introduction to electric circuit analysis · 2005. 9. 12. · 2003/2/20 advanced silicon device and...

2003/2/20 Advanced Silicon Device and Material Laboratory

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EE110300 Practice of Electrical and Computer Engineering

Lecture 2 and Lecture 4.1

Introductionto

Electric Circuit Analysis

Prof. Klaus Yung-Jane Hsu徐永珍

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NTHU, HsinChu, Taiwan, 30013

What Is An Electric Circuit?

• Electrical Systems– Information, Power, Control, etc.

• Behavioral Model• An electric circuit is a mathematical

model which approximates the behavior of an actual electrical system.

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What Is Electric Circuit Theory?

• A Special Case of Electromagnetic Field Theory

• The Study of Static and Moving Electric Charges

• 學習分析電荷的交通問題

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5 Basic Model Elements in Electric Circuit Theory

• Active Components– Voltage Source– Current Source

• Passive Components– Resistor– Capacitor– Inductor

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Atomic TheoryAtomic Theory

K L M NN ucleus

Simplified representation of the atom

Nucleus normally consists of neutrons and protons (positively charged)

Electrons orbit the nucleus in discrete orbits called shells (K, L, M, N, etc.)

Atom is electrically neutral since No. of protons = No. of electrons

The outer most shell is called the valence shell and electrons in this shell

are called valence electrons

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Different Types of Material

• Conductors are materials (e.g. copper, aluminum, gold) that have large numbers of free electrons.

• Insulators do not conduct (e.g. plastic, rubber, porcelain) because they have full or nearly full valence shells.

• Semiconductors have half-filled valence shells (e.g. silicon, germanium).

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What Is Electric Charge?

• A body is said to be charged when it has an excess or deficiency of electrons.

• The unit of electrical charge is the coulomb (C) = 6.24 x 1018 electrons.

• Coulomb’s Law: F = kQ1Q2 / r2 where k = 9 x 109, Q1 and Q2 are charges in coulombs, and r in m.

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Current

• 電流，即電荷的流量• 1 A of current is 1 C of charge passing a

given point in 1 s, i.e.

I = Q / t or Q = I x t.

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Direction of Current

• Electrons flow from negative terminal to positive terminal but conventional current flows in the opposite direction.

E+- I

Lamp

Direction of conventional current

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Voltage

• 電壓，即電位差• When charges are transferred from one body

to another, a potential difference or voltageresults between them.

• The voltage between two points is 1 V if it requires 1 J of energy to move 1 C of charge from one point to the other; i.e. V = W / Q.

• Symbol for DC Voltage Sources:

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Practical DC Voltage Source -Battery

• Primary batteries are not rechargeable;Secondary batteries are rechargeable.

• Batteries come in different shapes (e.g button), sizes (e.g. AAA, AA, C, D), types ( e.g. alkaline, carbon-zinc, lithium, NiCad, lead acid) and ratings.

• Battery capacity (Ah) = current drain x expected life.

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Other DC Voltage Sources

• Electronic power supplies rectify ac to dc for use in equipment or labs.

• Solar/photovoltaic cells convert sunlight to electrical energy for remote areas or space applications.

• DC generators convert mechanical energy to electrical energy by rotating a coil of wire through a magnetic field.

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Practical DC Current Sources

• Usually, a combination of DC voltage sources and other electrical devices (e.g. transistors, resistors, etc.) is required.

• Symbol of a DC Current Source:

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Resistor

• A resistor is defined as a component whose terminal voltage is proportional to the current flowing through. That is, a resistor is a device that obeys the Ohm’s Law.

• Ohm’s Law: V=IR• The constant R is called the resistance (Ω) of

the resistor.• Symbol:

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Resistor Color Code

Band

1 2 3 4 5

3

33

1

33

5

5533 5

4

2, Significant Figures

MultiplierTolerance

Reliability

Colour: Bk, Br, R, O, Y, Gn, Bl, V, Gr, W, Gl , S , No ColourBand 1: 1 2 3 4 5 6 7 8 9 Band 2: 0 1 2 3 4 5 6 7 8 9Band 3: 1 10 102 103 104 105 106 107 .1 .01 Band 4: 5% 10% 20%

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CapacitanceCapacitance

n A capacitor consists of two metal plates separated by an insulator(dielectric) which may be air, oil, mica, plastic, ceramic, etc.

n When a dc source is applied across the capacitor, one of the platesbecomes positive and the other negative.

n The amount of charge stored by a capacitor is: Q = CV (C)

MetalPlates

Lead Dielectric

Lead

Parallel-plate capacitor

EC

Circuit symbol

E

C

ψ

Electric fieldof capacitor

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Capacitance (contCapacitance (cont’’d)d)

n Capacitance of a parallel-plate capacitor is: C = ε A / d (F), where ε is the permittivity of the

dielectric, A is the area of each plate and d is theseparation of the plates. Further,ε = εr εo where εr is the relative permittivity or dielectricconstant of the dielectric and εo = 8.85 x 10-12 F/m isthe permittivity of air.

n Energy stored between the plates is given by W = 1/2CV2 (J)

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Induced Voltage & InductionInduced Voltage & Induction

dtdΦ

= Ne

8FaradayÕs Law: voltage is induced in a circuit whenever the flux linking the circuit is changing and the magnitude of the voltage is proportional to the rate of change of flux linkages:

(volts)

8LenzÕs Law: the polarity of the induced voltage (known as the counter emf or back emf) is such as to oppose the cause producing it.

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Self-InductanceSelf-Inductance

L vL= L d i

d t

+

-

I

Voltage acrossinductor

l

dA

Inductor Coil

dtdi

Lv L =

4Induced voltage across the coil is:

(V)

4Approximate inductance of coil (when l /d > 10) is:

lAN

orl

ANL or

22 µµµ=

: = permeability

(H)

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Power

• The Rate of Doing Work:

where W is the work (or energy) in joulesand t is in seconds.

• P=V I

tW

=P (watts, W)

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Series Circuits & KVLSeries Circuits & KVL

E R

+-

+

-+

-VR

R

+ -V

V

1

2

3

2

3

1

E

1

2+-

I

n KirchhoffÕs Voltage Law states that for a closed loop:ΣV = 0, or Σ Vrises = Σ Vdrops

n The total resistance of n resistors in series is:RT = R1 + R2 + . . . + Rn

n The total power is: PT = P1 + P2 + . . . + Pn

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Voltage Divider RuleVoltage Divider Rule

The voltage applied to a series circuit will bedropped across all the resistors in proportionto the magnitude of the individual resistors.

Vx = (Rx / RT) E

E R

+-

+

-+

-V

R

R

+ -V

V

1

2

3

2

3

1

I

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NTHU, HsinChu, Taiwan, 30013

Parallel CircuitParallel Circuit

n Elements/branches are said to be parallel when they have only2 nodes in common. The voltage across all parallel elements ina circuit will be the same.

n Voltage sources of different potentials should never beconnected in parallel.

IT

E+

I1 I2

R1 R2 I3R3

RT

Ix = E / Rx; KCL: IT = I1 + I2 + I3 = E / RT

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Parallel Circuits & KCLParallel Circuits & KCL

n KirchhoffÕs Current Law: ΣI = 0, or Σ Iin = Σ Iout

n Overall conductance: GT=G1 + G2 + . . + Gn =1/RT

i.e. Total resistance, RT = 1/(1/R1 + 1/R2 + . . . + 1/Rn)n For 2 resistors in parallel: RT= R1R2 / (R1 + R2)n For n equal resistors in parallel: RT = R/n where R is the

resistance of each resistor.

n Current divider rule: Ix = (RT/Rx)ITn Total power dissipated: PT = P1 + P2 + . . . + Pn

where P1 = E2/R1 or EI1; . . . . ; Pn = E2/Rn or EIn

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Capacitor ChargingCapacitor Charging

vc= E(1-e-t/τ) i = (E/R)e-t/τ

τ = RC

vR = Ee-t/τ

E C

a

b

R

+

- cTransientInterval

SteadyState

t

vc

v

E

t

i

0

0

ER

i

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Current Buildup Transient in InductorCurrent Buildup Transient in Inductor

vR = E(1-e-t/τ)

vL = Ee-t/τ

i = (E/R)(1-e-t/τ) τ = L/R

E+

-

TransientInterval

SteadyState

t

v

E

t

i

0

0

ER

i

R

L vL

L

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What Will You Get in Learning Electric Circuit Theory?

• Being equipped with basic common sense, language, and analysis skill for studying the hardware of any electrical systems

• Extensive examples will be encountered in the courses of Microelectronics, Power Electronics, and Power Systems

2003/2/20 Advanced Silicon Device and Material Laboratory

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Bon Voyage!旅途愉快！