z. ghassemlooy angle modulation professor z ghassemlooy electronics & it division scholl of...
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Z. Ghassemlooy
Angle Modulation
Professor Z Ghassemlooy
Electronics & IT DivisionScholl of Engineering
Sheffield Hallam UniversityU.K.
www.shu.ac.uk/ocr
Professor Z Ghassemlooy
Electronics & IT DivisionScholl of Engineering
Sheffield Hallam UniversityU.K.
www.shu.ac.uk/ocr
Z. Ghassemlooy
Contents
Properties of Angle (exponential) Modulation Types
– Phase Modulation– Frequency Modulation
Line Spectrum & Phase Diagram Implementation Power
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Properties
Linear CW Modulation (AM):– Modulated spectrum is translated message spectrum– Bandwidth message bandwidth
– SNRo at the output can be improved only by increasing the transmitted power
Angle Modulation: A non-linear process:-– Modulated spectrum is not simply related to the
message spectrum– Bandwidth >>message bandwidth. This results in
improved SNRo without increasing the transmitted power
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Basic Concept
First introduced in 1931
A sinusoidal carrier signal is defined as: )]([cos)( ttEtc ccc
For un-modulated carrier signal the total instantaneous angle is:
)()( ttt ccc
Thus one can express c(t) as:
][Re)(cos)( )(tjccc
ceEtEtc
Thus: • Varying the frequency fc Frequency modulation• Varying the phase c Phase modulation
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Basic Concept - Cont’d.
In angle modulation: Amplitude is constant, but angle varies (increases linearly) with time
t
Amplitude Ec
Initial phase c
Unmodulated carrier
Slope = c/t
t = 0
t(ms)
Unmodulated carrier
0
c(t) (red)
-/2
11/2
23/235/247/2
1 2 3 4
Phase-modulatedangle
Frequency-modulatedangle
2
0-1
m(t)
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Phase Modulation (PM)
PM is defined If 0180)()()( ppc KtmKtmt
Thus )]([cos)( tmKtEtc pccPM
Where Kp is known as the phase modulation index
Ec
c(t)
c(t)
c(t)
i(t)
Instantaneous frequency
Rotating Phasor diagram
)()(
)( tdt
tdt cc
ci
Instantaneous phase )()( tmKt pi
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Frequency Modulation (FM)
The instantaneous frequency is;
Where Kf is known as the frequency deviation (or frequency modulation index). Note: Kf < fc to make sure that f(t) >0.
Note that )()( tmKt fc
)()( tmKt fci
Integrating )()( tt cci
0)()(0
t
fcc dttmKtt
Substituting c(t) in c(t) results in: ])([cos)(0t
fccFM dttmKtEtc
Instantaneous phase
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Waveforms
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Important Terms
Carrier Frequency Deviation (peak)
Frequency swing pmpfpp EKf
Rated System Deviation (i.e. maximum deviation allowed)
FD =
75 kHz, FM Radio, (88-108 MHz band)25 kHz, TV sound broadcast5 kHz, 2-way mobile radio2.5 kHz, 2-way mobile radio
Percent Modulation
mfdc EKff
%100D
d
F
fm
Modulation Index m
d
f
f
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FM Spectral Analysis
Let modulating signal m(t) = Em cos mt
Substituting it in c(t)FM expression and integrating it results in:
]sin[cos])([cos)(0
tEK
tEdttmKtEtc mmm
fcc
t
fccFM
Since m
d
f
f mfdc EKff and
)sin(sinsin)sin(coscos]sin[cos)( ttEttEttEtc mccmccmccFM
the terms cos ( sin mt) and sin ( sin mt) are defined in trigonometric series, which gives Bessel Function Coefficient as:
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Bessel Function Coefficients
cos ( sin x) = J0 () + 2 [J2() cos 2x + J4() cos 4x + ....]
And sin ( sin x) = 2 [J1() sin x + J3() sin 3x + ....]
where Jn() are the coefficient of Bessel function of the 1st kind, of the order n and argument of .
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FM Spectral Analysis - Cont’d.
.........]3sin)(2sin)(2[sin
........]4cos)(22cos)(2)([cos/)(
31
420
tJtJt
tJtJJtEtc
mmc
mmccFM
Substituting the Bessel coefficient results in:
Expanding it results in:
.........}....................
)])3(cos)3()[cos({
)])2(cos)2()[cos({
)])(cos)()[cos({
cos)()(
3
2
1
0
ttJE
ttJE
ttJE
tJEtc
mcmcc
mcmcc
mcmcc
ccFM Carrier signal
Side-bands signal(infinite sets)
Since )()1))( nn
n JJ Then tnJEtc mn
cncFM )(cos)()(
tnJEtc mn
cncFM )(cos)()(
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FM Spectrum
J0()
c
J1()
c+ m
c+ 2m
c+ 3m
c+ 4m
J2()J3()
J4()
Side bands
Side bands
Bandwidth (?)
c- 3m
J2()
J3()
J4()
c- 2mc- 4m
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FM Spectrum - cont’d.
• The number of side bands with significant amplitude depend on see below
c
= 0.5
c
= 1.0
c
= 2.5
c
= 4
Bandwidth
Generation and transmission of pure FM requires infinite bandwidth, whether or not the modulating signal is bandlimited. However practical FM systems do have a finite bandwidth with quite well pwerformance.
Most practical FM systems have 2 < < 10
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FM Bandwidth BFM
The commonly rule used to determine the bandwidth is:– Sideband amplitudes < 1% of the un-modulated carrier can be
ignored. Thus Jn()> 0.01
For large values of , BFM = 2nfm= 2fm=2 (fc/ fm).fm = 2 fcBFM = 2nfm= 2fm=2 (fc/ fm).fm = 2 fc
For small values of , BFM = 2fmBFM = 2fm For limited cases
General case: use Carson equation BFM 2(fc + fm)
BFM 2 fm (1 + )BFM 2 fm (1 + )