introduction to electric circuit analysis · 2005. 9. 12. · 2003/2/20 advanced silicon device and...
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2003/2/20 Advanced Silicon Device and Material Laboratory
NTHU, HsinChu, Taiwan, 30013
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
2/20/2003 Advanced Silicon Device and Material Laboratory
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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NTHU, HsinChu, Taiwan, 30013
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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NTHU, HsinChu, Taiwan, 30013
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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NTHU, HsinChu, Taiwan, 30013
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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NTHU, HsinChu, Taiwan, 30013
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
2/20/2003 Advanced Silicon Device and Material Laboratory
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
2/20/2003 Advanced Silicon Device and Material Laboratory
NTHU, HsinChu, Taiwan, 30013
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
2/20/2003 Advanced Silicon Device and Material Laboratory
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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
2/20/2003 Advanced Silicon Device and Material Laboratory
NTHU, HsinChu, Taiwan, 30013
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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NTHU, HsinChu, Taiwan, 30013
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
NTHU, HsinChu, Taiwan, 30013
Bon Voyage!旅途愉快!