Chapter 2.
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 → Charge for reduction to silver
metal.
1Faraday = 9.649 x 104 coulombs
1Faraday ; Deposition of Ag 107.868g of 1 gram equivalent
(6.02 x 1023 charged particle),
I = dQ/dt (Q : charge, A : ampere)
Electrical Components:
2A Direct-Current Circuits and Measurements
- Direct current ; 전하가 시간에 비례
- Alternating current ; 전하가 주기적으로 변화하는 것 .
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
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.
Power Law
P = IVP = I2R = V2/R
1) Series circuits
2A-2 Direct-Current Circuits
Fig 2-1. A battery, a switch, & three resistors in series.
점 D 에서 kirchhoff's law 적용
I4 - I3 = 0 or I4 = I3 , I3 = I2 at point C.
* 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
∵
V1 = I1 R1 = IR1 (2-9)
Voltage dividers ; Fig 2-3 a → series connection of resistor discrete increment
- Potentiometer; continuously variable
AB
ACV
R
RVV
AB
AB
ACABAC
2) Parallel Circuits
Resistors in parallel at point A
Kirchhoff's current law to point A
I1 + I2 + I3 - It = 0
It = I1 + I2 + I3
- Applying 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
It = I1 + I2 + I3 에 위식 代入 V V V VIt = --- = --- + --- + --- V1 = V2 = V3 = V
Rp R1 R2 R3
so that 1 1 1 1 --- = --- + --- + ---
Rp R1 R2 R3
G=1/R Gp = G1 + G2 + G3
- Parallel resistances create a current divider.
I1 V/R1 1/R1 G1 Rp G1
--- = ----- = ----- = --- or I1 = It --- = It --- It V/Rp 1/Rp Gp R1 Gp
(Ex. 2-1)
Calculate
a) the total resistance,
b) the current from the battery,
c) the current present in each of the resistors, and
d) the potential drop across each of the resistors.
1 1 1a)( --- + --- ) = --- R2 R3 R2,3
1 1 1 3 --- = --- + --- = --- R2,3 = 13.3Ω R 20 40 40 V 15b) The current ; V = I·R I = --- = ----- = 0.67A Rs 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 = 0.67A I2 = 9.0/20 = 0.45A I3 = 9.0/40 = 0.22A
2A-3 Direct Current, Voltage, and Resistance Measurements
Digital Volmeters and Multimeters D’Arsonval moving-coil meter Digital Voltmeters and Multimeters.Power Source, display, A/D converter
The Loading Error in Potential Measurements
The Loading Error in Current Measurements
See equations 2-19 and 2-20
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.)
- Period (Tp); The time required for the completion of one cycle
- Cycle; one complete revolution
- Frequency(f) [HZ]; time number of cycles per second
f = 1/tp (2-21)
Sinusoidal signals ;
2B-1 Sinusoidal Signals
The AC: produced by rotation of a coil in a magnetic field.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 ω = 2π/tp = 2πf
Any time t 에서 instantaneous value → Vpsin ωtVp; maximum or peak voltage; the amplitude 순간 전류 : ⅰ= Ip sin ωt = Ip sin 2πft 순간 전압 : v = Vp sin ωt = Vp sin 2πft
Out of phase by 90o
Phase difference : phase angle(φ)일반식 ; ⅰ= Ip sin(ωt + φ) = Ip sin(2πft + φ)
(rms current & voltage) ;DC, AC 의 크기비교 ; 두 전류에 의한 저항에서 야기되는 Joule heatDC = the effective value of a sinusoidal, currentReport, heating effect of AC is calculated by averaging I2R losses even complete cycle
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
2B-2 Reactance in Electrical Circuits
Reactance - capacitance : capacitor
inductance : inductor
Use ; converting alternating current to DC or the converse①
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
Position 1 Position 2
Figure 2-8. (a) A series RC circuit. Time response of circuit when switch S is (b) in position 1 and (c) in position 2.
2B-3 Capacitors and Capacitance
1) Capacitance① a momentary current② current ceases → to be changed③ switch 을 2 로 discharge.
Capacitor
① 과 ② 사이에서 switch off; 측면 전하가 저장
The quantity of electricity Q
→ 판 넓이 , 모양 , 공간 , 절연체 의 유전상수에 의해 결정
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 Ip sin(wt - π/2)
∵ Vp = 1/wc Ip, V = (1/wc) I
1/wc = Xc → capacitive reactance 단위 Ω
Xc = -1/wc, V =XcI
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 ωt) = ωLIp cosωt = ωLIp sin(ωt + π/2)
전압의 위상이 전류보다 π/2 앞선다 .
V = ωLI
여기서 wL 을 inductive reactance 라 한다 .
XL = 2πfL
직류만 통과 , 교류 불통 ( 저주파 chopping coil)
직렬 연결 : L = L1 + L2 + L3
Rate of current changes in an RC circuit
By Kirchhoff 의 voltage law Vi = Vc + VR
Vi = constant Vi = q/C + iR
Rate of Voltage Change in an RC circuit
Phase relations between current and voltage in an RC circuit
use Ohm’s law to eq. 2-35
Rate of Current & Potential Change across RL circuit.
RC circuit 와 동일한 방법으로 처리
VR = Vi( I - e-tR/L )
VL = Vi e-tR/L
L/R : time constant
2B-4 Response of Series RC Circuits to Sinusoidal Inputs
Response of series RC & RL circuits to sinusoidal inputs signal (Vs)
Ip
At sufficiently high frequencies & capacitance, φ become negligible & I & v are in phase.1/ωC 은 저항 R 에 비해 무시 可 . 전류가 잘 흐름At very low frequencies, the phase angle; π/2
(1/ωC = Xc)
Voltage, current and phase Relationships for series RL circuit
Figure 2-9
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 phase difference
Figure 2-10
<Vector diagrams for Reactive Circuits>
V 가 ⅰ보다 90° 늦다 . at capacitanceV 가 ⅰ보다 90° 빠르다 . at inductance Z = √R2 + (XL - Xc)2
Z = √R2 + Xc2 , φ = -arctan 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
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
(a) high pass filter and (b)low-Pass Filters
Low pass filter
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.
Figure 2-13
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.
Semiconductor Device
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.
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.
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
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.
2C-3 Transistors
: Amplifying device
-Bipolar
-Field effect transistor.
① Bipolar Tr. : pnp, npn tr.
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
Figure 2-17.
Figure 2-18.
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.
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
Figure 2-19.
(n-channel junction FET)
current enhancement in brought about by application of a
positive potential to the gate:
Gate 에 “ +" induce “-“ substrate channel below the layer of SiO2
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.
2D Power Supplies and Regulators most ps contains a voltage regulator.
Figure 2-20.
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
Figure 2-21.
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.
Figure 2-22.
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.
Figure 2-23.
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.
Figure 2-24.
2E Readout Devices
Figure 2-25. Basic analog oscilloscope component
2E-1 Oscilloscopes
Cathode-Ray Tubes Horizontal and vertical Control Plates. Trigger Control.
Figure 2-26. Schematic of a CRT
2E-2 Recorders
Figure 2-27. Schematic of self-balancing recording potentiometer
2E-4 Computers
2E-3 Alphanumeric Displays