Lecture 2: Telegrapher Equations For Transmission Lines. Power Flow.

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Lecture 2: Telegrapher Equations For Transmission Lines. Power Flow."

Transcription

1 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 lane on one side of a PCB and lands on he oher: Microsri is an examle of a ransmission line, hough echnically i is only an aroximae model for microsri, as we will see laer in his course. Why TLs? Imagine wo ICs are conneced ogeher as shown: When he olage a A changes sae, does ha new olage aear a B insananeously? No, of course no Keih W. Whies

2 Whies, EE 481 Lecure 2 Page 2 of 13 If hese wo oins are searaed by a large elecrical disance, here will be a roagaion delay as he change in sae (elecrical signal) raels o B. No an insananeous effec. In microwae circuis, een disances as small as a few inches may be far and he roagaion delay for a olage signal o aear a anoher IC may be significan. This roagaion of olage signals is modeled as a ransmission line (TL). We will see ha olage and curren can roagae along a TL as waes! Fanasic. The ransmission line model can be used o sole many, many yes of high frequency roblems, eiher exacly or aroximaely: Coaxial cable. Two-wire. Microsri, sriline, colanar waeguide, ec. All rue TLs share one common characerisic: he E and H fields are all erendicular o he direcion of roagaion, which is he long axis of he geomery. These are called TEM fields for ranserse elecric and magneic fields. An excellen examle of a TL is a coaxial cable. On a TL, he olage and curren ary along he srucure in ime and

3 Whies, EE 481 Lecure 2 Page 3 of 13 saially in he direcion, as indicaed in he figure below. There are no insananeous effecs. E E H Fig. 1 A common circui symbol for a TL is he wo-wire (arallel) symbol o indicae any ransmission line. For examle, he equialen circui for he coaxial srucure shown aboe is: Analysis of Transmission Lines As menioned, on a TL he olage and curren ary along he srucure in ime () and in disance (), as indicaed in he figure aboe. There are no insananeous effecs.

4 Whies, EE 481 Lecure 2 Page 4 of 13 i, +, - i, How do we sole for (,) and i(,)? We firs need o deelo he goerning equaions for he olage and curren, and hen sole hese equaions. Noice in Fig. 1 aboe ha here is conducion curren in he cener conducor and ouer shield of he coaxial cable, and a dislacemen curren beween hese wo conducors where he elecric field E is arying wih ime. Each of hese currens has an associaed imedance: Conducion curren imedance effecs: o Resisance, R, due o losses in he conducors, o Inducance, L, due o he curren in he conducors and he magneic flux linking he curren ah. Dislacemen curren imedance effecs: o Conducance, G, due o losses in he dielecric beween he conducors, o Caaciance, C, due o he ime arying elecric field beween he wo conducors. To deelo he goerning equaions for, will consider only a small secion V and I,, we of he TL. This is so

5 Whies, EE 481 Lecure 2 Page 5 of 13 small ha he elecrical effecs are occurring insananeously and we can simly use circui heory o draw he relaionshis beween he conducion and dislacemen currens. This equialen circui is shown below: i, +, - R i, L C G +, - Fig. 2 The ariables R, L, C, and G are disribued (or er-uni lengh, PUL) arameers wih unis of /m, H/m, F/m, and S/m, reseciely. We will someimes ignore losses in his course. A finie lengh of TL can be consruced by cascading many, many of hese subsecions along he oal lengh of he TL. In he case of a lossless TL where R = G = 0 his cascade aears as: L L L L C C C C This is a general model: i alies o any TL regardless of is cross secional shae roided he acual elecromagneic field is TEM.

6 Whies, EE 481 Lecure 2 Page 6 of 13 Howeer, he PUL-arameer alues change deending on he secific geomery (wheher i is a microsri, sriline, wo-wire, coax, or oher geomery) and he consrucion maerials. Transmission Line Equaions To deelo he goerning equaion for,, aly KVL in Fig. 2 aboe (ignoring losses) i,, L, (2.1a),(1) Similarly, for he curren i, aly KCL a he node, i, C i, (2.1b),(2) Then: 1. Diide (1) by :,, i, L (3) In he limi as 0, he erm on he LHS in (3) is he forward difference definiion of deriaie. Hence,, i, L (2.2a),(4) 2. Diide (2) by :

7 Whies, EE 481 Lecure 2 Page 7 of 13,, 0, i i C (5) Again, in he limi as 0 he erm on he LHS is he forward difference definiion of deriaie. Hence, i,, C (2.2b),(6) Equaions (4) and (6) are a air of couled firs order arial differenial equaions (PDEs) for, and i,. These wo equaions are called he elegraher equaions or he ransmission line equaions. Reca: We exec ha and i are no consan along microwae circui inerconnecs. Raher, (4) and (6) dicae how and i ary along he TL a all imes. TL Wae Equaions We will now combine (4) and (6) in a secial way o form wo equaions, each a funcion of or i only. To do his, ake (4): of (4) and of (6): 2, 2 i, L 2 (7)

8 Whies, EE 481 Lecure 2 Page 8 of 13 2 i, 2, (6) : C 2 Subsiuing (8) ino (7) gies: 2, 2, LC 2 2 Similarly, 2 i, 2 i, LC 2 2 (8) (9) (10) Equaions (9) and (10) are he goerning equaions for he and deendence of and i. These are ery secial equaions. In fac, hey are wae equaions for and i! We will define he (hase) elociy of hese waeforms as 1 [m/s] (2.16) LC so ha (9) becomes 2, 1 2, (11) Volage Wae Equaion Soluions There are wo general soluions o (11): 1., (12)

9 Whies, EE 481 Lecure 2 Page 9 of 13 is any wice-differeniable funcion ha conains,, and in he form of he argumen shown. I can be erified ha (12) is a soluion o (11) by subsiuing (12) ino (11) and showing ha he LHS equals he RHS. Equaion (12) reresens a wae raeling in he + direcion wih seed 1/ LC m/s. To see his, consider he examle below wih = 1 m/s: A = 1 s, focus on he eak locaed a = 1.5 m. Then, 1.5 s The argumen s says consan for arying and. Therefore, a = 2 s, for examle, hen 2 s Therefore, 2.5 m So he eak has now moed o osiion = 2.5 m a = 2 s.

10 Whies, EE 481 Lecure 2 Page 10 of 13 Likewise, eery oin on his funcion moes he same disance (1 m) in his ime (1 s). This is called wae moion. The seed of his moemen is 1 m m 1 1 s s 2., (13) This is he second general soluion o (11). This funcion reresens a wae moing in he - direcion wih seed. The comlee soluion o he wae equaion (11) is he sum of (12) and (13), (14) and can be any suiably differeniable funcions, bu wih argumens as shown. Curren Wae Equaion Soluions A similar analysis can be erformed for curren waes on he TL. The goerning equaion for i, is 2 i, 1 2 i, (15) 2 2 2

11 Whies, EE 481 Lecure 2 Page 11 of 13 The comlee general soluion o his curren wae equaion can be deermined in a manner similar o he olage as i, i i (16) + wae - wae Furhermore, he funcion i can be relaed o he funcion and i can be relaed o. For examle, subsiuing i and differeniaing hen inegraing gies 1 i C ino (6), or i C (17) Bu, 1 C C C LC L We will define L Z0 [] (2.13),(18) C as he characerisic imedance of he ransmission line. (Noe ha in some exs, Z 0 is denoed as R c, he characerisic resisance of he TL). Wih (18), (17) can be wrien as

12 Whies, EE 481 Lecure 2 Page 12 of 13 Similarly, i can be shown ha i i 0 (19) Z 0 (20) The minus sign resuls since he curren is in he - direcion. Finally, subsiuing (19) and (20) ino (16) gies 1 1 i, (21) Z Z This equaion as well as (14) Z 0 0, (22) are he general wae soluions for and i on a ransmission line. Power Flow These olage and curren waes ransor ower along he TL. The ower flow carried by he forward wae, is 2,,, i, (23) Z0 which is osiie indicaing ower flows in he + direcion. Similarly, he ower flow of he reerse wae is

13 Whies, EE 481 Lecure 2 Page 13 of 13 2,,, i, (24) Z which is negaie indicaing ower flows in he - direcion. 0

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

PRESSURE BUILDUP. Figure 1: Schematic of an ideal buildup test

PRESSURE 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 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

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

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

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

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

Answer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1

Answer, 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 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

Random 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 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 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

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

4. International Parity Conditions

4. 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 information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 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 information

2.5 Life tables, force of mortality and standard life insurance products

2.5 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 information

ANALYTIC PROOF OF THE PRIME NUMBER THEOREM

ANALYTIC PROOF OF THE PRIME NUMBER THEOREM ANALYTIC PROOF OF THE PRIME NUMBER THEOREM RYAN SMITH, YUAN TIAN Conens Arihmeical Funcions Equivalen Forms of he Prime Number Theorem 3 3 The Relaionshi Beween Two Asymoic Relaions 6 4 Dirichle Series

More information

17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides

17 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 information

Two Compartment Body Model and V d Terms by Jeff Stark

Two Compartment Body Model and V d Terms by Jeff Stark Two Comparmen Body Model and V d Terms by Jeff Sark In a one-comparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics - By his, we mean ha eliminaion is firs order and ha pharmacokineic

More information

Term Structure of Prices of Asian Options

Term Structure of Prices of Asian Options Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:

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

Sensor Network with Multiple Mobile Access Points

Sensor Network with Multiple Mobile Access Points Sensor Newor wih Mulile Mobile Access Poins Parvahinahan Veniasubramaniam, Qing Zhao and Lang Tong School of Elecrical and Comuer Engineering Cornell Universiy, Ihaca, NY 4853, USA Email: v45@cornell.edu,{qzhao,long}@ece.cornell.edu

More information

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m

Chapter 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 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

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

Optimal Real-Time Scheduling for Hybrid Energy Storage Systems and Wind Farms Based on Model Predictive Control

Optimal Real-Time Scheduling for Hybrid Energy Storage Systems and Wind Farms Based on Model Predictive Control Energies 2015, 8, 8020-8051; doi:10.3390/en8088020 Aricle OPEN ACCESS energies ISSN 1996-1073 www.mdi.com/journal/energies Oimal Real-Time Scheduling for Hybrid Energy Sorage Sysems and Wind Farms Based

More information

AP Calculus AB 2007 Scoring Guidelines

AP 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 information

Motion Along a Straight Line

Motion 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 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

Usefulness of the Forward Curve in Forecasting Oil Prices

Usefulness 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 information

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper

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

Module 3 Design for Strength. Version 2 ME, IIT Kharagpur

Module 3 Design for Strength. Version 2 ME, IIT Kharagpur Module 3 Design for Srengh Lesson 2 Sress Concenraion Insrucional Objecives A he end of his lesson, he sudens should be able o undersand Sress concenraion and he facors responsible. Deerminaion of sress

More information

WHAT ARE OPTION CONTRACTS?

WHAT 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 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

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities

Table 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 information

The Kinetics of the Stock Markets

The Kinetics of the Stock Markets Asia Pacific Managemen Review (00) 7(1), 1-4 The Kineics of he Sock Markes Hsinan Hsu * and Bin-Juin Lin ** (received July 001; revision received Ocober 001;acceped November 001) This paper applies he

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

2.2 Time Series Analysis 2.2.1 Preliminaries 2.2.2 Various Types of Stochastic Processes 2.2.3 Parameters of Univariate and Bivariate Time Series

2.2 Time Series Analysis 2.2.1 Preliminaries 2.2.2 Various Types of Stochastic Processes 2.2.3 Parameters of Univariate and Bivariate Time Series . Time Series Analysis.. Preliminaries.. Various Tyes of Sochasic Processes..3 Parameers of Univariae and Bivariae Time Series..4 Esimaing Covariance Funcions and Secra . Time Series Analysis The cenral

More information

Lecture Note on the Real Exchange Rate

Lecture 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 information

Chapter 4: Exponential and Logarithmic Functions

Chapter 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 information

Circle Geometry (Part 3)

Circle Geometry (Part 3) Eam aer 3 ircle Geomery (ar 3) emen andard:.4.(c) yclic uadrilaeral La week we covered u otheorem 3, he idea of a convere and we alied our heory o ome roblem called IE. Okay, o now ono he ne chunk of heory

More information

Individual Health Insurance April 30, 2008 Pages 167-170

Individual 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 information

On the degrees of irreducible factors of higher order Bernoulli polynomials

On 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 information

SHB Gas Oil. Index Rules v1.3 Version as of 1 January 2013

SHB Gas Oil. Index Rules v1.3 Version as of 1 January 2013 SHB Gas Oil Index Rules v1.3 Version as of 1 January 2013 1. Index Descripions The SHB Gasoil index (he Index ) measures he reurn from changes in he price of fuures conracs, which are rolled on a regular

More information

Keldysh Formalism: Non-equilibrium Green s Function

Keldysh Formalism: Non-equilibrium Green s Function Keldysh Formalism: Non-equilibrium Green s Funcion Jinshan Wu Deparmen of Physics & Asronomy, Universiy of Briish Columbia, Vancouver, B.C. Canada, V6T 1Z1 (Daed: November 28, 2005) A review of Non-equilibrium

More information

Frequency Modulation. Dr. Hwee-Pink Tan http://www.cs.tcd.ie/hweepink.tan

Frequency 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 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

Full-wave Bridge Rectifier Analysis

Full-wave Bridge Rectifier Analysis Full-wave Brige Recifier Analysis Jahan A. Feuch, Ocober, 00 his aer evelos aroximae equais for esigning or analyzing a full-wave brige recifier eak-eecor circui. his circui is commly use in A o D cverers,

More information

Second Order Linear Differential Equations

Second Order Linear Differential Equations Second Order Linear Differenial Equaions Second order linear equaions wih consan coefficiens; Fundamenal soluions; Wronskian; Exisence and Uniqueness of soluions; he characerisic equaion; soluions of homogeneous

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

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

The option pricing framework

The 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 information

Stochastic Optimal Control Problem for Life Insurance

Stochastic 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 information

Automatic measurement and detection of GSM interferences

Automatic 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 information

CALCULATION OF OMX TALLINN

CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN 1. OMX Tallinn index...3 2. Terms in use...3 3. Comuaion rules of OMX Tallinn...3 3.1. Oening, real-ime and closing value of he Index...3 3.2. Index

More information

Morningstar Investor Return

Morningstar 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 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

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

Equation for a line. Synthetic Impulse Response 0.5 0.5. 0 5 10 15 20 25 Time (sec) x(t) m

Equation 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 information

AP Calculus AB 2010 Scoring Guidelines

AP 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 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

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

Return Calculation of U.S. Treasury Constant Maturity Indices

Return 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 information

Name: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling

Name: 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 information

Vector Autoregressions (VARs): Operational Perspectives

Vector 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 information

Option Pricing Under Stochastic Interest Rates

Option Pricing Under Stochastic Interest Rates I.J. Engineering and Manufacuring, 0,3, 8-89 ublished Online June 0 in MECS (hp://www.mecs-press.ne) DOI: 0.585/ijem.0.03. Available online a hp://www.mecs-press.ne/ijem Opion ricing Under Sochasic Ineres

More information

Does International Trade Stabilize Exchange Rate Volatility?

Does International Trade Stabilize Exchange Rate Volatility? Does Inernaional Trade Sabilize Exchange Rae Volailiy? Hui-Kuan Tseng, Kun-Ming Chen, and Chia-Ching Lin * Absrac Since he early 980s, major indusrial counries have been suffering severe muli-laeral rade

More information

Markov Chain Modeling of Policy Holder Behavior in Life Insurance and Pension

Markov Chain Modeling of Policy Holder Behavior in Life Insurance and Pension Markov Chain Modeling of Policy Holder Behavior in Life Insurance and Pension Lars Frederik Brand Henriksen 1, Jeppe Woemann Nielsen 2, Mogens Seffensen 1, and Chrisian Svensson 2 1 Deparmen of Mahemaical

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

Pricing Fixed-Income Derivaives wih he Forward-Risk Adjused Measure Jesper Lund Deparmen of Finance he Aarhus School of Business DK-8 Aarhus V, Denmark E-mail: jel@hha.dk Homepage: www.hha.dk/~jel/ Firs

More information

Capital Structure Effects on Prices of Firm Stock Options: Tests Using Implied Market Values of Corporate Debt

Capital Structure Effects on Prices of Firm Stock Options: Tests Using Implied Market Values of Corporate Debt Capial Srucure Effecs on Prices of Firm Sock Opions: Tess Using Implied Marke Values of Corporae Deb By Rober Geske and Yi Zhou* Noember, 2007 This reision January, 2009 JEL Classificaion: G12 Keywords:

More information

Package SJP. Parameter Symbol Conditions Rating Unit Remarks Transient Peak Reverse Voltage V RSM 30 V Repetitive Peak Reverse Voltage, V RM 30 V

Package SJP. Parameter Symbol Conditions Rating Unit Remarks Transient Peak Reverse Voltage V RSM 30 V Repetitive Peak Reverse Voltage, V RM 30 V V RM = 30 V, I F(AV) = A Schoky Diode Daa Shee Descripion is a Schoky diode ha is low forward volage drop, and achieves high efficiency recificaion circui. Package SJP (2) Feaures Low Sauraion Volage High

More information

Default Risk in Equity Returns

Default Risk in Equity Returns Defaul Risk in Equiy Reurns MRI VSSLOU and YUHNG XING * BSTRCT This is he firs sudy ha uses Meron s (1974) opion pricing model o compue defaul measures for individual firms and assess he effec of defaul

More information

Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Journal Of Business & Economics Research September 2005 Volume 3, Number 9 Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

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

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

Exotic electricity options and the valuation of electricity generation and transmission assets

Exotic electricity options and the valuation of electricity generation and transmission assets Decision Suppor Sysems 30 2001 383 392 wwwelseviercomrlocaerdsw Exoic elecriciy opions and he valuaion of elecriciy generaion and ransmission asses Shi-Jie Deng a,), Blake Johnson b, Aram Sogomonian c

More information

UNIT 3 POWER TRANSMISSION DEVICES

UNIT 3 POWER TRANSMISSION DEVICES UNI 3 POWER RANSMISSION DEVIES Power ransmission Devices Srucure 3. Inroducion Objecives 3. Power ransmission Devices 3.. Bels 3.. hain 3..3 Gears 3.3 ransmission Screw 3.4 Power ransmission by Bels 3.4.

More information

I. Basic Concepts (Ch. 1-4)

I. Basic Concepts (Ch. 1-4) (Ch. 1-4) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing

More information

An Optimal Control Approach to Inventory-Production Systems with Weibull Distributed Deterioration

An Optimal Control Approach to Inventory-Production Systems with Weibull Distributed Deterioration Journal of Mahemaics and Saisics 5 (3):6-4, 9 ISSN 549-3644 9 Science Publicaions An Opimal Conrol Approach o Invenory-Producion Sysems wih Weibull Disribued Deerioraion Md. Aiul Baen and Anon Abdulbasah

More information

Life insurance cash flows with policyholder behaviour

Life insurance cash flows with policyholder behaviour Life insurance cash flows wih policyholder behaviour Krisian Buchard,,1 & Thomas Møller, Deparmen of Mahemaical Sciences, Universiy of Copenhagen Universiesparken 5, DK-2100 Copenhagen Ø, Denmark PFA Pension,

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

Does the composition of wage and payroll taxes matter under Nash bargaining?

Does the composition of wage and payroll taxes matter under Nash bargaining? Economics Leers 64 (1999) 343 349 Does he comosiion of age and ayroll axes maer under Nash bargaining? Erkki Koskela *, Ronnie Schob a, b a Dearmen of Economics, Uniersiy of Helsinki, P.O. Box 54, Unioninkau

More information

Deployment Method for Real-Time Wireless Network Optimizer in CDMA Network

Deployment Method for Real-Time Wireless Network Optimizer in CDMA Network Deloymen Mehod for Real-Time Wireless Nework Oimizer in CDMA Nework Chi-Young Rhee, ang-jin Park, Yong-Hee Lee, Bum Kwon, and Jae-Hwang Yu Nework Engineering Develomen Team Nework R&D Cener, K Telecom

More information

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS Hao Wu and Qinfen Zheng Cenre for Auomaion Research Dep. of Elecrical and Compuer Engineering Universiy of Maryland, College Park, MD-20742 {wh2003, qinfen}@cfar.umd.edu

More information

Information Theoretic Approaches for Predictive Models: Results and Analysis

Information Theoretic Approaches for Predictive Models: Results and Analysis Informaion Theoreic Approaches for Predicive Models: Resuls and Analysis Monica Dinculescu Supervised by Doina Precup Absrac Learning he inernal represenaion of parially observable environmens has proven

More information

A closer look at Black Scholes option thetas

A closer look at Black Scholes option thetas J Econ Finan (2008) 32:59 74 DOI 0.007/s297-007-9000-8 A closer look a Black Scholes oion heas Douglas R. Emery & Weiyu Guo & Tie Su Published online: Ocober 2007 # Sringer Science & Business Media, LLC

More information

Smart Highside Power Switch

Smart 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 information

Time Series Analysis Using SAS R Part I The Augmented Dickey-Fuller (ADF) Test

Time Series Analysis Using SAS R Part I The Augmented Dickey-Fuller (ADF) Test ABSTRACT Time Series Analysis Using SAS R Par I The Augmened Dickey-Fuller (ADF) Tes By Ismail E. Mohamed The purpose of his series of aricles is o discuss SAS programming echniques specifically designed

More information

A Conceptual Framework for Commercial Property Price Indexes

A Conceptual Framework for Commercial Property Price Indexes Gran-in-Aid for Scienific Research(S) Real Esae Markes, Financial Crisis, and Economic Growh : An Inegraed Economic Approach Working Paper Series No.4 A Concepual Framework for Commercial Propery Price

More information

Hedging with Forwards and Futures

Hedging with Forwards and Futures Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buy-side of a forward/fuures

More information

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya. Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

More information

Conceptually calculating what a 110 OTM call option should be worth if the present price of the stock is 100...

Conceptually calculating what a 110 OTM call option should be worth if the present price of the stock is 100... Normal (Gaussian) Disribuion Probabiliy De ensiy 0.5 0. 0.5 0. 0.05 0. 0.9 0.8 0.7 0.6? 0.5 0.4 0.3 0. 0. 0 3.6 5. 6.8 8.4 0.6 3. 4.8 6.4 8 The Black-Scholes Shl Ml Moel... pricing opions an calculaing

More information

The 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. Heather D. Gibson, Stephan G. Hall and George S. Tavlas The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he

More information

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z o ffix uden abel ere uden ame chool ame isric ame/ ender emale ale onh ay ear ae of irh an eb ar pr ay un ul ug ep c ov ec as ame irs ame lace he uden abel ere ae uden denifier chool se nly rined in he

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

CLASSIFICATION OF REINSURANCE IN LIFE INSURANCE

CLASSIFICATION OF REINSURANCE IN LIFE INSURANCE CLASSIFICATION OF REINSURANCE IN LIFE INSURANCE Kaarína Sakálová 1. Classificaions of reinsurance There are many differen ways in which reinsurance may be classified or disinguished. We will discuss briefly

More information

IR Receiver Module for Light Barrier Systems

IR Receiver Module for Light Barrier Systems IR Receiver Module for Ligh Barrier Sysems MECHANICAL DATA Pinning: 1 = OUT, 2 = GND, 3 = V S 19026 APPLICATIONS Reflecive sensors for hand dryers, owel or soap dispensers, waer fauces, oile flush Vending

More information

COMPLEMENTARY RELATIONSHIPS BETWEEN EDUCATION AND INNOVATION

COMPLEMENTARY RELATIONSHIPS BETWEEN EDUCATION AND INNOVATION Discussion Paper No. 731 COMPLEMENTARY RELATIONSHIPS BETWEEN EDUCATION AND INNOVATION Kasuhiko Hori and Kasunori Yamada February 2009 The Insiue of Social and Economic Research Osaka Universiy 6-1 Mihogaoka,

More information

Dependent Interest and Transition Rates in Life Insurance

Dependent Interest and Transition Rates in Life Insurance Dependen Ineres and ransiion Raes in Life Insurance Krisian Buchard Universiy of Copenhagen and PFA Pension January 28, 2013 Absrac In order o find marke consisen bes esimaes of life insurance liabiliies

More information