11. Properties of alternating currents of LCR-electric circuits

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "11. Properties of alternating currents of LCR-electric circuits"

Transcription

1 WS. Properies of alernaing currens of L-elecric circuis. Inroducion So-called passive elecric componens, such as ohmic resisors (), capaciors () and inducors (L), are widely used in various areas of science and elecrical engineering. L-oscillaory circuis deliver he ime base for many elecrically generaed oscillaion processes and -elemens are uilised as frequency filers for signal forming. The resonance behaviour of L-oscillaory circuis feaures pleny of similariies compared o oscillaion-capable sysems in oher physical areas. In he firs par of his lab course, he behaviour of a serial circui compared o a square-wave volage shall be examined. In he second par we ake a look a he properies of conducors and inducors (coils) compared o harmonic alernaing volages (A), where in he hird par we invesigae on he resonance behaviour of a L parallel oscillaory circui.. Theoreical par a) Square-wave volage on he serial circui A capacior and a resisor are conneced o a direc curren volage (D) source, which creaes a consan volage, via a swich S as i is shown in Fig... S Figure.: Generaion of a square-wave volage wih a serial circui. A ime = 0, he capacior shall be compleely discharged and he volage is being plugged by urning he swich. Afer he power-up of he volage i follows by he nd Kirchhoff s circui law = V + V = I + Q = dq d + Q (.)

2 . Properies of alernaing currens of L-elecric circuis This is a firs-order differenial equaion for he charge Q which is sored on he capacior. onsidering he iniial condiions V = V = Q = 0 for = 0 he soluion of he differenial equaion becomes Q() = Q 0 ( e / ) mi Q 0 = (.) I() = dq d = I 0 e / mi I 0 = Q 0 = (.3) V () = Q() = V 0 ( e / ) mi V 0 = Q 0 = (.4) The characerisic ime consan which defines he behaviour of he circui is τ =. A ime T τ he capacior shall be compleely charged and he volage is being broken by urning he swich again. The iniial condiions a ime T become Q = Q 0, V = and I = 0. Saring wih he differenial equaion for > T i follows: 0 = V + V = I + Q = dq d + Q (.5) Q() = Q 0 e ( T 0)/ mi Q 0 = (.6) I() = dq d = I 0 e ( T 0)/ mi I 0 = Q 0 = (.7) V () = Q() = V 0 e ( T 0)/ mi V 0 = Q 0 = (.8) The emporal progress of he volage for periodic power-up and shu-off is shown in Fig.., in paricular for he case T τ. If his condiion is no fulfilled hen he capacior is no compleely charged and he curren hasn dropped down o zero ye when urning he swich. In his case he emporal progress for he volage is shown in Fig..3. b) Harmonic alernaing volage on he -circui and he L-circui When plugging a harmonic alernaing curren V () = cos (ω) (.9) of he frequency ω o an ordinary elecrical circui, hen a harmonic alernaing curren of he same frequency sreams which, in he general case, is shifed by a phase ϕ agains he volage V (): I() = I 0 cos (ω ϕ) (.0) Laboraory manuals for Physics Majors - PHY/

3 .. THEOETIAL PAT 3 a) V = Q b) T V = I c) τ = T Figure.: Temporal progress of he volage for periodic power-up and shu-off of he inpu volage for T 0. The dashed line shows he volage characerisic for a square-wave volage wih mean zero, as i is being delivered from a square-wave generaor. a) V b) V c) Figure.3: Temporal progress of he volage for periodic power-up and shu-off of he inpu volage when he condiion T 0 is no fulfilled. Laboraory manuals for Physics Majors - PHY/

4 4. Properies of alernaing currens of L-elecric circuis The behaviour of he circui is compleely described by his phase and he absolue value of he impedance Z = I 0 (.) If he circui conains only one single elemen, one receives he impedance wih he help of Kirchhoff s nd law: Ohmic resisor : ~ V () = cos (ω) = V () = I() I() = cos (ω) Z =, ϕ = 0 apacior of capaciy : ~ oil of inducance L: ~ L V () = cos (ω) = V () = Q() I() = dq = ω sin (ω) = ω cos (ω + π d ) Z = ω, ϕ = π V () = cos (ω) = V L () = L di d I() = ω L sin (ω) = ω L cos (ω π ) Z L = ω L, ϕ L = + π The phase and he absolue value of he impedance can be displayed as a vecor in he complex plane. For he hree described special cases his is shown in Fig..4 Im Im Im Z ϕ = 0 e Z _ π e Z L + π e Figure.4: Depicion of he impedance in he complex plane. In case he circui conains muliple impedances serially, he oal impedance is given by vecor sum of he single impedances. For he example of he serial circui one receives: Laboraory manuals for Physics Majors - PHY/

5 .. THEOETIAL PAT 5 ~ Z = ω Z = ϕ Z o V = V + V = I (Z + Z ) = I Z o (.) Z o = Z + Z = + /(ω ) (.3) an ϕ = ω and for he ampliude of he curren follows: I 0 = Z o = + /(ω ) (.4) (.5) The volage ampliudes a he capaciy and he resisor are given by V 0 = I 0 Z = V 0 = I 0 Z = + ω (.6) ω + ω (.7) Their dependence on he frequency ω of he inpu volage is shown in Fig..5. A he capaciy high frequencies and a he resisor low frequencies of he inpu signal are being suppressed. Therefore his circui can be used eiher as a high-pass or as a low-pass filer. The frequency response of he oupu volage V a can be adjused in boh cases by varying he resisor. A pracical usage of his circui are one conrols in audio amplifiers. Va = V V a = V Low pass High pass V 0 V0 V 0 V0 ω ω Figure.5: serial circui as high-pass or low-pass filer. In a similar manner one can combine a resisor and an inducance. In his case i holds ha: L Z o = Z ~ + Z L = w L + (.8) an ϕ = ωl (.9) Z o Z L = ω L ϕ Z = and he oupu ampliude a he resisor is: V 0 = I 0 = Z o = + ω L (.0) Laboraory manuals for Physics Majors - PHY/

6 6. Properies of alernaing currens of L-elecric circuis c) Elecrical parallel oscillaory circui (L-circui) ~ m I I I L I L p V p Figure.6: parallel oscillaory circui. In his experimen we use he circui which is shown in Fig..6. The oscillaory circui iself is made up of a coil of inducance L which is parallel-conneced wih a capaciy and an ohmic resisor p. Due o mero-logical reasons a furher resisor m is conneced in series wih he oscillaory circui. When a harmonic inpu volage V () = cos ω is applied o he circui wih Kirchhoff s second law follows V () = m I() + V p () and herefore (.) I() = m ( cos ω V p ()) (.) and wih Kirchhoff s firs law I() = I () + I () + I L () = dv p d + V p() + L V p d (.3) By equalling Equ.. and.3 and differeniaing one ime wih respec o ime he characerisic differenial equaion for his oscillaory circui follows: ω ( sin ω = d V p m d + + ) dv p p m d + V p() L (.4) I is of he same form as he one for he forced oscillaion of he harmonic oscillaor in classical mechanics (see lab course from he winer semeser). Is general soluion is a superposiion of a freely damped oscillaion and a forced oscillaion wih exciaion frequency ω. The free oscillaion decays wih he ime consan τ = L/ and for imes τ he sysem oscillaes only wih he frequency ω of he exciaion volage and is shifed by a phase ϕ o his exciaion. V p () = V p0 cos (ω + ϕ) (.5) The ampliude V p0 and he phase ϕ follow by plugging ino he differenial equaion: Laboraory manuals for Physics Majors - PHY/

7 .. THEOETIAL PAT 7 V p0 = an ϕ = / m ( ) ( ) (.6) p + m + ωl ω ( ) / ( ωl ω + ) (.7) p m Hence, he ampliude and he phase of he volage ha decays a he oscillaory circui are dependen on he exciaion frequency ω and show he ypical resonance behaviour of oscillaion-capable sysems. The ampliude of he volage drop is a he maximum for he resonance frequency ω = ω 0 = L (.8) Here, he impedances of he capaciy and he coil cancel each oher ou and he phase is ϕ = 0. The expression on he righ side of Equ..6 can be simplified for frequencies in he close region of he resonance frequency as follows. Firs of all wih ω0 = L one has V p0 (ω) = / m ( ) p + m + (ω (.9) ω 0 ω) Near by he resonance frequency we have ω ω 0 and wih ω = ω ω 0 i is approximaely rue ha Plugged ino Equ..6 his approximaion leads o ω 0 ω = (ω 0 + ω) (ω 0 ω) ω ω (.30) V p0 ( ω) / m ( ) = p + m + (ω ω) ω / m ( ) (.3) p + m + 4 ω The resonance curve is shown in Fig..7. Is widh is usually specified by he so-called half-power widh ω /, where ω / denoes he frequency difference for which he square of he ampliude of he volage drop i.e. he power in he parallel oscillaory circui has fallen off o half of he value a he resonance frequency ω 0. For ω / he ampliude of he volage drop iself has fallen off o / imes he value a he resonance frequency. From Equ..3 one ges ω / = ( + ) p m (.3) Laboraory manuals for Physics Majors - PHY/

8 8. Properies of alernaing currens of L-elecric circuis Vp0( ω) Vp0( ω) Vp0,max Vp0,max Vp0,max Vp0,max ω ω / ω/ ω.3 Experimenal par Figure.7: esonance curve. In his experimen we observe he measured quaniies wih a cahode-ray oscillograph (O). The funcional principle of he O is explained in he appendix of he lab course manual for EM. The O can only display volages. urrens can be displayed indirecly via he volage drop V on a known ohmic es resisor, due o V = I. Therefore he resisor has o be included ino he circui, whereby is value has o be small enough such ha i s no affecing he measuremen. In his experimen a es resisor of Ω is being used. For he abiliy o display wo measured quaniies a he same ime (e.g. inpu volage and curren in he circui) o read off heir phase relaion we use a wo-ray O. Le he assisan give you an inroducion o he working principles of he O Take ino accoun ha he ouer cable (shielding) of he inpus of he O are conneced inernally wih he ground! Therefore, always link he inpus such ha boh ouer cable lead o he same poin in he circui. For his experimen no error calculaion has o be done. a) Square-wave volage n he -serial circui For an applied square-wave volage he oupu volages a he capacior and he resisor of a serial circui shall be observed. Assemble he circui o arge he arrangemen of Fig..8. Use a resisor of = 470 Ω and a capacior wih a capaciy of = µf. Wih he volage generaor se up a square-wave volage wih an ampliude of 5 V and a frequency of 00 Hz. On he O, simulaneously sudy he inpu volage V () and he volage V () a he capacior. Plo he volage characerisic as a funcion agains he ime Laboraory manuals for Physics Majors - PHY/

9 .3. EXPEIMENTAL PAT 9 ~ V () ~ V () Figure.8: Measuremens on he serial circui. graphically and from he curves deermine he periods T and τ =. ompare your resuls wih he expeced values. epea he measuremen for a square-wave volage wih a frequency of 5000 Hz. ese he square-wave volage o a frequency of 00 Hz and simulaneously sudy he inpu volage V () and he volage V () a he resisor. Plo he volage characerisic as a funcion agains he ime graphically and from he curves deermine he periods T and τ =. ompare your resuls wih he expeced values. epea he measuremen for a square-wave volage wih a frequency of 5000 Hz. b) Harmonic inpu volage a conducor and coil For a harmonic inpu volage you shall explore he impedances of a single capacior and a single coil as well as he oupu volages of a serial circui. I() I() ~ L ~ Impedance of a capaciy: Figure.9: Measuremen of he impedance of a capacior and a coil. Assemble he circui as shown in Fig..9. Use a capacior wih a capaciy of = µf. Wih he volage generaor se up a square-wave volage wih an ampliude of 5 V and a frequency of 0 Hz. Simulaneously sudy he inpu volage V () and he curren I() (via he volage drop over he es resisor ) wih he aid of he O. Deermine Z and ϕ and compare your resuls wih he expeced values. epea he measuremens for frequencies of 50, 50, 500 and 000 Hz and plo Z as a funcion of he frequency. Impedance of a coil: Laboraory manuals for Physics Majors - PHY/

10 0. Properies of alernaing currens of L-elecric circuis Exchange he capaciy by a coil of inducance L = 35 mh. Wih he volage generaor se up a square-wave volage wih an ampliude of 5 V and a frequency of 00 Hz. Simulaneously sudy he inpu volage V () and he curren I() on he O. Deermine Z L and ϕ L and compare your resuls wih he expeced values. epea he measuremens for frequencies of 500, 000 and 000 Hz and plo Z L as a funcion of he frequency. c) esonance curve of he L parallel oscillaory circui The resonance curve of a L parallel oscillaory circui shall be measured for differen values of he resisor p. Assemble he circui afer Fig..0. Firs, use a resisor of p = 9. kω. Wih he O measure he oscillaion ampliude of he oscillaory circui as a funcion of he inpu (exciaion) frequency. Iniially, raise he inpu frequency in big seps of 00 khz o 600 khz and measure he range around he resonance frequency in more delicae seps. hose an appropriae sep size o do ha. Plo he ampliude as a funcion of he inpu frequency and deermine he half-power widh. epea he measuremen for a resisor of p = 57.6 kω. Plo he half-power widh agains / p and lay a sraigh line hrough boh measuremen poins. Deermine he capaciy from he slope of he line and he resisor m from he abscissa segmen. Finally, deermine he inducance L from he measured resonance frequency. Oscilloscope H H Ex. Z Ex. poeniomeer VG IN Signal generaor SWEEP OUT HI Frequency couner ~ ouner Generaor KO y m 50Ω L p KO Probe KO y Figure.0: Seup for he measuremen of he resonance curve of a L parallel oscillaory circui. Laboraory manuals for Physics Majors - PHY/

RC, RL and RLC circuits

RC, 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 information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 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 information

CHARGE AND DISCHARGE OF A CAPACITOR

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 information

Circuit Types. () i( t) ( )

Circuit 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 information

RC Circuit and Time Constant

RC Circuit and Time Constant ircui and Time onsan 8M Objec: Apparaus: To invesigae he volages across he resisor and capacior in a resisor-capacior circui ( circui) as he capacior charges and discharges. We also wish o deermine he

More information

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 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 information

9. Capacitor and Resistor Circuits

9. 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 information

Inductance and Transient Circuits

Inductance 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 information

Differential Equations and Linear Superposition

Differential 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 information

Using RCtime to Measure Resistance

Using 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 buil-in ADC (Analog o Digial Converer)

More information

PHYS245 Lab: RC circuits

PHYS245 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 information

Capacitors and inductors

Capacitors 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 information

Chabot College Physics Lab RC Circuits Scott Hildreth

Chabot 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 information

Chapter 2: Principles of steady-state converter analysis

Chapter 2: Principles of steady-state converter analysis Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer

More information

RC (Resistor-Capacitor) Circuits. AP Physics C

RC (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 information

Voltage level shifting

Voltage 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 information

5.8 Resonance 231. The study of vibrating mechanical systems ends here with the theory of pure and practical resonance.

5.8 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 information

Signal Processing and Linear Systems I

Signal 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 information

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

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1 - TRANSIENTS 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 resisor-capacior (R) and resisor-inducor (RL) D circuis

More information

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009

Full-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 information

Differential Equations. Solving for Impulse Response. Linear systems are often described using differential equations.

Differential 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 information

Pulse-Width Modulation Inverters

Pulse-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 information

Astable multivibrator using the 555 IC.(10)

Astable 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 information

DC-DC Boost Converter with Constant Output Voltage for Grid Connected Photovoltaic Application System

DC-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 information

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.

Appendix 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 information

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ

µ 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 information

The Transport Equation

The 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 information

Signal Rectification

Signal 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 information

Physics 1402: Lecture 21 Today s Agenda

Physics 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 Self-nducnce, R ircuis X X X X

More information

ECEN4618: Experiment #1 Timing circuits with the 555 timer

ECEN4618: 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 information

Rotational Inertia of a Point Mass

Rotational 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 information

Part II Converter Dynamics and Control

Part 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 information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. 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 information

Module 3. R-L & R-C Transients. Version 2 EE IIT, Kharagpur

Module 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 information

Transient Analysis of First Order RC and RL circuits

Transient 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 information

Switching Regulator IC series Capacitor Calculation for Buck converter IC

Switching 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 information

AP Calculus AB 2013 Scoring Guidelines

AP 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 information

s-domain Circuit Analysis

s-domain Circuit Analysis Domain ircui Analyi Operae direcly in he domain wih capacior, inducor and reior Key feaure lineariy i preered c decribed by ODE and heir Order equal number of plu number of Elemenbyelemen and ource ranformaion

More information

Physics 111 Fall 2007 Electric Currents and DC Circuits

Physics 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 information

Making Use of Gate Charge Information in MOSFET and IGBT Data Sheets

Making 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 information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT 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 information

AP Calculus BC 2010 Scoring Guidelines

AP 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 information

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A 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 information

Analogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar

Analogue 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 information

NOTES ON OSCILLOSCOPES

NOTES 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 information

A Novel Approach to Improve Diverter Performance in Liquid Flow Calibration Facilities

A Novel Approach to Improve Diverter Performance in Liquid Flow Calibration Facilities A Novel Approach o Improve Diverer Performance in Liquid Flow Calibraion Faciliies R. Engel Physikalisch-Technische Bundesansal (PTB) Braunschweig, Germany U. Klages Universiy of Applied Sciences a Wolfenbüel,

More information

Acceleration Lab Teacher s Guide

Acceleration 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 information

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)

Mathematics 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 information

Switched Mode Converters (1 Quadrant)

Switched 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 information

ALSO IN THIS ISSUE: For more information contact: Graham Robertson Media Relations, 310-726-8512 FOR DESIGNERS AND SYSTEMS ENGINEERS

ALSO 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 information

1. 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,

1. 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 information

Gate protection. Current limit. Overvoltage protection. Limit for unclamped ind. loads. Charge pump Level shifter. Rectifier. Open load detection

Gate 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 information

Steps for D.C Analysis of MOSFET Circuits

Steps 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 information

LLC Resonant Converter Reference Design using the dspic DSC

LLC 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 information

PI4ULS5V202 2-Bit Bi-directional Level Shifter with Automatic Sensing & Ultra Tiny Package

PI4ULS5V202 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 information

A Mathematical Description of MOSFET Behavior

A 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 information

Economics Honors Exam 2008 Solutions Question 5

Economics 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 information

CAPACITANCE AND INDUCTANCE

CAPACITANCE 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 information

AN Smart LED Lamp Driver IC with PFC Function. Introduction. Soft-Start Function. Internal Digital Reference by ZCD.

AN Smart LED Lamp Driver IC with PFC Function. Introduction. Soft-Start Function. Internal Digital Reference by ZCD. www.fairchildsemi.com AN-9744 Smar LED Lamp Driver IC wih PFC Funcion Inroducion The FL7701 is a PWM peak curren conroller for a buck converer opology operaing in Coninuous Conducion Mode (CCM) wih an

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking 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 information

Meßverfahren der EMV Bestimmung eines Nahfelds nach Betrag und Phase durch Messungen im Zeitbereich

Meßverfahren der EMV Bestimmung eines Nahfelds nach Betrag und Phase durch Messungen im Zeitbereich Meßverfahren der MV Besimmung eines Nahfelds nach Berag und Phase durch Messungen im Zeibereich Thiemo Sadler Jan Luiken er Haseborg Deparmen of Measuremen / MC Technical Universiy of Hamburg-Harburg Conen

More information

Thyristor Based Speed Control Techniques of DC Motor: A Comparative Analysis

Thyristor 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 information

The naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1

The 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 information

Monotonic, Inrush Current Limited Start-Up for Linear Regulators

Monotonic, 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 information

Chapter 2 Kinematics in One Dimension

Chapter 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 information

Photovoltaic Power Control Using MPPT and Boost Converter

Photovoltaic Power Control Using MPPT and Boost Converter 23 Phoovolaic Power Conrol Using MPP and Boos Converer A.Aou, A.Massoum and M.Saidi Absrac he sudies on he phoovolaic sysem are exensively increasing because of a large, secure, essenially exhausible and

More information

Multiprocessor Systems-on-Chips

Multiprocessor 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 information

4 Convolution. Recommended Problems. x2[n] 1 2[n]

4 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 information

DATA SHEET. 1N4148; 1N4446; 1N4448 High-speed diodes DISCRETE SEMICONDUCTORS. 1996 Sep 03

DATA 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 information

Lecture-10 BJT Switching Characteristics, Small Signal Model

Lecture-10 BJT Switching Characteristics, Small Signal Model 1 Lecure-1 BJT Swiching Characerisics, Small Signal Model BJT Swiching Characerisics: The circui in Fig.1(b) is a simple CE swich. The inpu volage waveform v s shown in he Fig.1(a) is used o conrol he

More information

Pulse Discharge Characteristics of Surface Mount Capacitors

Pulse Discharge Characteristics of Surface Mount Capacitors Pulse Discharge Characerisics of Surface Moun Capaciors W.J. Carey, A.J. Wiebe, L.L Algilbers, and W.C. Nunnally 3 ARC Technology 376 NW h Sree, Whiewaer, KS, USA Tel: + (36799-763; Email: carey@arc-ech.us,

More information

Markit Excess Return Credit Indices Guide for price based indices

Markit 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

Why Did the Demand for Cash Decrease Recently in Korea?

Why 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 information

Chapter 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

Chapter 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 information

RA 30 095/06.98 1/8. Replaces: 11.97 29 949, 29 951. Table of contents RA 30 095/06.98

RA 30 095/06.98 1/8. Replaces: 11.97 29 949, 29 951. Table of contents RA 30 095/06.98 RA 30 095/06.98 Elecronic amplifier for he conrol of proporional direcional valves ih elecrical posiion feedback Models T 5005 o T 5008, Series X RA 30 095/06.98 Replaces:.97 9 949, 9 95 The amplifiers

More information

Newton s Laws of Motion

Newton 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 information

Form measurement systems from Hommel-Etamic Geometrical tolerancing in practice DKD-K-02401. Precision is our business.

Form 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 information

Present Value Methodology

Present 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 information

TSG-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) 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 information

Section 7.1 Angles and Their Measure

Section 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 information

IR Receiver Modules for Mid Range Proximity Sensors

IR Receiver Modules for Mid Range Proximity Sensors IR Receiver Modules for Mid Range TSOP4P.. Vishay Semiconducors 2 3 MECHANICAL DATA Pinning = OUT, 2 =, 3 = V S 6672 FEATURES Low supply curren Phoo deecor and preamplifier in one package Inernal filer

More information

Duration 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.

Duration 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 information

SEMICONDUCTOR APPLICATION NOTE

SEMICONDUCTOR 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 information

Cointegration: The Engle and Granger approach

Cointegration: 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 information

A Probability Density Function for Google s stocks

A Probability Density Function for Google s stocks A Probabiliy Densiy Funcion for Google s socks V.Dorobanu Physics Deparmen, Poliehnica Universiy of Timisoara, Romania Absrac. I is an approach o inroduce he Fokker Planck equaion as an ineresing naural

More information

On Jitter by Dan Lavry, Lavry Engineering, Inc. email: dan@lavryengineering.com

On Jitter by Dan Lavry, Lavry Engineering, Inc. email: dan@lavryengineering.com On Jier by Dan Lavry, Lavry Engineering, Inc. email: dan@lavryengineering.com Copyrigh 1997 Lavry Engineering The firs par of his aricle for people who wan o gain some inuiive undersanding abou clock jier

More information

Product Operation and Setup Instructions

Product 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 information

THE PRESSURE DERIVATIVE

THE 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 information

BD FACSuite Software Quick Reference Guide for the Experiment Workflow

BD FACSuite Software Quick Reference Guide for the Experiment Workflow BD FACSuie Sofware Quick Reference Guide for he Experimen Workflow This guide conains insrucions for using BD FACSuie sofware wih he BD FACSVerse flow cyomeer using he experimen workflow. Daa can be acquired

More information

LECTURE 9. C. Appendix

LECTURE 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 information

Photo Modules for PCM Remote Control Systems

Photo Modules for PCM Remote Control Systems Phoo Modules for PCM Remoe Conrol Sysems Available ypes for differen carrier frequencies Type fo Type fo TSOP173 3 khz TSOP1733 33 khz TSOP1736 36 khz TSOP1737 36.7 khz TSOP1738 38 khz TSOP174 4 khz TSOP1756

More information

Smart Two Channel High-Side Power Switch

Smart Two Channel High-Side Power Switch Smar Two Channel igh-side Power Swich PROFET BTS6 Feaures Overload proecion Curren limiaion Shor circui proecion Thermal shudown Overvolage proecion (including load dump) Fas demagneizaion of inducive

More information

3 Runge-Kutta Methods

3 Runge-Kutta Methods 3 Runge-Kua Mehods In conras o he mulisep mehods of he previous secion, Runge-Kua mehods are single-sep mehods however, muliple sages per sep. They are moivaed by he dependence of he Taylor mehods on he

More information

Behavior Analysis of a Biscuit Making Plant using Markov Regenerative Modeling

Behavior Analysis of a Biscuit Making Plant using Markov Regenerative Modeling Behavior Analysis of a Biscui Making lan using Markov Regeneraive Modeling arvinder Singh & Aul oyal Deparmen of Mechanical Engineering, Lala Lajpa Rai Insiue of Engineering & Technology, Moga -, India

More information

CLOCK SKEW CAUSES CLOCK SKEW DUE TO THE DRIVER EROSION OF THE CLOCK PERIOD

CLOCK 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 information

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,

More information

Lecture 320 Differential Output Op Amps (3/27/02) Page 320-1

Lecture 320 Differential Output Op Amps (3/27/02) Page 320-1 Lecure 320 Differenial Oupu Op Amps (3/27/02) Page 3201 LECTURE 320 DIFFERENTIAL OUTPUT OP AMPS (READING: AH 384393, GHLM 808857) Objecive The objecive of his presenaion is: 1.) Design and analysis of

More information

Optimal Investment and Consumption Decision of Family with Life Insurance

Optimal Investment and Consumption Decision of Family with Life Insurance Opimal Invesmen and Consumpion Decision of Family wih Life Insurance Minsuk Kwak 1 2 Yong Hyun Shin 3 U Jin Choi 4 6h World Congress of he Bachelier Finance Sociey Torono, Canada June 25, 2010 1 Speaker

More information

The Torsion of Thin, Open Sections

The 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 information

Application of Fast Response Dual-Colour Pyroelectric Detectors with Integrated Op Amp in a Low Power NDIR Gas Monitor

Application 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 information