Transcript ekt 231 : communication system chapter 3 : angle modulation

EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
ANGLE MODULATION
CHAPTER 3
Review on Part 1
Part 2
1
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Review on
Part 1
ANGLE MODULATION
2
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Define the following…..
Modulation
Demodulation
Amplitude modulation (AM)
Angle modulation (FM,PM)
Modulating signal
Carrier signal
Bandwidth
3
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Introduction
• Angle modulation is the process by which
the angle (frequency or Phase) of the
carrier signal is changed in accordance
with the instantaneous amplitude of
modulating or message signal.
• also known as “Exponential modulation"
4
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Cont’d…
• Classified into two types ;
– Frequency modulation (FM)
– Phase modulation (PM)
• Used for :
–
–
–
–
–
Commercial radio broadcasting
Television sound transmission
Two way mobile radio
Cellular radio
Microwave and satellite communication system
5
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Cont’d…
Advantages over AM:
Freedom from interference: all natural and
external noise consist of amplitude variations,
thus receiver usually cannot distinguish
between amplitude of noise or desired signal.
AM is noisy than FM.
Operate in very high frequency
band(VHF):88M-108MHz
Can transmit musical programs with higher
degree of fidelity.
6
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FREQUENCY MODULATION
PRINCIPLES
• In FM the carrier amplitude remains constant, the
carrier frequency varies with the amplitude of
modulating signal.
• The amount of change (the relative displacement of
carrier frequency in hertz in respect to it un-modulated
value) in carrier frequency produced by the modulating
signal is known as frequency deviation.
7
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
PHASE MODULATION (PM) PRINCIPLES
• The process by which changing the phase of carrier
signal in accordance with the instantaneous of
message signal. The amplitude and frequency
remains constant after the modulation process.
• Mathematical analysis:
Let message signal:
 m t   Vm cos mt
And carrier signal:
 c t   Vc sin[ ct   ]
8
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
PM (cont’d)
• After phase modulation, with
  KVm (t )  KVm cosmt
the instantaneous voltage will be
vPM (t )  VC sin(Ct  KVm cosmt )
vPM (t )  VC sin(Ct  mp cosmt )
• where
mp = Modulation index of phase modulation
K = a constant and called deviation sensitivities of
the phase
 = phase angle of carrier signal .It is changed in
accordance with the amplitude of the message signal
9
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FREQUENCY MODULATION(FM)
• A process where the frequency of the carrier wave
varies with the magnitude variations of the
modulating or audio signal.
• The amplitude of the carrier wave is kept constant.
10
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM(cont’d)
• Mathematical analysis:
• Let message signal:
 m t   Vm cos mt
• And carrier signal:
 c t   Vc cos[ ct   ]
11
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM (cont’d)
• During the process of frequency modulations the
frequency of carrier signal is changed in
accordance with the instantaneous amplitude of
the message signal .Therefore the frequency of
carrier after modulation is written as
i  c  Kvm t   C  KVm cosmt
• To find the instantaneous phase angle of modulated
signal, integrate equation above w.r.t. t
i   i dt   C  KVm cosmt dt  C t 
KVm
m
sin mt
12
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM(cont’d)
• Thus, we get the FM wave as:
vFM (t )  Vc cos1  VC cos(C t 
KVm
m
sin mt )
vFM (t )  VC cos(Ct  m f sin mt )
• Where
mf 
KVm
m
Known as the modulation index for the FM
13
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM(cont’d)
• Frequency deviation: ∆f is the relative
displacement of carrier frequency (Hz) w.r.t its
unmodulated value. Given as:
max  C  KVm
min  C  KVm
d  max  C  C  min  KVm
d KVm
f 

2
2
• Where K is the deviation sensitivity in Hz/V
14
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM(cont’d)
• The peak to peak frequency deviation (2Δf) is
called the carrier swing.
• Therefore:
KVm
f 
2
• The modulation index is
f
mf 
fm
15
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
•
Example 3.1
(a) An FM modulator with
Deviation sensitivity, K1=5kHz/V
Modulating signal Vm(t)=2cos(2π2000t)
Determine
(i) The peak frequency deviation(Δf) : Ans:10kHz.
(ii) The modulation index (m) : 5 (unitless)
Hint:
KVm
f 
 K1Vm
2
f
mf 
fm
16
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Angle-modulated wave in the frequency domain.
17
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
•
Example 3.2
(a) A PM modulator with
Deviation sensitivity, K=2.5rad/V
Modulating signal Vm(t)=2cos(2π2000t)
Determine
(i) The peak phase deviation(m) : Ans: 5 rad
Hint: Peak phase shift for modulated wave is the modulation index itself.
m  KV m
18
Phase and frequency modulation of a sine-wave carrier by a sine-wave signal: (a) unmodulated
carrier; (b) modulating signal; (c) frequency-modulated wave; (d) phase-modulated wave
19
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM&PM (Bessel function)
• Thus, for general equation:
vFM (t )  VC cos(Ct  m f cosmt )
vFM (t )  VC sin(Ct  m f sin mt )
 VC sin Ct cos(m f sin mt )  cosct sin(m f sin mt )
20
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Bessel function
vt FM  VC [ J 0 (m f ) sin Ct  J1 (m f )sin(C  m )t  sin(C  m )t 
 VC [ J 2 (m f ) sin(C  2m )t  sin(C  2m )t
 VC [ J 3 (m f ) sin(C  3m )t  sin(C  3m )t ]  ..
21
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Representation of frequency spectrum
22
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Bessel Functions of the First Kind, Jn(m)
for some value of modulation index
23
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
•
Example 3.2
(a) An FM modulator with
m=1
Modulating signal Vm(t)=Vmsin(2π1000t)
Unmodulated carrier V c(t)=10sin(2π500kt)
Determine
(i) Number of sets of significant side frequencies
(Ans: 1 carrier + 3 sets sides freq.)
(ii) Their amplitudes
(iii) Draw the frequency spectrum
Hint: (i), (ii), (iii) use table of Bessel functions of the First Kind, Jnm
24
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Solution
(ii) Their amplitude
J0=0.77(10)
J1=0.44(10),
J2=0.11(10)
J3=0.02(10)
; Carrier
; 1st sideband pairs
; 2nd sideband pairs
; 3rd side band pairs
25
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Solution (cont’d)
(iii) Draw the frequency spectrum.
6kHz
26
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Angle Modulation
Part 2
•FM Bandwidth
•Power distribution of FM
•Generation & Detection of FM
•Application of FM
27
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM Bandwidth
• Theoretically, the generation and transmission of FM
requires infinite bandwidth. Practically, FM system have
finite bandwidth and they perform well.
• The value of modulation index determine the number of
sidebands that have the significant relative amplitudes
• If n is the number of sideband pairs, and line of frequency
spectrum are spaced by fm, thus the actual minimum
bandwidth using Bessel table:
B fm  2nfm
• With n = number of significant sidebands
fm
= modulating signal frequency
28
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM Bandwidth (cont’d)
Carson’s rule also can be used to estimate the
bandwidth regardless of modulation index
B fm  2(f  f m )
29
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
•Example 3.3
An FM modulator has the following information;
É f = 10kHz;
Vc = 10V
f m = 10kHz
f c = 500kHz
Determine
(a)Actual minimum bandwidth from the B.F table : Ans=60kHz.
(b)Approximate minimum bandwidth using Carson’s rule.
(c)Plot the output frequency spectrum for the Bessel
approximation
Hint: m  f
B  2nf
f
fm
fm
m
B fm  2(f  f m )
30
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Solution
Given;
É f = 10kHz;
Vc = 10V f m = 10kHz f c = 500kHz
(a)Actual minimum bandwidth from the B.F table.
m=10kHz/10kHz=1, from B.F table, B=2(3x10kHz)=60kHz.
(b) Approximate minimum bandwidth using Carson’s rule.
B fm  2(f  f m )  2(10kHz 10kHz)  40kHz.
31
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
(c) Plot the output frequency spectrum for the Bessel
approximation
32
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Deviation Ratio (DR)
• The worse case modulation index which produces the
widest output frequency spectrum.
DR 
f (max)
f m (max)
• Where
∆f(max) = max. peak frequency deviation
fm(max) = max. modulating signal frequency
33
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Example 3.4
An FM broadcast-band transmitter has a maximum
frequency deviation of 75kHz and a maximum
modulating signal frequency of 15kHz. Determine the
deviation ratio bandwidth.
Solution
The deviation ratio (i.e the worst case modulation index).
DR 
f (max)
f m (max)
75 kHz
 15
kHz  5
From the B.F table, a modulation index of 5 gives 8
significant sidebands.
Then B=2(8x15kHz)=240kHz.
34
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM Power Distribution
• As seen in Bessel function table, it shows that as the
sideband relative amplitude increases, the carrier
amplitude,J0 decreases.
• This is because, in FM, the total transmitted power is
always constant and the total average power is equal to
the unmodulated carrier power, that is the amplitude of
the FM remains constant whether it is modulated or not.
• The total power in angle-modulated wave is equal to the
power of the un-modulated wave.
35
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM Power Distribution (cont’d)
• In effect, in FM, the total power that is originally in the
carrier is redistributed between all components of the
spectrum, in an amount determined by the modulation
index, mf, and the corresponding Bessel functions.
• At certain value of modulation index, the carrier
component goes to zero, where in this condition, the power
is carried by the sidebands only.
36
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Average Power
•
The average power in unmodulated carrier
•
The total power in the angle modulated carrier.
m(t ) 2 Vc2
Pt 

cos2 [ct   (t )]
R
R
2
Vc2  1 1
 Vc
Pt 
  cos[2ct  2 (t )] 
R 2 2
 2R
•
Vc2
Pc 
2R
The modulated carrier power is the sum of the powers of the carrier and
the side frequency components as follow;
Vc2 2(V1 ) 2 2(V2 ) 2
2(Vn ) 2
Pt  P0  P1  P2  ..  Pn 


 .. 
2R
2R
2R
2R
Vc=peak unmodulated carrier voltage (volts), Vn= sidebands voltage
(volts), Pc=Carrier power, R=Resisitive load (ohms)
37
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Example 3.5
An FM modulator has the following information;
m = 1; vm( t ) = Vmsi n (2ù1000t )
vc( t ) = 10si n (2ù500kt )
Determine;
(i) The unmodulated carrier power for the FM modulator
(Assume RL=50Ω)
102
Vc2
Pc 

 1W
2R 2(50)
(i) The total power in the angle modulated wave.
Vc2 2(V1 ) 2 2(V2 ) 2 2(V3 ) 2
Pt 



 1.0051W
2R
2R
2R
2R
38