Chapter 4

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1
Communication Systems
Instructor: Engr. Dr. Sarmad Ullah Khan
Assistant ProfessorAssistant Professor
Electrical Engineering Department
CECOS University of IT and Emerging Sciences
Sarmad@cecos.edu.pk
Chapter 4
Dr. Sarmad Ullah Khan
Amplitude Modulations and
Demodulations
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Outlines
• Baseband versus Carrier Communication
D bl id b d A lit d M d l ti
• Double sideband Amplitude Modulation
• Amplitude Modulation
• Bandwidth Efficient Amplitude Modulation
• Amplitude Modulation: VESTIGIAL Sideband
3
Outlines
4

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Baseband versus Carrier Communication
• Modulation is a process that moves signal into a
specific frequency band
specific frequency band
• The bandwidth B represents a measure of frequency
range.
• It is typically measured in Hz with 1 Hz = 1/sec.
• The bandwidth of a signal indicates the frequency
range in which the signal‘s Fourier transform has ag g
power above a certain threshold (typically half of
the maximum power)
5
• Communication systems that do not use modulation
are called baseband communication
are called baseband communication
• Communication systems that use modulation are
called carrier communication
• Baseband is original message frequency band
• In telephony, baseband is audio band (0 – 3.5 kHz)
• In NTSC television, video baseband is 0 – 4.3 MHzIn NTSC television, video baseband is 0 4.3 MHz
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• Baseband Communication
Message signals are directly transmitted without any
Message signals are directly transmitted without any
modulation
Dedicated user channels are assigned to each long distance
communication
Baseband signals have overlapping bands
Severe interference
Waste of channel resourcesWaste of channel resources
Modulation and shifting to non overlapping bands save
channel resources
7
• Carrier Communication
Modulation techniques is used to shift the frequency
Modulation techniques is used to shift the frequency
spectrum of message signal
Modulation changes one of the basic parameter of carrier
signal (Amplitude, Frequency, Phase)
Carrier signal is a sinusoidal signal of high frequency fc
Parameter variation is proportional to message signal m(t)
Amplitude modulation is linearAmplitude modulation is linear
Frequency and Phase modulations are non linears
PAM, PWM, PPM, PCM and DM are baseband signals
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• Amplitude Modulation and Angle Modulation
Amplitude modulation (AM) varies the amplitude of a
Amplitude modulation (AM) varies the amplitude of a
carrier signal according to a modulating
signal m(t).
 The modulated signal is
)cos(
c
t
c
wA 
)cos()( twtm c
Source signal m(t) and its Fourier transform M(f)
9
Frequency Shifting Property
10
 )()(
2
1
cos)( ccc wwMwwMtwtm 

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Outlines
11
Double Sideband Amplitude Modulation
1
 M(f - fc) is M(f) shifted to the right of fc
 M(f + fc) is M(f) shifted to the left of fc
 The bandwidth changed from B to 2B
 The modulated signal is composed of two parts, above
 )()(
2
1
2cos)( ccc ffMffMtftm 
 The modulated signal is composed of two parts, above
fc and below fc
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The upper sideband (USB) containing the frequencies
The upper sideband (USB) containing the frequencies
|f| > |fc|
The lower sideband (LSB) containing the frequencies
|f| < |fc|
The modulated signal in this scheme does not have a
discrete component of the carrier frequency fc. For this
reason this is called double sideband suppressedreason this is called double-sideband suppressed
carrier (DSB-SC) modulation
13
B vs f
B vs fc
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15
Double Sideband Amplitude
Modulation
Spectrum
Spectrum of the DSB-SC signal m(t)cos10,000t
)cos()cos(
1
coscos  
16
)cos()cos(
2
coscos  

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Spectrum
Spectrum
17
Spectrum
Spectrum
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• Modulation and Demodulation
19
• Modulation and Demodulation
 )2cos()()(
2
1cos)()( 2
twtmtmtwtmte cc

20
 )2()2(
4
1)(
2
1)( cc
wwMwwMwMwE 

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• Modulators
Multiplier Modulators
Multiplier Modulators
Modulation is achieved directly by multiplying m(t) by
cos(wct) using an analog multiplier.
The output is proportional to the product of two input
signals.
Difficult to maintain linearity and are expansive.
21
Better to avoid
• Modulators
Non Linear Modulators
Modulation can be achieved by using non linear device
For example, diodes or transistors
Input-output characteristics of NL element is approx. by
power series as
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• Modulators
The summer output z(t) is given by
23
• Modulators
Substitution of x1(t)=coswct+m(t) and x2(t)=coswct-m(t)
24

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• Modulators
Spectrum of m(t) is centered at origin
Spectrum of m(t) coswct is centered at ±ω
The signal is ready for transmission but we do not need the
m(t) part of z(t)m(t) part of z(t)
Z(t) passed through band pass filter tuned to ωc
am(t) is suppressed and desire modulated signal
4bm(t)coswct pass without distortion
25
• Modulators
Non Linear Modulators (summary)
Non Linear Modulators (summary)
Two inputs m(t) and coswct
The summer output does not contain one of the input coswct
Circuits which have this characteristic are called balanced
circuits.circuits.
The previous circuitry is an example of balanced modulators.
26
This circuit is balanced to only one input carrier, the other input m(t) still
appear at the filter input, which must reject it…….for that reason it is
called a single balanced modulator

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• Modulators
Modulation through any periodic signal
Modulated signal can not only be obtained by a pure sinusoid but
by any periodic signal of fundamental frequency wc
Periodic signal can be expresses by trigonometric Fourier
Series
Spectrum of the modulated signal is the spectrum M(w) shifted to
±fc , ±2fc , ±3fc , ±4fc , …… ±nfc ,……
27
• Modulators
If we pass this modulated signal through band-pass filter of
bandwidth 2B tuned to wc
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• Modulators
Switching Modulators
Multiplication operation of modulation can be replaced by
switching operation. If a periodic signal having Fourier series as:
carrier
Modulated signal
Now consider a periodic square pulse train with Fourier series as
29
Modulated signal






 ....7cos
7
1
5cos
5
1
3cos
3
1
cos
2
2
1
)( twtwtwtwtw cccc

From example 2.8
• Modulators
The modulated signal m(t)w(t) is given by






 ....7cos)(
7
1
5cos)(
5
1
3cos)(
3
1
cos)(
2
)(
2
1
)()( twtmtwtmtwtmtwtmtmtwtm cccc

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Modulated signal m(t)w(t) consists of the component m(t) plus infinite
numbers of modulated signals with carrier frequencies ,.....5,3, ccc
www
Th f ( ) ( ) i f M( ) d M( ) hif d
The spectrum of m(t)w(t) consists of M(w) and M(w) shifted to
,.....5,3, ccc
www 
As we are interested in modulated component only. To
separate this component from others we pass m(t)w(t) through a
bandpass filter of bandwidth 2BHz, centered at
twtm c
cos)(
c
w
31
gives the required modulated signal twtm c
cos)(2

Therefore the multiplication of a signal by a square pulse train is is
reality a switching operation means turning off and on signal m(t)
periodically and can be accomplished by switching element controlled
by w(t)
• Modulators
Diode Bridge Modulator
Consider the following electronic switch circuit driven by
to produce the switching action
4321 ,, DDDD and
are matched pairs
32
During the next half cycle d is positive with respect to c, all the diodes open,
terminal a & b are open.
When terminal c is positive with respect to d, all the diodes conduct, terminal a
& b are effectively shortened.

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• Modulators
Therefore the the circuit act as a desired electronic switch, where
the terminal a & b open and close periodically with the carrier
frequency fc. When is applied across the terminal ab
To obtain m(t)w(t) we may place terminal ab in series or in parallel
as:
twA ccos
Switching on and off m(t) for each cycle of the carrier, resulting in
the switched signal m(t)w(t) and passing through band pass filter
gives the desired signal:
33
Series-bridge diode modulator Shunt-bridge diode modulator
• Modulators
Ring Modulator
Ring Modulator
Consider the following circuit
During the positive half cycle of the carrier D1 & D3 conduct and D2
& D4 are open, hence terminal a is connected to c & b to d
During the negative half cycle of the carrier D1 & D3 are open and
D2 & D4 conduct, hence terminal a is connected to d & b to c
Output is proportional to m(t) during positive cycle & -m(t) during
negative cycle
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• Modulators
Ring Modulator
Ring Modulator
The Fourier series of bipolar square wave is given by:






 ....7cos
7
1
5cos
5
1
3cos
3
1
cos
4
)(0 twtwtwtwtw cccc







 ....7cos)(
7
1
5cos)(
5
1
3cos)(
3
1
cos)(
4
)()( 0 twtmtwtmtwtmtwtmtwtm cccc

Filtering this signal to bandpass filter tuned to wc gives the required
modulated signal:
35
In this circuit there are two inputs m(t) and coswct, the input of the
final band pass filter does not contain either of the inputs……
This circuit is an example of double balanced modulator
• Demodulation of DSB-SC Signals
The demodulation involve multiplication of DSB SC
The demodulation involve multiplication of DSB-SC
with carrier signal
At receiver incoming signal multiply with local carrier
Local carrier must have frequency and phase
synchronization with incoming signal
Product is passed to low pass filter
Such demodulators are called synchronous or coherent
or homodyne demodulators
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Problem 4.2‐4
37
Problem 4.2‐4
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Problem 4.2‐4
At point b
39
At point c
Problem 4.2‐4
The minimum value of wc is to avoid overlapping
pp g
40
Will not work

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Problem 4.2‐4
This may be verified that the identity for contains
This may be verified that the identity for contains
a term when n is odd. This is not true when n is
even. Hence, the system works for a carrier only
when n is odd.
41
Example 4.2
Frequency mixer or converter:
Frequency mixer or converter is used to change the carrier frequency of the
modulated signal m(t)coswct to some other frequency wl
Can be achieved by multiplying m(t)coswct by
where or
42

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Example 4.2
In both cases the filter tuned to Wl will pass the term m(t)coswlt and suppress
the other term and giving the required output
m(t)coswct (the carrier frequency is translated to wl from wc)
43
Frequency mixing or frequency conversion is also known as heterodyning.
All the modulators discussed previously can be used for frequency mixing.
Frequency selected as operation called up-conversion
Frequency selected as operation called down-conversion
Outlines
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Amplitude Modulation
• The demodulation requires the receiver to possess a
carrier signal that is synchronized with incoming signal
• It is difficult to achieve in practice
• Unknown frequency shifts
• Require sophisticated receiver and costly
• Transmit a carrier Acoswct along with the modulated
signal m(t)coswct so no need to generate a carrier at the
receiver
45
• This type of modulation is called AM modulation and
denoted by and given by
)(ty g y
• Its Fourier spectrum is
)(tAM

• The spectrum of is the same as m(t)coswct plus two
additional impulses at ±ω
46
)(tAM


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• DSB-SC signal m(t)coswct and AM signal
are identical with A+m(t) as modulating signal instead of
are identical with A+m(t) as modulating signal instead of
m(t)
• To sketch ,we sketch A+m(t) & -(A+m(t) ) and fill
in between the carrier frequency.
)(tAM

47
• For signal e(t)coswct, if e(t) varies slowly, its envelop
would be |e(t)|
would be |e(t)|
• It means if A+m(t)≥0 for all t, the envelop of is
|A + m(t)| = A + m(t)
• For envelop detection to properly detect m(t)
• fc >> bandwidth of m(t)
)(tAM

• fc >> bandwidth of m(t)
• A + m(t) ≥ 0
48

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• Message signals m(t) with zero offset
 Let ±m be the maximum and minimum value of m(t)
 Let ±mp be the maximum and minimum value of m(t)
 m(t) ≥ -mp
Condition of envelop detection is
A ≥ - mmin = mp
Modulation index μ is
μ = mp/A
F l d t ti t b di t ti lFor envelop detection to be distortion less
0 ≤ μ ≤ 1
This is required condition for distortion less
demodulation of AM by envelop detector
49
• Message signals m(t) with nonzero offset
 It is rare that m(t) will have nonzero offset
 It is rare that m(t) will have nonzero offset
Maximum mmax and minimum mmin are not symmetric
mmin ≠ mmax
Change in offset does not change the envelop detector
output and
0 ≤ μ ≤ 1μ
But
μ = (mmax - mmin) / (2A + mmax + mmin)
50

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• Sideband and Carrier Power
 Th i di d t f l d t ti i t f
 There is a disadvantage of envelope detection in terms of
power waste, as the carrier term does not contain any
information
The carrier power Pc and sideband power Ps is given by
Power efficiency is given by
51
• Sideband and Carrier Power
For the special case of tone modulation:
For the special case of tone modulation:
Hence
With the condition 0 ≤ μ ≤ 1,
Thus under best condition only one third of the transmitted
power is used for carrying message, for practical signals
the efficiency is even worst
52

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• Generation of AM signal
AM signals can be generated by any DSB SC modulators
AM signals can be generated by any DSB-SC modulators.
 The input should be A + m(t) instead of just m(t).
 The modulating circuit do not have to be balanced because
there is no need to suppress the carrier
Switching action is provided by a single diode and
controlled by with twc ccos
53
c
• Generation of AM signal
The diode opens and short periodically with infect
multiplying the input signal by w(t).
The voltage across is:
54

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• Demodulation of AM signal
The AM signal can be demodulated coherently by a locally
The AM signal can be demodulated coherently by a locally
generated carrier. E.g.
There are two well known methods of demodulation of AM
signals:
 1) Rectifier detection 2) Envelope detection
   twtwtmA cc coscos)( No benefit of sending carrier on the channel
 1) Rectifier detection 2) Envelope detection
Rectifier detector:
AM signal is applied to a diode and resistor circuit, the negative
part of the AM wave will be suppressed.
The output across the resistor is the half wave rectified version of
the AM signal means multiplying AM with w(t).
55
The rectified output VR
  
56
   )(cos)( twt
c
wtmAvR

  











 ...5cos
5
1
3cos
3
1
cos
2
2
1
cos)( t
c
wt
c
wt
c
wt
c
wtmA

  otherTermstmA  )(
1


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57
Envelop detector:
In an envelope detector, the output follows the envelope
of the modulated signal
The following circuit act as an envelope detector
During the positive cycle of the input signal, the diode
conducts and the capacitor C charges up to the peak
voltage of the input signal
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When input signal falls below this peak value, the diode
i t ff (b th di d lt hi h i l this cut off. (because the diode voltage which is nearly the
peak voltage is greater than the input signal voltage
causing the diode to open )
At this stage the capacitor discharge at the slew rate
(with a time constant RC)
During the next positive cycle the process repeats 59
p
During each positive cycle the capacitor charges up to theDuring each positive cycle the capacitor charges up to the
peak voltage of the input signal and then decays slowly until
the next positive cycle
This behavior of the capacitor makes output voltage Vc(t)
follow the envelope of the input signal
Capacitor discharges during each positive peaks causes a
ripple signal of frequency wc at the output
60

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The ripple can be reduced by increasing the time
constant RC so the capacitor discharges very little
between positive peaks of the input signals
Making RC too large, makes capacitor voltage
impossible to follow the envelope
61
RC should be large compared to 1/wc, but should be small compared to
Where B is the highest frequency in m(t)
B2
1
Also requires a condition which is necessary for well defined envelope.
62
The envelope detector output is with a ripple of frequency wc
The DC term A can be blocked by a capacitor or a simple RC high pass filter, and
the ripple may be reduced further by another low-pass RC filter.

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Outlines
63
Bandwidth Efficient Amplitude
Modulation
• DSB spectrum has two sidebands (USB, LSB)
• Both carry complete information
• Both carry complete information
• Bandwidth requirement is 2B
• How to improve spectral efficiency?
– Utilize spectral redundancy
– remove spectral redundancy
• Single Sideband (SSB) removes either LSB or USBSingle Sideband (SSB) removes either LSB or USB
• Quadrature amplitude modulation (QAM) utilize
64

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Modulation
• Single Sideband (SSB) Modulation
LSB USB b d b b d filt
– LSB or USB can be suppressed by band pass filter
– A scheme in which only one sideband is
transmitted is known as single-sideband ( SSB)
transmission
– In SSB transmission the required bandwidth is half
compared to DSB signalp g
– An SSB signal can be coherently (synchronously)
demodulated. E.g
– For example multiplying USB signal by coswct
shifts its spectrum to the left and right by wc
65
Modulation
L filt i ill i th i d b b d
– Low pass filtering will give the required baseband
signal at the receiver
66

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Modulation
Hilb t T f
– Hilbert Transform
– xh(t) and H{x(t)} to denote Hilbert transform of
x(t)
Hilbert Transform of m(t)
and delays the phase of each component by
)(tmh
2

67
Modulation
Hilb t T f
– Hilbert Transform
– xh(t) and H{x(t)} to denote Hilbert transform of
x(t)
68

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Modulation
Ti d i t ti f SSB i
– Time domain representation of SSB is
– Where minus sign applies to USB and the plus
sign applies to LSB
twtmtwtmt chcSSB sin)(cos)()( 
69
Modulation
70

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Modulation
71
Example 4.7 p‐174
Tone Modulation:
Find for a simple case of tone modulation that is when the)(tSSB
Find for a simple case of tone modulation, that is, when the
modulating signal is a sinusoid
)(SSB
twtm mcos)( 
Solution:
72

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Example 4.7 p‐174
Hence
73
Example 4.7 p‐174
74

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Modulation
– Two methods are generally used to generate SSB
Two methods are generally used to generate SSB
signals
1) Sharp cutoff filters
2) Phase shifting networks
– In Sharp cutoff method, the DSB-SC signal is passed
through a sharp cutoff filter to eliminate the undesired
sidebandsideband
– To obtain USB, the filter should pass all components
above wc, attenuated and completely suppress all
components below wc
– Such an operation requires an ideal filter that is
practically not possible
75
Modulation
Thi th d f ti SSB i l b d
– This method of generating SSB signal can be used
when there is some separation between the passband
and stopband
– In some application this can be achieved e.g. voice
signals
– Voice signals spectrum shows little power content at
th i i Th filt i th t d id b d ithe origin. Thus filtering the unwanted sideband is
relatively easy
76
Tests have shown that frequency components below
300Hz are not important.
600Hz transition region around the cutoff frequency
wc , makes filtering easy and minimize the channel
interference

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Modulation
The basis of Phase shifting network method is the
– The basis of Phase shifting network method is the
following equation
77
Modulation
The basis of Phase shifting network method is the
– The basis of Phase shifting network method is the
following equation
78

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Modulation
• Quadrature Amplitude Modulation
The DSB signals of AM require twice the bandwidth
– The DSB signals of AM require twice the bandwidth
required for the baseband signal
– Try to send two signals m1(t) and m2(t) simultaneously by
modulating them with two carrier signals of same
frequency but shifted in phase by –/2
– The combined signal is
twtmtwtmtmtm sin)(cos)()()( 
79
twtmtwtmtmtm cc sin)(cos)()()( 2121 
Modulation
Both modulated signals occupy the same band
– Both modulated signals occupy the same band
– At the receiver the two baseband signals can be separated
by using a second carrier that is shifted in phase by –/2
– The first signal m1(t) can be detected by a multiplication
with 2cos(ct) followed by a low-pass filter
– The second signal m2(t) can be detected accordingly by a
multiplication with sin( t) followed by a low-pass filtermultiplication with sin(ct) followed by a low pass filter
80

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Modulation
Thus two baseband signals each of bandwidth B can be
– Thus, two baseband signals, each of bandwidth B, can be
simultaneously transmitted over a channel with bandwidth
2B
– This principle is called quadrature amplitude
modulation (QAM), because the carrier frequencies are in
phase quadrature
81
Outlines
82

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Amplitude Modulation: Vestigial
Sideband (VSB)
• VSB is a compromise between DSB and SSB
• It combines the advantages of DSB and SSB while avoid
It combines the advantages of DSB and SSB while avoid
disadvantages at small cost
• Its generation is relatively easy and bandwidth requirement is
25% greater than SSB
83
Sideband (VSB)
• If vestigial shaping filter produce VBS from DSB is Hi(f), Its
spectrum will bespectrum will be
• VBS filter allows transmission of one sideband but suppress
other side band gradually, NOT completely
84

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Sideband (VSB)
• For demodulation,
85

Chapter 4

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