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## Angle Modulation

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### 25 kHz, TV sound broadcast. 5 kHz, 2-way mobile radio. 2.5 kHz, 2-way mobile radio ... trigonometric series, which gives Bessel Function Coefficient as: Z. Ghassemlooy ... – PowerPoint PPT presentation

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Title: Angle Modulation

1
Angle Modulation
Professor Z Ghassemlooy Electronics IT
Division Scholl of Engineering Sheffield Hallam
University U.K. www.shu.ac.uk/ocr
2
Contents
• Properties of Angle (exponential) Modulation
• Types
• Phase Modulation
• Frequency Modulation
• Line Spectrum Phase Diagram
• Implementation
• Power

3
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 gtgtmessage bandwidth. This results in
improved SNRo without increasing the transmitted
power

4
Basic Concept
• First introduced in 1931

A sinusoidal carrier signal is defined as
For un-modulated carrier signal the total
instantaneous angle is
Thus one can express c(t) as
• Thus
• Varying the frequency fc ? Frequency
modulation
• Varying the phase ?c ? Phase
modulation

5
Basic Concept - Contd.
• In angle modulation Amplitude is constant, but
angle varies (increases linearly) with time

6
Phase Modulation (PM)
• PM is defined If

Thus
Where Kp is known as the phase modulation index
Instantaneous phase
Instantaneous frequency
Rotating Phasor diagram
7
Frequency Modulation (FM)
• The instantaneous frequency is

Where Kf is known as the frequency deviation (or
frequency modulation index). Note Kf lt fc to
make sure that f(t) gt0.
Instantaneous phase
Note that
Integrating
Substituting ?c(t) in c(t) results in
8
Waveforms
9
Important Terms
• Frequency swing
• Carrier Frequency Deviation (peak)
• Rated System Deviation (i.e. maximum deviation
allowed)
• Percent Modulation
• Modulation Index

10
FM Spectral Analysis
Let modulating signal m(t) Em cos ?mt
Substituting it in c(t)FM expression and
integrating it results in
the terms cos (? sin ?mt) and sin (? sin ?mt)
are defined in trigonometric series, which gives
Bessel Function Coefficient as
11
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 ?.
12
FM Spectral Analysis - Contd.
Substituting the Bessel coefficient results in
Expanding it results in
Carrier signal
Side-bands signal (infinite sets)
Since
Then
13
FM Spectrum
Bandwidth (?)
14
FM Spectrum - contd.
• The number of side bands with significant
amplitude depend on ?
• see below

Most practical FM systems have 2 lt ? lt 10
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.
15
FM Bandwidth BFM
• The commonly rule used to determine the bandwidth
is
• Sideband amplitudes lt 1 of the un-modulated
carrier can be ignored. Thus ?Jn(?)?gt 0.01

BFM 2nfm 2?fm2 (fc/ fm).fm 2 fc
For large values of ?,
For small values of ? ,
BFM 2fm
For limited cases
General case use Carson equation
BFM ? 2(fc fm)
BFM ? 2 fm (1 ?)