Lecture 1, 2 Premble and SignalsSystems 0921 Peng1

7/29/2019 Lecture 1, 2 Premble and SignalsSystems 0921 Peng1

1/20

Lecture Notes on Basic Electronicsfor Students in Computer Science

John Kar-kin Zao and Wen-Hsiao Peng

Department of Computer Science, National Chiao-Tung Univeristy

1001 Ta-Hsueh Rd., 30010 HsinChu, Taiwan

August 2006


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Contents

1 Preamble 1

1.1 Goal of This Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Content of This Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Relationship with Other Disciplines . . . . . . . . . . . . . . . . . . . . . . 1

I System and Circuit Analysis 2

2 Signals and Systems 3

2.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Types of Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3 Axiomatic Properties of Systems . . . . . . . . . . . . . . . . . . . . . . . . 5

2.4 Time-Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4.1 Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4.2 Step Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4.3 Sinusoidal Response . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4.4 Initial Value/Driving Free/Natural Response . . . . . . . . . . . . . 12

2.4.5 Transient Response . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4.6 Steady-State Response . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.5 Frequency-Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5.1 Phasor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5.2 Spectrum and Fourier Transform . . . . . . . . . . . . . . . . . . . 13

2.5.3 System Transfer Function Hs() . . . . . . . . . . . . . . . . . . . . 14

2.5.4 Time Domain versus Frequency Domain . . . . . . . . . . . . . . . 15

3 Electrical Circuits 16

3.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Circuit Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3 Circuit Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.4 Network Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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CONTENTS

3.4.1 One-Port Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4.2 Two-Port Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.5 Laplace Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.6 System Transfer Function in Time and Laplace Domains . . . . . . . . . . 26

3.7 Bode Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

II Devices Diode, BJT, MOSFETs 42

4 Semiconductor 43

4.1 Intrinsic Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2 Doped Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5 Diode 485.1 Physical Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.1.1 The pn Junction Under Open Circuit . . . . . . . . . . . . . . . . . 48

5.1.2 The pn Junction Under Reverse-Bias . . . . . . . . . . . . . . . . . 50

5.1.3 The pn Junction in the Breakdown Region . . . . . . . . . . . . . . 52

5.1.4 The pn Junction Under Forward Bias Conditions . . . . . . . . . . 52

5.2 Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.2.1 Forward Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.2.2 Reverse Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.2.3 Breakdown Region . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.3.1 Large Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.3.2 Small Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.3.3 Circuit Analysis with Diodes . . . . . . . . . . . . . . . . . . . . . . 62

5.4 Special Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.4.1 Zener diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.4.2 Switching Controlled Rectifier (SCR) . . . . . . . . . . . . . . . . . 655.4.3 LED/Varactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.5.1 Regulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.5.2 Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.5.3 Limiting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.5.4 Clamping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.5.5 Digital Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6 MOS Field-Effect Transistors (MOSFETs) 74

6.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

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CONTENTS

6.1.1 Physical Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.2 Characteristics (NMOS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.2.1 Regions of Operations . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.2.2 Saturation (vGS > Vt, vDS > vGS Vt) . . . . . . . . . . . . . . . . 78

6.2.3 Cut-off Region (vGS < Vt) . . . . . . . . . . . . . . . . . . . . . . . 79

6.2.4 Body Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80


6.3.2 Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . 80

7 Bipolar Junction Transistor (BJT) 82

7.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.1.1 PNP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.1.2 NPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.2 Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.2.1 Forward Biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.2.2 Reverse Biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.2.3 Early Effect and Voltage . . . . . . . . . . . . . . . . . . . . . . . . 82

7.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82


7.3.2 Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . 82

8 Summary and Comparison 83

III Analog Circuits 84

9 Amplifier 85

10 Single Transistor Amplifier with MOSFET 86

10.1 Common Source Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

10.1.1 Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

10.1.2 Time Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 86

10.1.3 Frequency Domain Analysis . . . . . . . . . . . . . . . . . . . . . . 86

10.2 Common Drain Voltage Follower . . . . . . . . . . . . . . . . . . . . . . . . 87

10.3 Common Gate Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

10.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

10.4.1 Differential Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . 87

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CONTENTS

11 Single Transistor Amplifier with BJT 88

11.1 Common Emitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

11.1.1 Time Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 88

11.1.2 Frequency Domain Analysis . . . . . . . . . . . . . . . . . . . . . . 88

11.2 Common Collector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

11.3 Common Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

11.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

11.4.1 Current Mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

11.4.2 Power Amplifier with Active Load . . . . . . . . . . . . . . . . . . . 89

12 Operational Amplifier (OP-AMP) 90

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1Preamble

1.1 Goal of This Course

Analysis and design of electronic circuits.

1.2 Content of This Course

Electric circuit (Passive Circuit ) analysis.

Only containing Resistor (R), Capacitor (C), and Inductor (L).

No signal amplification.

Electronic circuit (Active Circuit ) analysis.

Containing transistor.

Single transistor circuit. Signal amplification.

Operational amplifier and application.

1.3 Relationship with Other Disciplines

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Part I

System and Circuit Analysis

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2Signals and Systems

2.1 Basic Concepts

Definition 2.1 System stands for the transformation of signal from one to another. It

can be viewed as a process in which input signals are transformed by the system or causethe system to respond in some way, resulting in other signals as outputs.

Formalization

Systems

Abstraction

Decomposition

Analysis

Composition

Synthesis

Objects

Systems

Models

Components

System characteristics

/brhaviors

Figure 2.1: System from engineering perspective.

Approach Abstraction

Representing a real object by its special characteristics; that is, the relation

between its inputs and outputs, which becomes a system.

Decomposition

Dividing a system into several smaller systems (components) and studying

them to understand the large system.

Composition

Putting several systems together to form a larger system and studying it. Model

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Sec 2.2. Types of Systems

LTI SystemsInputs Outputs

States

Relative

StatesInput Output

Perspectives

Time domain.

Frequency domain.

2.2 Types of Systems

Temporal characteristic

Continuous-Time Systems Inputs/outputs of the systems are functions defined at continuous time.

Continuous-TimeSystem

Input x(t) Output y(t)

t

Magnitude

Figure 2.2: Continuous-time systems.

Discrete-Time Systems

Inputs/outputs of the systems are functions defined at discrete time.

Magnitude

Analog systems

Inputs/outputs of the system have continuously varying values.

Digital systems

Inputs/outputs of the system have discrete values.

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Lecture 2. Signals and Systems

Discrete-TimeSystem

Input x[n] Output y[n]

t

Magnitude

0 1 2 3 4 5

6 7 8 9

Figure 2.3: Discrete-time systems.

Digital System

Input x(t) Output y(t)

t

Magnitude

Figure 2.4: Digital system.

2.3 Axiomatic Properties of Systems

Linearity

If an input consists of the weighted sum of several signals, then the output is

the superposition of the responses of the system to each of those signals.

y1(t) = H{x1(t)}

y2(t) = H{x2(t)} (2.1)a y1(t) + b y2(t) = H{a x1(t) + b x2(t)}

Time-Invariant

The behavior and characteristics of the system are fixed over time.

For example, the magnitudes of resistors and capacitors of a circuit are un-

changed over time.

y(t) = H{x(t)}

y(t ) = H{x(t )} (2.2)

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Sec 2.4. Time-Domain Analysis

Systemx(t)

y(t)

Inverse

System

x(t)

Figure 2.5: Inverse system.

Causality

The output of the system depends only on the inputs at the present time and

in the past.

For example, y(t) =

Zt0

x()d.

Invertability

Distinct inputs of the system lead to distinct outputs, and an inverse system

exists.

For example, a system which is y(t) = 2x(t), for which the inverse system is

y(t) = 12

x(t).

Stability

If the input of the system is bounded, then the output must be bounded.

2.4 Time-Domain Analysis

Definition 2.2 The analysis of a LTI system that is based on the relationship between

time-varying inputs and their corresponding time-varying outputs.

Inputs/outputs are time functions (waveforms).

2.4.1 Impulse Response

Output of the system with a fictitious input of Direc-Delta function (t).

For LTI systems, the system characteristic in time domain is the system impulse response.

Direc-Delta function (t).

(t) =

(0 if t 6= 0

if t = 0. (2.3)

ZTT

(t)dt = 1, T > 0. (2.4)

Signal sampling using Direc-Delta function.

x() =

Z

x(t)(t )dt (2.5)

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t

Magnitude

-T/2 T/2

1/T

t0

Magnitude

Figure 2.6: Direc-Delta function

t

)(tx

2

T 2

T+

T

1 )(x

)( t

)(1

)(lim)()(0

xT

T

xdtttxT

==

Figure 2.7: Sampling using Direc-Delta function.

Signal reconstruction: any real time-functions can be represented by using theintegrals of Delta functions as in Eq. (2.6).

x(t) =

Z

x()( t)d (2.6)

Magnitude

t

1

)()( 11 tx

)(tx

)()( 22 tx

2

Figure 2.8: A time function represented by a set of delta functions.

Convolution

Outputs of the LTI system is the convolution of the input and the system

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impulse response.

y(t) = x(t) h(t) =

Z

x()h(t )d (2.7)

Magnitude

t

1

)()( 11 tx

)(tx

)()( 22 tx

2

LTISystem

)(th

0

Magnitude

t

Impulse Response

t

)()( 11 thx

Time-Invariant

1

1

2

Linearity

t

1 2

)(ty

)()( 22 thx

Figure 2.9: Continuous time convolution operation.

2.4.2 Step Response

Output of the system w.r.t. an input x(t) of step function.

0

t

)t(

1

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Magnitude

n

][]0[ nx

][nx

]2[]2[ nx

LTISystem

][nh

0

Magnitude

n

Impulse Response

43

21

1 2 3

0

]1[]1[ nx

]3[]3[ nx

1 2 3

4

54

3

0

1612

84

1 2 3

][]0[][]0[ nhxnx

0 1 2 3 4

]1[]1[]1[]1[ nhxnx

2015

105

]2[]2[]2[]2[ nhxnx

0 1 2 3 4 5

1612

84

0 1 2 3 4 5 6

129

63 ]3[]3[]3[]3[ nhxnx

0 1 2 3 4 5 6

16

=k

knhkxny ][][][

32

3938

22

10 3

n

Output

Input

n

n

n

n

Figure 2.10: Discrete time convolution operation.

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x(t) = u(t) =

(0 if t < 0

1 if t 0. (2.8)

du(t)

dt = (t). (2.9)

2.4.3 Sinusoidal Response

Output of the system w.r.t. sinusoidal function input x(t).

x(t) = cos(2t) with = 2f (2.10)

f is frequency.

= 2f is the angular frequency. T = 1

fis period.

52.50-2.5-5

1

0.5

0

-0.5

-1

t

x(t)=cos(t)

t

x(t)=cos(t)

Figure 2.11: Sinusoidal waveform.

For a real LTI system with a sinusoidal input function, the output is also a

sinusoidal function but with changes in both magnitude and phase.

x(t) = cos th(t) y(t) = kH()k cos(t +]H()) ,

where H() =Z

h()ej

d = kH()k ej]H()

(2.11)

Advanced Topics

Proof.

x(t) = cos th(t) y(t) = kH()k cos(t +]H())

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y(t) = x(t) h(t)

=

Z

x()h(t )d

= Z

cos()h(t )d

=1

2

Z

(ej + ej)h(t )d

=1

2

Z

ejh(t )d +1

2

Z

ejh(t )d

By defining 0

= t , the equation above can be written as follows:

y(t) =1

2 Z

ej(t0

)h(0

)d0 +1

2 Z

ej(t0)h(0)d0

Define H() =

Z

ej0

h(0

)d0 = kH()k ej]H() as a complex function of . Its

complex conjugate is H() =

Z

ej0

h

(0

)d0 = kH()k ej]H().Since h(t) is a real

function, h

(0

) = h(0

). Thus, y(t) can be formulized as follows:

y(t) =1

2ejt

Z

ej0

h(0

)d0 +1

2ejt

Z

ej0

h(0)d0

=1

2ejt kH()k ej]H() +

1

2ejt kH()k ej]H()

= kH()k cos(t +]H())

More generally, it is the output of the system w.r.t. complex exponential function

input x(t).

x(t) = ejt

= cos(t) +j sin(t) (2.12)

Complex exponential function ejt is the eigenfunction of any LTI systems.

x(t) = ejth(t) y(t) = H()ejt (2.13)

= kH()k cos(t +]H()) +j kH()k sin(t +]H())

H() =

Z

h(t)ejtdt.

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Sec 2.5. Frequency-Domain Analysis

LTI

System

)(th

)(tx

= dthxty )()()(

Input time function Output time function

LTI

System

)(th

tjetx =)( d tethHety tjtj === )()(,)(

LTI

System

)(th

tjeXtx )()( = )()(',')( XHety tj ==

Figure 2.12: The output of a LTI system with exponential complex function.

2.4.4 Initial Value/Driving Free/Natural Response

Output y(t) w.r.t. null input x(t) = 0 and possibly non-zero initial system states.

Equivalently, it is solution of Homogeneous System Equation.

2.4.5 Transient Response

The part of system output that will disappear (die down) as time progress.

yT(t) 0 as t . (2.14)

For Linear Time-Invariant (LTI) circuits, yT(t) = impulse response (with nec-

essary scaling and time-shifting).

2.4.6 Steady-State Response

The part of system output that will remain after transient response dies down.

yS(t) = y(t) yT(t). (2.15)

For Linear Time-Invariant (LTI) circuits, yT(t) = impulse response (with nec-

essary scaling and time-shifting).

2.5 Frequency-Domain Analysis

Definition 2.3 Determination of system output(s) w.r.t complex sinusoidal inputs at dif-ferent frequencies and with specific initial system state. Results are often displayed along

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frequency axis or expression as functions of angular frequency ().

Input X and Output Y are complex functions of angular frequency.

LTI Systems

Output

States

)(x )(y Input

2.5.1 Phasor

An electrical-engineering representation of sinusoidal signals in frequency domain.

A constant complex number that encodes the magnitude and the phase of thesinusoidal signals.

Example 2.4 Given sinusoidal signal x(t) = Kcos(t + ),Phasor X = Kej, whereX = K and phase]X = . x(t) =


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Sec 2.5. Frequency-Domain Analysis

X() is a complex function of angular frequency , which expresses the values

of the signal phasor in different frequencies.

X() = kX()k ej]X(). (2.17)

kX()k is called magnitude spectrum, specifying the magnitude for differ-

ent sinusoidal components.

]X() is called phase spectrum, specifying the phase for different sinu-

soidal components.

X() can be obtained by taking the Fourier Transform of x(t).

Definition 2.5 Givenf(t), its Fourier Transform, which is defined as follows, is a com-

plex function of the angular frequency .

F() =[f(t)] =

Z

f(t)ejtdt. (2.18)

Fourier Transform of f(t) is the projection of f(t) on the basis functions ejt.

Definition 2.6 Correspondingly, the Inverse Fourier Transform is as follows:

f(t) =1[F()] =1

2 Z

F()ejtd. (2.19)

2.5.3 System Transfer Function Hs()

A ratio between the spectra of input and output signals of a linear time-invariant

circuit.

It is also known as the frequency response of a LTI system.

Hs() Y()

X()

= kY()k ej]Y()

kX()k ej]X()

=kY()k

kX()kej(]Y()]X()) (2.20)

= kHs()k ej]Hs()

kHs()k = kY()k / kX()k is the magnitude response of the system.

]Hs() = ]Y()]X() is the phase response of the system.

From Eq. (2.13) and Eq. (2.16), each sinusoidal component X()ejt produces an

output signal ofY()ejt = X()H()ejt, as shown in Figure 2.13. Thus, y(t) can

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LTISystem

)(th

)(tx

= dthxty )()()(

LTISystem

)(th

deXtx tj= )(21

)(

deHXty tj= )()(21

)(

LTI

System

)(H

)(X )()()( XHY =

Input time function Output time function

Input Spectrum Output Spectrum

Time-Domain Analysis

Frequency-Domain Analysis

Figure 2.13: Relationship between time-domain analysis and frequency-domain analysis.

be written as follows.

y(t) =1

2 Z

Y()ejtd =1

2 Z

X()H()ejtd. (2.21)

The system transfer function Hs() = H(), which is the Fourier Transform of the

system impulse response h(t).

2.5.4 Time Domain versus Frequency Domain

The frequency response of a LTI system is the Fourier transform of the system

impulse response.

H() = = {h(t)} (2.22)

The convolution of two signals in time domain is equivalent to the multiplication of

their representations in frequency domain.

y(t) = x(t) h(t)= H()X() (2.23)

Documents

Lecture 1, 2 Premble and SignalsSystems 0921 Peng1