Chapter 2 Electrical Components and Circuits Electrical Components

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. 001111800 g of silver ion → Charge for reduction to silver metal. 1 Faraday = 9. 649 x 104 coulombs 1 Faraday ; Deposition of Ag 107. 868 g of 1 gram equivalent ↳ (6. 02 x 1023 charged particle), I = d. Q/dt (Q : charge, A : ampere)

2 A Direct-Current Circuits and Measurements - Direct current ; 전하가 시간에 비례 - Alternating current ; 전하가 주기적으로 변화하는 것. 2 A-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․d. Q/dt = V․I P = (I․R)․I = I 2 R. 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 = I 2 R = V 2/R

2 A-2 Direct-Current Circuits 1) Series circuits Fig 2 -1. A battery, a switch, & three resistors in series.

ⓐ 점 D에서 kirchhoff's law 적용 I 4 - I 3 = 0 or I 4 = I 3 , I 3 = I 2 at point C. * the current is the same at all points I = I 1 = I 2 = I 3 = I 4 ⓑ Voltage low V - V 3 - V 2 - V 1 = 0 or V = V 1 + V 2 + V 3 by ohm's law V = 1(R 1 + R 2 + R 3) = IReq ∵ Req = R 1 + R 2 + R 3 IR 1 = V 1 , V 2 = IR 2 , V 3 = IR 3 V 1 = I 1 R 1 = IR 1 (2 -9)

Voltage dividers ; Fig 2 -3 a → series connection of resistor ↳ discrete increment

- Potentiometer; continuously variable

2) Parallel Circuits Resistors in parallel at point A Kirchhoff's current law to point A I 1 + I 2 + I 3 - It = 0 It = I 1 + I 2 + I 3

- Applying Kirchhoff's voltage law I 1 = V/R 1 V - I 1/R 1 =0 V= I 1 R 1 I 2 = V/R 2 V - I 2/R 2 =0 V = I 2 R 2 I 3 = V/R 3 V = I 3 R 3 It = I 1 + I 2 + I 3에 위식 代入 V V It = --- + --Rp so that R 1 R 2 R 3 1 1 --- = --- + --Rp G=1/R V 1 = V 2 = V 3 = V R 1 R 2 R 3 G p = G 1 + G 2 + G 3 - Parallel resistances create a current divider. I 1 V/R 1 1/R 1 G 1 --- = ----- = --It V/Rp 1/Rp Gp Rp G 1 or I 1 = It --- = It --R 1 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) ( --- + --- ) = --R 2 R 3 R 2, 3 1 1 1 3 --- = --- + --- = --R 20 40 40 b) The current ; V = I·R R 2, 3 = 13. 3Ω V 15 I = ----- = 0. 67 A Rs 22. 3 c) V = V 1 + V 2 + V 3 V 1 = I 1 R 1 = 6. 03 I = I 2 = I 3 이므로 9. 0 V 1 = 15 x ------ = 6. 0 V (9. 0 + 13. 3) 13. 3 V 2 = V 3 = V 2, 3 = 15 x ------ = 9. 0 V 22. 3 d) R 1에서 I 1 = I = 0. 67 A I 2 = 9. 0/20 = 0. 45 A I 3 = 9. 0/40 = 0. 22 A

2 A-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

2 B 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 ;

2 B-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 90 o 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 I 2 R losses even complete cycle

2 B-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

2 B-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

Rate of current changes in an RC circuit By Kirchhoff 의 voltage law Vi = V c + V R Vi = q/C + i. R 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-t. R/L ) VL = Vi e-t. R/L L/R : time constant

2 B-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 phase. 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/w. C = 1/2πf. C XL = w. L = 2πf. L Impedance Z ; 교류회로에서 전압과 전류의 크기의 비(직류회로의 저항에 해당) At, RC circuit Z = √R 2 + Xc 2 Z = √R 2 + XL 2 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 = √R 2 + (XL - Xc)2 Z = √R 2 + Xc 2 , φ = -arctan Xc/R Z = √R 2 + XL 2 , φ = -arctan XL/R Z = √R 2 + (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. 186 A Vc = 0. 186 x 20 = 3. 7 V VR = 0. 186 x 50 = 9. 3 V VL = 0. 186 x 40 = 7. 4 V

2 B-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

2 B-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 ; 1/2πfo. C = 2πfo. L ∵ fo = 1/2π√LC ex) (Vp)i = 15. 0 V (peak voltage), L = 100 m. H, R = 20Ω, C = 1. 200μF.

Figure 2 -13

2 B-7 Alternating Current, Voltage, and Impedance Measurements Parallel Resonance Filters Xc = XL fo = 1/2π√LC Z of the parallel circuit Z = √R 2 + (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 p 29. 예제 참조 ☆ measurement of current and voltage.

Semiconductor Device

2 C 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.

2 C-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.

2 C-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 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.

2 C-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. 02 mm 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 흐 름 (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 Si. O 2 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.

2 D Power Supplies and Regulators most ps contains a voltage regulator. Figure 2 -20.

2 D-1 Transformers VX = 115 X N 2/N 1 N 2 and N 1 are the no of turns in the secondary and primary coils. 2 D-2 Rectifiers ①Half wave rectifier ②Full wave rectifier ③bridge rectifier ①: ②; 그림 ③ 그림

Figure 2 -21.

D 2, D 3 → conduct on the alternate D 4 and D 1 conduct Since two diodes are in series with the load, the output voltage is reduced by twice the diode drop. Figure 2 -22.

2 D-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.

2 D-3 Voltage Regulators Figure 2 -24. Zener diode : breakdown condition 하에서 작동. Under breakdown condition, a current change of 20 to 30 m. A may result from a potential change of 0. 1 V or less.

2 E Readout Devices Figure 2 -25. Basic analog oscilloscope component

2 E-1 Oscilloscopes Cathode-Ray Tubes Horizontal and vertical Control Plates. Trigger Control. Figure 2 -26. Schematic of a CRT

2 E-2 Recorders Figure 2 -27. Schematic recording potentiometer of self-balancing

2 E-3 Alphanumeric Displays 2 E-4 Computers