Chapter 2.
Electrical Components and Circuits
Electrical Components:
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)
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 1개의
전하를 움직이는데 는 일.
V ; volt → joule/conlomb (W/Q = V) = (I․R)
R ; ohm → R의 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 = I2R. 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 = IV
P = I2R = V2/R
2A-2 Direct-Current Circuits
1) Series circuits
Fig 2-1. A battery, a switch, & three resistors in series.
ⓐ 점 D에서 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
V1 = I1 R1 = IR1
V1
IR 1

V I(R 1  R2  R3 )
(2-9)
R3
R1
 V1 
 V, V 3 
V
Req
Req
Voltage dividers ; Fig 2-3 a → series connection of resistor
↳ discrete increment
- Potentiometer; continuously variable
VAC
R AC
 VAB
R AB
 VAB
AC
AB
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 + I3에 위식 代入
V
V
V
V
It = --- = --- + --- + --Rp
so that
R1
R2
R3
1
1
1
1
--- = --- + --- + --Rp
G=1/R
V1 = V2 = V3 = V
R1
R2
R3
Gp = G1 + G2 + G3
- Parallel resistances create a current divider.
I1 V/R1
1/R1 G1
--- = ----- = ----- = --It
V/Rp
1/Rp Gp
Rp
G1
or I1 = It --- = It --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
1
a) ( --- + --- ) = --R2
R3
R2,3
1
1
1
3
--- = --- + --- = --R
20
40 40
b) The current ; V = I·R
R2,3 = 13.3Ω
V
15
I = --- = ----- = 0.67A
Rs
22.3
c) 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
22.3
d) R1에서 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:
화가 계속 반복되는 전압 또는 전류.
시간에 따라 방향과 크기가 변화하며 똑같은 변
( 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) IP의 vector로
표시. (여기서 Ip : amplitude.)
주기 t 내에 2π radian 의 속도로 회전 할 때
ω = 2π/tp = 2πf
Any time t에서 instantaneous value → Vpsin ωt
Vp; 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, AC의 크기비교 ; 두 전류에 의한 저항에서 야기되는 Joule heat
DC = the effective value of a sinusoidal, current
Report, heating effect of AC is calculated by averaging I2R losses even
complete cycle
1 Hz 중의 평균 열손실 = 직류일 때의 ohm손실
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 ; 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
Position 1
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.
Position 2
2B-3 Capacitors and Capacitance
1) Capacitance
① a momentary current
② current ceases → to be changed
③ switch을 2로 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 V의 전위치에 의해 양극판에 축적된 전하의 크기가 1 C일 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 =│Xc│I
2) Inductance
Coil에 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 1volt의 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 wL을 inductive reactance라 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 = q/C + iR
Vi = constant
Rate of Voltage Change in an RC circuit
use Ohm’s law to eq. 2-35
Phase relations between
current and voltage in
an RC circuit
Rate of Current & Potential Change across RL circuit.
RC circuit와 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
(1/ωC = Xc)
At sufficiently high frequencies & capacitance, φ become negligible & I & v are in p
hase.
1/ωC은 저항 R에 비해 무시 可.
↳ 전류가 잘 흐름
At very low frequencies, the phase angle; π/2
Voltage, current and phase Relationships for series RL circuit
Figure 2-9
Capacitive & Inductive Reactance ; impedance
Xc = 1/wC = 1/2πfC
XL = wL = 2πfL
Impedance 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 current와 voltage 사이에 phase difference
Figure 2-10
<Vector diagrams for Reactive Circuits>
V가 ⅰ보다 90°늦다. at capacitance
V가 ⅰ보다 90°빠르다. at inductance
Z = √R2 + (XL - Xc)2
Z = √R2 + Xc2 , φ = -arctan Xc/R
Z = √R2 + XL2 , φ = -arctan XL/R
Z = √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 = 3.7V
VR = 0.186 x 50 = 9.3V
VL = 0.186 x 40 = 7.4V
2B-5 Filters Based on RC Circuits
High-pass & Low-Pass Filters
RC & RL circuits → low f component를 지나는 동안 high-f signals을 낮추기 위해
filter로 사용 (low pass filter) or 역이 성립.
① RC circuit에서 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 Z가 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 Measurements
Parallel Resonance Filters
Xc = XL fo = 1/2π√LC
Z of the parallel circuit
Z = √R2 + (XLXc/Xc-XL)2
At parallel circuit at resonance
→ Z는 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 → DC의 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 Diodes
Pn junction motion → diode is a nonlinear device that has greater conductance
in one direction than in another.
Figure 2-15 A pn junction dio
de
(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.
Figure 2-17.
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 2-18.
① P-type emitter junction 에서 hole 생성
② ①번의 hole 이 very thin n-type base 로 이동 - electron 과 결합 (base
current IB유발)
③ 대부분의 hole 은 base를 통해 drift 되어 collector junction 으로
attracting
④ 여기서 power supply로부터 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 dioxide로 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 conduct
Since two diodes are in series with the load, the output voltage is redu
ced by twice the diode drop.
Figure 2-22.
2D-2 Rectifiers and Filters
Figure 2-23.
In order to minimize the current fluctuations.
L section filter : S 은 직렬 C는 병렬 연결.
⇒ peak to peak ripple can be reduced.
2D-3 Voltage Regulators
Figure 2-24.
Zener diode : breakdown condition 하에서 작동.
Under breakdown condition, a current change of 20 to 30 mA may r
esult from a potential change of 0.1 V or less.
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-3 Alphanumeric Displays
2E-4 Computers