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M2Electric Circuit

LECTURE 7

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LECTURE 7

INTRODUCTION TO ELECTRIC CIRCUIT

Outline

Introduction

Circuit elements

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Circuit elements

Circuit terminologies

Basic laws

Time response

Responses: sinusoidal vs. non-sinusoidal excitations

Complex impedance and frequency response

Phasors and AC powers Three-phase systems

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Electricity: How they work?3

Electric Circuit4

• The battery, places a net positive charge at net positive charge at one terminal and a net negative charge on the other

• The free electrons (of negative charge) will drift toward the will drift toward the positive terminal

• The negative terminal is a “supply” of electrons

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall

3

Circuit Elements

5Active Elements Passive Elements

• A dependent source is an active

Independentsources

Dependentsources

pelement in which the source quantity is controlled by another voltage or current.

• There are four different types: VCVS, CCVS, VCCS, CCCS

C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill

A Voltage Source6

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall

4

A Current Source7

http://www.olympusmicro.com/primer/java/solarcell/

A Power Supply8

http://www.glentestco.com/product/product_pwrsupply01.htm

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9

Resistors

http://www.macnn.com/articles/12/05/24/well.designed.adapter.protects.phone.from.damage.malfunction/http://www.resistorguide.com/metal-film-resistor/http://www.colourbox.com/image/the-printed-circuit-board-with-computer-chips-resistors-and-condensers-image-2350532

Inductors & Capacitors10

http://www.splung.com/content/sid/3/page/capacitorshttp://www.area51esg.com/inductors-coils-chokes.htmlA.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

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Circuit Terminologies11

• A branch represents a single element such as a voltage source or a resistor

• A node is the point of connection between two or more branches

• A loop is a closed path (same beginning and end nodes) with no node passed more than once

• A mesh is a loop which does not contain any other loops within it

C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill

The Almighty Laws: Ohm’s Law12

• George Simon Ohm

• German (Erlangen, Cologne) (1789–1854)Ge a ( a ge , Co og e) ( 789 854)

• Physicist and Mathematician

• Professor of Physics,

• University of Cologne http://www-history.mcs.st-and.ac.uk/Mathematicians/Ohm.html

• v-i relationship of a resistor

Note: the negative current and voltage result in the graph extended in the 3rd quadrant

C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill

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Kirchhoff’s Laws: KCL13

• Kirchhoff’s current law

• German (Königsberg

http://www.biografiasyvidas.com/biografia/k/kirchhoff.htm

• German (Königsberg, Berlin) (1824-87)

• Physicist• Professor of Physics,• University of

Heidelberg

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall

Kirchhoff’s Laws: KVL14

Kirchhoff’s voltage law (KVL): the algebraic sum of thepotential rises and drops around a closed loop (or p p ppath) is zero.

These laws will be important bases of circuit theorems and analysis techniques

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall

8

Time Response: Resistor15

There is no limitation on the rate

Purely resistive circuit

There is no limitation on the rate of change imposed on the resistor voltage and current

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

Time Response: R-L16

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

9

An Inductor and a Fluorescent Lamp17

http://www.youtube.com/watch?v=z55566ep0Hg

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Breaking an Inductive Circuit

When the inductor current is interrupted the field begins to collapse causing a large induced voltage across the coil.

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

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19

Breaking an Inductive Circuit

http://www.youtube.com/watch?v=INbS-71KSz0

Charging a Capacitor20

http://www.youtube.com/watch?v=IvFVu7Jxa2I

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Discharging a Capacitor21

http://www.youtube.com/watch?v=5D2cLj28Pc8

Time Response: RC22

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

12

Time Response: RC23

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

A Sinusoidal Waveform24

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall

13

Periodic Functions25

Squarewave signal

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hallhttps://www.projectrhea.org/rhea/index.php/HW1.4_Ben_Laskowski_-_Periodic_and_Non-Periodic_Functions_ECE301Fall2008mboutin

Sawtooth signalTriangular signal

Full-wave signal

Fourier Series26

French (Auxerre, Grenoble, Paris) (1768–1830)Mathematician, Egyptologist, and AdministratorProfessor of Mathematics, École Polytechnique, y q

http://www2.math.umd.edu/~dlevy/photos2/photos/mathematical_lineage/jean-baptiste_fourier.html

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall

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27

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall

Phasor28

A phasor is a rotating line whose projection on a vertical axis can be used torepresent sinusoidally varying quantitiesaxis can be used torepresent sinusoidally varying quantities

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

15

Phasor Illustration29

http://www.ceb.cam.ac.uk/pages/impedance-analysis-basics.html

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

Resistance and Sinusoidal Excitation30

• Response in time domain

• Phasor (frequency) domain

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

16

Inductance and Sinusoidal Excitation31

• Response in time domain

• Phasor domain

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

Capacitance and Sinusoidal Excitation32

• Response in time domain

• Phasor domain

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

17

Resonance33

Resonant condition

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall

Resonance34

Practical implication: Capacitor and inductor voltages can be much larger than the supplied voltage

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall

18

An Application of a Resonant Circuit35

• Induction heating

f = 15 kHz

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall

One-Port vs. Two-Port Networks36

One-port networkTwo-port network

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall

19

37

Power38

• Instantaneous power

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

20

Power39

• Inductor

• Observation1) Average power is zero2) The power alternately flows into and out of the inductor

(also known as reactive power: Q)

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

Power40

• Capacitor

• Observation (similar to the inductor)1) Average power is zero2) The power alternately flows into and out of the inductor

(also known as reactive power: Q)

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

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Complex Power41

iv θθIVIVS

• Power triangle

iv

)θ (θsin I V j )θ (θ cos I VS iviv

S =      P +    j        Q

C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill

Why Rated VA?42

• Using only active power • Reactive power is in the picturepicture

A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning

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Three-Phase Systems43

http://www.ece.umn.edu/users/riaz/animations/alternator.html

Three-Phase System44

Wye connection

Delta connection

R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall