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