Chapter 5
AM, FM, and Digital Modulated Systems





Amplitude Modulation (AM)
Double Sideband Suppressed carrier (DSSC)
Assymetric Sideband Signals
Single sideband signals (SSB)
Frequency Division Multiplexing (FDM)
Huseyin Bilgekul
Eeng360 Communication Systems I
Department of Electrical and Electronic Engineering
Eastern Mediterranean University
Eeng 360 1
Bandpass Signaling Review
 The modulated bandpass signal can be described by
s(t )  Re{ g (t )e j C t }
Where
c  2f c ;
m(t) →g(t)
Modulation Mapping function: Convert
V( f ) 
 The voltage spectrum of the bandpass signal is
The PSD of the bandpass signal is
Where G f   F g t ;
Pv ( f ) 
f c - Carier Frequency

Ref : Table 4-1


1
G  f  f c   G *  f  f c 
2

1
Pg  f  f c   Pg  f  f c 
4
Pg  f  - PSD of the complex envelope g(t);
Eeng 360 2
Amplitude Modulation
 The Complex Envelope of an AM signal is given by
g (t )  Ac [1  m(t )]
Ac indicates the power level of AM and m(t) is the Modulating Signal
 Representation of an AM signal is given by
s(t )  Ac [1  m(t )]cos ct
 Ac[1+m(t)]
In-phase component x(t)
 If m(t) has a peak positive values of +1 and a peak negative value of -1
AM signal  100% modulated
 Envelope detection can be used if % modulation is less than 100%.
Eeng 360 3
Amplitude Modulation
An Example of a message signal m(t)
Waveform for Amplitude modulation of the message signal m(t)
Eeng 360 4
Amplitude Modulation
B
An Example of message energy spectral density.
Carrier component together
with the message
2B
Energy spectrum of the AM modulated message signal.
Eeng 360 5
AM – Percentage Modulation
 Definition: The percentage of positive modulation on an AM signal is
% Positive Modulation 
Amax  Ac
100  max  m(t )  100
Ac
 The percentage of negative modulation on an AM signal is
Ac  Amin
100   min  m(t )  100
Ac
 The percentage of overall modulation is
max  m(t )  min  m(t )
Amax  Amin
% Modulation 
100 
100
2 Ac
2
Amax - Maximum value of Ac [1  m(t )]
Amin - Minimum value of Ac [1  m(t )]
Ac - Level of AM envelope in the absence of modulation [i.e., m(t)  0]
If m(t) has a peak positive values of +1 and a peak negative value of -1
AM signal  100% modulated
Eeng 360 6
AM Signal Waveform
Amax = 1.5Ac
Amin = 0.5 Ac
% Positive modulation= 50%
% Negative modulation =50%
Overall Modulation = 50%
Eeng 360 7
AM – Percentage Modulation
Under modulated (<100%)
100% modulated
Over Modulated (>100%)
Envelope Detector
Envelope Detector
Can be used
Gives Distorted signal
Eeng 360 8
AM – Normalized Average Power
The normalized average power of the AM signal is
1
1
2
2
g t   Ac2 1  mt 
2
2
1
 Ac2 1  2mt   m 2 t 
2
1
1
 Ac2  Ac2 mt   Ac2 m 2 t 
2
2
s 2 t  


If the modulation contains no dc level, then mt   0
The normalized power of the AM signal is
s 2 t  
1 2
1 2 2
Ac 
Ac m t 
2
2
Discrete Carrier Power
Sideband power
Eeng 360 9
AM – Modulation Efficiency
 Definition : The Modulation Efficiency is the percentage of the total power
of the modulated signal that conveys information.
Only “Sideband Components” – Convey information
Modulation Efficiency:
E
m2  t 
1  m t 
2
100
Highest efficiency for a 100% AM signal : 50% - square wave modulation
Normalized Peak Envelope Power (PEP) of the AM signal:
PPEP
Ac2
1  max mt 2

2
Voltage Spectrum of the AM signal:
Ac
  f  f c   M  f  f c     f  f c   M  f  f c 
S( f ) 
2
Unmodulated Carrier
Spectral Component
Translated Message Signal
Eeng 360 10
Example 5-1. Power of an AM signal
Suppose that a 5000-W AM transmitter is connected to a 50 ohm load;
Then the constant Ac is given by
1 Ac2
 5,000  Ac  707 V
2 50
Without
Modulation
If the transmitter is then 100% modulated by a 1000-Hz test tone ,
the total (carrier + sideband) average power will be
 1  Ac2 
  1.5  5000   7,500W
1.5 
2
50
 

1
 2

 m t   2 for 100% modulation 


The peak voltage (100% modulation) is (2)(707) = 1414 V across the 50 ohm load.
The peak envelope power (PEP) is
 1  Ac2 
  4   5000   20,000W
4  
2
50
 

The modulation efficiency would be 33% since < m2(t) >=1/2
Eeng 360 11
Double Side Band Suppressed Carrier (DSBSC)
 Power in a AM signal is given by
s 2 t  
1 2
1 2 2
Ac 
Ac m t 
2
2
Carrier Power
 DSBSC is obtained by eliminating carrier component
If m(t) is assumed to have a zero DC level, then
Spectrum  S ( f ) 
Sideband power
s(t )  Ac m(t ) cos ct
Ac
M  f  f c   M  f  f c 
2
1 2 2
Power 
s t  
Ac m t 
2
m 2 t 
Modulation Efficiency 
E 2
100  100%
m t 
2
Disadvantages of DSBSC:
• Less information about the carrier will be delivered to the receiver.
• Needs a coherent carrier detector at receiver
Eeng 360 12
DSBSC Modulation
s(t )  Ac m(t ) cos ct
B
An Example of message energy spectral density.
No Extra Carrier
component
2B
Energy spectrum of the DSBSC modulated message signal.
Eeng 360 13
Carrier Recovery for DSBSC Demodulation
 Coherent reference for product detection of DSBSC can not be obtained by the
use of ordinary PLL because there are no spectral line components at fc.
Eeng 360 14
Carrier Recovery for DSBSC Demodulation
 A squaring loop can also be used to obtain coherent reference carrier for product
detection of DSBSC. A frequency divider is needed to bring the double carrier
frequency to fc.
Eeng 360 15
Single Sideband (SSB) Modulation
 An upper single sideband (USSB) signal has a zero-valued spectrum for
 A lower single sideband (LSSB) signal has a zero-valued spectrum for
f  fc
f  fc
 SSB-AM – popular method ~ BW is same as that of the modulating signal.
Note: Normally SSB refers to SSB-AM type of signal
USSB
LSSB
Eeng 360 16
Single Sideband Signal
 Theorem : A SSB signal has Complex Envelope and bandpass form as:
ˆ t 
g t   Ac mt   jm
ˆ (t ) sin ct 
st   Ac mt  cos ct  m
mˆ (t ) – Hilbert transform of m(t)  m
ˆ t   mt   ht 
H  f   ht 
 j ,
H f   
 j,
Hilbert Transform corresponds to a -900 phase shift
and
Upper sign (-)
Lower sign (+)
Where

USSB

LSSB
1
ht  
t
f 0
f 0
H(f)
j
-j
f
Eeng 360 17
Single Sideband Signal
Proof: Fourier transform of the complex envelope




G  f   Ac M  f   j mˆ  t   Ac M  f   jMˆ ( f )
Using
ˆ t   mt  ht 
m
2 Ac M  f ,
G f   
0,
Recall from Chapter 4
Upper sign  USSB
Lower sign  LSSB
 G f   Ac M  f 1  jH  f 
f  0

f  0
V( f ) 
1
G( f  f c )  G * [( f  f c )]
2
f   fc 
M  f  f c , f  f c 
0,
S  f   Ac 

A


c


0
,
f

f
M
f

f
,
f


f
c
c
c 


Upper sign  USSB
If lower signs were used  LSSB signal would have been obtained
Eeng 360 18
Single Sideband Signal
2 Ac M  f ,
G f   
0,
f  0

f  0
 M  f  f c  , f  f c 
S  f   Ac 

f  f c 
0,
f   f c 
0,
Ac 

M
f

f
,
f


f

c
c
 
Eeng 360 19
SSB - Power
The normalized average power of the SSB signal
s 2 t  
1
1
2
2
g (t )  Ac2 m 2 t   mˆ t 
2
2
Hilbert transform does not change
power.
SSB signal power is:
2
mˆ t   m 2 t 
s 2 t   Ac2 m 2 t 
Power gain factor
Power of the modulating signal
The normalized peak envelope (PEP) power is:
1
1 2 2
2
2
max g (t )  Ac m t   mˆ t 
2
2
Eeng 360 20
Generation of SSB
SSB signals have both AM and PM.
The complex envelope of SSB:
ˆ t 
g t   Ac mt   jm
For the AM component,
Rt   g t   Ac m 2 t   mˆ t 
For the PM component,
2
  mˆ t 
 t   g t   tan 

 mt  
1
Advantages of SSB
• Superior detected signal-to-noise ratio compared to that of AM
• SSB has one-half the bandwidth of AM or DSB-SC signals
Eeng 360 21
Generation of SSB

SSB Can be generated using two techniques
1.
2.

Phasing method
Filter Method
Phasing method g t   Ac mt   jmˆ t 
This method is a special modulation type of IQ canonical form
of Generalized transmitters discussed in Chapter 4 ( Fig 4.28)
Eeng 360 22
Generation of SSB

Filter Method
The filtering method is a special case in which RF processing (with a
sideband filter) is used to form the equivalent g(t), instead of using
baseband processing to generate g(m) directly. The filter method is the
most popular method because excellent sideband suppression can be
obtained when a crystal oscillator is used for the sideband filter.
Crystal filters are relatively inexpensive when produced in quantity at
standard IF frequencies.
Eeng 360 23
Weaver’s Method for Generating SSB.
Eeng 360 24
Generation of VSB
Eeng 360 25
Frequency Divison Multiplexing
Eeng 360 26