EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67  FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1  TRANSIENTS


 Ann Reed
 2 years ago
 Views:
Transcription
1 EDEXEL NAIONAL ERIFIAE/DIPLOMA UNI 67  FURHER ELERIAL PRINIPLE NQF LEEL 3 OUOME 2 UORIAL 1  RANIEN Uni conen 2 Undersand he ransien behaviour of resisorcapacior (R) and resisorinducor (RL) D circuis ransien behaviour of R circui: variaion of curren and volage wih ime when charging/scharging; ime consan; graphical deerminaion of growh and decay of volage and curren when charging/scharging; pracical R circui o demonsrae ransien behaviour; demonsrae he effec of he circui ime consan on a recangular waveform e.g. inegraor and ffereniaor circuis; calculaions e.g. ime consan, growh of capacior volage, iniial and seady sae values of curren, decay of resisor volage ransien behaviour of RL circui: variaion of curren and volage wih ime when conneced/sconneced o a D volage source; ime consan; graphical deerminaion of growh and decay of curren and volage when conneced/sconneced o a D volage source; pracical RL circui o demonsrae ransien behaviour; calculaions e.g. ime consan, growh of curren, decay of induced volage, curren decay I is assumed ha sudens have already sued elecrical principles. You will find more useful informaion on capacior charging and scharging a his web sie: hp:// D.J.Dunn 1
2 1. HARGING AND DIHARGING OF A APAIOR he circui shows a capacior in series wih a resisor and a D source. When he swich is in posiion 1, he baery will send curren hrough he resisor and charge he capacior. he volage is iniially zero and he volage R is he same as so he capacior charges a a fas rae. As he capacior charges, he volage increases and R decreases and he curren reduces unil he = and he curren is zero. he capacior is hen charged o. If he swich is moved o posiion 2, he charge rushes ou of he capacior hrough he resisor, ssipaing all he energy as hea unil no curren flows and = R =. If we recorded he volage c and R and I agains ime for charging and scharging we ge graphs like his. If he resisance and capaciance are boh large he charging will ake longer like filling a large conainer hrough a ap ha is nearly closed. If hey are small, he charging is fas like filling a small conainer wih he ap fully open. he agram shows his affec on charging. IME ONAN We call he produc R he ime consan and denoe i or someime 'τ'. If you refer o he absolue basic unis of Farads and Ohms you will see ha he unis are indeed seconds. When he volage and curren are changing, we say hey are in a RANIEN AGE. When hey reach a consan value we say hey are in a EADY AE. I is widely acceped ha i akes a ime of 5 or 5R o reach a seady sae. We need mahemaics o derive he equaions of hese curves bu you don' have o follow he derivaion in order o complee his uorial (alhough i helps). he following derivaion uses sraigh forward algebra and basic calculus. HARGING he curren hea flows from he source a rae i amps hrough he resisor and ino he capacior. ΔQ urren is he rae of charge wih ime so i Δ R he volage across he resisor is R = i R i. Equaing R ΔQ R R Δ dq Over an infiniesimally small change in ime his becomes he calculus form R R d dq Hence R R.(A) d D.J.Dunn 2
3 For he capacior, he we know Q = For a small change Q = For an infiniesimally small change dq = d.(b) ubsiue (B) ino (A) d R R d = R hence d d R d d his equaion ells us how varies wih ime bu in order o use i, we mus solve i. d In order o find we mus solve he equaion d Le = x Differeniae and since is a consan we find d = dx he equaion becomes dx d dx x x Rearranging d x Inegraing 1 dx d ln x x he limis become clear when we subsiue x = 1 dx d ln ln x ln ln ln 1 ake anilogs and e 1 Rearrange 1 e his relaes he volage over he capacior o ime from he momen when he swich is hrown o posiion 1. DIHARGING When he swich in he circui is hrown o posiion 2 he volage over he capacior is a = and if he derivaion is repeaed wih he correc limis of inegraion we find he relaionship is: e he graph below shows he resul for = 2 seconds and = 1. Noe he volage across he resisor is HE MEANING OF HE IME ONAN onsider he charging curve. 1 e he rae of change of volage a any ime is he graen of he curve and simply obained by ffereniaing. d e d onsider ha a = (he sar of he process) d (Remember ha e = 1) d If he change coninued a his rae, he volage would become afer seconds as illusraed on he graph. D.J.Dunn 3
4 We could define as he ime aken o reach he maximum value if he iniial rae of change is mainained. In oher words i is where he iniial graen inerceps he final value as shown. Anoher meaning is obained by examining he value afer seconds. Puing = we have 1 1 e 1 e.633 o he ime consan is he ime aken o change by 63.3% of he final value. his is useful when finng from a graph. If calculae he volage a = 4 we find = 98.2% and his is aken as anoher definiion of. I is widely acceped ha when = 5 he volage has reached is maximum. GRAPHIAL ONRUION MEHOD If we know he ime consan we can consruc he charge or scharge curves wih a graphical mehod as follows. ep 1  Draw he final value line and mark off he ime consan. onnec he origin o his poin. ep 2  hoose a poin on he las line drawn and mark off anoher ime consan from his poin. Projec o he final value line and connec he wo poins. Repea his process as shown and you will have a series of angens o he charging curve. his may be drawn in as shown in red. he closer you make your poins he more accurae he graph will be. he consrucion of a scharge curve is he same bu invered. D.J.Dunn 4
5 WORKED EXAMPLE No. 1 A capacior of value 5 μf is charged from zero o 1 hrough a 5 MΩ resisor. alculae he ime consan and he ime aken for he volage o rise o 5. OLUION = R = 5 x 16 x 5 x 1 6 = e e e 25 e ln(.5).6931 = 25 x.6931 = seconds WORKED EXAMPLE No. 2 A apaciance of 2 F is conneced in series wih a resisor of 2 k. he volage across he nework is suddenly changed from o 1. alculae he ime consan and deduce he ime aken for he volage on he capacior o rise o 5. OLUION = R = 2 x 1 3 x 2 x 16 = 4 seconds =5 = 1(1 e /4 ).5 =(1 e /4 ).5 = e /4 ln(.5) = / = /4 = 2.77 s when = 5 WORKED EXAMPLE No. 3 A apaciance of 1 F is charged up o 5. he capacior is scharged by connecing a 2 M resisor across he erminal. alculae he ime consan and deduce he ime aken for he volage on he capacior o fall o 1. OLUION = R = 2 x 1 6 x 1 x 16 = 2 seconds =1 = 5e /2 1/5 = e /2 ln(1/5) = / = /2 = s when = 1 D.J.Dunn 5
6 ELF AEMEN EXERIE No he graph shows a charging curve for a capacior and resisance. Work ou he ime consan and deermine he capaciance if he resisor value is 6 kω. (Answers.12 s and 2 μf) 2. alculae he ime consan for an R circui wih a resisance of 22 and capaciance of 47 nf in series. (13 s) How long es i ake for he volage o become a seady value? 3. A capacior of 2 μf is charged o 12 and hen a resisor of 5 Ω is conneced across i. alculae he charge sored. (.24 oulomb) alculae he energy sored. (.144 J) alculae ime aken o scharge o 1 (.25 s) 4. A capaciance of 15 μf is charged o 1 hrough a resisance of 2 MΩ. alculae he ime consan. onsruc he charging curve and deermine he ime aken o charge o 5. How long does i ake o reach a seady value? (21 s and 15 s approx) D.J.Dunn 6
7 2 HARGE DIHARGE OF AN INDUOR When a resisor is conneced in series wih an inducor we ge a similar charging and scharging effec. When he swich is hrown o posiion 1 here is a rush of curren. A his momen he rae of change of curren /d is a maximum so we ge maximum back emf on he inducor. Afer a ime he curren seles down o a maximum value of I = s /R so s = IR Le he curren a any ime be i. R = ir L = L /d ir L d IR ir L d R(I i) L d L (I i) R d If we examined he unis of L/R we would find ha his is seconds and L/R is he ime consan for he circui. = L/R (I i) d d I i If we subsiue x = I i hen dx =  dx dx i d d lnx lni i x x ake anilogs I i ln(i i) ln(i) ln ln 1 I i i e 1 1 e i I 1 e 1 e I I R his relaes he curren flowing in he circui o ime and he resul is a curren ha rises fas and hen levels off a he consan value. i I he graph shows he resul for = 1, R =.5 Ω and L = 2H giving are no pracical and only used o illusrae he resul) = 4 seconds (he values he ime consan may be defined as he ime aken o reach 63.3% of he maximum curren. Pure inducance is impossible and inducors always have some resisance in he conducor. ircuis usually show a pracical inducor as a pure inducance in series wih a resisance. In iems like ransformers, he resisance of he coil can be quie high. D.J.Dunn 7
8 WORKED EXAMPLE No. 3 An Inducance of 4 mh also has a resisance of.3 Ω. alculae he ime consan. Wha is he seady sae curren when 2 is applied across i? Wha is he curren.2 s afer he volage is suddenly changed from zero o 2? OLUION = L/R =.4/.3 =.13 s I = /R = 2/.3 = 66.7 A.2.13 i I1 e e 51.8 A ELF AEMEN EXERIE No alculae he ime consan for a series R L circui wih an inducance of 6 μh and resisance.2 Ω. (3 ms) 2. An inducor wih inducance 6 mh and resisance.7 Ω suddenly has 2 conneced across i. alculae he seady sae curren. (2.857A) alculae he energy sored and power ssipaed. (.245 J and W) alculae he ime aken for he curren o rise o.5 A. (16 ms) 3. he volage across he inducor shown is iniially zero. how ha when he swich is closed ha he volage across he inducor will be v = E e /τ where is he ime elapsed afer he swich is closed. Deermine an expression for he ime consan τ in erms of R and L. D.J.Dunn 8
9 3. APAIOR FOR INEGRAING AND DIFFERENIAING d he basic relaionship beween volage and curren flowing ino a capacior is i d capacior can be used inegrae and ffereniae a volage. INEGRAOR IRUI If a volage s is applied o he circui shown, he volage across he capacior is c 1 i d uppose ha a square wave form is applied o he inpu wih a frequency jus sufficien o allow he capacior o charge and scharge on each cycle. he oupu c will be a series a charging and scharging curves. so a If he frequency is slower he capacior will fully charge and dwell before scharging. If he frequency is faser, he capacior will no fully charge or scharge and he waveforms will look like his. If he consans are so arranged, a riangular wave form can be produced. DIFFERENIAOR IRUI If a square wave is applied o his circui, he volage R will be he inverse of he previous oupus ELF AEMEN EXERIE No kech he oupu of an inegraor and ffereniaor circui when a riangular wave form is applied o he inpu. Explain your reasoning. D.J.Dunn 9
RC (ResistorCapacitor) Circuits. AP Physics C
(ResisorCapacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationModule 4. Singlephase AC circuits. Version 2 EE IIT, Kharagpur
Module 4 Singlephase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,
More informationCircuit Types. () i( t) ( )
Circui Types DC Circuis Idenifying feaures: o Consan inpus: he volages of independen volage sources and currens of independen curren sources are all consan. o The circui does no conain any swiches. All
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 informationRC Circuit and Time Constant
ircui and Time onsan 8M Objec: Apparaus: To invesigae he volages across he resisor and capacior in a resisorcapacior circui ( circui) as he capacior charges and discharges. We also wish o deermine he
More informationChapter 2: Principles of steadystate converter analysis
Chaper 2 Principles of SeadySae Converer Analysis 2.1. Inroducion 2.2. Inducor volsecond balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer
More informationCapacitors and inductors
Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationChabot College Physics Lab RC Circuits Scott Hildreth
Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College  Physics 2426  Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
More informationTransient Analysis of First Order RC and RL circuits
Transien Analysis of Firs Order and iruis The irui shown on Figure 1 wih he swih open is haraerized by a pariular operaing ondiion. Sine he swih is open, no urren flows in he irui (i=0) and v=0. The volage
More information4kq 2. D) south A) F B) 2F C) 4F D) 8F E) 16F
efore you begin: Use black pencil. Wrie and bubble your SU ID Number a boom lef. Fill bubbles fully and erase cleanly if you wish o change! 20 Quesions, each quesion is 10 poins. Each quesion has a mos
More information9. Capacitor and Resistor Circuits
ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren
More informationPHYS245 Lab: RC circuits
PHYS245 Lab: C circuis Purpose: Undersand he charging and discharging ransien processes of a capacior Display he charging and discharging process using an oscilloscope Undersand he physical meaning of
More informationUsing RCtime to Measure Resistance
Basic Express Applicaion Noe Using RCime o Measure Resisance Inroducion One common use for I/O pins is o measure he analog value of a variable resisance. Alhough a builin ADC (Analog o Digial Converer)
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More information1. The graph shows the variation with time t of the velocity v of an object.
1. he graph shows he variaion wih ime of he velociy v of an objec. v Which one of he following graphs bes represens he variaion wih ime of he acceleraion a of he objec? A. a B. a C. a D. a 2. A ball, iniially
More informationPhysics 111 Fall 2007 Electric Currents and DC Circuits
Physics 111 Fall 007 Elecric Currens and DC Circuis 1 Wha is he average curren when all he sodium channels on a 100 µm pach of muscle membrane open ogeher for 1 ms? Assume a densiy of 0 sodium channels
More informationVoltage level shifting
rek Applicaion Noe Number 1 r. Maciej A. Noras Absrac A brief descripion of volage shifing circuis. 1 Inroducion In applicaions requiring a unipolar A volage signal, he signal may be delivered from a bipolar
More informationDifferential Equations and Linear Superposition
Differenial Equaions and Linear Superposiion Basic Idea: Provide soluion in closed form Like Inegraion, no general soluions in closed form Order of equaion: highes derivaive in equaion e.g. dy d dy 2 y
More informationModule 3. RL & RC Transients. Version 2 EE IIT, Kharagpur
Module 3  & C Transiens esson 0 Sudy of DC ransiens in  and C circuis Objecives Definiion of inducance and coninuiy condiion for inducors. To undersand he rise or fall of curren in a simple series
More informationFullwave rectification, bulk capacitor calculations Chris Basso January 2009
ullwave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal
More informationA Mathematical Description of MOSFET Behavior
10/19/004 A Mahemaical Descripion of MOSFET Behavior.doc 1/8 A Mahemaical Descripion of MOSFET Behavior Q: We ve learned an awful lo abou enhancemen MOSFETs, bu we sill have ye o esablished a mahemaical
More informationName: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling
Name: Algebra II Review for Quiz #13 Exponenial and Logarihmic Funcions including Modeling TOPICS: Solving Exponenial Equaions (The Mehod of Common Bases) Solving Exponenial Equaions (Using Logarihms)
More informationSection 7.1 Angles and Their Measure
Secion 7.1 Angles and Their Measure Greek Leers Commonly Used in Trigonomery Quadran II Quadran III Quadran I Quadran IV α = alpha β = bea θ = hea δ = dela ω = omega γ = gamma DEGREES The angle formed
More informationSwitching Regulator IC series Capacitor Calculation for Buck converter IC
Swiching Regulaor IC series Capacior Calculaion for Buck converer IC No.14027ECY02 This applicaion noe explains he calculaion of exernal capacior value for buck converer IC circui. Buck converer IIN IDD
More informationRotational Inertia of a Point Mass
Roaional Ineria of a Poin Mass Saddleback College Physics Deparmen, adaped from PASCO Scienific PURPOSE The purpose of his experimen is o find he roaional ineria of a poin experimenally and o verify ha
More informationChapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr
Chaper 2 Problems 2.2 A car ravels up a hill a a consan speed of 40km/h and reurns down he hill a a consan speed of 60 km/h. Calculae he average speed for he rip. This problem is a bi more suble han i
More informationTwo Compartment Body Model and V d Terms by Jeff Stark
Two Comparmen Body Model and V d Terms by Jeff Sark In a onecomparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics  By his, we mean ha eliminaion is firs order and ha pharmacokineic
More informationµ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ
Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high
More informationFourier series. Learning outcomes
Fourier series 23 Conens. Periodic funcions 2. Represening ic funcions by Fourier Series 3. Even and odd funcions 4. Convergence 5. Halfrange series 6. The complex form 7. Applicaion of Fourier series
More informationAcceleration Lab Teacher s Guide
Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion
More informationSteps for D.C Analysis of MOSFET Circuits
10/22/2004 Seps for DC Analysis of MOSFET Circuis.doc 1/7 Seps for D.C Analysis of MOSFET Circuis To analyze MOSFET circui wih D.C. sources, we mus follow hese five seps: 1. ASSUME an operaing mode 2.
More information2 Electric Circuits Concepts Durham
Chaper 3  Mehods Chaper 3  Mehods... 3. nroducion... 2 3.2 Elecrical laws... 2 3.2. Definiions... 2 3.2.2 Kirchhoff... 2 3.2.3 Faraday... 3 3.2.4 Conservaion... 3 3.2.5 Power... 3 3.2.6 Complee... 4
More informationChapter 2 Kinematics in One Dimension
Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More informationPulseWidth Modulation Inverters
SECTION 3.6 INVERTERS 189 PulseWidh Modulaion Inverers Pulsewidh modulaion is he process of modifying he widh of he pulses in a pulse rain in direc proporion o a small conrol signal; he greaer he conrol
More informationAppendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.
Appendi A: Area workedou s o OddNumbered Eercises Do no read hese workedou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa
More informationDifferential Equations. Solving for Impulse Response. Linear systems are often described using differential equations.
Differenial Equaions Linear sysems are ofen described using differenial equaions. For example: d 2 y d 2 + 5dy + 6y f() d where f() is he inpu o he sysem and y() is he oupu. We know how o solve for y given
More informationPart II Converter Dynamics and Control
Par II onverer Dynamics and onrol 7. A equivalen circui modeling 8. onverer ransfer funcions 9. onroller design 1. Inpu filer design 11. A and D equivalen circui modeling of he disconinuous conducion mode
More informationSignal Processing and Linear Systems I
Sanford Universiy Summer 214215 Signal Processing and Linear Sysems I Lecure 5: Time Domain Analysis of Coninuous Time Sysems June 3, 215 EE12A:Signal Processing and Linear Sysems I; Summer 1415, Gibbons
More informationMaking Use of Gate Charge Information in MOSFET and IGBT Data Sheets
Making Use of ae Charge Informaion in MOSFET and IBT Daa Shees Ralph McArhur Senior Applicaions Engineer Advanced Power Technology 405 S.W. Columbia Sree Bend, Oregon 97702 Power MOSFETs and IBTs have
More information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More informationAP Calculus AB 2013 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a missiondriven noforprofi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was
More information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuingedge
More informationAP Calculus BC 2010 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More information5.8 Resonance 231. The study of vibrating mechanical systems ends here with the theory of pure and practical resonance.
5.8 Resonance 231 5.8 Resonance The sudy of vibraing mechanical sysems ends here wih he heory of pure and pracical resonance. Pure Resonance The noion of pure resonance in he differenial equaion (1) ()
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More information23.3. Even and Odd Functions. Introduction. Prerequisites. Learning Outcomes
Even and Odd Funcions 23.3 Inroducion In his Secion we examine how o obain Fourier series of periodic funcions which are eiher even or odd. We show ha he Fourier series for such funcions is considerabl
More informationLecture 2: Telegrapher Equations For Transmission Lines. Power Flow.
Whies, EE 481 Lecure 2 Page 1 of 13 Lecure 2: Telegraher Equaions For Transmission Lines. Power Flow. Microsri is one mehod for making elecrical connecions in a microwae circui. I is consruced wih a ground
More informationCAPACITANCE AND INDUCTANCE
CHAPTER 6 CAPACITANCE AND INDUCTANCE THE LEARNING GOALS FOR THIS CHAPTER ARE: Know how o use circui models for inducors and capaciors o calculae volage, curren, and power Be able o calculae sored energy
More informationAstable multivibrator using the 555 IC.(10)
Visi hp://elecronicsclub.cjb.ne for more resources THE 555 IC TIMER The 555 IC TIMER.(2) Monosable mulivibraor using he 555 IC imer...() Design Example 1 wih Mulisim 2001 ools and graphs..(8) Lile descripion
More informationMOTION ALONG A STRAIGHT LINE
Chaper 2: MOTION ALONG A STRAIGHT LINE 1 A paricle moes along he ais from i o f Of he following alues of he iniial and final coordinaes, which resuls in he displacemen wih he larges magniude? A i =4m,
More informationI. Basic Concepts (Ch. 14)
(Ch. 14) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing
More informationPhysics 1402: Lecture 21 Today s Agenda
ecure 4 Physics 142: ecure 21 Tody s Agend Announcemens: nducion, R circuis Homework 6: due nex Mondy nducion / A curren Frdy's w ds N S B v B B S N B v 1 ecure 4 nducion Selfnducnce, R ircuis X X X X
More informationA Curriculum Module for AP Calculus BC Curriculum Module
Vecors: A Curriculum Module for AP Calculus BC 00 Curriculum Module The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy.
More informationDCDC Boost Converter with Constant Output Voltage for Grid Connected Photovoltaic Application System
DCDC Boos Converer wih Consan Oupu Volage for Grid Conneced Phoovolaic Applicaion Sysem PuiWeng Chan, Syafrudin Masri Universii Sains Malaysia Email: edmond_chan85@homail.com, syaf@eng.usm.my Absrac
More informationTHE PRESSURE DERIVATIVE
Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics THE PRESSURE DERIVATIVE The ressure derivaive has imoran diagnosic roeries. I is also imoran for making ye curve analysis more reliable.
More information4 Convolution. Recommended Problems. x2[n] 1 2[n]
4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discreeime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.11.
More informationSection A: Forces and Motion
I is very useful o be able o make predicions abou he way moving objecs behave. In his chaper you will learn abou some equaions of moion ha can be used o calculae he speed and acceleraion of objecs, and
More informationHOW RF TRANSFORMERS WORK AND HOW THEY ARE MEASURED
HOW RF TRANSFORMERS WORK AND HOW THEY ARE MEASURED ONTRIBUTIONS BY: DAXIONG JI HAIPING YAN WEIPING ZHENG AUTHORED BY: FRED LEFRAK REVIEWED BY: RADHA SETTY AN1 Rev.: B M1561 (/15/15) File: AN1.W61 This
More information23.3. Even and Odd Functions. Introduction. Prerequisites. Learning Outcomes
Even and Odd Funcions 3.3 Inroducion In his Secion we examine how o obain Fourier series of periodic funcions which are eiher even or odd. We show ha he Fourier series for such funcions is considerabl
More informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More information4.2 Trigonometric Functions; The Unit Circle
4. Trigonomeric Funcions; The Uni Circle Secion 4. Noes Page A uni circle is a circle cenered a he origin wih a radius of. Is equaion is as shown in he drawing below. Here he leer represens an angle measure.
More informationAP Calculus AB 2007 Scoring Guidelines
AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and
More informationCointegration: The Engle and Granger approach
Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be nonsaionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require
More informationECEN4618: Experiment #1 Timing circuits with the 555 timer
ECEN4618: Experimen #1 Timing circuis wih he 555 imer cæ 1998 Dragan Maksimović Deparmen of Elecrical and Compuer Engineering Universiy of Colorado, Boulder The purpose of his lab assignmen is o examine
More informationA Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)
A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke
More informationPrecision Dual Voltage Regulator Controller ADM1052
a FEAURES wo Independen Conrollers on One Chip wo 2.525 V Oupus Shudown Inpus o Conrol Each Channel 2.5% Accuracy Over Line, Load, and emperaure Low Quiescen Curren Low Shudown Curren Works wih Exernal
More informationPermutations and Combinations
Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes  ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he kvalue for he middle erm, divide
More informationDensity Dependence. births are a decreasing function of density b(n) and deaths are an increasing function of density d(n).
FW 662 Densiydependen populaion models In he previous lecure we considered densiy independen populaion models ha assumed ha birh and deah raes were consan and no a funcion of populaion size. Longerm
More informationFourier Series & The Fourier Transform
Fourier Series & The Fourier Transform Wha is he Fourier Transform? Fourier Cosine Series for even funcions and Sine Series for odd funcions The coninuous limi: he Fourier ransform (and is inverse) The
More informationDuration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVAF38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
More information6.5. Modelling Exercises. Introduction. Prerequisites. Learning Outcomes
Modelling Exercises 6.5 Inroducion This Secion provides examples and asks employing exponenial funcions and logarihmic funcions, such as growh and decay models which are imporan hroughou science and engineering.
More informationRandom Walk in 1D. 3 possible paths x vs n. 5 For our random walk, we assume the probabilities p,q do not depend on time (n)  stationary
Random Walk in D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More informationEntropy: From the Boltzmann equation to the Maxwell Boltzmann distribution
Enropy: From he Bolzmann equaion o he Maxwell Bolzmann disribuion A formula o relae enropy o probabiliy Ofen i is a lo more useful o hink abou enropy in erms of he probabiliy wih which differen saes are
More informationPRESSURE BUILDUP. Figure 1: Schematic of an ideal buildup test
Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics PRESSURE BUILDUP I is difficul o kee he rae consan in a roducing well. This is no an issue in a buildu es since he well is closed.
More informationUsefulness of the Forward Curve in Forecasting Oil Prices
Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,
More informationSEMICONDUCTOR APPLICATION NOTE
SEMICONDUCTOR APPLICATION NOTE Order his documen by AN1542/D Prepared by: C. S. Mier Moorola Inc. Inpu filer design has been an inegral par of power supply designs. Wih he adven of inpu filers, he designer
More informationAP Calculus AB 2010 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College
More informationChapter 4: Exponential and Logarithmic Functions
Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion
More informationLECTURE 9. C. Appendix
LECTURE 9 A. BuckBoos Converer Design 1. VolSec Balance: f(d), seadysae ransfer funcion 2. DC Operaing Poin via Charge Balance: I(D) in seadysae 3. Ripple Volage / C Spec 4. Ripple Curren / L Spec 5.
More informationThyristor Based Speed Control Techniques of DC Motor: A Comparative Analysis
Inernaional Journal of Scienific and Research Publicaions, Volume 2, Issue 6, June 2012 1 Thyrisor Based Speed Conrol Techniques of DC Moor: A Comparaive Analysis Rohi Gupa, Ruchika Lamba, Subhransu Padhee
More informationSignal Rectification
9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, halfwae and fullwae. Le s firs consider he ideal
More informationMotion Along a Straight Line
Moion Along a Sraigh Line On Sepember 6, 993, Dave Munday, a diesel mechanic by rade, wen over he Canadian edge of Niagara Falls for he second ime, freely falling 48 m o he waer (and rocks) below. On his
More informationImagine a Source (S) of sound waves that emits waves having frequency f and therefore
heoreical Noes: he oppler Eec wih ound Imagine a ource () o sound waes ha emis waes haing requency and hereore period as measured in he res rame o he ource (). his means ha any eecor () ha is no moing
More informationSmart Highside Power Switch
Smar ighside Power Swich Feaures Overload proecion Curren limiaion Shor circui proecion Thermal shudown Overvolage proecion (including load dump) Reverse baery proecion ) Undervolage and overvolage shudown
More informationThe Torsion of Thin, Open Sections
EM 424: Torsion of hin secions 26 The Torsion of Thin, Open Secions The resuls we obained for he orsion of a hin recangle can also be used be used, wih some qualificaions, for oher hin open secions such
More informationChapter 4. Properties of the Least Squares Estimators. Assumptions of the Simple Linear Regression Model. SR3. var(e t ) = σ 2 = var(y t )
Chaper 4 Properies of he Leas Squares Esimaors Assumpions of he Simple Linear Regression Model SR1. SR. y = β 1 + β x + e E(e ) = 0 E[y ] = β 1 + β x SR3. var(e ) = σ = var(y ) SR4. cov(e i, e j ) = cov(y
More informationNewton s Laws of Motion
Newon s Laws of Moion MS4414 Theoreical Mechanics Firs Law velociy. In he absence of exernal forces, a body moves in a sraigh line wih consan F = 0 = v = cons. Khan Academy Newon I. Second Law body. The
More informationGate protection. Current limit. Overvoltage protection. Limit for unclamped ind. loads. Charge pump Level shifter. Rectifier. Open load detection
Smar ighside Power Swich for ndusrial Applicaions Feaures Overload proecion Curren limiaion Shor circui proecion Thermal shudown Overvolage proecion (including load dump) Fas demagneizaion of inducive
More information17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides
7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion
More informationThe naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1
Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces imeseries smoohing forecasing mehods. Various models are discussed,
More informationTable of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities
Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17
More informationPI4ULS5V202 2Bit Bidirectional Level Shifter with Automatic Sensing & Ultra Tiny Package
Feaures can be Less han, Greaer han or Equal o V CCB 1.2V o 5.5V on A Por and 1.2V o 5.5V on B Por High Speed wih 20 Mb/s Daa Rae for pushpull applicaion High Speed wih 2 Mb/s Daa Rae for opendrain applicaion
More informationThe Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas
The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he
More information