Systematic Circuit Analysis (T&R Chap 3)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Systematic Circuit Analysis (T&R Chap 3)"

Transcription

1 Systematc Crcut Analyss TR Chap ) Nodeoltage analyss Usng the oltages of the each node relate to a ground node, wrte down a set of consstent lnear equatons for these oltages Sole ths set of equatons usng, say, Cramer s Rule Mesh current analyss Usng the loop currents n the crcut, wrte down a set of consstent lnear equatons for these arables. Sole. Ths ntroduces us to procedures for systematcally descrbng crcut arables and solng for them MAE4 Lnear Crcuts 4

2 Node oltages Nodal Analyss Pck one node as the ground node Label all other nodes and assgn oltages, B,, N and currents wth each branch,, M Recognze that the oltage across a branch B B s the dfference between the end node oltages A Thus B C wth the drecton as ndcated Wrte down the KCL relatons at each node Wrte down the branch relatons to express branch currents n terms of node oltages Accommodate current sources Obtan a set of lnear equatons for the node oltages 4 C C MAE4 Lnear Crcuts 4

3 Apply KCL Nodal Analyss Example p. Node A: Node B: Node C: 4 Wrte the element/branch eqns S G B ) G C ) G B 4 G 4 C S Substtute to get node oltage equatons Node A: G G ) G B G C S Node B: G G G ) B s Node C: G G G 4 ) C S Sole for, B, C then,,,, 4, G G G G B R R S R S 4 Reference node G G G G G G4 B C R 4 C S S S MAE4 Lnear Crcuts 4

4 G G G G G G G Systematc Nodal Analyss G G G4 B C S S S B R R S C S 4 Wrtng node equatons by nspecton Note that the matrx equaton looks just lke G for matrx G and ector and G s symmetrc and nonnegate defnte) R Reference node R 4 Dagonal,) elements: sum of all conductances connected to node Offdagonal,j) elements: conductance between nodes and j Rghthand sde: current sources enterng node There s no equaton for the ground node the column sums ge the conductance to ground MAE4 Lnear Crcuts 4

5 Nodal Analyss Example p.4 R/ Node A: Conductances G/ B G C.G Source currents enterng S Node B: S R B R R/ R C Conductances Node C: G/ A G/ C G ground G Source currents enterng Conductances G A G/ B G ground.g Source currents enterng MAE4 Lnear Crcuts.G.G G A S.G G.G B G.G.G C 44

6 Nodal Analyss some ponts to watch. The formulaton gen s based on KCL wth the sum of currents leang the node total G AtoB B ) G AtoC C ) G AtoGround leanga Ths yelds G AtoB G AtoGround ) G AtoB B G AtoC C enternga G AtoB G AtoGround ) G AtoB B G AtoC C enternga. If n doubt about the sgn of the current source, go back to ths basc KCL formulaton. Ths formulaton works for ndependent current source For dependent current sources ntroduced later) use your wts MAE4 Lnear Crcuts 4

7 Nodal Analyss Exercse p. KΩ B S KΩ S Ω O _ Sole ths usng standard lnear equaton solers Cramer s rule Gaussan elmnaton Matlab.. MAE4 Lnear Crcuts.. A B S S 46

8 Nodal Analyss wth Voltage Sources Current through oltage source s not computable from oltage across t. We need some trcks They actually help us smplfy thngs Method source transformaton R S Rest of the _ S crcut S RS R S Rest of the crcut B B Then use standard nodal analyss one less node MAE4 Lnear Crcuts 4

9 Nodal Analyss wth Voltage Sources Method groundng one node _ S B Rest of the crcut Ths remoes the B arable smpler analyss But can be done once per crcut MAE4 Lnear Crcuts 48

10 Nodal Analyss wth Voltage Sources Method Create a supernode Act as f A and B were one node KCL stll works for ths node Sum of currents enterng supernode box s Wrte KCL at all N other nodes N nodes less Ground node usng and B as usual Wrte one supernode KCL _ S B supernode Rest of the crcut Add the constrant B S These three methods allow us to deal wth all cases MAE4 Lnear Crcuts 49

11 Nodal Analyss Example 4 p. 6 _ S R _ R R S _ S R R S R R R _ Ths s method transform the oltage sources Applcable snce oltage sources appear n seres wth Rs Now use nodal analyss wth one node, A G G G ) A A G S G S G S G G G G S MAE4 Lnear Crcuts

12 S n _ Nodal Analyss Example p. R n R R/ B R R/ R C What s the crcut nput resstance ewed through S? S.G G B.G C G.G B. C Rewrte n terms of S, B, C Ths s method Sole. S 6. S B, C.. S B S C. S n R R /.R.R R n.8r. MAE4 Lnear Crcuts G B.G C.G S.G B.G C G S

13 Nodal Analyss Example 6 p. 8 S _ B supernode C Other consttuent relaton C S Two equatons n two unknowns MAE4 Lnear Crcuts R R R _ O S R 4 reference Method supernodes KCL for supernode: 4 Or, usng element equatons G G B ) G C B ) G 4 C Now use B S G G ) G G4 ) C G G ) S 4

14 Summary of Nodal Analyss. Smplfy the cct by combnng elements n seres or parallel. Select as reference node the one wth most oltage sources connected. Label node oltages and supernode oltages do not label the nodes drectly connected to the reference 4. Use KCL to wrte node equatons. Express element currents n terms of node oltages and ICSs. Wrte expressons relatng node oltages and IVSs 6. Substtute from Step nto equatons from Step 4 Wrte the equatons n standard form. Sole usng Cramer, gaussan elmnaton or matlab MAE4 Lnear Crcuts

15 MAE4 Lnear Crcuts 4 Solng sets of lnear equatons Cramer s Rule Thomas Rosa Appendx B pp. A to A x x x ) ) ) ) ) ) ) ) 8 ) ) ) 8 ) 8 ) 8 8 ) ) ) ) ) ) 6 ) ) 8 ) ) ) ) x

16 Solng sets of lnear equatons contd) ) ) x ) ) x.68 Notes: Ths Cramer s not as much fun as Cosmo Kramer n Senfeld I do not know of any trcks for symmetrc matrces MAE4 Lnear Crcuts

17 MAE4 Lnear Crcuts 6 Solng Lnear Equatons gaussan elmnaton x x x Augment matrx Row operatons only row row row row / row row row / row row row ) row row row )

18 Solng Lnear Equatons matlab A[ ; ; 8] A 8 B[4;;6] B 4 6 na) na)*b ans A\B ans ans MAE4 Lnear Crcuts

19 Mesh Current Analyss Dual of Nodal Voltage Analyss wth KCL Mesh Current Analyss wth KVL Mesh loop enclosng no elements Restrcted to Planar Ccts no crossoers unless you are really cleer) Key Idea: If element K s contaned n both mesh and mesh j then ts current s k j where we hae taken the reference drectons as approprate Same old trcks you already know R R Mesh A: Mesh B: 4 R S 4 S A B R A R B R A B ) S 4 S R R ) A R B S R A R R ) B S R R R R R R A B S S MAE4 Lnear Crcuts 8

20 Mesh Analyss by nspecton Matrx of Resstances R Dagonal elements: sum of resstances around loop Offdagonal j elements: resstance shared by loops and j Vector of currents As defned by you on your mesh dagram R S Voltage source ector S Sum of oltage sources assstng the current n your mesh R S R R S A If ths s hard to fathom, go back to the basc KVL to sort these drectons out C B R4 R R R R R R 4 R R R R A B C S S S MAE4 Lnear Crcuts 9

21 Mesh Equatons wth Current Sources Duals of trcks for nodal analyss wth oltage sources. Source transformaton to equalent TR Example 8 p. 9 KΩ KΩ KΩ KΩ 4KΩ V KΩ 4KΩ ma V O A O KΩ 8V B KΩ KΩ 6 A B 8 A.69 ma B.69 ma O A B.49 ma MAE4 Lnear Crcuts 6

22 Mesh Analyss wth ICSs method Current source belongs to a sngle mesh KΩ KΩ V O KΩ 4KΩ A B C ma Same example KΩ A 6 A B B 4 C C ma Same equatons Same soluton MAE4 Lnear Crcuts 6

23 Mesh Analyss wth ICSs Method Supermeshes easer than supernodes Current source n more than one mesh and/or not n parallel wth a resstance. Create a supermesh by elmnatng the whole branch noled. Resole the nddual currents last Supermesh R B R Excluded branch S S R B A ) R B R4 C R C A) A S A R C R 4 O B C S MAE4 Lnear Crcuts 6

24 Summary of Mesh Analyss. Check f cct s planar or transformable to planar. Identfy meshes, mesh currents supermeshes. Smplfy the cct where possble by combnng elements n seres or parallel 4. Wrte KVL for each mesh. Include expressons for ICSs 6. Sole for the mesh currents MAE4 Lnear Crcuts 6

25 Lnearty Superposton Lnear cct modeled by lnear elements and ndependent sources Lnear functons Homogenety: Addtty: fkx)kfx) fxy)fx)fy) Superposton follows from lnearty/addtty Lnear cct response to multple sources s the sum of the responses to each source. Turn off all ndependent sources except one and compute cct arables. Repeat for each ndependent source n turn. Total alue of all cct arables s the sum of the alues from all the nddual sources MAE4 Lnear Crcuts 64

26 Turnng off sources Voltage source Superposton Turned off when for all a short crcut S _ Current source Turned off when for all an open crcut S We hae already used ths n Théenn and Norton equ MAE4 Lnear Crcuts 6

27 Where are we now? Fnshed resste ccts wth ICS and IVS Two analyss technques nodal oltage and mesh current Preference depends on smplcty of the case at hand The am has been to deelop generalzable technques for access to analytcal tools lke matlab Where to now? Acte ccts wth resste elements transstors, opamps Lfe starts to get nterestng desgn ntroduced Capactance and nductance dynamc ccts Frequency response sdoman analyss Flters MAE4 Lnear Crcuts 66

+ + + - - This circuit than can be reduced to a planar circuit

+ + + - - This circuit than can be reduced to a planar circuit MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to

More information

EE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN

EE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson - 3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson - 6 Hrs.) Voltage

More information

LOOP ANALYSIS. The second systematic technique to determine all currents and voltages in a circuit

LOOP ANALYSIS. The second systematic technique to determine all currents and voltages in a circuit LOOP ANALYSS The second systematic technique to determine all currents and voltages in a circuit T S DUAL TO NODE ANALYSS - T FRST DETERMNES ALL CURRENTS N A CRCUT AND THEN T USES OHM S LAW TO COMPUTE

More information

Linear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits

Linear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.

More information

(6)(2) (-6)(-4) (-4)(6) + (-2)(-3) + (4)(3) + (2)(-3) = -12-24 + 24 + 6 + 12 6 = 0

(6)(2) (-6)(-4) (-4)(6) + (-2)(-3) + (4)(3) + (2)(-3) = -12-24 + 24 + 6 + 12 6 = 0 Chapter 3 Homework Soluton P3.-, 4, 6, 0, 3, 7, P3.3-, 4, 6, P3.4-, 3, 6, 9, P3.5- P3.6-, 4, 9, 4,, 3, 40 ---------------------------------------------------- P 3.- Determne the alues of, 4,, 3, and 6

More information

4. Basic Nodal and Mesh Analysis

4. Basic Nodal and Mesh Analysis 1 4. Basic Nodal and Mesh Analysis This chapter introduces two basic circuit analysis techniques named nodal analysis and mesh analysis 4.1 Nodal Analysis For a simple circuit with two nodes, we often

More information

Michał Tadeusiewicz. Electric Circuits. Technical University of Łódź International Faculty of Engineering. Łódź 2009

Michał Tadeusiewicz. Electric Circuits. Technical University of Łódź International Faculty of Engineering. Łódź 2009 Mchał Tadeusewcz Electrc Crcuts Techncal Unersty of Łódź Internatonal Faculty of Engneerng Łódź 9 Contents Preface.. 5. Fundamental laws of electrcal crcuts 7.. Introducton... 7.. Krchhoff s oltage Law

More information

2. Introduction and Chapter Objectives

2. Introduction and Chapter Objectives eal Analog Crcuts Chapter : Crcut educton. Introducton and Chapter Objectes In Chapter, we presented Krchoff s laws (whch goern the nteractons between crcut elements) and Ohm s law (whch goerns the oltagecurrent

More information

CIRCUIT ELEMENTS AND CIRCUIT ANALYSIS

CIRCUIT ELEMENTS AND CIRCUIT ANALYSIS EECS 4 SPING 00 Lecture 9 Copyrght egents of Unversty of Calforna CICUIT ELEMENTS AND CICUIT ANALYSIS Lecture 5 revew: Termnology: Nodes and branches Introduce the mplct reference (common) node defnes

More information

v a 1 b 1 i, a 2 b 2 i,..., a n b n i.

v a 1 b 1 i, a 2 b 2 i,..., a n b n i. SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are

More information

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by 6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng

More information

( ) Homework Solutions Physics 8B Spring 09 Chpt. 32 5,18,25,27,36,42,51,57,61,76

( ) Homework Solutions Physics 8B Spring 09 Chpt. 32 5,18,25,27,36,42,51,57,61,76 Homework Solutons Physcs 8B Sprng 09 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat = E. Please refer to Fgure EX32.5. We wll choose a clockwse

More information

Homework Solutions Physics 8B Spring 2012 Chpt. 32 5,18,25,27,36,42,51,57,61,76

Homework Solutions Physics 8B Spring 2012 Chpt. 32 5,18,25,27,36,42,51,57,61,76 Homework Solutons Physcs 8B Sprng 202 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat =. Please refer to Fgure EX32.5. We wll choose a clockwse

More information

Mesh-Current Method (Loop Analysis)

Mesh-Current Method (Loop Analysis) Mesh-Current Method (Loop Analysis) Nodal analysis was developed by applying KCL at each non-reference node. Mesh-Current method is developed by applying KVL around meshes in the circuit. A mesh is a loop

More information

Circuit Reduction Techniques

Circuit Reduction Techniques Crcut Reducton Technques Comnaton of KVLs, KCLs, and characterstcs equatons result n a set of lnear equatons for the crcut arales. Whle the aoe set of equaton s complete and contans all necessary nformaton,

More information

The circuit shown on Figure 1 is called the common emitter amplifier circuit. The important subsystems of this circuit are:

The circuit shown on Figure 1 is called the common emitter amplifier circuit. The important subsystems of this circuit are: polar Juncton Transstor rcuts Voltage and Power Amplfer rcuts ommon mtter Amplfer The crcut shown on Fgure 1 s called the common emtter amplfer crcut. The mportant subsystems of ths crcut are: 1. The basng

More information

Introduction: Analysis of Electronic Circuits

Introduction: Analysis of Electronic Circuits /30/008 ntroducton / ntroducton: Analyss of Electronc Crcuts Readng Assgnment: KVL and KCL text from EECS Just lke EECS, the majorty of problems (hw and exam) n EECS 3 wll be crcut analyss problems. Thus,

More information

Electric circuit components. Direct Current (DC) circuits

Electric circuit components. Direct Current (DC) circuits Electrc crcut components Capactor stores charge and potental energy, measured n Farads (F) Battery generates a constant electrcal potental dfference ( ) across t. Measured n olts (). Resstor ressts flow

More information

Multiple stage amplifiers

Multiple stage amplifiers Multple stage amplfers Ams: Examne a few common 2-transstor amplfers: -- Dfferental amplfers -- Cascode amplfers -- Darlngton pars -- current mrrors Introduce formal methods for exactly analysng multple

More information

Example: Determine the power supplied by each of the sources, independent and dependent, in this circuit:

Example: Determine the power supplied by each of the sources, independent and dependent, in this circuit: Example: Determine the power supplied by each of the sources, independent and dependent, in this circuit: Solution: We ll begin by choosing the bottom node to be the reference node. Next we ll label the

More information

Passive Filters. References: Barbow (pp 265-275), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6)

Passive Filters. References: Barbow (pp 265-275), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6) Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called

More information

Chapter 4: Methods of Analysis

Chapter 4: Methods of Analysis Chapter 4: Methods of Analysis 4.1 Motivation 4.2 Nodal Voltage Analysis 4.3 Simultaneous Eqs. & Matrix Inversion 4.4 Nodal Voltage Analysis with Voltage Sources 4.5 Mesh Current Analysis 4.6 Mesh Current

More information

Lesson 2 Chapter Two Three Phase Uncontrolled Rectifier

Lesson 2 Chapter Two Three Phase Uncontrolled Rectifier Lesson 2 Chapter Two Three Phase Uncontrolled Rectfer. Operatng prncple of three phase half wave uncontrolled rectfer The half wave uncontrolled converter s the smplest of all three phase rectfer topologes.

More information

07-Nodal Analysis Text: ECEGR 210 Electric Circuits I

07-Nodal Analysis Text: ECEGR 210 Electric Circuits I 07Nodal Analysis Text: 3.1 3.4 ECEGR 210 Electric Circuits I Overview Introduction Nodal Analysis Nodal Analysis with Voltage Sources Dr. Louie 2 Basic Circuit Laws Ohm s Law Introduction Kirchhoff s Voltage

More information

120 CHAPTER 3 NODAL AND LOOP ANALYSIS TECHNIQUES SUMMARY PROBLEMS SECTION 3.1

120 CHAPTER 3 NODAL AND LOOP ANALYSIS TECHNIQUES SUMMARY PROBLEMS SECTION 3.1 IRWI03_082132v3 8/26/04 9:41 AM Page 120 120 CHAPTER 3 NODAL AND LOOP ANALYSIS TECHNIQUES SUMMARY Nodal analysis for an Nnode circuit Select one node in the Nnode circuit as the reference node. Assume

More information

Small-Signal Analysis of BJT Differential Pairs

Small-Signal Analysis of BJT Differential Pairs 5/11/011 Dfferental Moe Sall Sgnal Analyss of BJT Dff Par 1/1 SallSgnal Analyss of BJT Dfferental Pars Now lets conser the case where each nput of the fferental par conssts of an entcal D bas ter B, an

More information

1E6 Electrical Engineering AC Circuit Analysis and Power Lecture 12: Parallel Resonant Circuits

1E6 Electrical Engineering AC Circuit Analysis and Power Lecture 12: Parallel Resonant Circuits E6 Electrcal Engneerng A rcut Analyss and Power ecture : Parallel esonant rcuts. Introducton There are equvalent crcuts to the seres combnatons examned whch exst n parallel confguratons. The ssues surroundng

More information

Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Alexander-Sadiku Fundamentals of Electric Circuits Chapter 3 Methods of Analysis Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Methods of Analysis - Chapter

More information

Series and Parallel Resistors

Series and Parallel Resistors Series and Parallel Resistors 1 Objectives To calculate the equivalent resistance of series and parallel resistors. 2 Examples for resistors in parallel and series R 4 R 5 Series R 6 R 7 // R 8 R 4 //

More information

21 Vectors: The Cross Product & Torque

21 Vectors: The Cross Product & Torque 21 Vectors: The Cross Product & Torque Do not use our left hand when applng ether the rght-hand rule for the cross product of two vectors dscussed n ths chapter or the rght-hand rule for somethng curl

More information

where the coordinates are related to those in the old frame as follows.

where the coordinates are related to those in the old frame as follows. Chapter 2 - Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of non-coplanar vectors Scalar product

More information

Chapter 4: Techniques of Circuit Analysis

Chapter 4: Techniques of Circuit Analysis 4.1 Terminology Example 4.1 a. Nodes: a, b, c, d, e, f, g b. Essential Nodes: b, c, e, g c. Branches: v 1, v 2, R 1, R 2, R 3, R 4, R 5, R 6, R 7, I d. Essential Branch: v 1 -R 1, R 2 -R 3, v 2 -R 4, R

More information

Electric Circuits. Overview. Hani Mehrpouyan,

Electric Circuits. Overview. Hani Mehrpouyan, Electric Circuits Hani Mehrpouyan, Department of Electrical and Computer Engineering, Lecture 5 (Mesh Analysis) Sep 8 th, 205 Hani Mehrpouyan (hani.mehr@ieee.org) Boise State c 205 Overview With Ohm s

More information

Problem set #5 EE 221, 09/26/ /03/2002 1

Problem set #5 EE 221, 09/26/ /03/2002 1 Chapter 3, Problem 42. Problem set #5 EE 221, 09/26/2002 10/03/2002 1 In the circuit of Fig. 3.75, choose v 1 to obtain a current i x of 2 A. Chapter 3, Solution 42. We first simplify as shown, making

More information

Chapter 6 Inductance, Capacitance, and Mutual Inductance

Chapter 6 Inductance, Capacitance, and Mutual Inductance Chapter 6 Inductance Capactance and Mutual Inductance 6. The nductor 6. The capactor 6.3 Seres-parallel combnatons of nductance and capactance 6.4 Mutual nductance 6.5 Closer look at mutual nductance Oerew

More information

Bipolar Junction Transistor (BJT)

Bipolar Junction Transistor (BJT) polar Juncton Transstor (JT) Lecture notes: Sec. 3 Sedra & Smth (6 th Ed): Sec. 6.1-6.4* Sedra & Smth (5 th Ed): Sec. 5.1-5.4* * Includes detals of JT dece operaton whch s not coered n ths course F. Najmabad,

More information

The Full-Wave Rectifier

The Full-Wave Rectifier 9/3/2005 The Full Wae ectfer.doc /0 The Full-Wae ectfer Consder the followng juncton dode crcut: s (t) Power Lne s (t) 2 Note that we are usng a transformer n ths crcut. The job of ths transformer s to

More information

s-domain Circuit Analysis

s-domain Circuit Analysis S-Doman naly -Doman rcut naly Tme doman t doman near rcut aplace Tranform omplex frequency doman doman Tranformed rcut Dfferental equaton lacal technque epone waveform aplace Tranform nvere Tranform -

More information

Faraday's Law of Induction

Faraday's Law of Induction Introducton Faraday's Law o Inducton In ths lab, you wll study Faraday's Law o nducton usng a wand wth col whch swngs through a magnetc eld. You wll also examne converson o mechanc energy nto electrc energy

More information

2 The TTL Inverter. (i) An input transistor, T 1, which performs a current steering function, can be thought of as a back-to-back diode arrangement.

2 The TTL Inverter. (i) An input transistor, T 1, which performs a current steering function, can be thought of as a back-to-back diode arrangement. The TTL Inverter.1 Crcut Structure The crcut dagram of the Transstor Transstor Logc nverter s shown n Fg..1. Ths crcut overcomes the lmtatons of the sngle transstor nverter crcut. Some of the notable features

More information

3. Bipolar Junction Transistor (BJT)

3. Bipolar Junction Transistor (BJT) 3. polar Juncton Transstor (JT) Lecture notes: Sec. 3 Sedra & Smth (6 th Ed): Sec. 6.1-6.4* Sedra & Smth (5 th Ed): Sec. 5.1-5.4* * Includes detals of JT dece operaton whch s not coered n ths course EE

More information

ECE 211 WORKSHOP: NODAL AND LOOP ANALYSIS. Tutor: Asad Akram

ECE 211 WORKSHOP: NODAL AND LOOP ANALYSIS. Tutor: Asad Akram ECE 211 WORKSHOP: NODAL AND LOOP ANALYSIS Tutor: Asad Akram 1 AGENDA Background: KCL and KVL. Nodal Analysis: Independent Sources and relating problems, Dependent Sources and relating problems. Loop (Mesh

More information

Loop Parallelization

Loop Parallelization - - Loop Parallelzaton C-52 Complaton steps: nested loops operatng on arrays, sequentell executon of teraton space DECLARE B[..,..+] FOR I :=.. FOR J :=.. I B[I,J] := B[I-,J]+B[I-,J-] ED FOR ED FOR analyze

More information

The eigenvalue derivatives of linear damped systems

The eigenvalue derivatives of linear damped systems Control and Cybernetcs vol. 32 (2003) No. 4 The egenvalue dervatves of lnear damped systems by Yeong-Jeu Sun Department of Electrcal Engneerng I-Shou Unversty Kaohsung, Tawan 840, R.O.C e-mal: yjsun@su.edu.tw

More information

Comparison of Control Strategies for Shunt Active Power Filter under Different Load Conditions

Comparison of Control Strategies for Shunt Active Power Filter under Different Load Conditions Comparson of Control Strateges for Shunt Actve Power Flter under Dfferent Load Condtons Sanjay C. Patel 1, Tushar A. Patel 2 Lecturer, Electrcal Department, Government Polytechnc, alsad, Gujarat, Inda

More information

INTRODUCTION. governed by a differential equation Need systematic approaches to generate FE equations

INTRODUCTION. governed by a differential equation Need systematic approaches to generate FE equations WEIGHTED RESIDUA METHOD INTRODUCTION Drect stffness method s lmted for smple D problems PMPE s lmted to potental problems FEM can be appled to many engneerng problems that are governed by a dfferental

More information

Analysis of Small-signal Transistor Amplifiers

Analysis of Small-signal Transistor Amplifiers Analyss of Small-sgnal Transstor Amplfers On completon of ths chapter you should be able to predct the behaour of gen transstor amplfer crcuts by usng equatons and/or equalent crcuts that represent the

More information

Semiconductor sensors of temperature

Semiconductor sensors of temperature Semconductor sensors of temperature he measurement objectve 1. Identfy the unknown bead type thermstor. Desgn the crcutry for lnearzaton of ts transfer curve.. Fnd the dependence of forward voltage drop

More information

greatest common divisor

greatest common divisor 4. GCD 1 The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no

More information

Node and Mesh Analysis

Node and Mesh Analysis Node and Mesh Analysis 1 Copyright ODL Jan 2005 Open University Malaysia Circuit Terminology Name Definition Node Essential node Path Branch Essential Branch Loop Mesh A point where two ore more branches

More information

The complex inverse trigonometric and hyperbolic functions

The complex inverse trigonometric and hyperbolic functions Physcs 116A Wnter 010 The complex nerse trgonometrc and hyperbolc functons In these notes, we examne the nerse trgonometrc and hyperbolc functons, where the arguments of these functons can be complex numbers

More information

Section B9: Zener Diodes

Section B9: Zener Diodes Secton B9: Zener Dodes When we frst talked about practcal dodes, t was mentoned that a parameter assocated wth the dode n the reverse bas regon was the breakdown voltage, BR, also known as the peak-nverse

More information

Chapter 2 Properties of resistive circuits

Chapter 2 Properties of resistive circuits Chaper 2 Properes of resse crcus 2.-2.2 (oponal) equalen ressance, resse ladder, dualy, dual enes 2.3 Crcus wh conrolled sources conrolled sources (VCVS, CCVS, VCCS, CCVS), equalen ressance 2.4 Lneary

More information

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of

More information

Sinusoidal Steady-State Analysis

Sinusoidal Steady-State Analysis // Snusdal Steady-State Analyss ntrductn dal Analyss Mesh Analyss Superpstn Therem Surce Transfrmatn Thevenn and rtn Equvalent Crcuts OP-amp AC Crcuts Applcatns ntrductn Steps t Analyze ac Crcuts: The

More information

HÜCKEL MOLECULAR ORBITAL THEORY

HÜCKEL MOLECULAR ORBITAL THEORY 1 HÜCKEL MOLECULAR ORBITAL THEORY In general, the vast maorty polyatomc molecules can be thought of as consstng of a collecton of two electron bonds between pars of atoms. So the qualtatve pcture of σ

More information

Circuit Analysis using the Node and Mesh Methods

Circuit Analysis using the Node and Mesh Methods Circuit Analysis using the Node and Mesh Methods We have seen that using Kirchhoff s laws and Ohm s law we can analyze any circuit to determine the operating conditions (the currents and voltages). The

More information

2. Linear Algebraic Equations

2. Linear Algebraic Equations 2. Lnear Algebrac Equatons Many physcal systems yeld smultaneous algebrac equatons when mathematcal functons are requred to satsfy several condtons smultaneously. Each condton results n an equaton that

More information

5. Simultaneous eigenstates: Consider two operators that commute: Â η = a η (13.29)

5. Simultaneous eigenstates: Consider two operators that commute:  η = a η (13.29) 5. Smultaneous egenstates: Consder two operators that commute: [ Â, ˆB ] = 0 (13.28) Let  satsfy the followng egenvalue equaton: Multplyng both sdes by ˆB  η = a η (13.29) ˆB [  η ] = ˆB [a η ] = a

More information

6. EIGENVALUES AND EIGENVECTORS 3 = 3 2

6. EIGENVALUES AND EIGENVECTORS 3 = 3 2 EIGENVALUES AND EIGENVECTORS The Characterstc Polynomal If A s a square matrx and v s a non-zero vector such that Av v we say that v s an egenvector of A and s the correspondng egenvalue Av v Example :

More information

L10: Linear discriminants analysis

L10: Linear discriminants analysis L0: Lnear dscrmnants analyss Lnear dscrmnant analyss, two classes Lnear dscrmnant analyss, C classes LDA vs. PCA Lmtatons of LDA Varants of LDA Other dmensonalty reducton methods CSCE 666 Pattern Analyss

More information

( ) B. Application of Phasors to Electrical Networks In an electrical network, let the instantaneous voltage and the instantaneous current be

( ) B. Application of Phasors to Electrical Networks In an electrical network, let the instantaneous voltage and the instantaneous current be World Academy of Scence Engneerng and echnology Internatonal Journal of Electrcal obotcs Electroncs and ommuncatons Engneerng Vol:8 No:7 4 Analyss of Electrcal Networks Usng Phasors: A Bond Graph Approach

More information

Graph Theory and Cayley s Formula

Graph Theory and Cayley s Formula Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll

More information

BERNSTEIN POLYNOMIALS

BERNSTEIN POLYNOMIALS On-Lne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful

More information

EE 201 ELECTRIC CIRCUITS. Class Notes CLASS 8

EE 201 ELECTRIC CIRCUITS. Class Notes CLASS 8 EE 201 ELECTRIC CIRCUITS Class Notes CLASS 8 The material covered in this class will be as follows: Nodal Analysis in the Presence of Voltage Sources At the end of this class you should be able to: Apply

More information

Optical Signal-to-Noise Ratio and the Q-Factor in Fiber-Optic Communication Systems

Optical Signal-to-Noise Ratio and the Q-Factor in Fiber-Optic Communication Systems Applcaton ote: FA-9.0. Re.; 04/08 Optcal Sgnal-to-ose Rato and the Q-Factor n Fber-Optc Communcaton Systems Functonal Dagrams Pn Confguratons appear at end of data sheet. Functonal Dagrams contnued at

More information

EECE251 Circuit Analysis Set 2: Methods of Circuit Analysis

EECE251 Circuit Analysis Set 2: Methods of Circuit Analysis EECE251 Circuit Analysis Set 2: Methods of Circuit Analysis Shahriar Mirabbasi Department of Electrical and Computer Engineering University of British Columbia shahriar@ece.ubc.ca 1 Reading Material Chapter

More information

What is Candidate Sampling

What is Candidate Sampling What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble

More information

Support Vector Machines

Support Vector Machines Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.

More information

A. Te densty matrx and densty operator In general, te many-body wave functon (q 1 ; :::; q 3N ; t) s far too large to calculate for a macroscopc syste

A. Te densty matrx and densty operator In general, te many-body wave functon (q 1 ; :::; q 3N ; t) s far too large to calculate for a macroscopc syste G25.2651: Statstcal Mecancs Notes for Lecture 13 I. PRINCIPLES OF QUANTUM STATISTICAL MECHANICS Te problem of quantum statstcal mecancs s te quantum mecancal treatment of an N-partcle system. Suppose te

More information

Laddered Multilevel DC/AC Inverters used in Solar Panel Energy Systems

Laddered Multilevel DC/AC Inverters used in Solar Panel Energy Systems Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) Laddered Multlevel DC/AC Inverters used n Solar Panel Energy Systems Fang Ln Luo, Senor Member IEEE

More information

FORCED CONVECTION HEAT TRANSFER IN A DOUBLE PIPE HEAT EXCHANGER

FORCED CONVECTION HEAT TRANSFER IN A DOUBLE PIPE HEAT EXCHANGER FORCED CONVECION HEA RANSFER IN A DOUBLE PIPE HEA EXCHANGER Dr. J. Mchael Doster Department of Nuclear Engneerng Box 7909 North Carolna State Unversty Ralegh, NC 27695-7909 Introducton he convectve heat

More information

Chapter 12 Inductors and AC Circuits

Chapter 12 Inductors and AC Circuits hapter Inductors and A rcuts awrence B. ees 6. You may make a sngle copy of ths document for personal use wthout wrtten permsson. Hstory oncepts from prevous physcs and math courses that you wll need for

More information

Chapter 08. Methods of Analysis

Chapter 08. Methods of Analysis Chapter 08 Methods of Analysis Source: Circuit Analysis: Theory and Practice Delmar Cengage Learning C-C Tsai Outline Source Conversion Mesh Analysis Nodal Analysis Delta-Wye ( -Y) Conversion Bridge Networks

More information

Chapter 2. Circuit Analysis Techniques

Chapter 2. Circuit Analysis Techniques Chapter 2 Circuit Analysis Techniques 1 Objectives To formulate the node-voltage equations. To solve electric circuits using the node voltage method. To introduce the mesh current method. To formulate

More information

PRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB.

PRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB. PRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB. INDEX 1. Load data usng the Edtor wndow and m-fle 2. Learnng to save results from the Edtor wndow. 3. Computng the Sharpe Rato 4. Obtanng the Treynor Rato

More information

Recurrence. 1 Definitions and main statements

Recurrence. 1 Definitions and main statements Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.

More information

An Alternative Way to Measure Private Equity Performance

An Alternative Way to Measure Private Equity Performance An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate

More information

Implementation of Deutsch's Algorithm Using Mathcad

Implementation of Deutsch's Algorithm Using Mathcad Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages - n "Machnes, Logc and Quantum Physcs"

More information

1 Approximation Algorithms

1 Approximation Algorithms CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons

More information

General Physics (PHY 2130)

General Physics (PHY 2130) General Physcs (PHY 30) Lecture 8 Moentu Collsons Elastc and nelastc collsons http://www.physcs.wayne.edu/~apetro/phy30/ Lghtnng Reew Last lecture:. Moentu: oentu and pulse oentu conseraton Reew Proble:

More information

VLSI Technology Dr. Nandita Dasgupta Department of Electrical Engineering Indian Institute of Technology, Madras

VLSI Technology Dr. Nandita Dasgupta Department of Electrical Engineering Indian Institute of Technology, Madras VLI Technology Dr. Nandta Dasgupta Department of Electrcal Engneerng Indan Insttute of Technology, Madras Lecture - 11 Oxdaton I netcs of Oxdaton o, the unt process step that we are gong to dscuss today

More information

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange

More information

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12 14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed

More information

3.4 Operation in the Reverse Breakdown Region Zener Diodes

3.4 Operation in the Reverse Breakdown Region Zener Diodes 3/3/2008 secton_3_4_zener_odes 1/4 3.4 Operaton n the everse Breakdown egon Zener odes eadng Assgnment: pp. 167171 A Zener ode The 3 techncal dfferences between a juncton dode and a Zener dode: 1. 2. 3.

More information

Chapter 4 Objectives

Chapter 4 Objectives Chapter 4 Engr228 Circuit Analysis Dr Curtis Nelson Chapter 4 Objectives Understand and be able to use the node-voltage method to solve a circuit; Understand and be able to use the mesh-current method

More information

Multivariate EWMA Control Chart

Multivariate EWMA Control Chart Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant

More information

State function: eigenfunctions of hermitian operators-> normalization, orthogonality completeness

State function: eigenfunctions of hermitian operators-> normalization, orthogonality completeness Schroednger equaton Basc postulates of quantum mechancs. Operators: Hermtan operators, commutators State functon: egenfunctons of hermtan operators-> normalzaton, orthogonalty completeness egenvalues and

More information

Experiment 8 Two Types of Pendulum

Experiment 8 Two Types of Pendulum Experment 8 Two Types of Pendulum Preparaton For ths week's quz revew past experments and read about pendulums and harmonc moton Prncples Any object that swngs back and forth can be consdered a pendulum

More information

Complex Number Representation in RCBNS Form for Arithmetic Operations and Conversion of the Result into Standard Binary Form

Complex Number Representation in RCBNS Form for Arithmetic Operations and Conversion of the Result into Standard Binary Form Complex Number epresentaton n CBNS Form for Arthmetc Operatons and Converson of the esult nto Standard Bnary Form Hatm Zan and. G. Deshmukh Florda Insttute of Technology rgd@ee.ft.edu ABSTACT Ths paper

More information

I. INTRODUCTION. 1 IRCCyN: UMR CNRS 6596, Ecole Centrale de Nantes, Université de Nantes, Ecole des Mines de Nantes

I. INTRODUCTION. 1 IRCCyN: UMR CNRS 6596, Ecole Centrale de Nantes, Université de Nantes, Ecole des Mines de Nantes he Knematc Analyss of a Symmetrcal hree-degree-of-freedom lanar arallel Manpulator Damen Chablat and hlppe Wenger Insttut de Recherche en Communcatons et Cybernétque de Nantes, rue de la Noë, 442 Nantes,

More information

Supplementary material: Assessing the relevance of node features for network structure

Supplementary material: Assessing the relevance of node features for network structure Supplementary materal: Assessng the relevance of node features for network structure Gnestra Bancon, 1 Paolo Pn,, 3 and Matteo Marsl 1 1 The Abdus Salam Internatonal Center for Theoretcal Physcs, Strada

More information

Analysis and Modeling of Magnetic Coupling

Analysis and Modeling of Magnetic Coupling Analyss and Modelng of Magnetc Couplng Bryce Hesterman Adanced Energy Industres Tuesday, Aprl 7 Dscoery earnng Center Unersty Of Colorado, Boulder, Colorado Dener Chapter, IEEE Power Electroncs Socety

More information

Basic circuit analysis

Basic circuit analysis EIE209 Basic Electronics Basic circuit analysis Analysis 1 Fundamental quantities Voltage potential difference bet. 2 points across quantity analogous to pressure between two points Current flow of charge

More information

Questions that we may have about the variables

Questions that we may have about the variables Antono Olmos, 01 Multple Regresson Problem: we want to determne the effect of Desre for control, Famly support, Number of frends, and Score on the BDI test on Perceved Support of Latno women. Dependent

More information

POLYSA: A Polynomial Algorithm for Non-binary Constraint Satisfaction Problems with and

POLYSA: A Polynomial Algorithm for Non-binary Constraint Satisfaction Problems with and POLYSA: A Polynomal Algorthm for Non-bnary Constrant Satsfacton Problems wth and Mguel A. Saldo, Federco Barber Dpto. Sstemas Informátcos y Computacón Unversdad Poltécnca de Valenca, Camno de Vera s/n

More information

Logistic Regression. Steve Kroon

Logistic Regression. Steve Kroon Logstc Regresson Steve Kroon Course notes sectons: 24.3-24.4 Dsclamer: these notes do not explctly ndcate whether values are vectors or scalars, but expects the reader to dscern ths from the context. Scenaro

More information

Module 2. AC to DC Converters. Version 2 EE IIT, Kharagpur 1

Module 2. AC to DC Converters. Version 2 EE IIT, Kharagpur 1 Module 2 AC to DC Converters erson 2 EE IIT, Kharagpur 1 Lesson 1 Sngle Phase Fully Controlled Rectfer erson 2 EE IIT, Kharagpur 2 Operaton and Analyss of sngle phase fully controlled converter. Instructonal

More information

4. Bipolar Junction Transistors. 4. Bipolar Junction Transistors TLT-8016 Basic Analog Circuits 2005/2007 1

4. Bipolar Junction Transistors. 4. Bipolar Junction Transistors TLT-8016 Basic Analog Circuits 2005/2007 1 4. polar Juncton Transstors 4. polar Juncton Transstors TLT-806 asc Analog rcuts 2005/2007 4. asc Operaton of the npn polar Juncton Transstor npn JT conssts of thn p-type layer between two n-type layers;

More information

Module 2. DC Circuit. Version 2 EE IIT, Kharagpur

Module 2. DC Circuit. Version 2 EE IIT, Kharagpur Module 2 DC Circuit Lesson 5 Node-voltage analysis of resistive circuit in the context of dc voltages and currents Objectives To provide a powerful but simple circuit analysis tool based on Kirchhoff s

More information