Chapter 5

3/23/2014
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 5
Dr. Sarmad Ullah Khan
Angle Modulation and
Demodulation
2

3/23/2014
2
Outlines
• Non Linear Modulation
B d idth f A l M d l t d W
• Bandwidth of Angle‐Modulated Waves
• Generating FM Waves
• Demodulation of FM Signals
3
Outlines
4

3/23/2014
3
Non Linear Modulation
• Modulation of carrier signal can be achieved by
amplitude phase and frequency
amplitude, phase and frequency
• Modulating amplitude results in amplitude
modulation
• Modulating frequency results in frequency
modulation
• Modulating phase results in phase modulationg p p
• Frequency modulation and phase modulation
collectively called angle modulation
5
• Noise power reduction
• Reduce bandwidth by using modulation schemes
• Reduce bandwidth by using modulation schemes
• Bandwidth reduction means more users
• FM varies frequency of carrier w.r.t. signal m(t)
w(t) = wc(t) + km(t)
• If mp is peak amplitude of m(t)
M d i l f i f ld b• Max. and min. value of carrier frequency would be
wc + kmp , wc - kmp
• Spectral component remains with the band of 2kmp
6

3/23/2014
4
• Means k control the bandwidth
• In practice it was not true
• In practice, it was not true
• FM bandwidth is greater than AM bandwidth
• AM varies the amplitude of carrier signal while FM
varies the instantaneous frequency of carrier signal
• Means carrier frequency change continuously• Means carrier frequency change continuously
• Consider a sinusoidal signal
7
)(cos)( tAt  
• (t) = instantaneous phase (radians)
• Hypothetical case of (t)
Hypothetical case of (t)
• Acos(wct + 0)
• (t) tangent to (wct + 0) at ‘t’
• When ∆t→0
Acos(wct + 0) = Acos(t)
• Angular frequency of is wc
8
)cos()( 0  tAt c 21 ttt 
)(t

3/23/2014
5
• (t) = instantaneous phase (radians)
• (w t +  ) is slop to (t)
• (wct + 0) is slop to (t)
• Instantaneous frequency wi at
any instant is a slop to (t)
dt
d
twi

)(
• Angle of carrier vary with m(t)
9
 dwt
t
ii )()(  

• In PM, angle (t) vary linearly with m(t):
• kp is constant and wc is carrier frequency
• When 0 = 0
PM  )(cos tmktwA pc 
  dtktdd )()()(
• The wi varies linearly with the derivative of modulating
signal
10
)(twi
 
dt
tdm
kwc
dt
tmktwd
dt
td
p
pci )()()(





3/23/2014
6
• As wi varies linearly with modulating signal, we
have FM
have FM
)(twi )(tmkw fc 
)(ti  dmktwdw
t
fc
t
i )()(  

FM 





 
t
fc dmktwA )(cos
11


)(ti )(tmktw pc 
PM
PM
)(twi
 )(cos tmktwA pc 
 
dt
tdm
kwc
dt
tmktwd
dt
td
p
pci )()()(




FM
)(twi )(tmkw fc 
12TASK: Make block diagrams of PM and FM modulators
f
t
fc
t
i )()(  

FM 





 
t

3/23/2014
7
)(ti
PM
)(tmktw pc 
 )(cos tmktwA pc 
PM
PM
)(tw i
 )(pc
 
dt
tdm
kwc
dt
tmktwd
dt
td
p
pci )()()(




Direct
Phase
modulator PM wave
Modulating
signal
source
twAcos
13
twA ccos
Indirect
Modulating
signal
source
Differentiator
Frequency
modulator
PM wave
twA ccos
FM )(twi )(tmkw fc 
t
fc
t
i )()(  
Direct
Modulating
signal source
Frequency
modulator FM wave
twAcos
fci  
FM 





 
t
14
Indirect
twA ccos
Integrator
Phase
modulator
FM wave
Modulating
signal source
twA ccos

3/23/2014
8
Example 5.1
15
Example 5.1
16

3/23/2014
9
Outlines
17
Bandwidth of Angle‐Modulated Waves
• Angle modulation is non linear
• Bandwidth analysis cannot be done directly by
• Bandwidth analysis cannot be done directly by
Fourier transform
• For bandwidth of FM, let
a(t) = 
t
dm )(
18

tjwtajktaktwj
FM
cffc
eAeAet
)()]([
)( 



)](Re[)( tt FMFM 



3/23/2014
10
• And
• Modulated wave consists of unmodulated carrier
plus various amplitude modulated terms
19
• The signal a(t) is the integral of m(t)
• If M(f) is band limited to B then A(f) is also band
• If M(f) is band limited to B, then A(f) is also band
limited to B
• Spectrum of a2(t) is simply A(f)*A(f) and is band
limited to 2B
• an(t) is band limited to nB
• Hence modulated wave has unmodulated carrierHence modulated wave has unmodulated carrier
and spectrum of a(t), a2(t),….., an(t) centered wc
• Modulated wave is not band limted
• However, in practice bandwidth of FM is finite
20

3/23/2014
11
• Because n! increases much faster than |kfa(t)|n
Narrow Band Angle Modulation
• When kf is very small such that
|k (t)| << 1
0
!
)(

n
tak nn
f
|kfa(t)| << 1
then
• This approximation is linear like AM expression
21
]sin)([cos)( ttaktAt cfcFM  
• Bandwidth of a(t) is B, bandwidth of is 2B
• Narrow band PM signal is approximated as
)(tFM
• Narrow band PM signal is approximated as
• NBPM has approximate bandwidth of 2B
]sin)([cos)( ttmktAt cPcPM  
22

3/23/2014
12
Wideband FM bandwidth Analysis
• FM signal is meaningful if frequency deviation is
• FM signal is meaningful if frequency deviation is
large enough
• Practically, kf is large such that |kfa(t)| << 1 not
satisfied
• Hence, we have wideband FM signal (WBFM)
• Consider m(t) and its stair case )(tm
Consider m(t) and its stair case
• Each pulse is called cell
23
)(tm
24

3/23/2014
13
• FM signal correspond to single cell has frequency
• FM signal correspond to single cell has frequency
wc+kfm(tk) and duration 1/2B
• Fourier transform of sinusoidal pulses correspond
to a cell is a sinc function
• Minimum and maximum frequencies are wc-kfmp
and wc+kfmpc f p
• Peak frequency deviation and estimate FM
bandwidth is
25
• In NBFM
• In NBFM
26

3/23/2014
14
Example
27
Outlines
28

3/23/2014
15
Generating FM Waves
• Two ways of generating FM waves
– Direct
– Direct
– Indirect
• NBFM Generation
29
Generating FM Waves
• Indirect method (Armstrong)
– NBFM is converted to WBFM using frequency
– NBFM is converted to WBFM using frequency
multiplier
– Frequency multiplier is realized by a non linear device
followed by bandpass filter
30

3/23/2014
16
Generating FM Waves
– Output spectra will be at wc, 2wc, ….., nwc
– Device having nonlinearity and bandpass filter called
frequency multiplierfrequency multiplier
– Such multiplier increase carrier freq. and freq. deviation
– This is basis of Armstrong freq. modulators
31
Generating FM Waves
– Generally freq deviation is increase by factor ‘n’ which
– Generally, freq. deviation is increase by factor n which
also increase carrier freq.
– Freq. mixing is applied to reduce carrier freq. to desire
value
32

3/23/2014
17
Generating FM Waves
• Direct method
– IN Hartley or Colpitt oscillators, frequency is given by
– If C varies by m(t) as
33
Generating FM Waves
• Direct method
– Then
– Then
34

3/23/2014
18
Generating FM Waves
• Direct method
35
Problem 5.3‐2
36

3/23/2014
19
Outlines
37
Demodulation of FM Signals
38

3/23/2014
20
39
40

3/23/2014
21
Problem 5.4‐2
41
Problem 5.4‐2
Solution:
42

Chapter 5

More Related Content

What's hot

Viewers also liked

Similar to Chapter 5

More from Fawad Masood

Recently uploaded

Chapter 5