INHA Univ.
전자회로 1
Chapter 1:
Introduction to
Electronics
인하대학교
정보통신공학부
2008년 2학기
Microelectronic Circuits Ch. 1 Introduction
1
Course Administration

Professor: 정 덕진





INHA Univ.
Office: Hi-Tech 빌딩 510호
TEL: (032) 860-7435
Email: djchung@inha.ac.kr
http://vlsi.inha.ac.kr/
Class Web Site: Cyber-class in Inha Univ.
Microelectronic Circuits Ch. 1 Introduction
2
Text and Reference books

INHA Univ.
Text:
 Microelectronics Circuits (5th Edition), Sedra/Smith
 Class notes on the web site
– Cyber-class in Inha Univ.

Reference:
Microelectronic Circuits Ch. 1 Introduction
3
Course Contents
INHA Univ.
Part I. Devices and Basic Circuits
Ch.1. Introduction to Electronics
•
Definition about signal / Analog-digital / Continuous-Discrete 등
Ch 2. Operational Amplifiers (OP-AMP)
•
•
Ideal OP-AMP
Practical OP-AMP 및 연결방법
Ch. 3. Diodes
•
•
Ideal Diode
Practical Diode condition 및 회로 / 특수 Diode / Zener Diode
Ch. 4. MOS Field-Effect Transistors (MOSFETs)
•
물리적인 특성, MOSFET circuits, amplifiers
Ch. 5. Bipolar Junction Transistors (BJTs)
•
•
•
물리적인 특성, npn/ pnp Tr., BJT circuits,
small-signal operation and models,
BJT amplifiers
Microelectronic Circuits Ch. 1 Introduction
4
Course Contents
INHA Univ.
Part II, Analog and Digital Integrated Circuits
Ch. 6. Single-Stage Integrated-Circuit amplifiers
Ch. 7. Differential and Multistage Amplifiers
Ch. 8. Feedback
Ch. 9. Operational-Amplifier and Data-Converter Circuits
Ch. 10. Digital CMOS Logic Circuits
Microelectronic Circuits Ch. 1 Introduction
5
INHA Univ.
Grading Information

Grade determinants
 Quiz/Homeworks
~ 10%
– Will be scheduled later.
 Exam-2
~ 25%
– Will be scheduled later
 Final Exam
~ 25%
– Will be scheduled later
 Projects
~ 30%
– Due at the beginning of class on the due date (No extensions).
 출석
Microelectronic Circuits Ch. 1 Introduction
~ 10%
6
INHA Univ.
Chapter 1
Introduction to Electronics
Microelectronic Circuits Ch. 1 Introduction
7
Introduction
INHA Univ.

Microelectronics: 작은 실리콘 (실리콘 칩)에 수백만개의 회로를
만들수 있는 능력을 가진 Integrated Circuit (IC) technology를
말한다.
 Microelectronics circuit example: Microprocessor
– Intel Pentium, AMD Athlon, DRAM, CDMA modem chip,
ASIC, FPGA etc.

Chapter 1 에서 배울점.
 Basic concept와 terminology를 이해하며, 주로 단일소자를
이용한 signal amplification (증폭)에 중점을 둔다.
 Linear amplifier에 대한 모델들을 이해하고, 그 모델을 이용해서
실질적인 amplifier circuits (증폭회로)들을 설계하고 분석한다.
Microelectronic Circuits Ch. 1 Introduction
8
The Transistor Revolution
INHA Univ.
First transistor
Bell Labs, 1948
Microelectronic Circuits Ch. 1 Introduction
9
The First Integrated Circuits
INHA Univ.
Bipolar logic
1960’s
ECL 3-input Gate
Motorola 1966
Microelectronic Circuits Ch. 1 Introduction
10
Intel 4004 Micro-Processor
INHA Univ.
• First microprocessor
designed In 1971
• 1000 transistors
• 1 MHz operation
Microelectronic Circuits Ch. 1 Introduction
11
Intel Pentium (IV) Microprocessor
INHA Univ.
• Released in 2000
• 42 million transistors
• 0.18 micron tech.
• > 1GHz
Microelectronic Circuits Ch. 1 Introduction
12
INHA Univ.
Silicon Wafer
Single die
Wafer
Microelectronic Circuits Ch. 1 Introduction
13
INHA Univ.
Transistor Counts
1 Billion
Transistors
K
1,000,000
100,000
10,000
1,000
i486
i386
80286
100
10
Pentium® III
Pentium® II
Pentium® Pro
Pentium®
8086
Source: Intel
1
1975 1980 1985 1990 1995 2000 2005 2010
Projected
Courtesy, Intel
Microelectronic Circuits Ch. 1 Introduction
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INHA Univ.
Design Abstraction Levels
SYSTEM
MODULE
+
GATE
CIRCUIT
DEVICE
G
S
n+
Microelectronic Circuits Ch. 1 Introduction
D
n+
15
Signals

INHA Univ.
Signals: 정보를 포함한 신호
 signal processing : 정보를 추출, 가공, 전송하는 과정
– Acoustic signal
– Electrical signal
– Optical signal
여기서는 주로 Electrical signal을 취급한다.
Microelectronic Circuits Ch. 1 Introduction
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INHA Univ.
1.1 Signals

In Fig.1.1(a), Signal is represented by a voltage Vs(t)
having a source resistance Rs.
Rs  0
Rs  
Figure 1.1 Two alternative representations of a signal source:
(a) the Thévenin form, and (b) the Norton form.
Microelectronic Circuits Ch. 1 Introduction
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INHA Univ.
Vs(t) = Rs is(t)
Figure 1.2 An arbitrary voltage signal vs(t).
Microelectronic Circuits Ch. 1 Introduction
18
1.2 Frequency Spectrum of Signals
INHA Univ.
1) Signal 의 표시방법
1)-1. Time Domain
Va(t) = Va sin t
Figure 1.3 Sine-wave voltage signal of amplitude Figure 1.4 A symmetrical squareVa and frequency f = 1/T Hz.
wave signal of amplitude V.
The angular frequency  = 2f rad/s.
Microelectronic Circuits Ch. 1 Introduction
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INHA Univ.
1)-2. Frequency domain
• Fourier series와 Fourier transform에
의하여 frequency spectrum이라는
신호표현이 얻어진다.
• 모든 signal은 Fourier transform에 의해
서 주파수 영역으로 구분 가능
Figure 1.5 The frequency spectrum (also known as the line
spectrum) of the periodic square wave of Fig. 1.4.
Microelectronic Circuits Ch. 1 Introduction
20
2)-2. Frequency domain
INHA Univ.
a0  
t
t
  an cos 2n  bn sin 2n 
2 n1
T
T
예)
2
2nt
an  0T f (t ) cos
dt
T
T
2
2nt
bn  0T f (t ) sin
dt
T
T
2
w

즉. Fig. 1-4의 파형은 ( 0
)
T
4v
1
1
v(t )  (sin wot  sin 3wot  sin 5wot    )

3
5
1
sin wot : fundamental frequency
sin 3wot : 3rd harmonic frequency
3
1
sin 5wot : 5th harmonic frequency
5
실효치(Root-Mean-Square, rms)로써 표시되기도 하며 sine wave시 peak
치의
1
이다
2
audio band : 20 ㎐~ 20 ㎑ (20 ㎑ 이상은 사람의 귀에서 인식 불가능)
Microelectronic Circuits Ch. 1 Introduction
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INHA Univ.

Unlike the case of periodic signals, where the spectrum
consists of discrete frequencies (at 0 and its
harmonics), the spectrum of nonperiodic signal
contains in general all possible frequencies, that is
continuous function of frequencies.
Figure 1.6 The frequency spectrum of an arbitrary
waveform such as that in Fig. 1.2.
Microelectronic Circuits Ch. 1 Introduction
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1.3 Analog and Digital Signals

특성에 의한 분류
 Analog signal : Fig. 1.2
 Digital signal :

형태에 의한 분류
 Continuous-time signal :
 Discrete-time signal :

Digital signal의 장점
 noise에 의한 문제를 쉽게 치유가능
 저전력으로 전송가능
Microelectronic Circuits Ch. 1 Introduction
INHA Univ.
23
INHA Univ.
Analog Signal

Sampling: At each intervals along the time axis we
have marked the time instants t0, t1, t2, and so on. At
each of these time instants the magnitude of the
signal is measured.
Continuous-time signal
Discrete-time signal
Figure 1.7 Sampling the continuous-time analog signal in (a) results in the
discrete-time signal in (b).
Microelectronic Circuits Ch. 1 Introduction
24
Digital Signal



INHA Univ.
After quantized, discretized, or digitized, the resulting digital signal is
a sequence of numbers that represent the magnitude of the
successive signal samples.
Binary number system results in the simplest possible digital signals
and circuits.
In binary system, each digit in the number takes on one of only two
possible values, denoted 0 and 1.
Figure 1.8 Variation of a particular binary digital signal with time.
From http://www.amd.com
Microelectronic Circuits Ch. 1 Introduction
25
Analog-to-Digital (A/D) Converter

INHA Univ.
A/D converter accepts at its input the samples of an
analog signal and provides for each input sample the
corresponding N-bit digital representation at its N
output terminals.
Microelectronic Circuits Ch. 1 Introduction
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INHA Univ.
1.4 Amplifiers

Signal Amplification
 Signal을 증폭할 때 선형성이 유지되어야 하며,
선형성이 유지되지 않으면 Nonlinear Distortion
이 발생.
vo (t )  Avi (t )
Transfer
characteristic
of a linear
amplifier
A : Amplifier gain, 만약 A=const. 이면 linear Amplifier 라고 부른다.
Voltage gain (Av) ≡
vo
vi
, current gain (Ai) ≡
io
,
ii
power gain (Ap) ≡
PL voio

Pi viii
∴ Ap = Av Ai
Microelectronic Circuits Ch. 1 Introduction
27
INHA Univ.

Expressing Gain in Decibels
 Voltage gain in decibels = 20 log |Av| dB
 Current gain in decibels = 20 log |Ai| dB
 Power gain in decibels = 10 log |Ap| dB


A negative gain Av means that there is a 180º phase difference
between input and output signals.
Amplifier Power Supplies
DC power
Pdc  V1I1  V2 I 2
Pdc  Pi  PL  Pdissipated

PL
 100 |
Pdc
Pi  0
: amplifier efficiency
V+ = 10V, V- = -10V
Vo = Vpeak, RL=1K
Microelectronic Circuits Ch. 1 Introduction
28

Example 1.1
INHA Univ.
 V+ = 10V, V- = -10V
 Vo = Vpeak, RL=1K,
I1  I 2  9.5mA
Av 

vo 9V peak

9
Vi 1V peak
Av  20 log10 9  19.1dB
vo 9V peak

 9mApeak
RL
1k
Io 
PL  Vorms I orms 
AP 
Vi  1Vpeak
Ii  0.1mA

Ai 

Ii
9 9
 40.5mW
2 2
PL 40.5

 810W / W
PI 0.05
Io

9
 90
0.1
Ai  20 log 90  39.1dB
PI  Virms I irms 
1 0.1
 0.05mW
2 2
AP  10 log 80  29.1dB
Pdc  10  9.5  10  9.5  190mW
Pdissipated  Pdc  PI  PL  190  0.05  40.5  149mW

PL
 100  21.3%
Pdc
Microelectronic Circuits Ch. 1 Introduction
29
INHA Univ.

Amplifier Saturation

The output voltage cannot
exceed a specified positive
limit and cannot decrease
below a specified negative
limit.
 L+ : Positive saturation level
 L-: Negative saturation level

Note that the peaks of the
larger waveform have been
clipped off because of
amplifier saturation.
Figure 1.13 An amplifier transfer characteristic that is linear except for output saturation.
Microelectronic Circuits Ch. 1 Introduction
30
Nonlinear Transfer Characteristic and Biasing
INHA Univ.
Figure 1.14 (a) An amplifier transfer characteristic that shows considerable nonlinearity.
(b) To obtain linear operation the amplifier is biased as shown, and the signal amplitude is
kept small. Observe that this amplifier is operated from a single power supply, VDD.
•
In practical amplifiers the transfer characteristic may exhibit nonlinearities of various
magnitude.
• The transfer characteristic is nonlinear and, because of the single-supply operation, is not
centered around origin.
• Biasing: signal의 전부분이 증폭될 수 있도록 DC voltage를 부가하여 중심점을 옮기는 것.
• See page.19.
Microelectronic Circuits Ch. 1 Introduction
31

Example 1.2
 v 10 10 e
11
INHA Univ.
( for v  0V and v  0.3V )
40 vI
0
I
O
 Find the limits L- and L+ and the corresponding v
 Find the VI that results in VO = 5V and the voltage gain at the corresponding
operating point
I
1) L- = 0.3V, v = 0.3V in Eq. (1.10)
v = 0.690V
O
I
2) L+ = 10 10
11
10V
3) VI = 0.673V by substituting v = 5V
in Eq. (1.10)
O
4) Av = -200 V/V by evaluating the
derivative dv / dv at v = 0.673V
O
I
I
Figure 1.15 A sketch of the transfer characteristic of
the amplifier of Example 1.2. Note that this amplifier
is inverting (i.e., with a gain that is negative).
Microelectronic Circuits Ch. 1 Introduction
32
Symbol Convention






INHA Univ.
IA: Direct-current (dc) current
VC: Direct-current (dc) Voltage
iA(t): Instantaneous current (Total current)
iC(t): Incremental current signal
VDD: Power-supply (dc) voltage
IDD: dc current drawn from the power supply
Microelectronic Circuits Ch. 1 Introduction
33
INHA Univ.
Circuit Models for Amplifiers

Circuit Model의 4가지 유형
Ro
Vi
Ri
Ri
A vo V i
Voltage Amplifier (Avo : unitless)
Ri
G m Vi
A isii
Ro
Current Amplifier (Ai : unitless)
ii
io
Vi
ii
Ro
Transconductance Amplifier
(Gm : conductance)
Microelectronic Circuits Ch. 1 Introduction
Ro
Ri
R m ii
Vo
Resistance Amplifier
(Rm : Resistance)
34
1.5.1 Voltage Amplifiers
INHA Univ.
Figure 1.17 (a) Circuit model for the voltage amplifier. (b) The voltage amplifier with input
signal source and load.
Microelectronic Circuits Ch. 1 Introduction
35
INHA Univ.
The Four Amplifier Types
ii
Ro
Vi
Ri
Ri
A vo V i
Voltage Amplifier (Avo : unitless)
Ri
G m Vi
Ro
Current Amplifier (Ai : unitless)
ii
io
Vi
A isii
Ro
Transconductance Amplifier
(Gm : conductance)
Microelectronic Circuits Ch. 1 Introduction
Ro
Ri
R m ii
Vo
Resistance Amplifier
(Rm : Resistance)
36
INHA Univ.
Frequency Response of Amplifiers


Amplifier frequency response: 다른 주파수들을 가지고 있는 Input
sinusoids에 대한 응답에 관한 특성.
Measuring the Amplifier Frequency Response
Figure 1.20 Measuring the frequency response of a linear amplifier. At the test frequency v, the
amplifier gain is characterized by its magnitude (Vo/Vi) and phase .
 Fig. 1.20 depicts a linear amplifier fed at its input with a sine-wave signal of
amplitude Vi and frequency 
 Whenever a sine-wave signal is applied to a linear circuit, the resulting output is
sinusoidal with the same frequency as the input.
 Linear Amplifier에서는 gain이 일정하나 일반적인 Amplifier에서는
frequency 에 따라 증폭율이 달라진다.
Microelectronic Circuits Ch. 1 Introduction
37
Measuring the Amplifier Frequency Response
INHA Univ.
Figure 1.20 Measuring the frequency response of a linear amplifier. At the test frequency , the
amplifier gain is characterized by its magnitude (Vo/Vi) and phase .



Magnitude of the amplifier gain (or transmission), or transfer function
 |T()| = Vo/Vi
Phase of the amplifier transmission:  T() = 
Amplifier의 Frequency response는 amplitude response와 phase response를
구성한다
 Amplitude response: gain magnitude |T()| versus frequency
 Phase response: phase angle  T() versus frequency
Microelectronic Circuits Ch. 1 Introduction
38
INHA Univ.
1.6.2 Amplifier Bandwidth
Figure 1.21 Typical magnitude response of an amplifier. |T()| is the magnitude of the amplifier
transfer function—that is, the ratio of the output Vo() to the input Vi().



Express the magnitude of transmission in decibels
The gain is almost constant over a wide frequency range, roughly
between 1 and 2.
Amplifier bandwidth: The band of frequencies over which the gain of
the amplifier is almost constant.
Microelectronic Circuits Ch. 1 Introduction
39
1.6.3 Evaluating the Frequency Response of
Amplifiers

INHA Univ.
In frequency-domain analysis
C
C
Vi
C
c
bc
S
C
Vo
be
C
E
the Amplifier transfer function T (w) = Vo()/Vi()
Microelectronic Circuits Ch. 1 Introduction
40
INHA Univ.
1.6.4 Single-Time-Constant Networks

Two examples of STC networks are
 Low-pass network
 High-pass network
Figure 1.22 Two examples of STC networks: (a) a low-pass network and (b) a high-pass network.
Microelectronic Circuits Ch. 1 Introduction
41
INHA Univ.
Low-pass network
R
Vi
Vo
C
20 log
1
2
w
   1
 w2 
  tan 1
1
1
Vo
1
jwC


T ( w)  

w
1
Vi R 
jwCR  1
j
1
wo
jwC
| w  20 log
wo
1
1
 3dB
2

1
RC
w w
|

wo wo
Vo ( s )
Vi ( s )
The transmission of low-pass network will decrease with frequency and
approach zero as  approach .
Low-pass filter passes low-frequency sine-wave inputs with little or no
attenuation (at =0, the transmission is unity)
jw 대신에 complex frequency variable s

w0 
Microelectronic Circuits Ch. 1 Introduction
T (s) 
42
INHA Univ.
Bode plots of Low-pass network
Magnitude response

3-dB frequency (0)
= corner frequency
= break frequency
Phase response
Microelectronic Circuits Ch. 1 Introduction
43
INHA Univ.
High-pass network
Vi
Vo
R
jw


1
Vi R  1
jw 
jwC
RC
1
w
1
 tan 1 o


w
1  j ( wo / w)
1  ( wo / w) 2
T ( w) 
C
R
Vo
w0 
예) C = 1 ㎋ , R = 1 ㏀
1
RC
1
1
6
sol) wo  1 


10
 Its transmission is unity at
RC 103  109 106
=  and decrease as  is
wo
f o  3dB frequency 
 159 KHz
reduced.
2
6
1
s
1 10
Transfer function : T ( s) 
 tan ( )

6
6
2
w
s  10
1  (10 / w)
Microelectronic Circuits Ch. 1 Introduction
44
Bode plots of High-pass network
INHA Univ.
Magnitude response
Phase response
Microelectronic Circuits Ch. 1 Introduction
45
Example 1.5
INHA Univ.
a) Amplifier voltage gain V0 / VS , dc gain and the 3-dB frequency ?
= 144V/VkΩ , Ro = 200Ω , RL = 1kΩ,
b) RS = 20kΩ, Ri = 100kΩ, Ci = 60pF,
Calculate dc gain, 3-dB frequency, unit gain frequency ?
c) V0 = ?
i) Vi = 0.1 sin102t V
ii) Vi = 0.1 sin105t V
iii) Vi = 0.1 sin106t V
iv) Vi = 0.1 sin108t V
Microelectronic Circuits Ch. 1 Introduction
46
Example 1.5: Solution (see pp. 36)
a)
INHA Univ.
Zi
1
1
 Vs
 Vs
1
Z i  Rs
1  RsYi
1  Rs (  sCi )
Ri
1
1
Vi
1


Rs 1  sCi Rs || Ri 
Vs (1  Rs )  sC R
1

i s
Ri
Ri
Vi  Vs
Vo  Vi
RL
RL  Ro
1
1
1
Vi
 
R
R
Vs
1  s 1  o 1  sCi Rs || Ri 
Ri
RL
1
Time constant
  Ci ( Ro || Ri ) 
wo
Vo
1
1
1
K


R
R
w
w
Vs
1 s 1 o 1 j
1 j
Ro
RL
wo
wo
Microelectronic Circuits Ch. 1 Introduction
47
Example 1.5: Solution (see pp. 36)
INHA Univ.
b) dc gain
K  144
1
1
 100V / V
20
200
1
1
100
1000
3 dB frequency
wo 
1
 106 r / s
60 pF  (20 K || 100 K)
106
f0 
 159.2kHz
2
8
unit gain frequency = 10 r / s
Microelectronic Circuits Ch. 1 Introduction
48
INHA Univ.
Example 1.5: Solution (see pp. 36)
c)
T ( jw) 
vo
100
( jw) 
vs
1  jw / 106
5
w
1 10

ii)   tan
  tan

5
.
7
wo
106
1
Gain =
2
w
1 10
i )   tan
  tan
0
6
wo
10
1
 vo (t )  10 sin 2 t
6
w
1 10
iii)   tan
  tan
 45
6
wo
10
1
gain 
100
1
 
106
106
2
 70.7
 vo (t )  70.7 sin(106 t  45 )V
Microelectronic Circuits Ch. 1 Introduction
100
gain 
1
 
2
105
106
 9.95
 vo (t )  9.95 sin(105 t  5.7 )V
8
w
1 10

iv)   tan
  tan


89
.
4
wo
106
1
gain 
100
1
 
2
108
106
 89.4
 vo (t )  0.1sin(108 t  89.4 )V
49
1.6.5 Classification of Amplifier Based on
Frequency Response
INHA Univ.
Figure 1.26 Frequency response for (a) a capacitively coupled amplifier, (b) a directcoupled amplifier (Low-pass filter), and (c) a tuned or bandpass amplifier (bandpass filter).
Microelectronic Circuits Ch. 1 Introduction
50
1.7 Digital Logic Inverters
1.7.1 Function of the Inverter
INHA Univ.
Figure 1.28 A logic inverter operating from a dc supply VDD.

A logical variable is associated with a nominal voltage
level for each logic state
 1  VOH
and 0  VOL
Microelectronic Circuits Ch. 1 Introduction
51
INHA Univ.
1.7.2 The Voltage Transfer Characteristic (VTC)
VOH
VIH
“1”
Vout
VOH
Slope = -1
Undefined
Region
Slope = -1
VIL
“0”
VOL
VOL
VIL VIH
Vin

The regions of acceptable high and low voltages are delimited by VIH
and VIL that represent the points where the gain of VTC curve = -1.

VIL ~ VIH: transition region
Microelectronic Circuits Ch. 1 Introduction
52
1.7.3 Noise Margins

INHA Univ.
For a gate to be robust and insensitive to noise
disturbance, “0” and “1” intervals (noise margins) should
be as large as possible.
"1"
V
OH
Noise margin high
NM H
V
IH
Undefined
Region
V
OL
NM L
"0"
Gate Output
Stage M
Microelectronic Circuits Ch. 1 Introduction
V
IL
Gate Input
Stage M+1
Noise margin low
* Noise Margin High
NMH = VOH - VIH
* Noise Margin Low
NML = VIL - VOL
53
1.7.4 Ideal VTC

INHA Univ.
The ideal gate should have




infinite gain in the transition region
a gate threshold located in the middle of the logic swing
high and low noise margins equal to half the swing
input and output impedances of infinity and zero, respectively.
g=
Ri = 
Ro = 0
Fanout = 
NMH = NML = VDD/2
Ideal voltage-transfer characteristic of an
Ideal inverter
Microelectronic Circuits Ch. 1 Introduction
54
1.7.5 Inverter Implementation
INHA Univ.
Its Layout
CMOS Inverter
VDD
N Well
VDD
PMOS
2l
Contacts
PMOS
In
Out
In
NMOS
Out
Metal 1
Polysilicon
NMOS
GND
Microelectronic Circuits Ch. 1 Introduction
55
INHA Univ.
VDD
PMOS
In
Out
NMOS
Figure 1.31 (a) The simplest implementation of a logic inverter using a
voltage-controlled switch; (b) equivalent circuit when vI is low; and (c)
equivalent circuit when vI is high. Note that the switch is assumed to
close when vI is high.
Microelectronic Circuits Ch. 1 Introduction
56
INHA Univ.
VDD
PMOS
In
Out
NMOS
Figure 1.32 A more elaborate implementation of the logic inverter utilizing two
complementary switches. This is the basis of the CMOS inverter studied in Section
4.10.
Microelectronic Circuits Ch. 1 Introduction
57
1.7.6 Power Dissipation


INHA Univ.
Power dissipation: how much energy is consumed per
operation and how much heat the circuit dissipates
Two important power consumption: Dynamic and static
power dissipation
 P (watts) = CLVdd²f01+ tscVddIpeakf01+VddIleakage

f01 = P01  fclock
 Dynamic power dissipation = CLVdd²f01
 Static power dissipation = tscVddIpeakf01+VddIleakage
– CL: load capacitance

Capacitance between the output node and ground
– Vdd: power-supply voltage
Microelectronic Circuits Ch. 1 Introduction
58
1.7.7 Propagation Delay

INHA Univ.
Propagation delay: time delay between switching of v1
(from low to high or vice versa) and the corresponding
change appearing at the output.
 Propagation arises for two reasons:
– The transistors that implement the switches exhibit finite
(nonzero) switching times
– The capacitance that is inevitably present between the inverter
output node and ground needs to charge (or discharge) before
the output reaches its required level of VOH or VOL
Microelectronic Circuits Ch. 1 Introduction
59
Modeling Propagation Delay

INHA Univ.
Model circuit as first-order RC network
R
vin
vout
where   RC (time constant)
Time to reach 50% point is
C
tp = ln (2)  = 0.69 
Time to reach 90% point is
tp = ln (9)  = 2.2 
Important model – matches delay of inverter
Microelectronic Circuits Ch. 1 Introduction
60
Example 1.6
INHA Univ.
Figure 1.34 Example 1.6: (a) The inverter circuit after the switch opens (i.e., for t  0). (b)
Waveforms of vI and vO. Observe that the switch is assumed to operate instantaneously. vO
rises exponentially, starting at VOL and heading toward VOH .
Microelectronic Circuits Ch. 1 Introduction
61
INHA Univ.
Solution)
iii)
i)
V V 
OL
offset
V V
R
RR
DD
offset
on
on
5  0.1
 0.1
 0.1 0.55V
1.1
ii) by substituting in Eq. (1.33)
v (t )  5  (5  0.55) e
 t /
O
1
v (t )  (V V )
2
1
 (5  0.55)
2
O
PLH
OH
iv) The result is
t  0.69
PLH
 0.69 RC
 0.6910 10
 6.9 ns
3
Microelectronic Circuits Ch. 1 Introduction
OL
11
62