9. Capacitor and Resistor Circuits
|
|
- Kelly Heath
- 7 years ago
- Views:
Transcription
1 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 (volage) DC. Now we sar o consider various combinaions of componens and much of he ineresing behavior depends upon ime so we will also consider AC or alernaing curren (volage) sources which are signal generaors. he firs combinaion we consider is a resisor in series wih a capacior and a baery. he RC Circui Consider he resisor-capacior circui indicaed below: When he swich is closed, Kirchoff's loop equaion for his circui is V= Q C + ir (1) for >0 where boh Q[] and i[] are funcions of ime. here are wo unknown quaniies Q[] and i[] in equaion (1) and we need an addiional equaion namely
2 ElecronicsLab9.nb d i@d = d () Q@D You can eliminae one of he unknowns beween equaions (1) and () by aking he derivaive of equaion (1) wih respec o ime obaining 0= 1 d d Q@D + R C d d (3) i@d and using equaion () o eliminae he derivaive of he charge 0= 1 C d i@d + R d () i@d I is easy enough o solve equaion () since by rearrangemen d d i@d = -1 RC (5) i@d Furher à 1 i âi = -1 RC à â () Inegraion yields LogB i@d i0 F- (7) RC where i0 is a consan of inegraion which we will deermine shorly. Using a propery of he exponenial funcion, we obain from equaion (7) i@d = i0 ExpB- RC F () Iniially a =0, when he swich is closed, he capacior has zero charge and herefore here is zero poenial across i. he curren in he circui is deermined enirely by he baery poenial V and he resisance R hrough Ohm's law i@0d R = V or i@0d = V (9) R as iniially he capacior C play no role. Seing =0 in equaion () and using equaion (9) yields i@0d = i0 = V R so we have deermined he consan of inegraion. finally he soluion as () Uilizaion of equaion () in equaion () yields
3 ElecronicsLab9.nb 3 à i@d = V R ExpB- RC F (11) he produc RC has unis of ime and usually is called he ime consan =RC (1) Graph of he Soluion for he curren Suppose he numerical values V= vols, R=,000 ohms, and C=.5 microfarads as indicaed hen V = ; R = 000.; Cap =.5 * - ; = R * Cap; Prin@"ime Consan =",, " sec"d ime Consan =0.0 sec IMPORAN: C is a proec variable assigned o somehing specific in Mahemaica so insead we use Cap as he symbol for capaciance. i@_d := V R ExpB- F Plo@i@D,, 0, * <, AxesLabel "ime", "i@d"<d i@d ime So iniially, righ afer he swich is closed, he curren i[] is a maximum and hereafer is decreases exponenially. he iniial curren is
4 ElecronicsLab9.nb So iniially, righ afer he swich is closed, he curren i[] is a maximum and hereafer is decreases exponenially. he iniial curren is i@0d which agrees wih he graph above. he ime consan (=0.0 seconds in his case) deermines he rae of decay. Afer a ime he curren has decreased o i@d and his is equal o equaion (11) wih = namely i@0d * ã Noe ha ã so afer one ime = he curren has dropped 37% in is value. Afer =, he curren is i@ * D which is 1% of he original value of he curren since ã and so on. he volage across he resisor is i*r so we may graph his volage as
5 ElecronicsLab9.nb 5 Vr = Plo@i@D * R,, 0, * <, AxesLabel "ime", ime Graph of he Charge Q[] Combining equaions () and (11) yields d d Q@D = V R ExpB- RC F (13) and inegraion yields Q@D = Q@0D + V R à ExpB 0 ' F â' (1) where he iniial charge on he capacior is zero Q[0]=0. he inegral is easily obained Clear@D; ' F â' à ExpB 0 - ã- Combining his wih equaion (1) and recalling equaion (1) we obain Q@D = VC 1 - ExpBwhich we can also graph. F (15)
6 ElecronicsLab9.nb V = ; R = 000.; Cap =.5 * - ; = R * Cap; Q@_D := V * Cap 1 - ExpB- F Plo@Q@D,, 0, * <, AxesLabel "ime", "Q@D"<D Q@D ime Iniially he charge on he capacior is zero Q@0.D 0. and his agrees wih he above graph. Afer a ime = he charge on he capacior is Q@D and his can also be obained approximaely from he graph. Afer a very long ime he charge has is maximum value Q@5 * D which is almos he same as
7 ElecronicsLab9.nb 7 V * Cap he volage across he capacior is VC = PloB Q@D Cap Q C and we may graph his using,, 0, * <, AxesLabel "ime", ime Replace he Baery and Swich by a Signal Generaor having a Square Wave he circui diagram now appears
8 ElecronicsLab9.nb Suppose he square wave generaor has a frequency f given by he square of he signal generaor can be graph using = ; 1 f= ; Prin@"frequency =", f, "Hz"D frequency =50.Hz Noice ha he period of he signal generaor is chosen o be he same as he ime consan in he RC circui. We will discuss his more laer. Suppose he volage ampliude of he signal generaor is vols (he same as he baery volage) he square wave of he signal generaor is graphed using
9 ElecronicsLab9.nb 9 V0 =.; SqWave@_D := IfB <, V0, 0F Plo@SqWave@D,, 0, <D Effecively having he signal generaor in he circui is he same as having he baery in he circui for ime 0<< seconds so he equaion (11) for he curren and equaion (15) for he charge hold for hese imes. he Volage Across he Capacior We may graph he volage across he capacior ogeher wih he signal generaor volage and obain
10 ElecronicsLab9.nb = ; PloB: Q@D Cap, SqWave@D>, :, 0, >F If he period of he signal generaor is longer, for example =*, hen he capacior has more ime o charge = ; Q@D PloB:, SqWave@D>, :, 0, >F Cap Furher if he period of he signal generaor is longer sill, for example =3*, hen he capacior has more ime o charge
11 ElecronicsLab9.nb 11 = 3 ; Q@D PloB:, SqWave@D>, :, 0, >F Cap and he capacior almos has ime o fully charge and have all he vols appear across i. Abou vols now appears across he capacior. he Volage Across he Resisor We may graph he volage across he resisor ogeher wih he signal generaor volage and obain = ; PloBi@D R, SqWave@D<, :, 0, >, PloRange 0, <F If he period of he signal generaor is longer, for example =*, hen he curren ges smaller sill and he volage across he resisor is reduced furher
12 ElecronicsLab9.nb 1 If he period of he signal generaor is longer, for example =*, hen he curren ges smaller sill and he volage across he resisor is reduced furher = ; PloBi@D R, SqWave@D<, :, 0, >, PloRange 0, <F If he period of he signal generaor is longer, for example =3*, hen he curren ges smaller sill and he volage across he resisor is reduced furher = 3 ; PloBi@D R, SqWave@D<, :, 0, >, PloRange 0, <F Abou vols now appears across he resisor. he Second Par of he Square Wave of he Signal Generaor.
13 ElecronicsLab9.nb 13 he Second Par of he Square Wave of he Signal Generaor. During he second par of he period of he signal generaor for imes < <, he volage is zero in he original circui. I helps make he analysis simpler o change he wave form a lile and have he signal generaor volage zero during he firs par of he cycle and a consan V0 during he second par of he cycle = ; V0 =.;, 0, V0 F SigGen = Plo@SqWave@D,, 0, <D SqWave@_D := IfB < his corresponds o he imes in he range sec < < 0.0 sec in he previous diagram. Effecively for he firs par of he cycle he baery is removed from he circui and replaced by a shoring wire and he circui looks like
14 ElecronicsLab9.nb 1 Kirchoff circui law afer he swich is closed is 0= Q C + ir (1) which is he same as equaion (1) wihou he baery. aking he ime derivaive of equaion (1) and using equaion () yields d d i=- i (17) RC Equaion (17) can be solved using he same echniques as before and we obain again equaion (11) d d Q@D = i@d = i0 ExpB- F (1) However, he iniial condiion i0 is differen his ime as we shall see. Equaion (1) can be inegraed for he charge Q[] obaining Q@D = Q@0D + i0 1 - ExpB- F (19) he capacior is assumed fully charged iniially (which can happen if he ime consan is shor compared wih he period of he square wave) so iniially Q@0D = C V (0) and when =0 he par of equaion (19) involving he exponenial funcion vanishes. For long imes here is no charge on he capacior Q[ ]=0. Since ExpA- E=0 and equaion (19) reduces o Q@ D = C V + i0 = 0 (1) and i follows ha i0 = - CV =- V () R Combining equaions (0) and () wih equaion (19) yields Q@D = C V + VC ExpB- F - 1 = V C ExpB- F (3) Equaion (3) should make inuiive sence, since during he second half of he square wave cycle, he Q capacior is discharging. he volage across he capacior is V= C iniially so
15 ElecronicsLab9.nb 15 = ; V =.; SqWave@_D := IfB < PloB:V * ExpB-, 0, VF F, SqWave@D>, :, 0, >F Furher if he signal generaor is longer say hree imes he ime consan, =3 hen he capacior has even more ime o discharge
16 ElecronicsLab9.nb 1 = 3 * ; V =.; SqWave@_D := IfB < PloB:V * ExpB-, V0, 0F F, SqWave@D>, :, 0, >F he Volage Across he Resisor he curren in he circui is obained by aking he derivaive of he charge equaion (3) obaining i@d = - VC ExpB- F=- V R ExpB- F () and he volage across he resisor is jus R*i[]. Graphing he volage across he capacior and he volage across he resisor for he second half he cycle yields
17 ElecronicsLab9.nb 17 = ; V =.; PloB:V * ExpB- F, - V * ExpB- F>, :, 0, >F Noice he sum of he volage of he capacior and he volage of he resisor is jus zero as required by Kirchoff's law. If he signal generaor period is wice he ime consan hen we obain = * ; V =.; PloB:V * ExpB- F, - V * ExpB- F>, :, 0, >F
18 ElecronicsLab9.nb 1 If he signal generaor period is hree he ime consan hen we obain = 3 * ; V =.; PloB:V * ExpB- F, - V * ExpB- F>, :, 0, >F Laboraory Exercises PAR A: Place a signal generaor in series wih a resisor and capacior. Prey much any oupu level (he oupu volage) of he signal generaor will do OK bu afer you ge he oscilloscope working properly make a noe of he maximum volage in your lab noebook. Choose a square wave and make he 1 frequency f of he signal generaor such ha f= wih ==RC a firs. Wih channel 1 of he oscilloscope, measure he volage across he signal generaor and wih channel measure he volage across he capacior. Compare wih he graphs of he firs example above. Make he frequency f of he signal generaor smaller ( larger) so he capacior has more ime o charge. Keep decreasing f. Skech he oscilloscope figures you ge and indicae he values of he volage on he verical scale and he ime on he horizonal scales. Example: Suppose C=0.1 mf and R=. kw hen he ime consan =RC=0.000 sec. as indicaed below:
19 ElecronicsLab9.nb 19 R =. 3 ; c = ; = R c NOE: he value of R and C you use need no be he values given above. Use your digial ohmmeer o measure he value of he resisor and make sure i is he same as given by he color code. Use your digial capacior meer o measured he value of he capacior and i should agree wih he capacior code (which is no ha sandardized so check wih he maker of he capacior and use your meer For example, a capacior labeled 50 B means 1 is he firs digi and 5 is he second digi for he capaciance. is he muliplier in powers of so his capacior is C=5 0 mf = 5 mf where mf=- F. Capaciors can be much smaller and pf = -1 F is ofen used is he ime i ake he capacior o charge o 7% of he maximum volage (which is he maximum volage of he signal generaor). he signal generaor frequency should be se o have a period = a firs bu wha you acually conrol is he frequency f of he signal generaor where f=1/. For he example above, = ; f = So he frequency f=1,70 Hz= 1.5 khz corresponds o one ime consan. he horizonal ime scale of he oscilloscope had beer be somehing like his frequency f. If he oscilloscope is se a oo high a frequency, he ime will be oo shor o see he volage rise. On he oher hand, if he oscilloscope is se a oo low a frequency, here will no be enough ime o see he volage rise across he capacior. You also mus make sure o se he volage scale a roughly he oupu volage of he oscilloscope which you should have measured firs before connecing he capacior and resisor in he circui. PAR B: Wih channel 1 of he oscilloscope, measure he volage across he signal generaor and wih channel measure he volage across he resisor. Compare wih he graphs of he second example above. Make he frequency f of he signal generaor smaller ( larger) so he capacior has more ime o charge. Keep decreasing f he frequency of he signal generaor. Skech he oscilloscope figures you ge. PAR C: Call he capacior used above C1. ake a second capacior and call i C. Combine he wo capaciors in SERIES wihou he signal generaor and oscilloscope aached. he effecive capaciance is given by 1 Ceff = 1 C1 + 1 C Compue he numerical value of he effecive capaciance and check i wih he digial capaciance meer. Noe he effecive capaciance of wo capaciors in SERIES is less han boh C1 and C. Use he SERIES combinaion of C1 and C ogeher wih he signal generaor and oscilloscope and repea he measuremens of PAR A above.
20 ElecronicsLab9.nb 0 Compue he numerical value of he effecive capaciance and check i wih he digial capaciance meer. Noe he effecive capaciance of wo capaciors in SERIES is less han boh C1 and C. Use he SERIES combinaion of C1 and C ogeher wih he signal generaor and oscilloscope and repea he measuremens of PAR A above. PAR D: Call he capacior used above C1. ake a second capacior and call i C. Combine he wo capaciors in PARALLEL wihou he signal generaor and oscilloscope aached. he effecive capaciance is given by Ceff = C1 + C Compue he numerical value of he effecive capaciance and check i wih he digial capaciance meer. Noe he effecive capaciance of wo capaciors in PARALLEL is less han boh C1 and C. Use he PARALLEL combinaion of C1 and C ogeher wih he signal generaor and oscilloscope and repea he measuremens of PAR A above.
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationThe option pricing framework
Chaper 2 The opion pricing framework The opion markes based on swap raes or he LIBOR have become he larges fixed income markes, and caps (floors) and swapions are he mos imporan derivaives wihin hese markes.
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 information2.5 Life tables, force of mortality and standard life insurance products
Soluions 5 BS4a Acuarial Science Oford MT 212 33 2.5 Life ables, force of moraliy and sandard life insurance producs 1. (i) n m q represens he probabiliy of deah of a life currenly aged beween ages + n
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 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 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 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 informationCredit Index Options: the no-armageddon pricing measure and the role of correlation after the subprime crisis
Second Conference on The Mahemaics of Credi Risk, Princeon May 23-24, 2008 Credi Index Opions: he no-armageddon pricing measure and he role of correlaion afer he subprime crisis Damiano Brigo - Join work
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 informationMultiprocessor Systems-on-Chips
Par of: Muliprocessor Sysems-on-Chips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,
More informationSINAMICS S120 drive system
SINAMICS S120 drive sysem Design PM340, frame sizes FSA o FSF The PM340 feaure he following connecions as sandard: DCP/R1 and DCN DC link Terminals DCP/R1 and R2 for connecion of an exernal braking PM-IF
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 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 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 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 informationII.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal
Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.
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 informationSuggested Reading. Signals and Systems 4-2
4 Convoluion In Lecure 3 we inroduced and defined a variey of sysem properies o which we will make frequen reference hroughou he course. Of paricular imporance are he properies of lineariy and ime invariance,
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 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 informationPresent Value Methodology
Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer
More informationWhy Did the Demand for Cash Decrease Recently in Korea?
Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in
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 informationOn the degrees of irreducible factors of higher order Bernoulli polynomials
ACTA ARITHMETICA LXII.4 (1992 On he degrees of irreducible facors of higher order Bernoulli polynomials by Arnold Adelberg (Grinnell, Ia. 1. Inroducion. In his paper, we generalize he curren resuls on
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 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 informationTSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999
TSG-RAN Working Group 1 (Radio Layer 1) meeing #3 Nynashamn, Sweden 22 nd 26 h March 1999 RAN TSGW1#3(99)196 Agenda Iem: 9.1 Source: Tile: Documen for: Moorola Macro-diversiy for he PRACH Discussion/Decision
More informationNikkei Stock Average Volatility Index Real-time Version Index Guidebook
Nikkei Sock Average Volailiy Index Real-ime Version Index Guidebook Nikkei Inc. Wih he modificaion of he mehodology of he Nikkei Sock Average Volailiy Index as Nikkei Inc. (Nikkei) sars calculaing and
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 informationApplication of Fast Response Dual-Colour Pyroelectric Detectors with Integrated Op Amp in a Low Power NDIR Gas Monitor
Applicaion of Fas Response DualColour Pyroelecric Deecors wih Inegraed Op Amp in a Low Power NDIR Gas Monior Infraec GmbH, Gosrizer Sr. 663, 027 Dresden. Inroducion Monioring he concenraion of carbon dioxide
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 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 informationImprovement of a TCP Incast Avoidance Method for Data Center Networks
Improvemen of a Incas Avoidance Mehod for Daa Cener Neworks Kazuoshi Kajia, Shigeyuki Osada, Yukinobu Fukushima and Tokumi Yokohira The Graduae School of Naural Science and Technology, Okayama Universiy
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 informationWHAT ARE OPTION CONTRACTS?
WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be
More informationMaking a Faster Cryptanalytic Time-Memory Trade-Off
Making a Faser Crypanalyic Time-Memory Trade-Off Philippe Oechslin Laboraoire de Securié e de Crypographie (LASEC) Ecole Polyechnique Fédérale de Lausanne Faculé I&C, 1015 Lausanne, Swizerland philippe.oechslin@epfl.ch
More informationIndividual Health Insurance April 30, 2008 Pages 167-170
Individual Healh Insurance April 30, 2008 Pages 167-170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More informationForecasting, Ordering and Stock- Holding for Erratic Demand
ISF 2002 23 rd o 26 h June 2002 Forecasing, Ordering and Sock- Holding for Erraic Demand Andrew Eaves Lancaser Universiy / Andalus Soluions Limied Inroducion Erraic and slow-moving demand Demand classificaion
More informationThe Fourier Transform
The Fourier Transform As we have seen, an (sufficienl smooh) funcion f() ha is periodic can be buil ou of sin s and cos s. We have also seen ha complex exponenials ma be used in place of sin s and cos
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 informationGoRA. For more information on genetics and on Rheumatoid Arthritis: Genetics of Rheumatoid Arthritis. Published work referred to in the results:
For more informaion on geneics and on Rheumaoid Arhriis: Published work referred o in he resuls: The geneics revoluion and he assaul on rheumaoid arhriis. A review by Michael Seldin, Crisopher Amos, Ryk
More informationLecture Note on the Real Exchange Rate
Lecure Noe on he Real Exchange Rae Barry W. Ickes Fall 2004 0.1 Inroducion The real exchange rae is he criical variable (along wih he rae of ineres) in deermining he capial accoun. As we shall see, his
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 information