Matakuliah : H0122 / Dasar Telekomunikasi
Tahun
: 2008
Modulasi Frekuensi
Pertemuan 4
Learning Outcomes
Mahasiswa dapat menjelaskan teknik modulasi frekuensi
dan karakteristiknya.
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Outline Materi
• Prinsip Modulasi Frekuensi
• Bandwidth
• Hubungan dengan Modulasi Fasa
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Angle Modulation
• The angle modulation can be expressed mathematically as:
m(t) = Vccos [ωct + (t)]
 m(t)= angle modulated wave
 Vc = peak carrier amplitude (Volt)
 c = carrier radian frequency (rad/sec)
 (t ) = instantaneous phase deviation (radians)
• The magnitude of the frequency (f) and phase deviation () is
proportional to the amplitude of the modulating signal, V m and the
rate at which the changes are occurring is equal to the modulating
signal frequency, fm.
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Angle Modulation
• Frequency & Phase Modulation (FM & PM) are both forms of Angle
Modulation.
• Because of its superior performance than AM, it is used extensively
for commercial broadcasting radio broadcasting, television sound
transmission, 2-way mobile radio, cellular radio, microwave and
satellite communications systems.
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Frequency Modulation
• Frequency Modulation is the process of changing carrier
frequency by the modulating signal while the carrier amplitude
remains constant.
• As the modulating signal amplitude increases, the carrier
frequency increases and vice versa.
• The amount of change in carrier frequency produced by the
modulating signal is called Frequency Deviation (f).
Meanwhile, the change in phase is called Phase Deviation ()
• The deviation is proportional to the amplitude of the modulating
signal.
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Frequency Modulation
• FM produces pairs of sidebands spaced from the carrier in
multiples of the modulating frequency.
• The modulation index m of FM signal is the ratio of the frequency
deviation fd to the modulating frequency, fm (m = f d / fm)
• The modulation index determines the number of significant pairs of
sidebands in FM signals.
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Frequency Modulation
The frequency of a harmonic carrier signal is varied in such a way
that the instantaneous frequency deviation i.e. the difference
between the instantaneous frequency and the carrier frequency
is linearly related to the size of the modulating signal at a given
instant of time.
inst  t   c  K f vm  t 
t
t
0
0
inst  t    inst  t  dt ct   K f vm  t  dt
vFM
t


 t   Vc cos  ct   K f vm  t  dt   c 
0


Kf is the frequency deviation sensitivity
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 rad / s 
 Volt 
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Modulation Index
• Frequency modulation index is defined as
m = Kf Vm/ωm
• Frequency deviation which is the change in carrier when acted on
by a modulating signal frequency is given by:
 Peak frequency shift in hertz
 Peak-to-peak frequency deviation of carrier swing
• Therefore m can be rewritten as
m=Δf /fm
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PM & FM Waveform
Carrier
Modulating
signal
FM
PM
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Spektrum
vangle  t   Vc cos c t  m cos  mt  
cos   m cos   
n 

J
m
cos


n




 n


2 

n 

Jn (m) is the Bessel function of the first kind
vangle  t   Vc
n 

J
m
cos

t

n

t



 n
m
 c

2 

n 

 J 0  m  cos c t 









vangle  t   Vc  J1  m  cos c  m  t    J1  m  cos c  m  t   

2
2






 J  m  cos   2  t     J  m  cos   2  t     .....
m
2
m
 c

 c

 2

FM:
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m
K f Vm
m
PM:
m  K pVm
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Spektrum
•
•
•
•
m
= modulation index
Vc = peak amplitude of the unmodulated carrier
J0(m) = carrier component
J1(m)= first set of side frequencies displaced from
the carrier by ωm
• J2(m) = second set of side frequencies displaced
from the carrier by 2ωm
• Jn(m) = nth set of side frequencies displaced from
the carrier by nωm
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Spektrum
FM modulator: f = 10 kHz, fm = 10 kHz, Vc = 10 V, fc = 500 kHz, m=1
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Bandwidth
Low-index modulation (narrowband FM)
m <1 (fm>>f), B = 2fm
High-index modulation (wideband FM)
m >10 (f >>> fm), B = 2fm
Actual bandwidth
B = 2nfm
(use Bessel table, n = number of significant sidebands)
Carson’s rule (approx 98% of power)
B = 2 (f + fm)
Δf = peak frequency deviation
fm = modulating frequency
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FM & PM Modulator
• FM modulator = integrator followed by a PM Modulator
• FM Demodulator = PM demodulator followed by a
differentiator
• PM Modulator = Differentiator followed by an FM Modulator
• PM Demodulator = FM demodulator followed by an integrator
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Frequency Modulator
Modulating
signal
source
Frequency
modulator
FM wave
Direct
Vccos(2πfct)
inst  t   c  K f vm  t 
t
t
inst  t    inst  t  dt ct   K f vm  t  dt
0
0


 t   Vc cos  ct   K f vm  t  dt 
0


t
vFM
Kf is the deviation sensitivity
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Summary
• Telah dipelajari karakteristik modulasi sudut
• Telah dipelajari modulasi frekuensi
• Telah dipelajari peran sidebands.
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