Angle Modulation 2 (1)

7/27/2019 Angle Modulation 2 (1)

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Angle Modulation

"All of RF is Truly FM"

SIGA2800Basic SIGINT Technology


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Objectives

1. Identify which modulations are also

known as angle modulations.

2. Given a maximum modulating frequency

and either a frequency of deviation or

deviation ratio of a frequency modulated

signal, determine signal bandwidth as

given by Carson's rule.


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Objectives

3. Given a bandwidth and either a maximum

frequency deviation or deviation ratio,

compute the maximum modulating

frequency that will comply with Carson's

rule.


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Objectives

4. Given a carrier being frequency

modulated by a sine wave at a fixed

deviation ratio, compute:

a. Average signal power

b. Bandwidth in accordance with Carson's rule.

c. Signal power present at the carrier frequency,

any frequency harmonic, and at a frequencyequal to the frequency deviation.


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Objectives

5. For angle modulated signals, identify what

factors drive overall power in the signal.

6. State what factors affect the bandwidth of

signals modulated using angle modulation.


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Sinusoids

Sinusoid

waveform

Cosinusoid

waveform

A sinusoid, meaning a sine wave -or- a cosine wave, is the basic

building block of all signals.


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Sinewave Characteristics

Amplitude

PeriodPhase

Period

1Frequency

A sinusoid has three properties .These are its amplitude, period

(or frequency), and phase.

Amplitude

Time


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Types of Modulation

Amplitude Modulation

Frequency Modulation

Phase Modulation

With very few

exceptions, phase

modulation is used fordigital information.

)t*sin(V

)t*sin(V

)t*sin(V


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Types of Modulation

Carrier Variations

Amplitude

Frequency Phase

Types of Information

Analog

Digital

These two

constitute angle

modulation.(Objective #1)


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Modulation Process

ModulatingSignal

ModulatorInformation /

Baseband Modulated

Signal

The modulation general process is the same regardless of the how

the carrier is modulated. For our purposes, modulation means the

variation of a carrier wave in order to transfer information.


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What is Angle Modulation?

phase)tfsin(2V(t)v cc

Angle modulation is a variation

of one of these two parameters.


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Understanding Phase vs. Frequency

phaseV

To understand the difference

between phase and frequency,

a signal can be thought of

using a phasor diagram. Thedistance from the center is the

signal's amplitude. The angle

from the positive horizontal

axis is the phase.


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The change in the phase over

time (the phase velocity) is

the signal's frequency.


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t

Frequency

Phase


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Signals vs NASCAR

In NASCAR, we track each car

by its position on the track.

In signals, we track the signal by

its phase. This is its position on

the phasor diagram.


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Signals vs NASCAR

In NASCAR, we track a car's

velocity by how fast it goes

around the track.

In signals, we track the signal's

velocity by its frequency. This

is how fast it goes around the

phasor diagram.


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Understanding Angle Modulation

Angle modulation, either PM or FM,

varies the frequency or phase of thecarrier wave. Because of the

practicalities of implementation, FM

is predominant; analog PM is only

used in rare cases.

)t*sin(V

Vary one of these

parameters


Phase Modulation


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In either analog FM or PM, theamplitude remains constant.

)t*sin(V

This remains

constant!


Phase Modulation

V

V


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V

2

VPower

Envelope

The envelope, meaning the difference between

the maximum and minimum of the carrier, is

constant in an FM signal. That's why FM is

called a constant envelopesignal. The power

of an FM signal is shown at right. It does not

depend upon the modulating signal or the

amount of deviation (Objectives #4a, 5).


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Calculating Total Power

The total power of an FM signal is simply V2. Therefore, the total

power of an FM signal is the power of the carrier. Period. This is

regardless of the information or the deviation ratio (Objectives

#4a, 5).

))t(tfsin(2V(t)v cc

2VPowerTotal


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Varying the Frequency

VCOInformationSignalFrequency

Modulation

The voltage-controlled oscillator (VCO) is a device whose outputfrequency changes with the amplitude of the modulating signal. The

amount of change, called its deviation constant, is dependent upon

its design.


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Understanding Terms

Center

Frequency

An FM signal has its energy spread over an infinite number of

spectral components. It's center frequency is the average center

of the energy.


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Understanding Terms

Deviation

The deviationis the maximum frequency change from the

center frequency.


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Understanding Terms

Excursion

The excursionis the difference between the maximum and

minimum frequency changes. This is also called the maximum

deviationor total deviation.


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Amplitude vs Angle Modulation

))t(tfsin(2V(t)vcc

)tfsin(2V(t)(t)v cc Amplitude Modulation

Angle Modulation


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Calculating FM Bandwidth

The Fourier transform for an FM signal modulated by a real signalwould be extremely difficult. Instead, engineers use the special case

of an FM signal modulated by sinusoid, which boils down to:

-

sin(x))-xj(n- dxe21

This integral cannot be solved in closed form. In order to figure

out actual numerical answers, we use Bessel functions,

specifically Bessel functions of the first kind of order nand

argument .


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t)sin((t) m

))t(tfsin(2V(t)v cc Angle Modulation

For PM

dtt)sin((t) mFor FM


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m

d

f

Vf


The beta value, called the modulation index, is

the ratio of the deviation of the modulator, fd,

multiplied by the amplitude of the modulating

signal and divided by the modulating frequency,fm(Objectives 2, 3, 4b, 6).


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Understanding FM Bandwidth

b=0.5 b=1

b=5 b=10


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W

VfD d


The designator when looking at real signals is

the deviation ratio, D, which is the product of

the modulator deviation, fd, multiplied by the

amplitude of the modulating signal, V, dividedby the maximum frequency of the modulating

signal, W (Objectives 2, 3, 4b, 6).


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Carson's Rule

)f(f2

1)(f2BW

devmax

max

Carson's Rule, named after an engineer who did not think that

FM would provide any improvement over AM, provides a

rough calculation of the bandwidth of an FM signal basedupon its design parameters and the parameters of the

modulating signal (Objectives 2, 3, 4b, 6).


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FM Broadcast Signal


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FM Spectrum

The spectrogram of an FM signal shows how the spectrum varieswith time. Note how it is asymmetric.

This is the spectrum of an AM signal modulated with the same

information as above. But it has a symmetric spectrum.


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FM Signal

This shows anFM signal.

Note the

constant

envelope(amplitude).


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FM Signal

This is a constellationdiagram of an FM

signal. Note how it has

a constant amplitude

(distance from the

center).


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Why FM and not PM?

Broadcast analog television chrominance(color)

Apollo spacecraft communications

AM stereo

For practical implementation reasons, analog FM is easier togenerate than analog PM, and FM provides better performance in

most common environments. However, analog PM has been (and

continues to be) used for a few, isolated systems.


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Using Analog Phase Modulation


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n 0.1 0.2 0.5 1 2 5

0 0.997 0.99 0.938 0.765 0.224 -0.178

1 0.05 0.1 0.242 0.44 0.577 -0.3282 0.001 0.005 0.031 0.115 0.353 0.047

3 0.129 0.365

4 0.391

5 0.261

6 0.131

bValue

S

pectralLine#

Angle Modulation 2 (1)

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