Introduction
 IN THIS CHAPTER YOU WILL LEARN…
 That electronic circuits process signals, and thus understanding
electrical signals is essential to appreciating the material in this book.
 The Thevenin and Norton representations of signal sources.
 The representation of a signal as sum of sine waves.
 The analog and digital representations of a signal.
Chapter #1: Signals and
Amplifiers
Assoc. Prof. Bui Thanh Tung
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
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Assoc. Prof. Bui Thanh Tung
2
Introduction
1.1. Signals
 IN THIS CHAPTER YOU WILL LEARN…
 The most basic and pervasive signal-processing function: signal
amplification, and correspondingly, the signal amplifier.
 How amplifiers are characterized (modeled) as circuit building
blocks independent of their internal circuitry.
 How the frequency response of an amplifier is measured, and how it
is calculated, especially in the simple but common case of a singletime-constant (STC) type response.
Assoc. Prof. Bui Thanh Tung
3
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
 signal – contains information
 e.g. voice of radio announcer reading the news
 process – an operation which allows an observer to
understand this information from a signal
 generally done electrically
 transducer – device which converts signal from non-electrical
to electrical form
 e.g. microphone (sound to electrical)
Faculty of Electronics and Telecommunications
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Assoc. Prof. Bui Thanh Tung
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Principle of Analog Electronics (ELT-2050)
1.1: Signals
Example 1.1: Thevenin and Norton Equivalent Sources
 Q: How are signals represented?
 A: thevenin form – voltage source vs(t)
with series resistance RS
 preferable when RS is low
 A: norton form – current source is(t)
with parallel resistance RS
 preferable when RS is high
 Consider two source / load combinations to upper-right.
 note that output resistance of a source limits its ability to deliver a signal
at full strength
 Q(a): what is the relationship between the source and output when
maximum power is delivered?
 for example, vs < vo??? vs > vo??? vs = vo???
 Q(b): what are ideal values of RS for norton and thevenin representations?
Figure 1.1: Two alternative representations of a signal source: (a) the
Thévenin form; (b) the Norton form.
Assoc. Prof. Bui Thanh Tung
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
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6
1.2. Frequency Spectrum of Signals
What is a Fourier Series?
 frequency spectrum – defines the
a time-domain signal in terms of
the strength of harmonic
components
 Q: What is a Fourier Series?
 A: An expression of a periodic
function as the sum of an
infinite number of sinusoids
whose frequencies are
harmonically related
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Assoc. Prof. Bui Thanh Tung
 decomposition – of a periodic function into the
(possibly infinite) sum of simpler oscillating
functions
Fourier
Series Representation
of f
(x )



a0
f(x)   ak cos(kx)  bk sin(kx)
2
k 1



1
ak   f( x)cos(kx)dx , n0
 
bk 
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1
 f( x)sin(kx)dx , n1
 
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What is a Fourier Series? (2)
Fourier Series Example
step #1: define ak for the square wave
note that the piece-wise square wave must be divided in two dc functions
 Q: How does one calculate Fourier Series of square
wave below?
 A: See upcoming slides…

0

Va
Va
ak 
cos(kx)dx   cos(kx)dx  0
 
 0



0
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1
sin kx 
k

1
sin kx 
k
0
1
1
sin k 0  sin  k 
k
k
1
1
sin k  sin k 0 
k
k
00
00
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
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Fourier Series Example
Fourier Series Example
step #2: define bk for the square wave if k is even


0

Va
V
bk 
Va sin(kx)dx  a  sin(kx)dx

 
 0




0
Assoc. Prof. Bui Thanh Tung
11

1
 cos kx 
k

1
 cos kx 
k
0
1
1
 cos k 0  cos  k 
k
k
1
1
 cos k   cos k 0 
k
k
1 1
  (-1)k
k k
1
1
 (-1)k 
k
k
4Va

 k is odd
bk  
k
k is even 0
step #3: define Fourier Series

4Va
0
0


k


a0   
f(x )    ak cos(kx)  bk sin(kx)
2 k 1 



1

sin(k0t )
4V   k is odd
f( x )  a  
k
 k 1 k is even
0

f( x ) 
Faculty of Electronics and Telecommunications
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
x  0t
4Va 
1
1

sin(0t )  sin(30t )  sin(50t )  
 
3
5

Assoc. Prof. Bui Thanh Tung
12
this series may be truncated
because the magnitude of each
terms decreases with k…
Faculty of Electronics and Telecommunications
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Fourier Series Example
1.2. Frequency Spectrum of Signals
 Examine the sinusoidal wave below…
v a (t )  Va sin(t   )


Va  amplitude in volts
  angular frequency in rad/sec
 = phase shift in rad
t  time in sec
root mean square magnitude =
sine wave amplitude / square root of two
Figure 1.6: The frequency spectrum (also known as the
line spectrum) of the periodic square wave of Fig. 1.5.
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Assoc. Prof. Bui Thanh Tung
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1.2. Frequency Spectrum of Signals
1.3. Analog and Digital Signals
 Q: Can the Fourier Transform be applied to a non-periodic function of time?
 A: Yes, however (as opposed to a discrete frequency spectrum) it will yield
a continuous…
 analog signal – is continuous with respect to both value and time
 discrete-time signal – is continuous with respect to value but
sampled at discrete points in time
 digital signal – is quantized (applied to values) as well as sampled
at discrete points in time
Figure 1.9 Block-diagram representation of the analog-to-digital converter (ADC).
Assoc. Prof. Bui Thanh Tung
15
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Assoc. Prof. Bui Thanh Tung
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
1.3. Analog and Digital Signals
1.3. Analog and Digital Signals
analog signal
sampling
discrete-time signal
digital signal
quantization
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Assoc. Prof. Bui Thanh Tung
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Assoc. Prof. Bui Thanh Tung
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
18
1.3. Analog and Digital Signals
digital
digital and
binary
1.4. Amplifiers
 Q: Are digital and binary
synonymous?
 A: No. The binary number
system (base2) is one way to
represent digital signals.
 Q: Why is signal amplification needed?
 A: Because many transducers yield output at low power
levels (mW)
 linearity – is property of an amplifier which ensures a signal
is not “altered” from amplification
 distortion – is any unintended change in output
base 10  base 2



y  b0 20  b1 21  b2 22  

LSB
n 1
  b3 23  b
n1 2
MSB
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
1.4.1. Signal Amplification
1.4.2. Amplifier Circuit Symbol
 voltage amplifier – is used to boost voltage levels for
increased resolution.
 power amplifier – is used to boost current levels for
increased “intensity”.
output / input relationship for amplifier



v o (t )  Av v i (t )
Figure 1.11: (a) Circuit symbol for amplifier. (b) An amplifier with a
common terminal (ground) between the input and output ports.
voltage gain
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22
1.4.4. Power and Current Gain
1.4.5. Expressing Gain in Decibels
 Q: What is one main difference between an amplifier and
transformer? …Because both alter voltage levels.
 A: Amplifier may be used to boost power delivery.
power gain ( Ap ) 
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Assoc. Prof. Bui Thanh Tung
 Q: How may gain be expressed in decibels?
voltage gain in decibels  20 log Av dB
load power (PL ) vo io

input power (PI ) vi ii
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current gain in decibels  20 log Ai dB
power gain in decibels  10 log(Ap )dB
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
1.4.6. Amplifier Power Supply
1.4.6. Amplifier Power Supply
 conservation of power – dictates that
power input (Pi) plus that drawn from
supply (Pdc) is equal to output (PL) plus
that which is dissipated (Pdis).
 Pi + Pdc = PL + Pdissapated
 supplies – an amplifier has two power supplies
 VCC is positive, current ICC is drawn
 VEE is negative, current IEE is drawn
 power draw – from these supplies is defined below
 Pdc = VCC ICC + VEE IEE
 efficiency – is the ratio of power output
to input.
 efficiency = PL / (Pi + Pdc)
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Assoc. Prof. Bui Thanh Tung
Figureof 1.13:
An amplifier
that requires two dc
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Electronics
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supplies
batteries)
for operation.
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of Analogas
Electronics
(ELT-2050)
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1.4.7. Amplifier Saturation
1.5. Circuit Models for Amplifiers
 limited linear range – practically,
amplifier operation is linear over a
limited input range.
 saturation – beyond this range,
saturation occurs.
 output remains constant as
input varies
 model – is the description of component’s (e.g. amplifier) terminal behavior
 neglecting internal operation / transistor design
L
Lminus
 vi  plus
Av
Av


or...
L
v L
Assoc. Prof. Bui Thanh Tung minus o plus
27
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
1.5.1. Voltage Amplifiers
model of amplifier input terminals


Ri
input voltage  vi  (v s )
 R R
i
source 
s
volt.
source and
input
resistances
1.5.1. Voltage Amplifiers
model of amplifier output terminals



RL
output voltage  vo  (Avovi )
 R R
L
open-ckt 
o
output
 Q: How can one model the amplifier behavior from
previous slide?
 A: Model which is function of: vs, Avo, Ri, Rs, Ro, RL
voltage output and
load
resistances






R
RL
i
 RL  Avov s Ri
vo   Avo (v s )
 R R R R
 source
R

R
R
i
L
i
s L  Ro

s  
o

volt.
source and output and
input 
load

resistances  resistances

open-ckt output voltage
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1.5.1. Voltage Amplifiers
1.5.1. Voltage Amplifiers
 ideal amplifier model – is function of vs and Avo only!!
 It is assumed that Ro << RL…
 It is assumed that Ri << Rs…
non-ideal model
ideal model
 Q: What is one “problem” with this behavior?
 A: Gain (ratio of vo and vs) is not constant, and
dependent on input and load resistance.






R
RL
i
 RL  Avov s Ri
vo   Avo (vs )

 source Ri  Rs  RL  Ro
Ri  Rs RL  Ro
  

volt.
source and output and
input

 load
resistances  resistances

open-ckt output voltage
The ideal amplifier model neglects this
Facultynonlinearity.
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Assoc. Prof. Bui Thanh Tung
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Principle of Analog Electronics (ELT-2050)
key characteristics of ideal voltage amplifier model = high input
impedance, low output impedance
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Principle of Analog Electronics (ELT-2050)
1.5.1. Voltage Amplifiers
1.5.2. Cascaded Amplifiers
 In real life, an amplifier is not ideal and will not have infinite
input impedance or zero output impedance.
 Cascading of amplifiers, however, may be used to emphasize
desirable characteristics.
 first amplifier – high Ri, medium Ro
 last amplifier – medium Ri, low Ro
 aggregate – high Ri, low Ro
 ideal amplifier model – is function of vs and Avo only!!
 It is assumed that Ro << RL…
 It is assumed that Ri << Rs…
Ri
RL
vo  Avov s
 Avov s
Ri  Rs RL  Ro 
ideal

 model
non-ideal model
key characteristics of ideal voltage amplifier model = source
resistance RS and load resistance RL have no effect on gain
Assoc. Prof. Bui Thanh Tung
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Assoc. Prof. Bui Thanh Tung
34
Example 1.3: Cascaded Amplifier Configurations




Example 1.3: Cascaded Amplifier Configurations
Examine system of cascaded amplifiers on next slide.
Q(a): What is overall voltage gain?
Q(b): What is overall current gain?
Q(c): What is overall power gain?
aggregate amplifier
with gain
Av 
vL
v s  i i Rs
Figure 1.17: Three-stage amplifier for Example 1.3.
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Principle of Analog Electronics (ELT-2050)
1.5.3. Other Amplifier Types
Voltage amplifier
Transconductance amp.
1.5.3. Other Amplifier Types
Current amplifier
Av 0 
37
i0
vi
Assoc. Prof. Bui Thanh Tung
Av 0 
i0
ii
with
v 0 0
with
v0 0
Ri  0
Ro  
current amplifier
transresistance amplifier
Ri  
Ro  
Rm 
Ri  0
v0
with
R
ii Faculty
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i 0of Electronics and Telecommunications
0
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38
1.5.4. Relationship Between Four Amp Models
1.5.5. Determining Ri and Ro
 interchangeability – although these four types exist,
any of the four may be used to model any amplifier
 they are related through Avo (open circuit gain)
current
to voltage
amplifier
transcond.
to voltage
amplifier
 Q: How can one calculate input resistance from terminal behavior?
 A: Observe vi and ii, calculate via Ri = vi / ii
 Q: How can one calculate output resistance from terminal behavior?
 A:
 Remove source voltage (such that vi = ii = 0)
 Apply voltage to output (vx)
 Measure negative output current (-io)
 Calculate via Ro = -vx / io
transres.
to voltage
amplifier




 Ro  
R
Avo  Ais    GmRo  m
Ri
 Ri 
Assoc. Prof. Bui Thanh Tung
39
i0 0
Ri  
Ro  0
transconductance amplifier
Gm 
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with
voltage amplifier
Transresistance amp.
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v0
vi
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Principle of Analog Electronics (ELT-2050)
Assoc. Prof. Bui Thanh Tung
40
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Section 1.5.5:
Determining Ri and Ro
1.5.6. Unilateral Models
 question: how can we calculate input
resistance from terminal behavior?
 answer: observe vi and ii, calculate via
Ri = vi / ii
 question: how can we calculate output
resistance from terminal behavior?
 answer:
 remove source voltage (such
that vi = ii = 0)
 apply voltage to output (vx)
 measure negative output
current (-io)
 calculate via Ro = -vx / io
 unilateral model – is one in which signal flows only from input to output (not
reverse)
 However, most practical amplifiers will exhibit some reverse
transmission…
Figure 1.18: Determining the output resistance.
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Faculty of Electronics and Telecommunications
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Assoc. Prof. Bui Thanh Tung
42
Example 1.4: Common-Emitter Circuit
Examplebase
1.4.
 Examine the bipolar junction transistor (BJT).
 three-terminal device
 when powered up with dc source and operated with small signals, may be
modeled by linear circuit below.
input resistance (r)
output resistance (ro)
collector
 examine:
 bipolar junction transistor (BJT):
 three-terminal device
 when powered up with dc source and operated with small signals, may be modeled
by linear circuit below.
C
B
E
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43
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
short-circuit
conductance
(gm)
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44
emitter
Figure 1.19 (a) small-signal
circuit model for a bipolar
junction transistor (BJT)
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input and output share common terminal
Example 1.4: Common-Emitter Circuit
 Q(a): Derive an expression for the voltage gain vo / vi of common-emitter
circuit with:
 Rs = 5kohm
 r = 2.5kohm
 gm = 40mA/V
 ro = 100kohm
 RL = 5kohm
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
45
source
load
Figure 1.19(b): The BJT connected as an amplifier with
the emitter as a common terminal between input and
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output (called a common-emitter amplifier).
Assoc. Prof. Bui Thanh Tung
Principle of Analog Electronics (ELT-2050)
46
1.6.1. Measuring the
Amplifier Frequency Response
1.6.1: Measuring the
Amplifier Frequency Response
input and output are similar for linear
amplifier
 Q: How does one examine frequency response?
 A: By applying sine-wave input of amplitude Vi and frequency .
 Q: Why?
 A: Because, although its amplitude and phase may change, its shape and
frequency will not.
this characteristic of sine wave applied to linear circuit is
unique
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47
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Assoc. Prof. Bui Thanh Tung
48
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
1.6.1. Measuring the
Amplifier Frequency Response
1.6.2. Amplifier Bandwidth
 Q: What is bandwidth of a device?
 A: The range of frequencies over which its magnitude response is constant
(within 3dB).
 Q: For an amplifier, what is main bandwidth concern?
 A: That the bandwidth extends beyond range of frequencies it is expected
to amplify.
 amplifier transfer function (T) – describes the inputoutput relationship of an amplifier – or other device –
with respect to various parameters, including
frequency of input applied.
 It is a complex value, often defined in terms of
magnitude and phase shift.
V
T( )  o
V

i
and

T(
) 


phase shift
magnitude gain
Assoc. Prof. Bui Thanh Tung
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
49
50
1.6.4. Single Time-Constant Networks
1.6.4. Single Time-Constant Networks
 low pass filter (LPF)
attenuates output at
high s
 single time–constant (STC) network – is composed of (or may be
reduced to) one reactive component and one resistance.
 low pass filter – attenuates output at high frequencies, allow low
to pass
 high pass filter – attenuates output at low frequencies, allow
high to pass
 time constant (t.) – describes the length of time required for a
network transient to settle from step change (t = L / R = RC)
Assoc. Prof. Bui Thanh Tung
51
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Assoc. Prof. Bui Thanh Tung
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
high pass filter (HPF)
Figure 1.22: Two examples of STC networks: (a) a low-pass network and
(b) a high-pass network.
Faculty of Electronics and Telecommunications
Assoc. Prof. Bui Thanh Tung
52
Principle of Analog Electronics (ELT-2050)
1.6.4. Single Time-Constant Networks
1.6.4. Single Time-Constant Networks
Figure 1.2 : Characteristics of Various STC
low-pass:
1
vo
Zo
1
jC


k
vi Z i  Z o R  1

jC
high-pass:
vo
Zo
R


 k
vi Zi  Z o R  1
jC
transfer function
transfer function
(for physical freq.)
magnitude response
phase response
transmission at   0
transmission at   
3db Frequency
Bode Plots
Assoc. Prof. Bui Thanh Tung
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
53
Assoc. Prof. Bui Thanh Tung
high - pass
K
1  (s / 0 )
Ks
1  0
K
1  j( / 0 )
K
1  j(0 /  )
K
K
1  j( / 0 )2
1  j(0 /  )2
 tan( / 0 )
K
tan(0 /  )
0
0
0 
K
1
t
refer to
same
next slide
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-20dB/decade drop, beginning
-45 degrees/decade drop,
from maximum gain at corner
moving outward from -45
Figure:
Low-Filter Magnitude degree
(top-left)
andatPhase
frequency
shift
corner(topfrequency
right) Responses as well as High-Pass Filter (bottom-left)
and Phase (bottom-right) Responses
-45 degrees/decade drop,
+20dB/decade incline, until
moving outward from +45
maximum gain is reached at
degree shift at corner frequency
corner frequency
Figure: Low-Pass Filter Magnitude (top-left) and Phase (top-right) Responses as well as
High-Pass Filter (bottom-left) and Phase (bottom-right) Responses
Assoc. Prof. Bui Thanh Tung
55
low - pass
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Assoc. Prof. Bui Thanh Tung
56
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Example 1.5: Voltage Amplifier
Example 1.5: Voltage Amplifier
 Examine voltage amplifier with:
 input resistance (Ri)
 input capacitance (Ci)
 gain factor (m)
 output resistance (Ro)
 Q(a): Derive an expression for
the amplifier voltage gain Vo / Vs
as a function of frequency.
From this, find expressions for
the dc gain and 3dB frequency.
Assoc. Prof. Bui Thanh Tung
 Q(b): What is unity-gain frequency? How is it calculated?
 A: Gain = 0dB
 A: It is known that the gain of a low-pass filter drops at 20dB per
decade beginning at 0. Therefore unity gain will occur two
decades past 0 (40dB – 20dB – 20dB).
 Q(c): Find vo(t) for each of the following input: vs = 0.1sin(102t), vs =
0.1sin(105t)
Faculty of Electronics and Telecommunications
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Assoc. Prof. Bui Thanh Tung
58
1.6.5. Classification of
Amps Based on Frequency Response
1.6.5. Classification of Amps Based on Frequency Response
 internal capacitances – cause the falloff of gain at high frequencies
 like those seen in previous example
 coupling capacitors – cause the falloff of gain at low frequencies
 are placed in between amplifier stages
 generally chosen to be large
Assoc. Prof. Bui Thanh Tung
59
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
 directly coupled / dc amplifiers – allow passage of low frequencies
 capacitively coupled amplifiers – allow passage of high frequencies
 tuned amplifiers – allow passage of a “band” of frequencies
Assoc. Prof. Bui Thanh Tung
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Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Conclusion
Conclusion (2)
 An electrical signal source can be represented in either Thevenin form
(a voltage source vs in series with source resistance Rs) or the Norton
form (a current source is in parallel with resistance Rs). The Thevenin
voltage vs is the open-circuit voltage between the source terminals.
The Norton current is is equal to the short-circuit current between the
source terminals. For the two representations to be equivalent, vs
and Rsis must be equal.
 A signal can be represented either by its waveform vs time or as the
sum of sinusoids. The latter representation is known as the
frequency spectrum of the signal.
Assoc. Prof. Bui Thanh Tung
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
61
 The sine-wave signal is completely characterized by its peak value (or
rms value which is the peak / 21/2), frequency ( in rad/s of f in Hz;  =
2f and f = 1/T, where T is the period is seconds), and phase with
respect to an arbitrary reference time.
 Analog signals have magnitudes that can assume any value. Electronic
circuits that process analog signals are called analog circuits. Sampling
the magnitude of an analog signal at discrete instants of time and
representing each signal sample by a number results in a digital signal.
Digital signals are processed by digital circuits.
Assoc. Prof. Bui Thanh Tung
62
Conclusion (3)
Conclusion (4)
 The simplest digital signals are obtained when the binary number system
is used. An individual digital signal then assumes one of only two
possible values: low and high (e.g. 0V and 5V) corresponding to logic 0
and logic 1.
 An analog-to-digital converter (ADC) provides at its output the digits of
the binary number representing the analog signal sample applied to its
input. The output digital signal can then be processed using digital
circuits.
 A transfer characteristic, vo vs. vi, of a linear amplifier is a straight line
with a slope equal to the voltage gain.
Assoc. Prof. Bui Thanh Tung
63
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
 Amplifiers increase the signal power and thus require dc power supplies
for their operation.
 The amplifier voltage gain can be expressed as a ratio Av in V/V or in
decibels, 20log|Av| in dB.
 Depending on the signal to be amplified (voltage or current) and on the
desired form of output signal (voltage or current) there are four basic
amplifier types: voltage, current, transconductance, and transresistance.
A given amplifier may be modeled by any of these configurations, in
which case their parameters are related by (1.14) through (1.16) in the
text.
Assoc. Prof. Bui Thanh Tung
64
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Conclusion (5)
Conclusion (6)
 Single-time-constant (STC) networks are those networks that are
composed of, or may be reduced to, one reactive component (L or C) and
one resistance. The time constant (t) is L/R or RC.
 STC networks can be classified into two categories: low-pass (LP) and
high-pass (HP). LP network pass dc and low-frequencies while
attenuating high-frequencies. The opposite is true for HP.
 The gain of an LP (HP) STC circuit drops by 3dB below the zero-frequency
(infinite-frequency) value at a frequency 0 = 1/t. At high-frequencies
(low-frequencies) the gain falls of at a rate of 6dB/octave or
20dB/decade.
 The sinusoid is the only signal whose waveform is unchanged through a
linear circuit. Sinusoidal signals are used to measure the frequency
response of amplifiers.
 The transfer function T(s) = Vo(s)/Vi(s) of a voltage amplifier may be
determined from circuit analysis. Substituting s = j gives T(j) whose
magnitude (|T(j)| is the magnitude response and () is the phase
response.
 Amplifiers are classified according to the shape of their frequency
response.
 Refer to Table 1.2. on page 34 and Figs. 1.23 and 1.24. Further details are provided in Appendix E.
Assoc. Prof. Bui Thanh Tung
65
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)
Assoc. Prof. Bui Thanh Tung
66
Faculty of Electronics and Telecommunications
Principle of Analog Electronics (ELT-2050)