Electrical Components and Circuits Electric current ; the motion of a charge through a medium.
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Transcript of Electrical Components and Circuits Electric current ; the motion of a charge through a medium.
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Electrical Components and Circuits
Electric current ; the motion of a charge through a medium.
Electric units ; the unit of charge (or quantity of electricity) ; C(coulomb) →
0.001111800g of silver ion → silver metal 로 환원시키는데 필요로 하는
전하량 .
1Faraday = 9.649 x 104 coulombs
1Faraday ; 107.868g 의 은 석출
1g 당량의 원소나 화합물을 석출 .
(6.02 x 1023 charged particle 에 대응하는 ) I = dQ/dt (Q : charge, A : ampere)
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2A-1 Laws of Electricity
두 점 사이의 electrical potential (V) ; 공간의 한 점에서 다른 점까지 1
개의 전하를 움직이는데 는 일 .
V ; volt → joule/conlomb (W/Q = V) = (I R)․
R ; ohm → R 의 단위 Ω(R = ρℓ/A) ohm's law
G ; 저항의 역수 (electrical conductance) Ω-1, S
I ; Ampere
P ; electrical power. joules/sec, W
P = dw/dt = V dQ/dt = V I․ ․
P = (I R) I = I․ ․ 2R. joule's law
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Kirchhoff's Laws
Current low ; the algebraic sum of currents around any point in a circuit is zero.
Voltage low ; the algebraic sum of the voltages around a closed electrical
loop is zero.
Direct current ; 전하가 시간에 비례
Alternating current ; 전하가 주기적으로 변화하는 것 .
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1) series circuitsFig 2-1. a battery, a switch, & three resistors in series.
2A-2 Direct-Current Circuits
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점 D 에서 kirchhoff's law 적용
I4 - I3 = 0 or I4 = I3 at point C. I3 = I2
* the current is the same at all points
I = I1 = I2 = I3 = I4
Voltage low
V - V3 - V2 - V1 = 0 or V = V1 + V2 + V3
by ohm's law V = 1(R1 + R2 + R3) = IReq
∵ Req = R1 + R2 + R3
IR1 = V1 , V2 = IR2 , V3 = IR3
VR
R VV,
R
RV
)RRI(R
IR
V
V
eq
33
eq
11
321
11
∵
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Voltage dividers ; Fig 2-3 a → series connection of resistor discrete increnents
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Potentiometer ; continuously variable
AB
ACV
R
RVV
AB
AB
ACABAC
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2) Parallal Circuits
Resistor in parallel at point A
Kirchhoff's current law
I1 + I2 + I3 - I = 0
I = I1 + I2 + I3
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Kirchhoff's voltage law
I1 = V/R1 V - I1/R1 =0 V= I1R1
I2 = V/R2 V - I2/R2 =0 V = I2R2
I3 = V/R3 V = I3R3
I = I1 + I2 + I3 에 위식 代入 V V V VI = --- = --- + --- + --- V1 = V2 = V3 = V
Req R1 R2 R3
so that 1 1 1 1 --- = --- + --- + ---
Req R1 R2 R3
G=1/R G = G + G + GParallal resistances create a current divider
I1 V/R1 1/R1 G1 R G1
--- = ----- = ----- = --- or I1 = I--- = I--- I V/R 1/R G R1 G
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(Ex. 2-1)
a) the total resistance
b) the current from the battery
c) the current present in each of the resistors
d) the potential drop across each of the resistors
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1 1 1a)( --- + --- ) = --- R2 R3 R2,3
1 1 1 3 --- = --- + --- = --- R2,3 = 13.3Ω R 20 40 40 V 1.5b) The current ; V = I·R I = --- = ----- = 0.67A R 22.3c) V = V1 + V2 + V3
V1 = I1R1 = 6.03 I = I2 = I3 이므로 9.0 V1 = 15 x ------------ = 6.0V (9.0 + 13.3) 13.3 V2 = V3 = V2,3 = 15 x ------ = 9.0V 22.3d) R1 에서 I1 = I = 0.67G I2 = 9.0/20 = 0.45A I3 = 9.0/40 = 0.22A
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2A-3 Direct Current, Voltage, and Resistance Measurements
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2B Alternating current Circuits
Alternating voltage and current: 시간에 따라 방향과 크기가
변화하며 똑같은 변화가 계속 반복되는 전압 또는 전류 .
; the simplest alternating waveform is sine-wave volt or current
Cycle; one complete revolution
Frequency(f) [HZ]; time number of cycles per second
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Sinusoidal signals ;
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2B-1 Sinusoidal Signals
The AC: produced by rotation of a coil in a magnetic fiedd.A pure sine wave → 일정한 각속도로 회전 하는 ( 시계방향 ) IP 의 vector 로 표시 . ( 여기서 Ip : amplitude.) 주기 t 내에 2π radian 의 속도로 회전 할 때 W = 2π/t = 2πf
Any time t 에서 instantaneous value → VpsinwtVp ; maximum or peak voltage; the amplitude 순간 전류 : ⅰ= Ip sin wt = Ip sin 2πft 순간 전압 : v = Vp sin wt = Vp sin 2πft
Out of phase by 90o
Phase difference : phase angle(φ)일반식 ; ⅰ= Ip sin(wt + φ) = Ip sin(2πft + φ)(rms current voltage) ;
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DC, AC 의 크기비교 ; 두 전류에 의한 저항에서 야기되는 Joule heat
DC = the effective value of a sinusoidal, currentReport, heating effect of AC is calculated by averaging I2R losses even complete cycle
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1 Hz 중의 평균 열손실 = 직류일 때의 ohm 손실
square wave ; 파행도 1.00 파고율 1.00
sine wave ; 파행율 = 1.11 파고율 =
1.41
삼각파 ; 파행율 = 1.15 파고율 = 1.73
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2B-2 Reactance in Electrical Circuits
Reactance - capacitance : capacitor
inductance : inductor
Use ; ① converting alternating current to DC or the converse
② discriminating among signals of different frequencies or
separating ac & dc signals.
Capacitors
구성 ; a pair of conductors separated by a thin layer of a dielectric
substance
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Position 1 Position 2
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1) Capacitance① a momentary current② current ceases → to be changed③ switch 을 2 로 discharge.
Capacitor : 전류의 측정可
① 과 ② 사이에서 switch 껌 ; 측면 전하가 저장
The quantity of electricity Q
→ 판 넓이 , 모양 , 공간 , 절연체 의 유전상수에 의해 결정
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1 Faraday ; 1 V 의 전위치에 의해 양극판에 축적된 전하의 크기가 1 C 일 때의
capacitance.
μF, PF
V = 1/C ∫idt = 1/C∫ Ip sin wt dt
= -1/wc Ip cos wt = 1/wc Im sin(wt - π/2)
∵ Vp = 1/wc Ip, V = (1/wc) I
1/wc = Xc → capacitive reactance 단위 Ω
Xc = -1/wc V =XcI
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2) Inductance
Coil 에 직류 통과 → 자기작용에 의한 유기전압으로 인해 다른 전류 발생
자기장이 변화 → emf 발생
V = -L(di/dt) - : 전류의 방향과 반대
L : inductance [Henrys] → [H]
1 Henry : 전류변화속도가 one A/1 sec 일 때 1volt 의 전압 발생 , μH ~ H
범위
V = L(d/dt)(Ip sin wt) = WLIp coowt = WLIp sin(wt + π/2)
전압의 위상이 전류보다 π/2 앞선다 .
V = wLI
여기서 wL 을 inductive reactance 라 한다 .
XL = 2πfL
직류만 통과 , 교류 불통 ( 저주파 chohing coli)
직렬 연결 : L = L1 + L2 + L3
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Rate of current & potential changes in an RC circuit
By Kirchhoff 의 voltage law Vi = Vc + VR
Vi : const Vi = q/C + iR
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Rate of Current & Potential Change across RL circuit.
RC circuit 와 유사한 방법으로 처리
VR = Vi( I - e-tR/L )
VL = Vi e-tR/L
L/R : time constant
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2B-4 Response of Series RC Circuits to Sinusoidal
Inputs
Response of series RC & RL circuits to sinusoidal inputs
signal (Vs)
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At sufficiently high frequencies & capacitance, φ become negligible & e vs are in phase.1/wC 은 저항 R 에 비해 무시 可 . 전류가 잘 흐름At very low frequencies, the phase angle π/2
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Voltage, current and phase Relationships for series RL circuit
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Figure 2-9
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Capacitive & Inductive Reactance ; impedance
Xc = 1/wC = 1/2πfC XL = wL = 2πfLImpedance Z ; 교류회로에서 전압과 전류의 크기의 비 ( 직류회로의 저항에 해당 )
At, RC circuit Z = √R2 + Xc2
Z = √R2 + XL2
Ip = Vp/Z
저항과 차이점 :
① frequency dependent
② current 와 voltage 사이에 phafe diffrence
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Figure 2-10
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<Vector diagrams for Reactive Circuits>
V 가 ⅰ보다 90° 늦다 . at capacitenceV 가 ⅰ보다 90° 빠르다 . at inductance Z = √R2 + (XL - Xc)2
Z = √R2 + Xc2 , φ = -anctan Xc/RZ = √R2 + XL
2 , φ = -arctan XL/RZ = √R2 + (XL
+ Xc)2
φ = -arctan (XL + Xc) / R (XL
> Xc 인 경우 )
ex) ① peak current ② voltage drop
Z = √(50)2 + (40 - 20)2 = 53.8Ω Ip = 10 v/53.8 = 0.186A Vc = 0.186 x 20 = 3.7VVR = 0.186 x 50 = 9.3V VL = 0.186 x 40 = 7.4V
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2B-5 Filters Based on RC Circuits
High-pass & Low-Pass FiltersRC & RL circuits → low f component 를 지나는 동안 high-f signals 을 낮추기 위해 filter 로 사용 (low pass filter) or 역이 성립 .① RC circuit 에서 high-pass filter Vo : across the resistor R
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Low pass filter
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2B-6 The Response of RC Circuits to Pulsed
Inputs
<Resonant Circuits>
impedance Z 가 최소 즉 XL = Xc 일 때
전류 I = E/Z = E/R the condition of Resonance
resonant frequency fo ;
1/2πfoC = 2πfoL
∵ fo = 1/2π√LC
ex) (Vp)i = 15.0 V (peak voltage), L = 100mH, R = 20Ω, C = 1.200μF.
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2B-7 Alternating Current, Voltage, and Impedance MeasurementsParallel Resonance Filters
Xc = XL fo = 1/2π√LCZ of the parallel circuit
Z = √R2 + (XLXc/Xc-XL)2
At parallel circuit at resonance → Z 는 최대 → maximum voltage drop 生 → tank circuit Behavior of RC Circuits with pulsed inputs RC 회로에 pulse 加 → various form (with of pulse time const) 사이의 관계에 의존
Simple Electrical Measurements Galvanometers → DC 의 전류 , 저항 측정 원리 : the current in duceol motion of a coil suspended in a yixed magnetic yiedd.⇒ D'arsonval movement or coil.
He Ayrton Shunt : to vary the range of a galvanometers
p29. 예제 참조 measurement of current and voltage.
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2C Semiconductors and Semiconductor Devices
Semiconductors
- Electronic circuits contain one or more nonlinear devices such
as transistors, semiconductor diodes, and vacuum or gas-filled
tubes.
Nonlinear components ; rectification (from ac to dc ) amplitude
modulation or frequency modulation vacuum tube →
Semiconductor based diodes and transistors → integrated circuits
(Tr, R, C & conductor)
-Semiconductor 장점 : low cost, low power consumption, small
heat generation, long life and compactness.
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2C-1 Properties of silicon & germanium semiconductors.
-Sufficient thermal agitation occurs at room temp. to liberate an
occasional electron from its bonded state, leaving it free to more
through the crystal lattice and thus to conduct electricity.
-Hole : positively charged region.
-Electron: negatively charged region.
-Hole & electron 의 이동방향 반대 .
-Doping of arsenic or antimony (Group Ⅴ) → n type
of indium or gallium (Group Ⅲ) → p type
Positive holes are less mobile them free electrons.
Conductivity of n type >conductivity of p type.
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2C-2 . Semiconductor DiodesPn junction motion → diode is a nonlinear device that has greater conductance in one direction than in another.
Figure 2-15 A pn junction
diode
(c) forward - bias
(d) reverse - bias
→ depletion layer 생성
: conductance 10-6~10-8
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Figure 2-16 I - V cures for semiconductor Diodes
The voltage at which
the sharp increase in
current occurs under
reverse bias is called
the Zener breakdown
voltage.
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2C-3 Transistors
: Amplifying device
-Bipolar
-Field effect transistor.
① Bipolar Tr. : pnp, npn tr.
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The mechanism of amplification with a bipolar transistor.Pnp on ∽ n layer ~ 0.02mm thickness, p>>n layer. ( 수백배 이상 ), ∴The concentration of holes in p >> that of electrons in n layer
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① P-type emitter junction 에서 hole 생성② ① 번의 hole 이 very thin n-type base 로 이동 - electron 과 결합 (base current IB 유발 )
③ 대부분의 hole 은 base 를 통해 drift 되어 collector junction 으로 attracting
④ 여기서 power supply 로부터 나온 electron 과 combined 되어 전류 흐름 (Ic)
The no of current carrying holes is a fixed multiple of the number of electrons supplied by the input base current.
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Field Effect Transistors (FET)
FET - The insulated gate field effect transistor.
→109~1014 Ω 의 imput impedence
→ MOSFET (metal oxide semiconductor FET)
n- chanel MOSFET
The gate is a cylindrical p-type semiconductor surrounding a
center core of n -doped material called the channel.
Two isolated n regions are formed in a p-type substrate.
위의 n.p regions 을 silicon dioxide 로 insulating
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(n-channel junction FET)
current enhancement in brought about by application of a
positive potential to the gate.
Gate 에 "t" →substrate "_"
Depletion mode →in the absence of a gate voltage reverse bias is
applied to the gate the supply of electrons in the channel is
depleted. → channel 저항 증가→전류감소 .
The width of the reverse biased gate junction determined (the
wide of the channel and consequently). The magnitude of the
current between source and drain.
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2D Power Supplies and Regulators most ps contains a voltage regulator.
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2D-1 Transformers
VX = 115 X N2/N1
N2 and N1 are the no of turns in the secondary and primary coils.
2D-2 Rectifiers
①Half wave rectifier
②Full wave rectifier
③bridge rectifier
①:②; 그림
③ 그림
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D2, D3 → conduct on the alternate D4 and D1 conductSince two diodes are in series with the load, the output voltage is reduced by twice the diode drop.
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2D-2 Rectifiers and Filters
In order to minimize the current fluctuations.
L section filter : S 은 직렬 C 는 병렬 연결 .
⇒ peak to peak ripple can be reduced.
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2D-3 Voltage Regulators
Zener diode : breakdown condition 하에서 작동 .
Under breakdown condition, a current change of 20 to 30 mA
may result from a potential change of 0.1 V or less.
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2E Readout Devices
Basic analog oscilloscope component
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Schematic of a CRT
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2E-2 Recorders
Schematic of self-balancing recording potentiometer