Prof. Dong‐Weon Lee
MEMS & Nanotechnology Laboratory School of Mechanical Systems Engineering
Chonnam National University
Summary
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• Semiconductor, energy band gap and MOS structure
• Charge, current and voltage
• Measurement tools (ohm meter, voltmeter & ammeter)
• Voltage and current divider rule
• Ideal voltage and current sources
• KCL & KVL for network analysis
Electrical network
an interconnection of electrical elements such as resistors, inductors,
capacitors, transmission lines, voltage sources, current sources, switches and active electronic components.
Electrical circuit
a network that has a closed loop, giving a return path for the current. A
network is a connection of two or more components.
Semiconductor, energy band gap and MOS structure
1. Semiconductor
2. Energy band gap
3. MOS structure
Basic in Electrical Engineering
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• Circuit elements: electrical devices for making circuits – R, C, I, and OP‐AMP etc.
• 전기공학에서는 모든 현상을 회로로 표현하며, 이런 현상을 수학적으로 표현하는 것을 모델링이라 정의
(a natural phenomena circuit modeling mathematical modeling)
Basic in Electrical Engineering Current
Definition: the flow of electric charge
SI unit: A(amperes) which is equal to a flow of one coulomb of charge per second, C/s
(1 A는 1 초에 1 coulomb의 전하가 흐른다는 의미)
Voltage
Definition: the difference of electrical potential between two points of an electrical or electronic circuit
SI unit: J/C = V (volts)
(1 V는 1 Joule의 에너지로 1 coulomb의 전하를 분리시켰다는 의미)
Current density
The density of electrical current. It is defined as a vector whose magnitude is the
electric current per cross‐sectional area. SI units: A/m
2Basic in Electrical Engineering
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Ideal Sources Representation
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도체의 한 끝에 전자를 공급하고,
다른 한 끝에서 전자를 제거하는
장치(a kind of electron pump)
Concept of Voltage Source
Q. Find the total charge in a cylindrical conductor and compute the current flowing in the wire
Total charge current (C/s)?
2r = 210
‐3m
Charge density(n) = 10
29carriers/m
3Charge quantity(q) = 1.6910
‐19C Drift velocity() = 19.910
‐6m/s 2r
1 m
Vol (V)= 3.1410
‐6m
3# of carriers (N) = Vn = 3.14 10
23carriers
Total charges = qN = (1.6910
‐19C)(3.1410
23)=5310
3C Charge density(Q) per unit length? 5310
3C/m
Current(A) : Q = (5310
3)C/m(19.910
‐6)m/s
I = ~1 A(C/s)
Example in Electrical Engineering
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Q. What power do you need to heat 1l of wafer?
Assumption: Electric kettle의 소비전력 1.8kW, 물의 온도는 20도, 끓는 온도 100도 (1 cm
3의 water를 1도 올리는데 필요한 calorie는 1 cal)
A) 결국 1,000 cm
3* (100‐20) = 80,000[cal]의 calorie 이 필요 전력량 [W∙s] = 열량 [Joule] cal =0.24*I
2*R*t [J W∙s]
~ 333,333[W∙s]의 전력량 필요
1초에 500 [W∙s]이므로 약 666초 의 시간이 필요
; 1l의 물을 끓이기 위해서는 약 11분 6초의 시간이 필요 Example
Electric kettle
뒤에서 다시 언급
Independent Sources
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Dependent Sources (Electronic circuit)
Dependent Sources (Electronic circuit)
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Equivalent circuits for series and parallel resistors
Basic in Electrical Engineering
Voltage divider rule
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Current divider rule
Basic in Electrical Engineering
Ideal Voltage Sources: 출력전압은 다른 회로소자들에 공급하여야 하는 전류의 양에 의해서 영향을 받지 않음
Ideal Current Sources: 자신에 연결된 회로에 관계없이 규정된 전류를 발생시키는 회로 소자
vs(t)=VS vs(t)
a
b
+ v
-
i +
-
v i
VS 0
i
is(t)
a
b
+
v
- v
i IS
0 is(t)=IS
가정: 부하저항 무한 가정: 부하저항 0
Ideal Sources
MEMS@chonnam.ac.kr 0
Power conservation : 어떤 회로의 모든 회로 요소에서 흡수되는 전력의 합은 항상 0 이다. 즉 흡수된 전력의 합은 발생된 전력의 합과 항상 같다
Non‐ideal source: Practical source
• Node
‐ Common connection point between any elements
• 직렬 (series) 및 병렬 (parallel) 연결
• Super node: a region that encloses more than one node – 하나의 node로 취급
Terminologies: voltage source, current source, node, branch, loop, mesh etc
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• Branch
‐ Two‐terminal circuit element
Terminologies: voltage source, current source, node, branch, loop, mesh etc
• Loop: any closed connection of branches
(branch의 한쪽 단자에서 시작하여 동일한 branch의 반대쪽 단자에서 끝나는 폐회로를 의미)
• Mesh: a loop that does not contain other loop
Terminologies: voltage source, current source, node, branch, loop, mesh etc
Basic in Electric Engineering : Measuring devices
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Circuit analysis : network analysis
Define unknown branch current & unknown node voltage
• Kirchhoff’s Voltage Law (KVL)
• Kirchhoff’s Current Law (KCL)
Terminologies: KVL and KCL?
Basic in Electric Engineering
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Assumption for the circuit theory: needs for circuit analysis
‐ Circuit theory는 물리적 현상을 수학적으로 모델링 한 전자기학의 일부
‐ 몇몇 assumption을 통해 theory를 단순화 함
‐ 회로 이론을 적용할 때에는 가정을 만족하는 지를 따져야 함
가정
(1) Propagation(傳播) effect가 무시될 만큼 계가 작다(외부로 빠져나가는 E?) 즉, 계가 순간적으로, 동시적으로 변화한다 → 집중정수 계
(2) 계에 알짜 전하는 없다 (R,L,C) – no charges exist in a curciut (3) 계의 구성 부품 간에 자기적인 결합은 없다
Concentrated constant: 통상적인 저항기의 저항 코일의 인덕턴스 커패시터의 정전 용량 등은 그 소자에 특유한 어떤 주파수보다 충분히 낮은 주파수 영역에서는 회로의 어느 한곳에 전기 정수가 집중되어 있다고 볼 수 있는데 여기서 그 정수를 가리키는 용어
KCL
5A
2A ‐3A
I
3I
41.5A
?
?
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Series and parallel resistor: 등가저항 구하기
KCL: use a node voltage as a variable Known quantity:
V
1=12V, V
2=8V, R
1=5, R
2=2, R
3=4
Find: node voltage v
Ausing KCL
Ref.
A
B +
‐
+ V
1‐
V
1R
1R
3V
2V
2R
2i
1i
2i
3v
AV
A={(12/5)+(8/4)}/{(1/5)+(1/2)+(1/4)}=4.6V
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KCL: find an unknown resistance value
is 20 W.
R1 Req
20W
KVL
6V
1V 12V
Known quantities: V
1, V
3, V
S2Find V
2?
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KVL
Practical Voltage & Current Sources: Remind
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KVL & KCL: Remind
The sum of all the voltages around the loop is equal to zero. v1 + v2 + v3 + v4 = 0
The current entering any junction is equal to the current leaving that junction. i1 + i4 = i2 + i3
KVL: loop current: simultaneous equations by two loops
R
2R
1I G
A B
C
R
3Vs +
-
1I
2R
4Find two loop currents using the KVL method when parameters are Vs=10V,
R
1=1k, R
2=2k, R
3=3k, R
4=4k
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Power consumption: Rated power
mA
P
R=60 W, P
OR= 820 lumens (Average), 1lm = 1/680 W, 1500 h (Average), V
R= 115 V
Resistance value of a filament of a light bulb measured with a general multimeter 16.7
The reason of the difference in resistance?
Power consumption: Efficiency
Efficiency is defined as the ratio of the useful power dissipated by or supplied by the load to the total power supplied by the source.
In this case, the useful power supplied by the load is the optical power. From
any handbook containing equivalent units: 680 lumens=1 W
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Ex. Power consumption:
75 W and 100 W
Resistor
a two‐terminal electrical or electronic component that resists an electric current by producing a voltage drop between its terminals in accordance with Ohm's law.(저항은 자신을 통과하는 전자로부터 에너지를 흡수하여 열로 발산)
Example:
1. 전기난로에서
저항선(전열선)은 열을 발산
2. 전구에서
저항선(필라멘트)은 가열되어 빛을 발산 3. DC모터의 속도(전류)를
조절하기 위하여 저항을 사용
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Resistor (Cont.)
Resistance value : 1, 2선은 수로 3선은 승(power)으로 읽는다
Ex.1 등백적(orange‐white‐red) = 3900 = 3.9kW Ex.2 황보갈(yellow‐violet‐brown) = 470 W
Ex.3 회적초(gray‐red‐blue) = 82x10
5=8.2MW Ex.4 청회등(blue‐gray‐orange) = 68x10
3= 68kW Tollence‐우측 마지막 선의 색으로 판별: 갈색 1%, 금색 5%, 은색 10%
Capacity of a resistor: 일반 기판용 저항은 1/4W
Review of measurement of current and voltage
Practical applications
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1. Wheatstone bridge
2. Node voltage & mesh current methods
‐ Compute the solution of circuits containing linear resistors and independent and dependent sources using node analysis.
‐ Compute the solution of circuits containing linear resistors and independent and dependent sources using mesh analysis.
40
Wheatstone bridge circuit: to measure R more preciously
Known quantities:
Source voltage, resistance value, bridge voltage Find:
Unknown resistance value R
x1 k 1 k
1 k
12 V
12 mV
This result is very useful and quite general
저항을 보다 정밀하게 측정하기 위해서 사용
알고 있는 저항을 이용하여 모르는 저항을 정밀하게 측정하는 장치
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Micromachined transducer: Ex. Pressure sensor
‐ Fiber optic sensors
This technology uses the properties of fiber optics to affect light propagating in a fiber such that it can be used to form sensors. Pressure sensors can be made by constructing miniaturized fiber optic
interferometers to sense nanometer scale displacement of membranes. Pressure can also be made to induce loss into a fiber to form intensity based sensors.
‐ Mechanical deflection
This technology uses the mechanical properties of a liquid to measure its pressure. Such as, the effect of pressure on a spring system and the changes of compression of spring can be used to measure pressure.
‐ Strain gauge
This technology makes use of the changes in resistance that some materials experience due to change in its stretch or strain. This technology makes use of the change of conductivity of material when
experiencing different pressures and calculates that difference and maps it to the change of pressure.
‐ Semiconductor Piezoresistive
This technology uses the change in conductivity of semiconductors due to the change in pressure to measure the pressure.
‐ Vibrating elements (silicon resonance, for example)
This technology uses the change in vibration on the molecular level of the different materials elements due to change in pressure to calculate the pressure.
‐ Variable capacitance
This technology uses the change of capacitance due to change of the distance between the plates of a capacitor because of change in pressure to calculate the pressure.
Micromachined transducer: Ex. Two types of pressure sensor
Piezoresistive type Capacitive type
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Micromachined transducer: Comparison
Historically, capacitive sensors have benefited from the same advances in diaphragm etching and wafer bonding that piezoresistive sensors have.
However, the piezoresistive approach generally has a complex transducer with simple circuit requirements, while the converse is true of the
capacitive approach. For this reason, capacitive sensors have benefited
more from advances in circuit design than piezoresistive sensors.
Micromachined transducer: Ex. Piezoresistive pressure sensor
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Wheatstone bridge circuit: Voltage measurement
SPECIFY THE ASSUMED POLARITY OF THE
VOLTAGE BETWEEN NODES A AND B
Focus on Measurements: Strain gauge
Measure of strain, stress, force, torque, pressure, etc.
The relationship between length and resistance Gauge factor (GF)
Since the strain is defined as
R
0: zero strain resistance
Compression: decrease of length & increase of cross section decrease of resistance Tension: increase of length & decrease of cross section increase of resistance
A
L
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Focus on Measurements: Strain gauge (Cont.)
Ex) foil strain gauge (GF: metal foil is usually about 2) maximum strain: 0.4 ~ 0.5 %
for a 120 gauge 0.96 ~ 1.2 , it can be measured by electrical circuits
Wheatstone bridge & Force measurement
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Wheatstone bridge & Force measurement (Cont.)
Relationship between voltage and force
k: force transducer
Wheatstone bridge & Force measurement: Ex.
Tensile stress on the top of the beam
Compressive stress on the bottom This causes a voltage of 50 mV at node B with respect to node A.
Determine the applied force to the free end of the cantilever
R =1k , V =12V, L=0.3m, w=25mm, h=100mm, Y=69GPa(N/m2)
Schematic of the circuit and geometry of the beam shown in Figure, characteristics of the material, reads on the bridge.
Al cantilevered beam loaded by the force
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