Fall 2005 Lecture 12: 10.19.05 Chemical reactin equilibria Tday: LAST TIME...2 EQUATING CHEMICAL POTENTIALS DURING REACTIONS...3 The extent f reactin...3 The simplest

More information

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came. MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the

More information

NONISOTHERMAL OPERATION OF IDEAL REACTORS Plug Flow Reactor. F j. T mo Assumptions:

NONISOTHERMAL OPERATION OF IDEAL REACTORS Plug Flow Reactor. F j. T mo Assumptions: NONISOTHERMAL OPERATION OF IDEAL REACTORS Plug Flw Reactr T T T T F j, Q F j T m,q m T m T m T m Aumptin: 1. Hmgeneu Sytem 2. Single Reactin 3. Steady State Tw type f prblem: 1. Given deired prductin rate,

More information

ECE 5318/6352 Antenna Engineering. Spring 2006 Dr. Stuart Long. Chapter 6. Part 7 Schelkunoff s Polynomial

ECE 5318/6352 Antenna Engineering. Spring 2006 Dr. Stuart Long. Chapter 6. Part 7 Schelkunoff s Polynomial ECE 538/635 Antenna Engineering Spring 006 Dr. Stuart Lng Chapter 6 Part 7 Schelkunff s Plynmial 7 Schelkunff s Plynmial Representatin (fr discrete arrays) AF( ψ ) N n 0 A n e jnψ N number f elements in

More information

NUMBERS, MATHEMATICS AND EQUATIONS

NUMBERS, MATHEMATICS AND EQUATIONS AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t

More information

Lab 11 LRC Circuits, Damped Forced Harmonic Motion

Lab 11 LRC Circuits, Damped Forced Harmonic Motion Physics 6 ab ab 11 ircuits, Damped Frced Harmnic Mtin What Yu Need T Knw: The Physics OK this is basically a recap f what yu ve dne s far with circuits and circuits. Nw we get t put everything tgether

More information

B. Definition of an exponential

B. Definition of an exponential Expnents and Lgarithms Chapter IV - Expnents and Lgarithms A. Intrductin Starting with additin and defining the ntatins fr subtractin, multiplicatin and divisin, we discvered negative numbers and fractins.

More information

Death of a Salesman. 20 formative points. 20 formative points (pg 3-5) 25 formative points (pg 6)

Death of a Salesman. 20 formative points. 20 formative points (pg 3-5) 25 formative points (pg 6) Death f a Salesman Essential Questins: What is the American Dream? What des it mean t be successful? Wh defines what it means t be successful? Yu? Yur family? Sciety? Tasks/Expectatins Pints Yu will be

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

3/22/18. Onward to Galaxies, starting with our own! Warping of Space by Gravity. Three aspects of falling into a black hole: 1) Spaghettified

3/22/18. Onward to Galaxies, starting with our own! Warping of Space by Gravity. Three aspects of falling into a black hole: 1) Spaghettified ASTR 1040: Stars & Galaxies Prf. Juri Tmre TAs: Peri Jhnsn, Ryan Hrtn Lecture 20 Thur 22 Mar 2018 zeus.clrad.edu/astr1040-tmre M51 Whirlpl Onward t Galaxies, starting with ur wn! Revisit Our Milky Way

More information

Final Exam Spring 2014 SOLUTION

Final Exam Spring 2014 SOLUTION Appled Opts H-464/564 C 594 rtland State nverst A. La Rsa Fnal am Sprng 14 SOLTION Name There are tw questns 1%) plus an ptnal bnus questn 1%) 1. Quarter wave plates and half wave plates The fgures belw

More information

Lead/Lag Compensator Frequency Domain Properties and Design Methods

Lead/Lag Compensator Frequency Domain Properties and Design Methods Lectures 6 and 7 Lead/Lag Cmpensatr Frequency Dmain Prperties and Design Methds Definitin Cnsider the cmpensatr (ie cntrller Fr, it is called a lag cmpensatr s K Fr s, it is called a lead cmpensatr Ntatin

More information

lecture 5: Nucleophilic Substitution Reactions

lecture 5: Nucleophilic Substitution Reactions lecture 5: Nuclephilic Substitutin Reactins Substitutin unimlecular (SN1): substitutin nuclephilic, unimlecular. It is first rder. The rate is dependent upn ne mlecule, that is the substrate, t frm the

More information

LaPlace Transforms in Design and Analysis of Circuits Part 3: Basic Parallel Circuit Analysis

LaPlace Transforms in Design and Analysis of Circuits Part 3: Basic Parallel Circuit Analysis LaPlace Tranfrm n Degn and Analy f Crcut Part : Bac Parallel Crcut Analy Cure N: E-7 Credt: PDH Thma G. Bertenhaw, Ed.D., P.E. Cntnung Educatn and Develpment, Inc. 9 Greyrdge Farm Curt Stny Pnt, NY 98

More information

6. Frequency Response

6. Frequency Response 6. Frequency esnse eading: Sedra & Sith: hater.6, hater 3.6 and hater 9 (MOS rtins, EE 0, Winter 0, F. Najabadi Tyical Frequency resnse an liier U t nw we have ignred the caacitrs. T include the caacitrs,

More information

Lab #3: Pendulum Period and Proportionalities

Lab #3: Pendulum Period and Proportionalities Physics 144 Chwdary Hw Things Wrk Spring 2006 Name: Partners Name(s): Intrductin Lab #3: Pendulum Perid and Prprtinalities Smetimes, it is useful t knw the dependence f ne quantity n anther, like hw the

More information

ECE 2100 Circuit Analysis

ECE 2100 Circuit Analysis ECE 2100 Circuit Analysis Lessn 25 Chapter 9 & App B: Passive circuit elements in the phasr representatin Daniel M. Litynski, Ph.D. http://hmepages.wmich.edu/~dlitynsk/ ECE 2100 Circuit Analysis Lessn

More information

Name Student ID. A student uses a voltmeter to measure the electric potential difference across the three boxes.

Name Student ID. A student uses a voltmeter to measure the electric potential difference across the three boxes. Name Student ID II. [25 pt] Thi quetin cnit f tw unrelated part. Part 1. In the circuit belw, bulb 1-5 are identical, and the batterie are identical and ideal. Bxe,, and cntain unknwn arrangement f linear

More information

Purchase Order Workflow Processing

Purchase Order Workflow Processing P a g e 1 Purchase Order Wrkflw Prcessing P a g e 2 Table f Cntents PO Wrkflw Prcessing...3 Create a Purchase Order...3 Submit a Purchase Order...4 Review/Apprve the PO...4 Prcess the PO...6 P a g e 3

More information

Feedback Principle :-

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

More information

Averaged Modeling of Non-ideal Boost Converter Operating in DCM

Averaged Modeling of Non-ideal Boost Converter Operating in DCM Internatnal Jurnal f Cmputer and lectrcal ngneerng l.3 N. February 793-863 Averaged Mdelng f Nn-deal Bt Cnverter Operatng n DCM Guang-jun Xe Senr Member IACSI Xuan Zha Ha-bn Fang and Hu-fang Xu Abtract

More information

Lecture 6: Phase Space and Damped Oscillations

Lecture 6: Phase Space and Damped Oscillations Lecture 6: Phase Space and Damped Oscillatins Oscillatins in Multiple Dimensins The preius discussin was fine fr scillatin in a single dimensin In general, thugh, we want t deal with the situatin where:

More information

Differentiation Applications 1: Related Rates

Differentiation Applications 1: Related Rates Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm

More information

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

More information

Oscillator. Introduction of Oscillator Linear Oscillator. Stability. Wien Bridge Oscillator RC Phase-Shift Oscillator LC Oscillator

Oscillator. Introduction of Oscillator Linear Oscillator. Stability. Wien Bridge Oscillator RC Phase-Shift Oscillator LC Oscillator Oscillatr Intrductin f Oscillatr Linear Oscillatr Wien Bridge Oscillatr Phase-Shift Oscillatr L Oscillatr Stability Oscillatrs Oscillatin: an effect that repeatedly and regularly fluctuates abut the mean

More information

Introduction to Smith Charts

Introduction to Smith Charts Intrductin t Smith Charts Dr. Russell P. Jedlicka Klipsch Schl f Electrical and Cmputer Engineering New Mexic State University as Cruces, NM 88003 September 2002 EE521 ecture 3 08/22/02 Smith Chart Summary

More information

Module B3. VLoad = = V S V LN

Module B3. VLoad = = V S V LN Mdule B Prblem The -hase lads are cnnected n arallel. One s a urely resste lad cnnected n wye. t cnsumes 00kW. The secnd s a urely nducte 00kR lad cnnected n wye. The thrd s a urely caacte 00kR lad cnnected

More information

Exercises for Frequency Response. ECE 102, Fall 2012, F. Najmabadi

Exercises for Frequency Response. ECE 102, Fall 2012, F. Najmabadi Eecses Fequency espnse EE 0, Fall 0, F. Najabad Eecse : Fnd the d-band an and the lwe cut- equency the aple belw. µ n (W/ 4 A/, t 0.5, λ 0, 0 µf, and µf Bth capacts ae lw- capacts. F. Najabad, EE0, Fall

More information

You need to be able to define the following terms and answer basic questions about them:

You need to be able to define the following terms and answer basic questions about them: CS440/ECE448 Sectin Q Fall 2017 Midterm Review Yu need t be able t define the fllwing terms and answer basic questins abut them: Intr t AI, agents and envirnments Pssible definitins f AI, prs and cns f

More information

Electrical Circuits II (ECE233b)

Electrical Circuits II (ECE233b) Electrcal Crcut II (ECE33b) Applcaton of Laplace Tranform to Crcut Analy Anet Dounav The Unverty of Wetern Ontaro Faculty of Engneerng Scence Crcut Element Retance Tme Doman (t) v(t) R v(t) = R(t) Frequency

More information

Ch5 Appendix Q-factor and Smith Chart Matching

Ch5 Appendix Q-factor and Smith Chart Matching Ch5 Appedx -factr ad mth Chart Matchg 5B-1 We-Cha a udwg, F Crcut Deg hery ad Applcat, Chapter 8 -type matchg etwrk w-cmpet Matchg Netwrk hee etwrk ue tw reactve cmpet t trafrm the lad mpedace t the dered

More information

Astro 102 Lab #2. 1) Learning the user interface and setting up your home location

Astro 102 Lab #2. 1) Learning the user interface and setting up your home location Name: Astr 102 Lab #2 Lab bjectives 1) Learn hw t use the Stellarium planetarium prgram by becming familiar with the user interface and cnfiguring the planetarium t yur present lcatin n Earth 2) Learn

More information

The Simple Linear Regression Model: Theory

The Simple Linear Regression Model: Theory Chapter 3 The mple Lear Regress Mdel: Ther 3. The mdel 3.. The data bservats respse varable eplaatr varable : : Plttg the data.. Fgure 3.: Dsplag the cable data csdered b Che at al (993). There are 79

More information

EEO 401 Digital Signal Processing Prof. Mark Fowler

EEO 401 Digital Signal Processing Prof. Mark Fowler EEO 401 Digital Signal Prcessing Prf. Mark Fwler Intrductin Nte Set #1 ading Assignment: Ch. 1 f Prakis & Manlakis 1/13 Mdern systems generally DSP Scenari get a cntinuus-time signal frm a sensr a cnt.-time

More information

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y= Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents

More information

RN53 Radon Detector. RN53-STK Starter Kit

RN53 Radon Detector. RN53-STK Starter Kit The RN53-STK Starter Kit has everything yu need t kick-start yur prject and is a great tl fr develpers: Prf f cncept prttypes as well as final cmmercial slutins. fr educatinal use: Natural science curses

More information

Invertebrate Biodiversity

Invertebrate Biodiversity Invertebrate Bidiversity Backgrund infrmatin Insects and ther invertebrates are essential fr any healthy ecsystem. Invertebrates aerate the sil, eat plant pests, pllinate flwers, and prvide fd fr ther

More information

Medium Scale Integrated (MSI) devices [Sections 2.9 and 2.10]

Medium Scale Integrated (MSI) devices [Sections 2.9 and 2.10] EECS 270, Winter 2017, Lecture 3 Page 1 f 6 Medium Scale Integrated (MSI) devices [Sectins 2.9 and 2.10] As we ve seen, it s smetimes nt reasnable t d all the design wrk at the gate-level smetimes we just

More information