RC, RL and RLC circuits
|
|
- Rolf Barrett
- 7 years ago
- Views:
Transcription
1 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. We will sudy he way volages and currens change in hese circuis when volages are suddenly applied or removed. To change he volage suddenly, a funcion generaor will be used. In order o observe hese rapid changes we will use an oscilloscope. 1. The square wave generaor Inroducion We can quickly charge and discharge a capacior by using a funcion generaor se o generae a square wave. The oupu of his volage source is shown in Figure T Figure 1: Oupu of square-wave generaor One conrol on he generaor les you vary he ampliude, 0. You can change he ime period over which he cycle repeas iself, T, by adjusing he repeiion frequency f = 1/T. The generaor is no an ideal volage source because i has an inernal resisance 50Ω. Thus, for purpose of analysis, he square-wave generaor may be replaced by he wo circuis shown in Figure 2. When he volage is on, he circui is a baery wih an EMF of 0 vols in series wih a 50Ω resisor. When he volage is off, he circui is simply a 50Ω resisor. R R 0 + On Of f Figure 2: Square-wave generaor equivalen circui 1
2 Procedure To learn how o operae he oscilloscope and funcion generaor, se he funcion generaor for square wave oupu and connec he generaor o he verical inpu of he oscilloscope. Adjus he oscilloscope o obain each of he paerns shown in Figure 3. Try changing he ampliude and repeiion frequency of he generaor and observe wha corresponding changes are needed in he oscilloscope conrols o keep he race on he screen he same. Now se he funcion generaor o a frequency of abou 100 Hz. Observe he paern and adjus he frequency unil he period T = 10.0 ms. Funcion Generaor Oscilloscope Figure 3: Observing he oupu of he square-wave generaor 2. Resisance-capaciance circuis Inroducion We have previously sudied he behavior of capaciors and looked a he way a capacior discharges hrough a resisor. Theory (see exbook) shows ha for a capacior, C, charging hough a resisor, R, he volage across he capacior,, varies wih ime according o ( ) ( - RC = 0 1- e ) (1) where 0 is he final seady-sae volage. When he same capacior discharges hrough he same resisor, ( ) - RC = 0 e (2) The produc of he resisance and capaciance, RC, governs he ime scale wih which he changes ake place. For his reason i is called he ime consan, which we call τ (au). I can be found indirecly by measuring he ime required for he volage o fall o 0 /2 (see Figure 4 below). This ime inerval is called he half-life, T 1/2, and is given by he equaion T 1/2 = (ln2)τ, so T 1 2 T1 2 = = (3) ln
3 / T 1/2 Figure 4: Discharge of a capacior Procedure Assemble he circui shown in Figure 5. R = 10 k C = 0.1 F Funcion Generaor Figure 5: Invesigaing an RC circui Oscilloscope Wih iniial values R = 10 kω, C = 0.1 µf, and f = 100 Hz, observe one period of he charge and discharge of he capacior. Make sure he repeiion frequency is low enough so ha he volage across he capacior has ime o reach is final values, 0 and 0. Figure 6 shows one complee cycle of he inpu square-wave ha is being applied across he resisor and capacior. Superimpose on he square-wave a skech of he waveform you observed, which illusraes he volage across he capacior as a funcion of ime. Figure 6: Capacior volage vs. ime 3
4 Wha is he larges volage, 0, across he capacior? Wha is he larges charge, q 0, on he capacior? 0 = q 0 = Use he ohmmeer o measure R. (Recall ha a resisor should be removed from he circui before you measure is resisance wih an ohmmeer.) R = To measure T 1/2 change oscilloscope gain (vols/cm) and sweep rae (ms/cm) unil you have a large paern on he screen, like he paern shown in Figure 7a. Make sure he sweep speed is in he calibraed posiion so he ime can be read off he x- axis. Cener he paern on he screen so ha he horizonal axis is in he cener of he paern. Tha is, so ha he waveform exends equal disances above and below he axis. Move he waveform o he righ unil he sar of he discharge of he capacior is on he verical axis as shown in Figure 7b. The half-life is jus he horizonal disance shown on Figure 7b. Figure 7a and b: Measuring he half-life Measure he half-life, T 1/2, and from his compue he ime consan τ using Equaion 3. Make sure o include unis wih your resuls T 1/2 = τ = 4
5 You have jus deermined his circui s ime consan from he capacior discharging curve. Theoreically, he ime consan is given by he produc of he resisance and capaciance in he circui, RC. Compue RC from componen values. Show your calculaion in he space below. Noe ha, as described above, he square-wave generaor has an inernal resisance of 50Ω. Thus, he oal resisance hrough which he RC circui charges and discharges is R + 50Ω. τ = When his calculaion is carried ou using ohms for resisance and Farads for capaciance, he produc has unis of seconds. Use dimensional analysis o show ha his is indeed he case. Wihin he uncerainies of he olerances (10%) of he resisor and capacior, do your measuremens suppor he equaion τ = RC? (If here is more han 20% disagreemen, consul your insrucor.) Alhough you have been old ha he inernal resisance of he funcion generaor is 50Ω, le s say we had kep his piece of informaion from you. Wihou using an ohmmeer, ouline a procedure for measuring he inernal resisance of your funcion generaor. 5
6 Adjus he funcion generaor o ry differen values of f and hence, T, while keeping τ fixed by no changing eiher R or C. On he lef graph below skech wha you saw when he period T of he square wave was much less han he ime consan, τ. On he righ graph below skech wha you saw when he period T of he square wave was much greaer han he ime consan. >> T = T = << T = T = 3. Resisance-inducance circuis Inroducion In his secion we conduc a similar sudy of a circui conaining a resisor and an inducor, L. Consider he circui shown in Figure 8 below. The ex shows ha if we sar wih he baery conneced o he LR circui, afer a long ime he curren reaches a seady-sae value, i 0 = 0 /R. R 0 L Figure 8: A model circui wih an inducor and resisor If we call = 0 he ime when we suddenly hrow he swich o remove he baery, allowing curren o flow o ground, hen curren changes wih ime according o he equaion ( ) -( R/L) i = i0 e (4) If, a a new = 0, we hrow he swich so he baery is conneced, he curren increases according o he equaion ( ) ( -( R/L) i = i0 1- e ) (5) The ime consan for boh equaions is L/R and 6
7 T 1 L 2 = = (6) R We can find he curren as a funcion of ime by measuring he volage across he resisor wih he oscilloscope and using he relaionship i() = ()/R. Noe ha wha we would see firs is he growh of curren given by Equaion 5, where he final curren depends on he square-wave ampliude 0. Then, when he square wave drops o zero, he curren decays according o Equaion 4. The ime consan should be he same in boh cases. Procedure Se up he circui shown in Figure 9 below. L = 25 mh R = 1 k Funcion Generaor Oscilloscope Figure 9: Invesigaing he LR circui Wih iniial values R = 1kΩ and L = 25mH, se he oscilloscope o view one period of exponenial growh and decay. Again, make sure ha f is low enough for he curren o reach is final values, i 0 and 0. Sar wih f = 5 khz. Superimpose a skech of he waveform you observe on he single cycle of he inpu square-wave shown below. Wha is he larges curren hrough he inducor? i 0 = Measure he half-life. From his value, compue he ime consan. T 1/2 = τ = 7
8 Measure he value of R and he dc resisance of he inducor wih an ohmmeer. Finally add he inernal resisance of he square-wave generaor o obain he oal resisance. Compue he value of L/R from he componens values. R (of resisor) = R (of inducor) = R (of funcion generaor) = R (oal) = τ = L/R = Wihin he uncerainies of he manufacuring olerances (10%) of he resisor and inducance, do your measuremens suppor he equaion = L/R? When his calculaion is carried ou using ohms for resisance and Henries for inducance, he raio has unis of seconds. Use dimensional analysis o show ha his is indeed he case. Adjus he funcion generaor o ry differen values of f and hence, T, while keeping τ fixed by no changing eiher R or L. On he lef graph below skech wha you saw when he period T of he square wave was much less han he ime consan, τ. On he righ graph below skech wha you saw when he period T of he square wave was much greaer han he ime consan. 8
9 >> T = T = << T = T = 4. Resisance-inducance-capaciance circuis Inroducion As discussed in he exbook, a circui conaining an inducor and a capacior, an LC circui, is an elecrical analog o a simple harmonic oscillaor, consising of a block on a spring fasened o a rigid wall. L C k M Figure 10: LC Circui and is analog, a mechanical SHM Sysem In he same way ha, in he mechanical sysem, energy can be in he form of kineic energy of he block of mass M, or poenial energy of he spring wih spring consan k; in 1 2 he LC circui energy can reside in he magneic field of he inducor U = 2 Li, or he 1 2 elecric field of he capacior, U = 2 q C. Boh he curren and he charge hen change in a sinusoidal manner. The frequency of he oscillaion is given by 1 0 = (7) LC All circuis have some resisance, and in he same way fricional forces damp mechanical SHM, resisance causes energy loss (i 2 R) which makes he charge decay in ime. ( ) - q q e cos( ) (8) = 0 1 ( ) = 0 1 (9) 9
10 where τ = 2L/R or T = ln2(2l R) = 0.693(2L ) (10) 1 2 R For large τ he sysem is underdamped and he charge oscillaes, aking a long ime o reurn o zero. 2 2 Noe from Equaion 9 ha when 0 = 1, 1, which appears in he argumen of he cosine funcion of Equaion 8, is zero a all imes. This condiion is called criical damping. Criical damping occurs when R = 2 L C. When he resisor is larger han he criical value he sysem is overdamped. The charge acually akes longer o reurn o zero han in he criically damped case. The decaying oscillaions in he LRC circui can be observed using he same echnique as used o observe exponenial decay. Again, a square-wave generaor produces he same effec as a baery swiched on and off periodically. The oscilloscope measures he volage across C as a funcion of ime. a. Observing oscillaions in a RLC circui Procedure Assemble he circui of Figure 11. Use a small value of R, say, 47Ω. Be sure o reduce he signal generaor frequency o 100 Hz or below so you can see he enire damped oscillaion. R L = 25 mh C = 0.1 F Funcion Generaor Oscilloscope Figure 11: Invesigaing he LRC circui Measure he period and calculae he frequency of he oscillaions. (The period is NOT 0.01 s = 1/100 Hz, he repeiion frequency of he square wave.) Measured period = Calculaed f 1 = = f = Calculae 0 from componen values. 0 =1 LC = 10
11 Compare he 1 you measured wih 0 ha you calculaed from componen values. In heory, 1, he damped frequency, is only slighly less han 0, he undamped frequency, making his a valid comparison of heory wih experimen. b. Criical damping and overdamping in a RLC circui Procedure Noe ha in he equaions for his circui, R represens he sum of he resisance of he inducor, he inernal resisance of he square-wave generaor, 50Ω, and he resisance of he resisor. To sudy criical damping and overdamping, remove your fixed resisor and pu in is place a 5-kΩ variable resisor. Sar wih he variable resisor se o a small value of R. For small R you should see he oscillaions ha are characerisic of underdamping. On he firs graph below skech he waveform ha appears on he oscilloscope. Increase R unil criical damping is reached; ha is, unil he oscillaions disappear. Skech his curve on he middle graph above. Use he ohmmeer o measure he value of he variable resisor a criical damping. (Don forge o disconnec he variable resisor from he circui when measuring is resisance.) R (variable resisor a criical damping) = Calculae he oal resisance in he circui a criical damping by adding he dc resisance of he inducor and 50Ω for he funcion generaor o he resul above. R (oal a criical damping) = Compare his value of he circui resisance a criical damping o he prediced value for criical damping, R = 2 L C. 11
12 Wha happens o he waveform when he resisance is larger han he criicaldamping value? Skech your resuls on he righmos graph above. c. Underdamping in a RLC circui Inroducion When he circui is underdamped, Equaion (8) applies. This means ha he ampliude of he oscillaion will decay exponenially, wih he ime consan for he decay being: 2L (11) R Recall ha when an exponenial decay is ploed on a semi-log scale he resuling graph is a sraigh line wih a slope equal o -1/. You can find he slope of a line on a semi-log graph by idenifying he wo end poins of he line. Noe he ime and volage a each poin 1 and 1, 2 and 2. Calculae he naural log of he wo volages. Then, ln( 2 ) ln( 1 ) 1 slope 2 1 The following seps describe how o measure he ime consan of he decay of he oscillaions. (12) Procedure Adjus he variable resisor so ha he circui is underdamped and oscillaes abou seven or eigh imes before he oscillaions become oo small o be easily seen on he oscilloscope. Cener he oscillaion paern verically on he screen so ha when he oscillaions have decayed he line on he oscilloscope coincides wih he ime axis. In he able below record he volage of each oscillaion peak, and he corresponding ime for each peak. When your able is complee you should have six or seven ses of daa recorded. Peak Heigh () Time ( ) Table 1 12
13 Creae a semi-log graph of your daa. (You can use Excel o creae a semi-log graph.) Following he procedure described above, deermine he ime consan for your circui. This is your experimenal value for he ime consan. Show your calculaion and resul here. τ experimen = Remove he variable resisor from he circui and measure is resisance. Add his value o he resisance of he square-wave generaor (50 ohms) and he resisance of he inducor o ge he oal resisance of your circui. Show your calculaion and resul here. R oal = Using Equaion (11) calculae he heoreical decay ime consan for your circui. Show your work. τ heory = Compare his heoreical value o he experimenal value you found above. They should agree wihin en or weny percen. If hey do no, consul your insrucor. 13
CHARGE 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 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 informationRC (Resistor-Capacitor) Circuits. AP Physics C
(Resisor-Capacior 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 First-Order RL and RC Circuits
Chaper 7. esponse of Firs-Order 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 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 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 informationModule 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur
Module 4 Single-phase 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 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 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 informationFull-wave rectification, bulk capacitor calculations Chris Basso January 2009
ull-wave 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 informationAppendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.
Appendi A: Area worked-ou s o Odd-Numbered Eercises Do no read hese worked-ou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa
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 bi-polar
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, half-wae and fullwae. Le s firs consider he ideal
More informationSignal Processing and Linear Systems I
Sanford Universiy Summer 214-215 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 14-15, Gibbons
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 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 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 informationDC-DC Boost Converter with Constant Output Voltage for Grid Connected Photovoltaic Application System
DC-DC Boos Converer wih Consan Oupu Volage for Grid Conneced Phoovolaic Applicaion Sysem Pui-Weng Chan, Syafrudin Masri Universii Sains Malaysia E-mail: edmond_chan85@homail.com, syaf@eng.usm.my Absrac
More informationPulse-Width Modulation Inverters
SECTION 3.6 INVERTERS 189 Pulse-Widh Modulaion Inverers Pulse-widh 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 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 information1. y 5y + 6y = 2e t Solution: Characteristic equation is r 2 5r +6 = 0, therefore r 1 = 2, r 2 = 3, and y 1 (t) = e 2t,
Homework6 Soluions.7 In Problem hrough 4 use he mehod of variaion of parameers o find a paricular soluion of he given differenial equaion. Then check your answer by using he mehod of undeermined coeffiens..
More information11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic D-S 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 cuing-edge
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 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 informationModule 3. R-L & R-C 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 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 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 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 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 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 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 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 informationRandom Walk in 1-D. 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 informationNOTES ON OSCILLOSCOPES
NOTES ON OSCILLOSCOPES NOTES ON... OSCILLOSCOPES... Oscilloscope... Analog and Digial... Analog Oscilloscopes... Cahode Ray Oscilloscope Principles... 5 Elecron Gun... 5 The Deflecion Sysem... 6 Displaying
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 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 informationAnalogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar
Analogue and Digial Signal Processing Firs Term Third Year CS Engineering By Dr Mukhiar Ali Unar Recommended Books Haykin S. and Van Veen B.; Signals and Sysems, John Wiley& Sons Inc. ISBN: 0-7-380-7 Ifeachor
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 ime-series smoohing forecasing mehods. Various models are discussed,
More informationLECTURE 9. C. Appendix
LECTURE 9 A. Buck-Boos Converer Design 1. Vol-Sec Balance: f(d), seadysae ransfer funcion 2. DC Operaing Poin via Charge Balance: I(D) in seady-sae 3. Ripple Volage / C Spec 4. Ripple Curren / L Spec 5.
More informationAP Calculus BC 2010 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board
More informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
More informationChapter 8 Student Lecture Notes 8-1
Chaper Suden Lecure Noes - Chaper Goals QM: Business Saisics Chaper Analyzing and Forecasing -Series Daa Afer compleing his chaper, you should be able o: Idenify he componens presen in a ime series Develop
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 informationAP Calculus AB 2013 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a mission-driven no-for-profi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was
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 informationLLC Resonant Converter Reference Design using the dspic DSC
LLC Resonan Converer Reference Design using he dspic DSC 2010 Microchip Technology Incorporaed. All Righs Reserved. LLC Resonan Converer Webinar Slide 1 Hello, and welcome o his web seminar on Microchip
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 informationCointegration: The Engle and Granger approach
Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require
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 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 informationProduct Operation and Setup Instructions
A9 Please read and save hese insrucions. Read carefully before aemping o assemble, insall, operae, or mainain he produc described. Proec yourself and ohers by observing all safey informaion. Failure o
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 UVA-F-38 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 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 discree-ime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.1-1.
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 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 informationCHAPTER FIVE. Solutions for Section 5.1
CHAPTER FIVE 5. SOLUTIONS 87 Soluions for Secion 5.. (a) The velociy is 3 miles/hour for he firs hours, 4 miles/hour for he ne / hour, and miles/hour for he las 4 hours. The enire rip lass + / + 4 = 6.5
More informationStability. Coefficients may change over time. Evolution of the economy Policy changes
Sabiliy Coefficiens may change over ime Evoluion of he economy Policy changes Time Varying Parameers y = α + x β + Coefficiens depend on he ime period If he coefficiens vary randomly and are unpredicable,
More informationFrequency Modulation. Dr. Hwee-Pink Tan http://www.cs.tcd.ie/hweepink.tan
Frequency Modulaion Dr. Hwee-Pink Tan hp://www.cs.cd.ie/hweepink.tan Lecure maerial was absraced from "Communicaion Sysems" by Simon Haykin. Ouline Day 1 Day 2 Day 3 Angle Modulaion Frequency Modulaion
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 informationAnswer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prin-ou should hae 1 quesions. Muliple-choice quesions may coninue on he ne column or page find all choices before making your selecion. The
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 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 informationWATER MIST FIRE PROTECTION RELIABILITY ANALYSIS
WATER MIST FIRE PROTECTION RELIABILITY ANALYSIS Shuzhen Xu Research Risk and Reliabiliy Area FM Global Norwood, Massachuses 262, USA David Fuller Engineering Sandards FM Global Norwood, Massachuses 262,
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 informationReturn Calculation of U.S. Treasury Constant Maturity Indices
Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion
More informationPI4ULS5V202 2-Bit Bi-directional 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 push-pull applicaion High Speed wih 2 Mb/s Daa Rae for open-drain applicaion
More informationOPERATION MANUAL. Indoor unit for air to water heat pump system and options EKHBRD011ABV1 EKHBRD014ABV1 EKHBRD016ABV1
OPERAION MANUAL Indoor uni for air o waer hea pump sysem and opions EKHBRD011ABV1 EKHBRD014ABV1 EKHBRD016ABV1 EKHBRD011ABY1 EKHBRD014ABY1 EKHBRD016ABY1 EKHBRD011ACV1 EKHBRD014ACV1 EKHBRD016ACV1 EKHBRD011ACY1
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 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 information1 HALF-LIFE EQUATIONS
R.L. Hanna Page HALF-LIFE EQUATIONS The basic equaion ; he saring poin ; : wrien for ime: x / where fracion of original maerial and / number of half-lives, and / log / o calculae he age (# ears): age (half-life)
More informationName: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 2204 FINAL EXAMINATION. June 2009.
Name: Teacher: DO NOT OPEN THE EXMINTION PPER UNTIL YOU RE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 2204 FINL EXMINTION June 2009 Value: 100% General Insrucions This examinaion consiss of wo pars. Boh pars
More informationALSO IN THIS ISSUE: For more information contact: Graham Robertson Media Relations, 310-726-8512 FOR DESIGNERS AND SYSTEMS ENGINEERS
www.powerelecronics.com JUNE 2009 Vol. 35, No. 6 FOR DESIGNERS AND SYSTEMS ENGINEERS ALSO IN THIS ISSUE: For more informaion conac: Graham Roberson Media Relaions, 310-726-8512 New PWM Slope Compensaion
More informationAutomatic measurement and detection of GSM interferences
Auomaic measuremen and deecion of GSM inerferences Poor speech qualiy and dropped calls in GSM neworks may be caused by inerferences as a resul of high raffic load. The radio nework analyzers from Rohde
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
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 no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy.
More informationMTH6121 Introduction to Mathematical Finance Lesson 5
26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random
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 informationVIPer12ADIP VIPer12AS
VIPer12ADIP VIPer12AS LOW POWER OFF LINE SMPS PRIMARY SWITCHER TYPICAL POWER CAPABILITY Mains ype SO-8 DIP8 European (195-265 Vac) 8 W 13 W US / Wide range (85-265 Vac) 5 W 8 W n FIXED 60 KHZ SWITCHING
More informationVector Autoregressions (VARs): Operational Perspectives
Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101-115. Macroeconomericians
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 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 k-value for he middle erm, divide
More informationCLOCK SKEW CAUSES CLOCK SKEW DUE TO THE DRIVER EROSION OF THE CLOCK PERIOD
DESIGNING WITH HIGH SPEED CLOCK DRIERS CONFERENCE PAPER CP-19 Inegraed Device Technology, Inc. By Sanley Hronik ABSTRACT Today s high speed sysems are encounering problems wih clocking ha were no consideraions
More informationTrends in TCP/IP Retransmissions and Resets
Trends in TCP/IP Reransmissions and Reses Absrac Concordia Chen, Mrunal Mangrulkar, Naomi Ramos, and Mahaswea Sarkar {cychen, mkulkarn, msarkar,naramos}@cs.ucsd.edu As he Inerne grows larger, measuring
More informationCLASSICAL TIME SERIES DECOMPOSITION
Time Series Lecure Noes, MSc in Operaional Research Lecure CLASSICAL TIME SERIES DECOMPOSITION Inroducion We menioned in lecure ha afer we calculaed he rend, everyhing else ha remained (according o ha
More informationAP Calculus AB 2010 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College
More informationMonotonic, Inrush Current Limited Start-Up for Linear Regulators
Applicaion epor SLA156 March 2004 Monoonic, Inrush urren Limied Sar-Up for Linear egulaors Jeff Falin PMP Porable Producs ABSA he oupu volage of a linear regulaor ends o rise quickly afer i is enabled.
More informationDATA SHEET. 1N4148; 1N4446; 1N4448 High-speed diodes DISCRETE SEMICONDUCTORS. 1996 Sep 03
DISCETE SEMICONDUCTOS DATA SHEET M3D176 Supersedes daa of April 1996 File under Discree Semiconducors, SC01 1996 Sep 03 specificaion Diodes rapides Caracerisiques Encapsulees hermeiquemen dans un boiier
More informationForm measurement systems from Hommel-Etamic Geometrical tolerancing in practice DKD-K-02401. Precision is our business.
Form measuremen sysems from Hommel-Eamic Geomerical olerancing in pracice DKD-K-02401 Precision is our business. Drawing enries Tolerance frame 0.01 0.01 Daum leer Tolerance value in mm Symbol for he oleranced
More informationKinematics in 1-D From Problems and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, morin@physics.harvard.
Chaper 2 Kinemaics in 1-D From Problems and Soluions in Inroducory Mechanics (Draf ersion, Augus 2014) Daid Morin, morin@physics.harard.edu As menioned in he preface, his book should no be hough of as
More informationEquation for a line. Synthetic Impulse Response 0.5 0.5. 0 5 10 15 20 25 Time (sec) x(t) m
Fundamenals of Signals Overview Definiion Examples Energy and power Signal ransformaions Periodic signals Symmery Exponenial & sinusoidal signals Basis funcions Equaion for a line x() m x() =m( ) You will
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 no-for-profi membership associaion whose mission is o connec sudens o college success and
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 informationStochastic Optimal Control Problem for Life Insurance
Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian
More informationSwitched Mode Converters (1 Quadrant)
(1 Quadran) Philippe Barrade Laboraoire d Elecronique Indusrielle, LEI STI ISE Ecole Polyechnique Fédérale de Lausanne, EPFL Ch-1015 Lausanne Tél: +41 21 693 2651 Fax: +41 21 693 2600 Philippe.barrade@epfl.ch
More informationNovelty and Collective Attention
ovely and Collecive Aenion Fang Wu and Bernardo A. Huberman Informaion Dynamics Laboraory HP Labs Palo Alo, CA 9434 Absrac The subjec of collecive aenion is cenral o an informaion age where millions of
More informationMarkit Excess Return Credit Indices Guide for price based indices
Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semi-annual
More informationOM02 Optical Mouse Sensor Data Sheet
OM0 Opical Mouse Sensor Daa Shee Index. General descripion Page. Feaures Page. Pin configuraions (package) and descripions Page. Absolue maximum raing Page. Elecrical characerisics Page. Applicaion circui
More informationAN1207. Switch Mode Power Supply (SMPS) Topologies (Part II) REQUIREMENTS AND RULES INTRODUCTION CONTENTS. Microchip Technology Inc.
Swich Mode Power Supply (SMPS) opologies (Par II) Auhor: INRODUCION his applicai noe is he secd of a wo-par series Swich Mode Power Supply (SMPS) opologies. he firs applicai noe in his series AN1114 -
More informationInnovation + Quality. Product range Valves and controls for cooling systems
Innovaion + Qualiy Produc range Valves and conrols for cooling sysems Cooling sysems Chilled ceiling sysems make up a growing share in he cooling secor for office buildings. Wih due consideraion o some
More information