Loading...

PPT – Angle Modulation PowerPoint presentation | free to download - id: 1d274c-ZDc1Z

The Adobe Flash plugin is needed to view this content

Angle Modulation

Professor Z Ghassemlooy Electronics IT

Division Scholl of Engineering Sheffield Hallam

University U.K. www.shu.ac.uk/ocr

Contents

- Properties of Angle (exponential) Modulation
- Types
- Phase Modulation
- Frequency Modulation
- Line Spectrum Phase Diagram
- Implementation
- Power

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

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

Basic Concept - Contd.

- In angle modulation Amplitude is constant, but

angle varies (increases linearly) with time

Phase Modulation (PM)

- PM is defined If

Thus

Where Kp is known as the phase modulation index

Instantaneous phase

Instantaneous frequency

Rotating Phasor diagram

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

Waveforms

Important Terms

- Frequency swing

- Carrier Frequency Deviation (peak)

- Rated System Deviation (i.e. maximum deviation

allowed)

- Percent Modulation

- Modulation Index

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

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 ?.

FM Spectral Analysis - Contd.

Substituting the Bessel coefficient results in

Expanding it results in

Carrier signal

Side-bands signal (infinite sets)

Since

Then

FM Spectrum

Bandwidth (?)

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.

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 ?)