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; Q -> proportional to time.

- Alternating current; Q -> periodically change.

2A-1 Laws of Electricity Electrical potential (V) ; 공간의 한 점에서 다른 점까지 1개의 전하를

움직이는데 필요로 하는 일.

V ; volt → joule/coulomb (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/t

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

1) Series circuits

2A-2 Direct-Current 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

VRR VV,

RRV

)RRI(RIR

VV

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

ABACV

RRVV

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 + I3에 위식 代入

V V V V It = --- = --- + --- + --- 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 1 a) ( --- + --- ) = --- R2 R3 R2,3 1 1 1 3 --- = --- + --- = --- R2,3 = 13.3Ω R 20 40 40

V 15 b) The current ; V = I·R 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: 시간에 따라 방향과 크기가 변화하며 똑같은 변

화가 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)

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)

Sinusoidal signals ;

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

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; 전하가 저장

The quantity of electricity Q

→ 판 넓이 , 모양, 공간, 절연체 의 유전상수에 의해 결정 (one-farad

capacitor stores 1 Q of charge per applied volt.)

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 =XcI

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.

Rate of current and voltage changes in an RC circuit

By Kirchhoff 의 voltage law Vi = vc + vR Vi = constant Vi = q/C + iR

: Instantaneous voltage across the resistor

Phase relations between current and voltage in an RC circuit

: Ohm’s law to eq. 2-35

Fig.2-8c

2B-4 Response of Series RC Circuits to Sinusoidal Inputs signal ftVtVv pps πω 2sinsin ==

ftIdtdvC p

C π2sin=

Ip

At sufficiently high frequencies & capacitance, φ become negligible & I & v are in phase. 1/ωC은 저항 R에 비해 무시 可. 전류가 잘 흐름 At very low frequencies, the phase angle; π/2

(1/ωC = Xc)

Figure 2-10

Figure 2-9

90o phase difference between v and 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 & 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

<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 + XL

2 , 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

Voltage, current and phase Relationships for series RL circuit

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 + XL

2 Ip = Vp/Z

저항과 차이점 :

① frequency dependent

② current와 voltage 사이에 phase difference

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.

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 fixed magnetic field. ⇒ D'arsonval movement or coil.

He Ayrton Shunt : to vary the range of a galvanometers

p29. 예제 참조 measurement of current and voltage.

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 (in the 1950s)→ 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.

Bipolar Junction Transistors

: pnp, npn tr.

Bipolar junction transistors(BJTs) may be viewed as two back-to-back

semiconductor diodes.

Electrical Characteristics of a BJT

The discussion that follows focuses on the behavior of

a pnp-type BJT.

Mechanism of Amplification with a BJT

Turning again to Fig 2-18, holes are formed at the p-

type emitter junction through removal of electrons by

the two dc sources, namely, the input signal and the

power supply.

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

Fig 2-17. Two types of BJTs.

Fig 2-18. Current in a common-emitter circuit with a transistor.

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 input impedance

→ MOSFET (metal oxide semiconductor FET)

n- channel 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

Fig 2-19. An n-channel enhancement mode MOSFET: (a) structure, (b) symbol, (c) performance characteristics.

(n-channel junction FET)

Current enhancement is brought about by application of a positive

potential to the gate:

Gate 에 “+" induce “-“ substrate channel below the layer of SiO2

Depletion mode →to conduct in the absence of a gate voltage and

to become nonconducting as potential is applied to the gate.

The reverse bias is applied to the gate -> the supply of electrons

in the channel is depleted. → channel 저항 증가→전류감소.

2D Power Supplies and Regulators most ps contains a voltage regulator.

Fig 2-20. Diagram showing the components of a power supply and their effects on the 115-V line voltage.

2D-1 Transformers

The voltage from the ac power lines is readily increased or decreased by

means of a powe transformer such as that shown schematically in Fig 2-

21.

VX = 115 X N2/N1

N2 and N1 are the no of turns in the secondary and primary coils.

2D-2 Rectifiers

Fig 2-22 shows three type of rectifiers and their output-signal forms.

①Half wave rectifier

②Full wave rectifier

③bridge rectifier

①:②;그림

③ 그림

Fig 2-21. Schematic of a typical power transformer with multiple secondary windings.

D2, D3 → conduct on the alternate D4 and D1 conduct Since two diodes are in series with the load, the output voltage is reduced by twice the diode drop.

Fig 2-22. Three types of rectifiers: half-wave, full-wave, and bridge.

Fig 2-23. Filtering the output from a rectifier.

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

Fig 2-24 illustrates a simple voltage regulator that use a Zener

diode.

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.

Fig 2-24. Zener-stabilized voltage regulator.

2E Readout Devices

Fig 2-25. Basic analog oscilloscope component

2E-1 Oscilloscopes Cathode-Ray Tubes Fig 2-26 is a schematic that shows the main components of a CRT. Horizontal and vertical Control Plates Input signals are applied to two sets of two set of plates, one of which deflects the beam horizontally and the other vertically. Trigger Control To steadily display a repetitive signal, such as a sine wave, on the screen, it is essential that each sweep begin at an identical place on the signal profile.

2E-4 Computers Many modern instruments use computers and computer monitors as readout devices.

2E-3 Alphanumeric Displays The output from digital equipment is most conveniently displayed in terms of decimal numbers and letters, that is, in alphanumeric form.