communication system Chapter 4

Communication System
Ass. Prof. Ibrar Ullah
BSc (Electrical Engineering)
UET Peshawar
MSc (Communication & Electronics Engineering)
UET Peshawar

PhD (In Progress) Electronics Engineering
(Specialization in Wireless Communication)
MAJU Islamabad

E-Mail: ibrar@cecos.edu.pk
Ph: 03339051548 (0830 to 1300 hrs)

1

Chapter-4 Amplitude Modulation

1. Bandwidth and baseband
2. Amplitude modulation
3 Quadrature amplitude modulation
4. Single side band Modulation
5. Vestigial side band Modulation

2

Baseband and carrier Communication
•
•
•

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 a power above a certain threshold
(typically half of the maximum power)

• Often the frequency f = ω / 2π is used instead of the angular frequency
ω.
3

Baseband and carrier Communication
• The term baseband designates a frequency range starting
at 0 Hz
• Example of a baseband signal spectrum:

• In baseband communication baseband signals are sent
without any shift in the range of frequencies
• Any communication that uses modulation of a highfrequency carrier signal is called carrier communication
4

Amplitude Modulation (DSB)
•Amplitude modulation (AM) varies the amplitude of a carrier
signal according to a modulating signal m(t).
A cos( wct + θ c )
• The modulated signal is m(t ) cos( wct )

5

Amplitude Modulation (DSB) cont…

Frequency-Shifting Property of Fourier transform:

6

• This type of modulation shifts the spectrum of m(t) to the carrier
frequency.
If

m(t ) ⇔ M ( w)
1
m(t ) cos wc t ⇔ [ M ( w + wc ) + M ( w − wc )]
2

7

m(t ) cos wc t ⇔

1
[ M (w + wc ) + M ( w − wc )]
2

•This modulation shifts the frequency spectrum to the right and the
left by wc
wc
• The modulated signal is composed of two parts, above     and
below wc
wc
–  the upper sideband (USB) containing the frequencies |w| > |     |
wc
–  the lower sideband (LSB) containing the frequencies  |w| < |     |
•The modulated signal in this scheme does not have a discrete
wc
component of the carrier frequency      for this reason this is called
double-sideband suppressed carrier (DSB-SC) modulation

8

B   Vs wc

•If the bandwidth of the original signal m(t) is 2   B, then the
π
π
bandwidth of the modulated signal will be 4  B, consisting of
wc
–  the upper sideband (USB) containing the frequencies |w| > |     |
wc
–  the lower sideband (LSB) containing the frequencies  |w| < |     |

To avoid overlap of the two spectral parts, wc > 2πB must be fulfilled
(if ωc  < 2πB , the information of m(t) will be partly lost in the process of
modulation)

9


10


Spectrum

Spectrum of the DSB-SC signal m(t)cos10,000t
1
cos α cos β = cos(α + β ) + cos(α − β )
2

11


Spectrum


12


Spectrum


13

Modulation / Demodulation
Modulation

Demodulation

14

Demodulation
• The process of receiving the original signal from the modulated
signal is called demodulation.
• Demodulation is similar to modulation and can be performed by
multiplying the modulated signal again with the carrier signal cos( w t )
c

The resulting signal

e(t ) = m(t ) cos w t = 1 [ m(t ) + m(t ) cos(2 w t )]
2
2

c

c

It has the Fourier transform

E ( w) = 1 M ( w) + 1 [ M ( w + 2 w ) + M ( w − 2 w )]
2
4
c

c

15

Modulators
Multiplier modulators:
•Modulation is achieved directly by multiplying m(t) by t
cos wc
using an analog multiplier.
•The output is proportional to the product of two input signals.
•Difficult to maintain linearity and are expansive.
Better to avoid
Better to avoid

17

Modulators (cont…)
Nonlinear modulators:
Modulation is achieved by using nonlinear devices such as
semiconductor diode or a transistor
NL: Two identical
NL: Two identical
nonlinear elements
nonlinear elements

Let output characteristics of NL be approximated by the power series as:

Where x(t) and y(t) are input & output

18


Changing inputs

Gives:
19


•Spectrum m(t) is centered at the origin, while of m(t)coswct is centered at
+-wc
•The signal is ready for transmission but we do not need the m(t) part of z(t)
•Z(t) is passed through a band-pass filter tuned to wc , the signal m(t) is
suppressed while 4bm(t)coswct passed unharmed.

20

Summary nonlinear modulator:
•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.
•The previous circuitry is an example of balanced modulators.
This circuit is balanced to only one input carrier, the other input m(t) still appear at the
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 ititis called aasingle balanced modulator
filter input, which must reject it…….for that reason is called single balanced modulator

21

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. E.g:

Trigonometric Fourier series

Spectrum of the modulated signal is the spectrum M(w) shifted to
If we pass this modulated signal through band-pass filter of
bandwidth 2B tuned to wc

22

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. E.g:


Spectrum of the modulated signal is the spectrum M(w) shifted to
If we pass this modulated signal through band-pass filter of
bandwidth 2B tuned to wc

23

Switching Modulators
Multiplication operation of modulation can be replaced by switching
operation. If we a periodic signal having Fourier series as:
carrier
Modulated signal
Now consider a periodic square pulse train with Fourier series as

1 2
1
1
1

w(t ) = +  cos w t − cos 3w t + cos 5w t − cos 7 w t + .... 
2 π
3
5
7

c

c

c

From example 2.8
From example 2.8

c

24

The modulated signal m(t)w(t) is given by

25

Modulated signal m(t)w(t) consists of the component m(t) plus infinite
numbers of modulated signals with carrier frequencies w ,3w ,5w ,.....
c

c

c

The spectrum of m(t)w(t) consists of M(w) and M(w) shifted to
± w ,±3w ,±5w ,.....
c

c

c

As we are interested in modulated component m(t ) cos w t only. To
separate this component from others we pass m(t)w(t) through a
bandpass filter of bandwidth 2BHz, centered at ± w
c

c

gives the required modulated signal

2 m(t ) cos w t
π
c

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
26
controlled by w(t)

Diode bridge modulator:
Consider the following electronic switch circuit driven by A cos w t to produce
the switching action
c

D ,D
1

2

andD 3 , D 4

are matched pairs

When terminal c is positive with respect to d, all the diodes conduct, terminal
a & b are effectively shortened.
During the next half cycle d is positive with respect to c, all the diodes open,
terminal a & b are open.
27

Therefore the the circuit act as a desired electronic switch, where the terminal a
& b open and close periodically with the carrier frequency f c . When A cos wct
is applied across the terminal ab
To obtain m(t)w(t) we may place terminal ab in series or in parallel as:

Series-bridge diode modulator

Shunt-bridge diode modulator

Switching on and off m(t) for each cycle of the carrier, resulting in the
switched signal m(t)w(t) and passing through bandpass filter gives the
desired signal:
28

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

29

The Fourier series of bipolar square wave is given by:
Example 2.8 p-52
Example 2.8 p-52

Gives modulated signal as:

Filtering this signal to bandpass filter tuned to wc gives the
required modulated signal:

In this circuit there are two inputs m(t) and coswcct,the input of the final
In this circuit there are two inputs m(t) and cosw t, the input of the final
bandpass filter does not contain either of the inputs……
bandpass filter does not contain either of the inputs……
this circuit is an example of double balanced modulator
this circuit is an example of double balanced modulator

30

Problem 4.2-4

At point b

At point c
33

Problem 4.2-4
The minimum value of wc is

to avoid overlapping

Will not work

34

Problem 4.2-4

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.

35

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

36

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)

Frequency mixing or frequency conversion is also known as heterodyning.
All the modulators discussed previously can be used for frequency mixing.
Frequency selected as
Frequency selected as

operation called up-conversion
operation called down-conversion
37

Amplitude Modulation (AM)
For DSB-SC a receiver must generate a carrier in frequency and phase synchronism
with the carrier at the transmitter.
Problem:
Transmitter and receiver may be located thousands of miles away, this call for a
sophisticated receiver and could be costly.
Solution:
Transmit a carrier Acoswct along with the modulated signal m(t)coswct so no
need to generate a carrier at the receiver.

38

This type of modulation is called amplitude modulation and denoted by ϕ (t )
and is given by:
AM

It has the Fourier spectrum

The spectrum of ϕ (t ) is the same as m(t)coswct plus two additional impulses at± wc
AM

•DSB-SC signal m(t)coswct and AM signal
A+m(t) as modulating signal instead of m(t)

are identical with

•To sketch ϕ (t ) ,we sketch A+m(t) & -(A+m(t) ) and fill in between the carrier
frequency.
AM

39

As we sketch A+m(t) & -(A+m(t) ):
Consider two cases:

A + m(t ) ≥ 0 and

A + m(t ) ≤ 0

40

For simple envelope detection for AM signal is:

A = 0, also satisfies the condition. In this case there is no need to add carrier,
because the envelope of DSB-SC signal m(t)coswct is m(t)
Such a DSB-SC signal can be detected by envelope detection

Assume

for all t

Let mp is the peak amplitude (positive or negative) of m(t)
Then
Hence the condition is equivalent to
Thus the minimum carrier amplitude required for the envelope detection is mp
41

We define the modulation index

µ

as:
A = carrier amplitude
mp = constant of m(t)

As A is the carrier amplitude and there is no
upper bound on A,

This is the condition for the viability of demodulation of Am signal by an
envelope detector
42

Sideband and carrier power:
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 is given by
The sideband power Ps is given
by
Hence the power efficiency
is given by:

η

44

For the special case of tone modulation:

m(t ) = µA cos wmt

and

Hence
With condition
Thus under best condition only one third of the transmitted power is used for
carrying message, for practical signals the efficiency is even worst

45

Generation of AM signals
• 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 aasingle diode
Switching action is provided by single diode
and controlled by c cos wc t with
and controlled by
with

46

Generation of AM signals

The diode opens and short periodically with
The diode opens and short periodically with
multiplying the input signal by w(t).
multiplying the input signal by w(t).

infect
infect

The voltage across bb / is:

47

Demodulation of AM Signals
The AM signal can be demodulated coherently by a locally generated carrier. E.g.

[[ A + m(t )] cos wct ] cos wct

No benefit of sending carrier on the channel
No benefit of sending carrier on the channel

There are two well known methods of demodulation of AM signals:
1) Rectifier detection 2) Envelope detection

Rectifier detector:
AM signal is applied to a diode and resistor circuit, the negative part of the 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).
48

Rectifier Detector

The rectified output VR

{[

]}

vR = A + m(t ) cos w t w(t )
c
1 2 
1
1

= [ A + m(t )] cos w t  +  cos w t − cos 3w t + cos 5w t − ...
c 2 π 
c 3
c 5
c


=

1
[ A + m(t )] + otherTerms
π

49

Rectifier Detector (cont…)

50

Envelope 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.
•When input signal falls below this peak value, the diode is 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.

51

Envelope Detector (cont…)

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

52

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.

Conditions:
RC should be large compared to 1/wc, but should be small compared to 1 2πB
Where B is the highest frequency in m(t)

Also requires

a condition which is necessary for well defined envelope.

53

The envelope detector output is

with a ripple of frequency w c

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.

54

Quadrature Amplitude Modulation
The DSB signals of AM require twice the bandwidth required for the baseband
signal!
Idea: 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 –π/2
The combined signal is

m1 (t ) + m2 (t ) = m1 (t ) cos wc t + m2 (t ) sin wc t

55

Quadrature Amplitude Modulation (cont…)
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 –π/2
• The first signal m1(t) can be detected by a multiplication with 2cos(ωct) followed
by a low-pass filter

The second signal x2(t) can be detected accordingly by a multiplication with
sin(ωct) followed by a low-pass filter
56

Quadrature Amplitude Modulation
(cont…)
• 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.

57

Amplitude Modulation (Single Sideband SSB)
• The DSB spectrum has two sidebands: USB and LSB
• Both USB and LSB contain complete information of the baseband
signal.
• 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
signal.
• An SSB signal can be coherently (synchronously) demodulated. E.g.
For example multiplying USB signal by cos wc t shifts its spectrum to
the left and right by wc
58

Single Sideband SSB (cont..)

Low pass filtering will give the required baseband signal at the
receiver.
59

Single Sideband SSB (cont..)
Time domain representation of SSB signals:

ϕ SSB (t ) = m(t ) cos wct ± mh (t ) sin wc t
mh (t ) Hilbert Transform of m(t)
Hilbert Transform of m(t)

π
and delays the phase of each component by 2
and delays the phase of each component by

Where minus sign applies to USB and the plus sign applies to LSB

60

Example 4.7 p-174
Tone Modulation:
Find ϕ SSB (t ) for a simple case of tone modulation, that is, when the
modulating signal is a sinusoid m(t ) = cos wmt
Solution:

ϕ SSB (t ) = m(t ) cos wc t ± mh (t ) sin wc t

61

Generation of SSB Signals
Two methods are generally used to generate SSB signals.
1) Sharp cutoff filters
2) Phase shifting networks
Selective Filtering Method:
• In this method the DSB-SC signal is passed through a sharp cutoff
filter to eliminate the undesired sideband.
• 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.
64

Generation of SSB Signals
• 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 the
origin. Thus filtering the unwanted sideband is relatively
easy.

Tests have shown that frequency components
Tests have shown that frequency components
below 300Hz are not important.
below 300Hz are not important.

600Hz transition region around the cutoff
600Hz transition region around the cutoff
frequency w cc, ,makes filtering easy and
frequency w makes filtering easy and
minimize the channel interference
minimize the channel interference
65

Generation of SSB Signals(cont…)
Phase-Shift Method:
The basis of this method is the following equation

ϕ SSB (t ) = m(t ) cos wc t ± mh (t ) sin wc t

66

Generation of SSB Signals(cont…)

67

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