Electronic Circuits I

Prof. Yong-Joo Doh

• 과기대 9-222 (E-mail: yjdoh@korea.ac.kr, tel: 1376)

• Lecture materials can be found in EKU-강의자료실

Teaching Assistant – 장영재 (phyjyj@gmail.com, tel: 010-9487-3434)

• Home work ~ every Chapter

Textbook:

• “전자회로공학” (최성재 옮김, 7판) – 교우사 출판사

• “Introductory Electronic Devices and Circuits” by R. T. Paynter (7th ed. Pearson

and Prentice Hall press)

What do we learn?

0. Circuit Basic

1. Semiconductor Basic

2. Diode

3. Diode Application – 1

4. Diode Application – 2

5. Bipolar Junction Transistor

7. DC Bias Circuit

8. Amplification

Grade

• Mid-term Exam. = 40 %

• Final Exam = 40 %

• Homework = 15 %

• Attendance & Attitude = 5 % (One petition; -1 for an absence; -0.3 for a lateness)

• Not allowed : smart phone, sleeping, other reports, chatting… 앙대영~

• Pardon : Active questions and answers 대영~

English : Course materials (ppt & exam), summary in English (class & homework)

Some Important Electrical Units

SI Fundamental Units

Current

Charge

Voltage

Resistance

Ampere A

Coulomb C

Volt V

Ohm W

Watt W

Quantity Unit Symbol

Power

These derived units are

based on fundamental

units from the meter-

kilogram-second system,

hence are called mks

units.

Except for current, all electrical and magnetic units

are derived from the fundamental units.

Current is a fundamental unit.

Unit Symbols

Metric Prefixes

Error, Accuracy, and Precision

Experimental uncertainty is part of all measurements.

Error is the difference between the true or best accepted value and the measured value.

Accuracy (정확도) is an indication of the range of error in a measurement.

Precision (정밀도) is a measure of repeatability or consistency.

Error } Precise,

but not

accurate.

교정(correction)이 필요함

Tolerance (허용오차)

~ 1 %, 5 %, 10 %

Significant Digits

(유효숫자) When reporting a measured value, one uncertain digit may be

retained but other uncertain digits should be discarded. Normally this is the

same number of digits as in the original measurement.

1. Nonzero digits are always considered to be significant.

2. Zeros to the left of the first nonzero digit are never significant.

3. Zeros between nonzero digits are always significant.

4. Zeros to the right of the decimal point for a decimal number are

significant.

5. Zeros to the left of the decimal point with a whole number may or may

not be significant depending on the measurement.

Example: 23.92 has four nonzero digits – they are all significant.

Example: 0.00276 has three zeros to the left of the first nonzero digit.

There are only three significant digits.

Example: 806 has three significant digits.

Example: 9.00 has three significant digits.

Example: 4000 does not have a clear number of significant digits.

Electrical Safety

Safety is always a concern with electrical circuits. Knowing the rules and

maintaining a safe environment is everyone’s job.

• Do not work alone, or when you are drowsy.

• Do not wear conductive jewelry.

• Know the potential hazards of the equipment you are working on; check equipment

and power cords frequently.

• Avoid all contact with energized circuits; even low voltage circuits.

• Maintain a clean workspace.

• Know the location of power shutoff and fire extinguishers.

• Don’t have food or drinks in the laboratory or work area. (컴퓨터 옆에 둔 커피잔은

반드시 엎어진다)

Body resistance ~ 20 kW

Current

Current (I) is the amount of charge (Q) that flows past a point in a unit of time (t).

The defining equation is: Q

It

Current sources are not as common as voltage sources, but they are useful for

production testing. The units shown here include current sources as well as

measurement instruments.

Resistance

Resistance is the opposition to current.

One ohm (1 W) is the resistance if one ampere (1 A) is in a material when one

volt (1 V) is applied.

Conductance is the reciprocal of resistance. 1

GR

Components designed to have a specific amount of resistance are called

resistors.

lR

A

Resistance color-code

Color

Black

Brown

Red

Orange

Yellow

Green

Blue

Violet

Gray

White

Gold

Silver

No band

0

1

2

3

4

5

6

7

8

9

±5%

± 10%

Digit

± 20%

100

101

102

103

104

105

106

107

108

109

10-1

10-2

Multiplier

1% (five band)

5% (four band)

Tolerance

2% (five band)

10% (four band)

Resistance value, first three bands:

First band – 1st digit

Second band – 2nd digit

*Third band – Multiplier (number of

zeros following second digit)

Fourth band - tolerance

* For resistance values less than 10 W, the third band is either gold or silver.

Gold is for a multiplier of 0.1 and silver is for a multiplier of 0.01.

흑 갈 빨 주 노 초 파 보 회 흰

5.1 kW ± 5% 47 W ± 10%

Alphanumeric Labeling

• Two or three digits, and one of the letters R, K, or M are used to identify a resistance value.

• The letter is used to indicate the multiplier, and its position is used to indicate decimal point position.

Variable resistors include the potentiometer and rheostat. The center terminal

of a variable resistor is connected to the wiper.

R

Variable resistor

(potentiometer) 분압기

R

Variable resistor

(rheostat) 가감저항기

Switches

Voltage

The defining equation for voltage is

WV

Q

One volt is the potential difference (voltage) between two points when one

joule of energy is used to move one coulomb of charge from one point to

the other.

Ideally, a voltage source can provide a

constant voltage for any current required

by a circuit.

The IV curve for an ideal voltage source

has a constant voltage for all current.

In practice, ideal sources do not exist,

but they can be closely approximated by

actual sources.

A basic power supply

The DMM

The DMM (Digital Multimeter) is an important multipurpose instrument which

can measure voltage, current, and resistance. Many include other measurement

options.

Voltmeter connection to measure voltage in a simple circuit.

31⁄2-digit DMM illustrates how the resolution changes with

the number of digits in use

A typical analog multimeter

Ohm’s law

The most important fundamental law in electronics is Ohm’s law,

which relates voltage, current, and resistance. Georg Simon Ohm (1787-1854) formulated the equation that

bears his name:

VI

R

If you need to solve for voltage,

Ohm’s law is:

V IR

If you need to solve for resistance,

Ohm’s law is:

VR

I

115 V

V

1 s

1 s

40 mA

10 A

COM

Range

Autorange

Touch/Hold

Fused

OFF V

V

Hz

mV

A

What is the (hot)

resistance of the bulb?

Graph of Current versus Voltage

Notice that the plot of current versus

voltage for a fixed resistor is a line with

a positive slope. What is the resistance

indicated by the graph?

Voltage (V)

Curr

ent

(mA

)

0 10 20 300

2.0

4.0

6.0

8.0

10

What is its conductance?

2.7 kW

0.37 mS

Power Supply

+15 V- + - +5 V 2A

DC Ammeter

+

-

Gnd

V A

The resistor is green-blue brown-gold.

What should the ammeter read?

초-파-갈 ~ 560 W

“흑갈빨주노초파보”

Energy and Power

Energy is closely related to work. Energy is the ability to do work. It is measured

in the same units as work, namely the newton-meter (N-m) or joule (J).

What amount of energy is converted to heat in sliding a box

along a floor for 5 meters if the force to move it is 400 N?

W = Fd = (400 N)(5 m) = 2000 N-m = 2000 J

Power is the rate of doing work. Because it is a rate, a time unit is required.

The unit is the joule per second (J/s), which defines a watt (W).

WP

t

What power is developed if the box in the previous example

is moved in 10 s? 2000 J

10 s

WP

t 200 W

Electrical Energy and Power

In electrical work, the rate energy is dissipated can be determined from any of

three forms of the power formula.

2P I R P VI2V

PR

Together, the three forms are called Watt’s law.

What power is dissipated in a 27 W resistor is the current is 0.135 A?

Given that you know the resistance and current, substitute the

values into P =I 2R.

2

2(0.135 A) 27

0.49 W

P I R

W

Resistor failures

Relative sizes of metal-film resistors

with standard power ratings of 1⁄8 W,

1⁄4 W, 1⁄2 W, and 1 W.

Typical resistors with high power ratings

A triple output power supply

Series circuits

A series circuit is one that has only one current path.

If you break one of the resistors in series circuit, current does not flow at all.

The current everywhere is the same, because there is only one path.

The total resistance of resistors in series is the sum of the individual resistors.

Kirchhoff’s voltage law

The sum of all the voltage drops around a single closed path in a circuit

is equal to the total source voltage in that closed path.

KVL applies to all circuits, but you must apply it to only one closed path.

In a series circuit, this is (of course) the entire circuit.

A mathematical shorthand way of writing KVL is 1

0n

i

i

V

VS

Sum of n voltage drops equals the source

voltage.

Voltage divider

What is the voltage across R2? R1

VSR2+

10 kW

15 kW

20 V2

2 S

T

10 k20 V

25 k

RV V

R

W

W 8.0 V

Notice that 40% of the source voltage

is across R2, which represents 40% of

the total resistance.

VS

VOUT

R2

R1

+

10 kW

20 kW

15 V

What is the largest output voltage available?

5.0 V

Voltage dividers can be set

up for a variable output using

a potentiometer. In the circuit

shown, the output voltage is

variable.

Power in Series Circuits

R1

VSR2+330 W

470 W

20 V

Use the voltage divider rule to find V1 and V2.

Then find the power in R1 and R2 and PT.

Applying the voltage divider rule:

1

470 20 V

800 V

W

W 2

330 20 V

800 V

W

W

The power dissipated by each resistor is:

2

1

11.75 V

470 P

W

2

2

8.25 V

330 P

W

PT = P1 + P2

Voltage measurements

VS

R2

R1

+

10 kW

5.0 kW

12 V

A

B

C

Voltage is relative and is measured with respect to another point in the circuit.

For example, VA means the voltage at point A with

respect to ground (called reference ground). VB means

the voltage at point B with respect to ground. VAB

means the voltage between points A and B.

Q1. What are VA, VB, and VAB for the circuit shown?

VA = 12 V VB = 8 V VAB = 4 V

VS

R2

R1

+

10 kW

5.0 kW

12 V

A

B

C

Q2. What are VA, VB, and VC for the circuit?

VA = 4 V VB = 0 V VC = -8 V

Q3. Has VAB changed from the previous circuit?

Resistors in parallel

Resistors that are connected to the same two points are said to be in

parallel. (병렬 저항)

A parallel circuit is identified by the fact that it has more than

one current path (branch) connected to a common voltage source.

Voltage across parallel branches is the same

Parallel circuit rules

Because all components are connected across the same

voltage source, the voltage across each is the same.

+5.0 V+-

+5.0 V+-

+5.0 V+-

+5.0 V+-

R2 R3R1

VS

680 W 2.2 kW1.5 kW+5.0 V

The total resistance of resistors in parallel is the reciprocal of

the sum of the reciprocals of the individual resistors.

R1 R2

T

1 2

1

1 1R

R R

or

1 2T

1 2

R RR

R R

Connecting resistors in parallel reduces total resistance and

increases total current.

Circuit with n resistors in parallel.

Kirchhoff’s current law

The sum of the currents entering a

node is equal to the sum of the

currents leaving the node.

VS

+R1 R2 R3

680 W 1.5 kW 2.2 kW

5.0 V

Tabulating current, resistance, voltage and power is a useful

way to summarize parameters in a parallel circuit.

IT = I1+I2+I3 =VS/RT

Current divider

When current enters a node (junction) it divides into currents

with values that are inversely proportional to the resistance

values. The most widely used formula for the current divider is the

two-resistor equation. For resistors R1 and R2,

Notice the subscripts. The resistor in the numerator is not the

same as the one for which current is found.

Notice that the larger resistor has the smaller current.

R1 R2

Power in parallel circuits

Power in each resistor can be calculated with any of the standard power

formulas.

2VP

R

As in the series case, the total power is the sum of the powers

dissipated in each resistor.

Combination circuits

Most practical circuits have various combinations of series and

parallel components. You can frequently simplify analysis by

combining series and parallel components.

An important analysis method is to form an equivalent circuit. An

equivalent circuit is one that has characteristics that are electrically

the same as another circuit but is generally simpler

Equivalent circuits

Kirchhoff’s voltage law and Kirchhoff’s current law can be

applied to any circuit, including combination circuits.

Kirchhoff’s Law

R1

R3

470 W

270 W

R2

330 W

VS +10 V

Tabulating current, resistance, voltage and power is a useful way to summarize

parameters. Solve for the unknown quantities in the circuit shown.

Kirchhoff’s laws can be applied as a check on the answer.

Notice that the current in R1 is equal to the sum of the branch currents in R2

and R3.

The sum of the voltages around the outside loop is zero.

Loaded voltage divider

The voltage-divider equation was developed for a

series circuit. Recall that the output voltage is

given by A R1

R2 R3

+

2 22 S S

T 1 2

R RV V V

R R R

A voltage-divider with a resistive load is a combinational circuit and the voltage

divider is said to be loaded. The loading reduces the total resistance from node A

to ground.

A R1

R2 R3

+

Form an equivalent series circuit by combining R2

and R3; then apply the voltage-divider formula to the

equivalent circuit:

2,3 2 32 3 S 2,3

1 2,3 2 3

32

2 3 2 22 S S S

3 2 3 1 21 2 1 2 1 2

2 3 3 3

, R R R

V V V RR R R R

RR

R R R RV V V V

R R R R RR R R R R RR R R R

Stiff voltage divider

A stiff voltage-divider is one in which the

loaded voltage nearly the same as the no-load

voltage.

To accomplish this, the load current must be

small compared to the bleeder current (or RL is

large compared to the divider resistors).

R1

R2 RL

VS

If R1 = R2 = 1.0 kW, what value of RL will make the divider a stiff

voltage divider? What fraction of the unloaded voltage is the loaded

voltage?

RL > 10 R2; RL should be 10 kW or greater. For a 10 kW load,

2 L 2L S S S

1 2 L 1 21 2

3

||0.476

||

R R RV V V V

R R R R RR R

R

This is 95% of

the unloaded

voltage.

Loading effect of a voltmeter

R1

470 kW

R2

47 k0 W

VS +10 V

+ 10 V +4.04 V

+4.04 V

Assume VS = 10 V, but the

meter reads only 4.04 V when

it is across either R1 or R2.

Can you explain what is happening?

All measurements affect the quantity being measured. A

voltmeter has internal resistance, which can change the

resistance of the circuit under test. In this case, a 1 MW

internal resistance of the meter accounts for the readings.

Wheatstone bridge

-

+

R1R3

R4R2

VS

Output

The Wheatstone bridge consists of a

dc voltage source and four resistive

arms forming two voltage dividers.

The output is taken between the

dividers. Frequently, one of the bridge

resistors is adjustable.

When the bridge is balanced, the output voltage is zero, and the

products of resistances in the opposite diagonal arms are equal.

1 4 2 3R R R R

How to prove it:

Thevenin’s theorem

Thevenin’s theorem states that any two-

terminal, resistive circuit can be replaced

with a simple equivalent circuit when

viewed from two output terminals.

Step 0: The original circuit.

Step 1: Calculating the

equivalent output voltage.

Assume an infinite load

between A and B

Step 2: Calculating the

equivalent resistance.

Assume current flow

between A and B

Thevenin’s equivalent

circuit

VTH

RTH

Superposition theorem

The superposition theorem is a way to determine currents and

voltages in a linear circuit that has multiple sources by taking one

source at a time and algebraically summing the results.

+-

-

+

-

+

R1R3

R2

I2

VS2VS1

12 V

2.7 kW 6.8 kW

6.8 kW

18 V

What does the ammeter read for I2?

6.10 kW 1.97 mA 0.98 mA

8.73 kW 2.06 mA 0.58 mA

1.56 mA

Source 1: RT(S1)= I1= I2=

Source 2: RT(S2)= I3= I2=

Both sources I2=

The total current is the algebraic sum.

Capacitor

Capacitor is composed of two conductive plates

separated by an insulating dielectric.

The ability to store charge is the definition of

capacitance.

DielectricConductors

Capacitance is the ratio of charge to voltage ~ Q

CV

[Farad] = [Coulomb]/[Volt]

A capacitor stores energy in the form of an electric field that is

established by the opposite charges on the two plates. The energy of

a charged capacitor is given by the equation

2

2

1CVW

128.85 10 F/m r AC

d

-

C is directly proportional to the relative dielectric constant

and the plate area.

C is inversely proportional to the distance between the plates

Mica capacitor Electrolytic capacitors Variable capacitors

+++

+

VT

TV

TT

47

MF

.022

++++

VTT VTT47 MF

.022

Mica

Foil

Foil

Mica

Foil

Foil

Mica

Foil

When capacitors are connected in series, the total capacitance

is smaller than the smallest one. T

1 2 3 T

1

1 1 1 1...

C

C C C C

When capacitors are connected in parallel, the total capacitance

is the sum of the individual capacitors. T 1 2 3 ... nC C C C C

For an RC circuit, the time constant for charging or

discharging is t = RC [seconds] ~ exponential curve

100%

80%

60%

40%

20%

00 1t 2t 3t 4t 5t

99%98%

95%

86%

63%

37%

14%

5%2% 1%

Number of time constants

Perc

ent o

f final v

alu

e

C

R

C

R

Capacitive reactance

Capacitive reactance is the opposition to ac by a capacitor. 1 1

2πCX

fC C

The reactance of a 0.047 mF capacitor when a frequency of 15 kHz is applied is 226 W

When capacitors are in series, the total reactance is

the sum of the individual reactances. C( ) C1 C2 C3 Ctot nX X X X X

When capacitors are in parallel, the total reactance is

the reciprocal of the sum of the reciprocals of the

individual reactances.

C( )

C1 C2 C3 C

1

1 1 1 1tot

n

X

X X X X

Capacitive Voltage Divider

Vout

1000 pF

0.01 µF

C2

C1

1.0 V

f = 33 kHz

1

1

1 14.82 k

2π 2π 33 kHz 1000 pFCX

fC W

2

2

1 1482

2π 2π 33 kHz 0.01 μFCX

fC W

( ) 1 2 5.30 kC tot C CX X X W

2

( )

482 1.0 V

5.30 k

Cout s

C tot

XV V

X

W W

When a signal is applied to an RC circuit, and the

output is taken across the capacitor as shown, the

circuit acts as a low-pass filter.

Low-Pass Filters

10 V dc

VoutVin

100 W

1 Fm

10 V dc

0

10 V dc

0

As the frequency increases, the output amplitude decreases.

1ƒ = 1 kHz

8.46 V rms10 V rms W100

Fm

1.57 V rms

10 V rms

1ƒ = 10 kHz

W100

Fm

Vout (V)

9.98

8.46

1.57

0.79

0.1 1 10 20 100f (kHz)

9

8

7

6

5

4

3

2

1

0.79 V rms

10 V rms

1ƒ = 20 kHz

W100

Fm

Reversing the components, and taking the output across the

resistor as shown, the circuit acts as a high-pass filter.

As the frequency increases, the output amplitude also

increases.

Vout (V)

f (kHz)

9.87

5.32

0.6300.01 0.1 1

10

9

8

7

6

5

4

3

2

1

10

Vin

10 V dc

0

Vout

0 V dc10 V dc 100 W1 Fm

ƒ = 100 Hz

0.63 V rms10 V rms

100 W1 Fm

ƒ = 1 kHz

5.32 V rms10 V rms

100 W1 Fm

ƒ = 10 kHz

9.87 V rms10 V rms

100 W1 Fm

High-Pass Filters

Inductor

When a length of wire is formed into a coil, it

becomes a basic inductor. When there is current in

the inductor, a three-dimensional magnetic field is

created. [henry]

Faraday’s law The amount of voltage induced in a coil is directly

proportional to the rate of change of the magnetic

field with respect to the coil.

NS

V- +

Lenz’s law

When the current through a coil changes and an induced voltage is created as a result of the

changing magnetic field, the direction of the induced voltage is such that it always opposes

the change in the current.

Practical inductors

Actual inductors have winding resistance (RW) due to the resistance of

the wire and winding capacitance (CW) between turns. An equivalent

circuit for a practical inductor including these effects is shown: L

RW

CW

0

2

0 0

/

total

B ni Ni

NBA Li

NBAL NA n n A

i

m m

m m

Series inductors

When inductors are connected in series, the total

inductance is the sum of the individual inductors. T 1 2 3 ... nL L L L L

Parallel inductors

When inductors are connected in parallel, the total

inductance is smaller than the smallest one.

T

1 2 3 T

1

1 1 1 1...

L

L L L L

For an RL circuit, the time constant is τL

R

i =IF + (Ii - IF)e-Rt/L

IF = final value of current

Ii = initial value of current

i = instantaneous value of current

Inductive reactance is the opposition to ac by an

inductor. The equation for inductive reactance is

R

L

t0

Current after switch closure

t0

Inductor voltage after switch closure

Vinitial

Ifinal

Inductive reactance

Inductive reactance is the opposition to ac by an inductor. 2πLX fL L

When inductors are in series, the total reactance is

the sum of the individual reactances. That is, L( ) L1 L2 L3 Ltot nX X X X X

When inductors are in parallel, the total reactance is

the reciprocal of the sum of the reciprocals of the

individual reactances.

L( )

L1 L2 L3 L

1

1 1 1 1tot

n

X

X X X X