Chapter 4 · Chapter 4 Amplitude Modulation. ... Define AM concepts ... modulation index, voltage ,power distribution

Chapter 4

Amplitude Modulation

Communication System Chart

Communication

System

Continuous Wave Digital Wave

Amplitude

Modulation

(AM)

Pulse

Modulation

(PM)

Angle

Modulation

Frequency

Modulation

(FM)

Analogue Pulse

Modulation

Digital Pulse

Modulation

What is modulation?

“Modulation is defined as the process of modifying a carrier

wave (radio wave) systematically by the modulating signal

(audio)”

This process makes the signal suitable for the transmission and

compatible with the channel. The resultant signal is called the

modulated signal

In the other words, it is the process of changing/varying one of

the parameters of the carrier wave by the modulating signal

Introduction

Modulation is operation performed at the transmitter to achieve efficient and reliable information transmission

For analogue modulation, it is frequency translation method caused by changing the appropriate quantity in a carrier signal

It involves two waveforms:

A modulating signal/baseband signal – represents the message

A carrier signal – depends on type of modulation

Introduction

Introduction

Analogue modulations - frequency translation

methods caused by changing the appropriate

quantity in a carrier signal.

MODULATIONModulated

signal

Carrier

Baseband

signal

Introduction

•Once this information is received, the low frequency information

must be removed from the high frequency carrier.

•This process is known as “ Demodulation”.

Introduction

Types of Modulation

Three main type of modulations:

Analog Modulation

Amplitude modulation

Example: Double sideband with carrier (DSB-WC), Double sideband suppressed carrier (DSB-SC), Single sideband suppressed carrier (SSB-SC), Vestigial sideband (VSB)

Angle modulation (frequency modulation & phase modulation)

Example: Narrow band frequency modulation (NBFM), Wideband frequency modulation (WBFM), Narrowband phase modulation (NBPM), Wideband phase modulation (NBPM)

Types of Modulation

Pulse Modulation

Carrier is a train of pulses

Example: Pulse Amplitude Modulation (PAM), Pulse width modulation (PWM) , Pulse Position Modulation (PPM)

Digital Modulation

Modulating signal is analog Example: Pulse Code Modulation (PCM), Delta Modulation

(DM), Adaptive Delta Modulation (ADM), Differential Pulse Code Modulation (DPCM), Adaptive Differential Pulse Code Modulation (ADPCM) etc.

Modulating signal is digital (binary modulation) Example: Amplitude shift keying (ASK), frequency Shift Keying

(FSK), Phase Shift Keying (PSK) etc.

Summary of Modulation Techniques

v(t) = V sin )2( ftASK FSK PSK

Digital Modulation

AM FM PM

Analogue Modulation

Volt Hertz Radians

•Changing of the amplitude produces

Amplitude Modulation signal

•Changing of the frequency produces

Frequency Modulation signal

•Changing of the phase produces

Phase Modulation signal

Types of Modulation

Learning Outcomes

Define AM concepts

Calculate the AM voltage distribution,

modulation index, voltage ,power

distribution

Calculate and draw AM in time and

frequency domain, bandwidth

Revision..

Why do we need modulation?

What are the types of modulation?

What is AM?

What is bandwidth?

Basic Amplitude Modulation

• Amplitude Modulation is the process of changing the Amplitude of a relatively high frequency carrier signal in accordance with the amplitude of the modulating signal (Information).

The carrier amplitude varied linearly by the modulating signal which usually consist of a range of a audio frequencies. The frequency of the carrier is not affected

Application of AM - Radio broadcasting, TV pictures

(video), facsimile transmission

Frequency range for AM - 535 kHz – 1600 kHz

Bandwidth - 10 kHz


Various forms of Amplitude Modulation

• Conventional Amplitude Modulation (Alternativelyknown as Full AM or Double Sideband Large carriermodulation (DSBLC) /Double Sideband Full Carrier(DSBFC)

• Double Sideband Suppressed carrier (DSBSC)modulation

• Single Sideband (SSB) modulation

• Vestigial Sideband (VSB) modulation

Amplitude Modulation ~ DSBFC (Full AM)

“Amplitude Modulation is the process of changing the

amplitude of the radio frequency (RF) carrier wave by the amplitude variations of modulating signal”

The carrier amplitude varied linearly by the modulating signal which usually consist of a range of a audio

frequencies. The frequency of the carrier is not affected

Application of AM - Radio broadcasting, TV pictures

(video), facsimile transmission

Frequency range for AM - 535 kHz – 1600 kHz

Bandwidth - 10 kHz

17

Basic Amplitude Modulation

Envelope

AM Envelope

Carrier

Envelope is the original modulating

signal

•Wave and the shape of the Modulated Wave is called AM Envelope.

Amplitude Modulation – What really happened?? (you are not required to memorized this)

carrier

We now know how AM wave looks like,

but how do we represent it

mathematically?

Can you write the general equation of a

sinusoid wave?

The expression of voltage in the electric circuit is given

by :

or

V = Amplitude of the signal in Volts

f = The signal frequency in Herzt

(2ft + ) = The phase of the signal in radian

AM wave equation

)2cos()(

)2sin()(

ftVtv

ftVtv

An unmodulated modulating signal :

vm (t) = Em sin (2fmt)

Or vm (t) = Vm sin (2fmt)

22

AM wave equation

Em = Vm= peak modulating signal amplitude(volts)

AM Modulation

Envelope of the modulating signal varies above &

below the peak carrier amplitude

In general Em < Ec, otherwise distortion will occur.

The modulating signal values adds or subtracts from

the peak value of the carrier.

This instantaneous value either top or bottom voltage

envelope (new expression for Vm) :

)2sin(1

1

tfvvv

vvv

mmc

mc

v1

An unmodulated carrier (carrier signal) is described by the following equation :-

vc (t) = Ec sin (2fct)

Or vc (t) = Vc sin (2fct)

25

AM wave equation

Ec = Vc = peak carrier amplitude (volts)

26

AM Concepts

Figure 3-3: Amplitude modulator showing input and output signals.

(Low frequency)

(High frequency)

(nonlinear devices)

carrier

Modulation x carrier

The modulated wave can be expressed as :-

Vam(t) =[Ec + Em sin (2fmt)] (sin 2fct) .........(1)

WHERE:

Ec + Em sin (2fmt) = Amplitude of the modulated wave

Em = peak change in the amplitude of the envelope

fm = frequency of the modulating signal

27

Expanding eq (1) we get:

28

AM wave equation

)2........()2sin()2sin()2sin( tftfEtfEV cmmccam

Carrier signalModulating

signal

Later we will see how this equation can be further improved to make it more

meaningful

2

9

AM wave equation

)2)........(2sin()]2sin([ tftfEEV cmmcam

AM Concepts

In AM, it is particularly important that the

peak value of the modulating signal be

less than the peak value of the carrier.

Vm < Vc

Distortion occurs when the amplitude of

the modulating signal is greater than the

amplitude of the carrier.

The amplitude-modulated wave can then be expressed as

)cos()()cos()( ttvtVtv cmccAM

)cos()()( ttvVtv cmcAM

)cos()cos()( ttVVtv cmmcAM

tV

VtVtv m

c

mccAM cos1)cos()(

tmtVtv maccAM cos1)cos()(


where notation m is termed the modulation index. It is

simply a measurement for the degree of modulation and

bears the relationship of Vm to Vc

c

ma

V

Vm

Therefore the full AM signal may be written as

tmtVtv maccAM cos(1)cos()(


Modulation Index and Percentage of

Modulation

modulation index (m) is a value that describes the

relationship between the amplitude of the modulating signal and the amplitude of the carrier signal.

Percentage of modulation.

c

m

E

Em

100c

m

E

EM

modulating factor or

coefficient, or degree of

modulation.

modulation index (m) can also calculate it using

34


Modulation

mc

mc

EEV

EEV

min

max

minmax

minmax

minmax

minmax

21

21

VV

VV

VV

VVm

where

• The modulating signal (information signal) is often a complex form consists of many sinusoidal wave with different Amplitude and Frequencies;

v(t) = V1sin(2f1t) + V2sin(2f2t) + V3sin(2f3t)+V4sin(2f4t) + V5sin(2f5t) + ….

• Thus, after modulation, the output wave will be in the form of :

vam(t) = Ecsin(2fct) - ½ m1Ec cos[2(fc+fm1)t] + ½m1Ec cos[2(fc-fm1)t] - ½ m2Ec cos[2(fc+fm2)t] +½ m2Ec cos[2(fc-fm2)t] - ½ m3Ec cos[2(fc+fm3)t]+ ½ m3 Ec cos[2(fc-fm3)t] - …

• The Total Modulation Index will be :

m = sqrt (m12 + m2

2 + m32 + mn

2)

Modulation of complex signal

Modulation Index for Multiple

Modulating Frequencies Two or more sine waves of different, uncorrelated

frequencies modulating a single carrier is calculated

by the equation:

m m1

2m2

2

Modulation Index for Multiple Modulating Frequencies

Consider

these

envelopes:

Do they

look the

same?


Modulation

Overmodulation and Distortion

The modulation index should be a number

between 0 and 1.

If the amplitude of the modulating voltage is

higher than the carrier voltage, m will be

greater than 1, causing distortion.

If the distortion is great enough, the

intelligence signal becomes unintelligible.


Modulation

Overmodulation and Distortion

Distortion of voice transmissions produces

garbled, harsh, or unnatural sounds in the

speaker.

Distortion of video signals produces a

scrambled and inaccurate picture on a TV

screen.

Over Modulation

http://www.williamson-labs.com/480_am.htm


Modulation

Figure : Distortion of the envelope caused by overmodulation where the

modulating signal amplitude Vm is greater than the carrier signal Vc.

AM Modulation

Draw AM wave in time domain and

frequency domain

Voltage Distribution

An unmodulated carrier (carrier signal) is described by the following equation :-

Vc (t) = Ec sin (2fct)

The Amplitude of the AM Wave varies proportional to the amplitude of the modulation signal, and the maximum of the modulated wave equal to Ec + Em.

Thus the amplitude of the modulated wave can be expressed as :-

Vam(t) =[Ec + Emsin(2fmt)] sin (2fct)

Ec + Emsin(2fmt) Amplitude of modulated wave.

Em= Peak Change in the Amplitude of Envelope

fm= Frequency of Modulating signal

Voltage Modulation

• Since Em = mEc and by developing the equation for modulated wave, the final equation of the modulated wave can be expressed in term of its Carrier Component and Side FrequenciesComponent (usf & lsf):-

Where Ecsin(2fct) carrier signal (V)

upper side frequency signal (V)

lower side frequency signal (V)

• Carrier wave is 90˚ out of phase with the upper and lower side frequencies

• The upper and lower side frequencies are 180 ˚ out of phase with each other

])(2cos[2

])(2cos[2

)2sin( tffmE

tffmE

tfEV mcc

mcc

ccam

])(2cos[2

tffmE

mcc

])(2cos[2

tffmE

mcc

The frequency domain provides an alternative

description of signal in which the time axis is

replaced by a frequency axis.

Frequency Domain

The relationship between the time

and frequency domains

Sidebands and

the Frequency Domain

Side frequencies, or sidebands are generated as

part of the modulation process and occur in the

frequency spectrum directly above and below the

carrier frequency.

• Single-frequency sine-wave modulation generates two

sidebands.

• Complex wave (e.g. voice or video) modulation generates a

range of sidebands.

Sidebands and


Frequency

Amplitude

fLSB fC fUSB

fUSB = fc + fmfLSB = fc - fm

2

musblsb

EEE

Sidebands and


Figure : The AM wave is the

algebraic sum of the

carrier and upper and

lower sideband sine

waves.

(a) Intelligence or modulating

signal.

(b) Lower sideband.

(c ) Carrier.

(d ) Upper sideband.

(e ) Composite AM wave.

Bandwidth

Signal bandwidth is an important characteristic of any

modulation scheme

In general, a narrow bandwidth is desirable

Bandwidth is calculated by:

mfB 2

Bandwidth

Bandwidth is the difference between the upper and lower sideband frequencies.

BW = fUSB−fLSB

Sidebands and the Frequency

Domain

Example:

A standard AM broadcast station is allowed to transmit modulating frequencies up to 5 kHz. If the AM station is transmitting on a frequency of 980 kHz, what are sideband frequencies and total bandwidth?

54

fUSB = fc +fm =980 + 5 = 985 kHz

fLSB = fc -fm = 980 – 5 = 975 kHz

BW = fUSB – fLSB = 985 – 975 = 10 kHz

Or

BW = 2 (5 kHz) = 10 kHz

1. Highlight and identify important information in the question: fm

fc2. Use the formulas to solve the problem:

A standard AM broadcast station is allowed to transmit modulating frequencies up to 5 kHz. If the AM station is transmitting on a frequency of 980 kHz, what are sideband frequencies and total bandwidth?

EXAMPLE :

AM DBSFC Modulator with a carrier frequency, fc = 100 kHz and maximum modulating signal frequency, fm of 10 kHz, determine the following :

a. LSB & USB

b. Bandwidth

c. Upper and Lower side frequencies if the modulating signal is a single frequency of 5kHz.

d. Draw the output frequency spectrum

Solution:

Frequency

Lower side band Upper side bandCarrier

fc-fm(max fc+m(maxfcfLSF

fUSF

100kHz95kHz 105kHz90kHz 110kHz

If fm consists of a range frequencies f1 to f2, the component of the sidebands become:

Upper sideband (USB) range is from (fc+f1) to (fc+f2)

Lower sideband (LSB) range is from (fc-f2) to (fc-f1)

Bandwidth for this case,B = (fc+f2) - (fc-f2)

= 2f2

AM spectrum when the modulating signal is a baseband signal from frequency f1 to f2

f1 f2 fc-f2 fc-f1 fc+f1 fc+f2

Amplitude,V Amplitude,V

Baseband signal lower sideband upper sideband

Modulatedsignal

freq freq


For example, if voice signal with the band of frequency of

0 – 4 kHz is transmitted using a carrier of 100 kHz, the

modulated signal consists of

Carrier signal with frequency of 100 kHz

upper side band with frequency of range of 100 – 104 kHz

lower side band with frequency of range 96 – 100 kHz

The bandwidth is 104 – 96 = 8 kHz


Given the first input to AM Modulator is 500 kHz Carrier signal

with Amplitude of 20V. The second input to AM Modulator is the

10kHz modulating signal with ± 7.5 Vp. Determine the following :-

a) USB & LSB

b) Modulation Index and percent modulation, M

c) Peak Amplitude of modulated carrier and Upper & Lower side

frequency voltage

d) Maximum & Minimum Amplitude of the envelope, Vmax and Vmin

e) Draw output in frequency domain & time domain

59

Group Activity

(a) Upper and lower side frequencies:

(b) Modulation Index and percent modulation, M

60

Solution

%5.37100375.0

375.020

5.7

M

E

Em

c

m

kHzf

kHzf

lsb

usb

49010500

51010500

(c) Peak Amplitude of modulated carrier and Upper & Lower side

frequency voltage

We can find Elsb and Eusb by using equation:

Thus

61

Solution (c)-method 1

pcc VulatedunEulatedE 20)mod()(mod

pm

usblsb VE

EE 75.32

5.7

2

2

musblsb

EEE

(c) Peak Amplitude of modulated carrier and Upper &

Lower side frequency voltage

Let’s say Em is unknown. Em can be found from

Thus

62

Solution (c)- method 2

pc

usblsb VmE

EE 75.32

)20)(375.0(

2

cm

c

m mEEE

Em

(d) Maximum & Minimum Amplitude of the

envelope, Vmax and Vmin

63

Solution

pmc

pmc

VEEV

VEEV

5.125.720

5.275.720

min

max

(e) frequency domain

64

Solution

f (kHz)

Amplitude (Vp)

fLSB =490 fC = 500 fUSB = 510

3.75

20

3.75

(e) time domain

65

Solution

Vmax=27.5 Vp Vmin =12.5 Vp

Frequency

Amplitude

fLSB fC fUSB

How to

calculate AM

power ???

PT ????

Pc

PUSBPLSB

AM Power

The AM signal is a composite of the

carrier and sideband signal voltages.

Each signal produces power in the

antenna.

Total transmitted power (PT) is the sum

of carrier power (Pc ) and power of the

two sidebands (PUSB and PLSB).

AM Power

Power in a transmitter is important, but the most important power measurement is that of the portion that transmits the information

Power in an AM transmitter is calculated according to the formula at the right

Pt Pc 1m 2

2

Measuring AM signal power

The greater the percentage of modulation, the higher the

sideband power and the higher the total power transmitted.

Power in each sideband is calculated

PSB = PLSB = PUSB = Pcm2 / 4

Maximum power appears in the sidebands when the carrier is

100 percent modulated.

Pc = (Vc )2 / 2R

where Pc = carrier power (W)

Vc =peak carrier voltage(V)

R= load resistance (Ohm)

Measuring AM signal power

In reality it is difficult to determine AM

power by measuring the output voltage.

However, antenna current is easy to

measure and output power can be

expressed

where IT is measured RF current and R is antenna

impedance

22 where 1

2T T T c

mP I R I I

AC average power dissipation

Recall that the average power dissipated

by resistor R is with a sinusoidal source

of amplitude Vpk is given

2

22pkrms

/ 2

2

pkV VVP

R R R

AM signal power

Since the vAM is composed of three sinusoids

the total average power dissipated by the antenna R is

given

LSB USB

2 2 2

2 2 2

/ 2 / 2 2 / 2 2

2 8 8

T c

c m m

c m m

P P P P

V V V

R R R

V V V

R R R

AM sin 2 sin 2 ( ) sin 2 ( )2 2

m mc c c m c m

V Vv V f t f f t f f t

AM signal power

Remembering that the modulation index

m = Vm /Vc we can write

The common term is the just the carrier

power, thus the total power can also be

written

2 2 2 2 2 2

12 8 8 2 4 4

c c c cT

V mV mV V m mP

R R R R

2

12

T C

mP P

AM power efficiency

Therefore given the equation for power of

an AM waveform, the efficiency is:

It can be seen from this equation that the

efficiency of AM modulation increases as

the modulation index, μ, increases.

%1002

2

2

m

mh

An AM transmitter has a carrier power of 30 W. The

percentage modulation is 85%. Calculate (a) the total

power, and (b) the power in one sideband.

Example Problem 1

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time (sec)

Vo

ltag

e (V

)

0 1000 2000 3000 4000 5000 60000

0.1

0.2

0.3

0.4

0.5

Frequency (Hz)

Vo

ltag

e (V

)

AM power efficiency

From the previous example, what percentage of the total

power was dedicated to transmitting the carrier?

Is any information conveyed by the carrier itself?

How could we maximize the power in the sidebands?

PT= 42.75 W

PUSB = 5.4 WPLSB = 5.4 W

Pc = 30 W

AM power efficiency

Sideband power is maximized by setting m

= 1.

For m = 1, what percentage of the total

power is dedicated to the sidebands?

2

12

T c

mP P

2

4c

mP

2

4c

mP

cP

AM power efficiency

At maximum modulation, the sideband power is at most

33% of the total transmitted power.

2

12

T c

mP P

2

4c

mP

2

4c

mP

cP

Percentage modulation (% m)

Per

cen

tag

e o

f to

tal

po

wer

(%

PT)

Power in sidebands (PSB

)

Power in carrier (Pc)

100 90 80 70 60 50 40 30 20 10 00

20

40

60

80

100

AM power efficiency

Two-thirds of the power is wasted in the carrier.

Further, 100% modulation only occurs at peaks in the

modulating signal, thus the average sideband power is

considerably worse than the ideal.

0 0.5 1 1.5 2 2.5 3

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time (sec)

Vo

ltag

e (V

)

Speech as a modulating signal100% modulation only occurs

at peaks

Improving on AM

Besides the 67% power loss due to the carrier,

the sidebands contain redundant information.

To maximize the efficiency of AM we need to

Suppress the carrier

Eliminate one of the sidebands

AM modulated speech signal

Upper and lower

sidebands contain the

same information.

Why is still widely used?

AM is still widely used because it is simple

and effective.

AM broadcast radio

CB radio (11m range)

TV broadcasting

Air traffic control radios

Garage door opens, keyless remotes

Aircraft VHF Communications Transceiver

Types of AM

1) Double sideband full carrier (DSBFC)

- Contains USB, LSB and Carrier

- This is the most widely used type of AM modulation. In fact, all radio channels in the AM band use this type of modulation.

2) Double sideband suppressed carrier (DSBSC)

- Contains only USB & LSB

- A circuit that produces DSBSC is Balanced modulator

3) Single sideband (SSB)

- In this modulation, only half of the signal of the DSBSC is used

- Contains either LSB or USB

- Produce efficient system in term of power consumption and bandwidth

4) Vestigial Sideband (VSB):

- This is a modification of the SSB to ease the generation and reception of the signal.

EXAMPLE :

For AM DSBFC wave with an unmodulated

carrier voltage, Vc = 10 Vp , a load resistance

of 10 and modulation index of 1, determine

the following :

a. Power of the carrier, and sideband

frequencies (Plsf & Pusf)

b. Total Power of sideband, PT

c. Draw Power Spectrum

EXAMPLE :

An AM Transmitter has a carrier power output of 50W. Determine

the total power that produced 80% modulation.

SOLUTION :

1. Total Power is defined as :

PT = Pc[1 + (m2 /2)]

Thus,

PT = (50 W)[1 + ((0.8)2 /2)]

= 66 W

EXAMPLE:

• For AM DSBFC transmitter with an unmodulated

carrier Power, Pc = 100 W is modulated

simultaneously with 3 other modulating signals with

coefficient index of m1 = 0.2, m1 = 0.4, m1 = 0.5,

determine the following :-

a. Total Modulation Index or Coefficient

b. Upper and Lower sideband power

c. Total transmitted power

m m1

2m2

2

Chapter 4 · Chapter 4 Amplitude Modulation. ... Define AM concepts ... modulation index, voltage ,power distribution

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