Dr. Ahmed El-Mahdy COMM 601: Modulation I

COMM 601: Modulation I

Lecture 2

Conventional Amplitude Modulation

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Amplitude Modulation

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Amplitude Modulation

• Also known as “Linear Modulation”.

• Applications:

- AM radio

- TV video broadcasting (VSB)

- Point to point communications (SSB)

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Double Side Band

Suppressed

Carrier

(DSB)

Conventional

AM

Amplitude Modulation

Single side band

(SSB)

Vestigial side

Band

(VSB)

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional Amplitude Modulation

frequencycarriertheis

amplitude.carriertheis:where

2cos

:by defined vecarrier wa sinusoidal aConsider

c

c

cc

f

A

tfAc(t)

c(t)

modulator. theof senstivity amplitude theis:

2cos)(1

:as described becan signal (AM) modulated amplitudeAn

signal). g(modulatin signalmessagethedenotes)(Let

a

cac

kwhere

tftmkAs(t)

tm

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional Amplitude Modulation

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Spectrum of AM Signal

M(f)

-W 0 W f fc -W fc fc+ W f-fc -W -fc -fc+ W 0

Wf c

S(f)

1

BT=2W

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Spectrum of AM Signal

f

Wf c

BT=2W

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Spectrum of AM Signal (Cont.)

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Transmission Bandwidth of Conventional AM

AM is Wasteful of Bandwidth

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional Amplitude Modulation

The envelope of s(t) has the same shape as

the baseband signal m(t) provided that two

requirements are satisfied:

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional Amplitude Modulation

(c)). Fig.in (asdistortion

envelope exhibits signal modulated thecase, In this

zero. thecrosses)]([1 whenever reversal

phasecarrier in resulting modulated,over becomes

signalcarrier then the,1)(such that large

ismodulator theof senstivity amplitude he When t

envelope. therepresents]1[

Then positive.alwaysis)]([1

that ensurescondition this(b), Fig.in shown As

allfor1)(

:unity than less is of magnitude The (1)

tmk

tmk

m(t)k A

tmk

ttmk

m(t)k

a

a

ac

a

a

a

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional Amplitude Modulation

distorted. be willand 0 around be will

spectrum theofpart becauserily satisfacto detected be

not can envelope thesatisfied,not iscondition thisIf

:isThat(t).

signal theof component frequency hightest the

an greater thmuch is frequency carrier The)2(

c

c

f

Wf

m

W

f

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional AM: Basic definitions

2

-

-ve sign

)](1[ tmkA ac

Envelope

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional AM: Average transmitted power

See Appendix

(At the end of this

Lecture)

Assume m(t) has zero mean

])(1[2

])()(21[2

)](1[2

)(2

1

222

222

22

2

tmkA

tmktmkA

tmkA

tCP

ac

aac

ac

avg

)(1)(

2cos)(1

tmkAtCThen

tftmkAs(t)Since

ac

cac

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional AM: Modulation efficiency

Modulation Efficiency:

is the ratio between side band power (that conveys information) to

the total power

)(1

)(

)(2

1

2

1

)(2

1

100powerTotal

power band side

22

22

2222

222

tmk

tmk

tmkAA

tmkA

a

a

acc

ac

Dr. Ahmed El-Mahdy COMM 601: Modulation I

22

2

2

2

])(max1[2

]])(max1[[2

1

])](1[[max2

1

)(max2

1

tmkA

tmkA

tmkA

tCP

ac

ac

ac

PEP

Peak Envelope Power of Conventional AM:

Conventional AM: Peak Envelope Power

is the power that would be obtained if the envelope attains its

maximum value

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Remarks on Transmitted Power of Conventional AM

AM is Wasteful of Power

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional AM with single tone modulating signal

mamamm

a

mm

a

AkAkAA

k

tfAtm

tmtmk

2

)(Then

)2cos)( :signal modulating sinusiodalFor

2

)(min)(max(factor)index Modulation Since

10

Then

1)2cos(.1)(Since

tfAkeitmk mmaa

tftfAs(t) cmc 2cos2cos1

For single tonee

Dr. Ahmed El-Mahdy COMM 601: Modulation I

tfAtm mm 2cos

mmm ffff

AfM

2

MODULATING SIGNAL

MODULATED (AM) SIGNAL

CARRIER UPPER SIDEBNAND LOWER SIDEBNAND

Conventional AM with single tone modulating signal

tftfAts cmc 2cos2cos1

tftfAtfAts mcccc 2cos.2cos2cos

tfftffA

tfAts mcmcc

cc

2cos2cos2

2cos

mcmcc

mcmcc

ccc

ffffffA

ffffffA

ffffA

fS

4

4

2

Dr. Ahmed El-Mahdy COMM 601: Modulation I

AMPLITUDE MODULATED SIGNAL

MODULATING SIGNAL

VAc 52

VAm 5.22

mTfB 2V

Ac 25.14

Hzf

Hzf

VA

k

VA

m

c

c

a

m

10

200

10

1.0

5

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional AM with single tone modulating signal

2

2

2

2

2

2

2

2

22

22

2

21

2

)(1

)(

m

m

m

m

a

a

A

A

A

A

tmk

tmk

3

1max 1When

For sinusoidal

modulating signal

ma Ak tfAtm mm 2cos

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional AM with single tone modulating signal

]2

1[2

]2

1[2

)(22

222

2

222

22 c

avgm

m

ca

ccavg

AP

A

A

Atmk

AAP

22

22

22

]1[2

]1[2

])(max1[2

cPEPm

m

ca

cPEP

APA

A

Atmk

AP

tfAtm mm 2cos

ma Ak

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Conventional AM with multi-tone modulating signal

: efficiency theand formulaspower above in the thisUse

...

,...;Then

2cos....)2cos)2cos1

2cos....))2cos)2cos(1

2cos)(1:signalmodulatedThe

....)2cos)2cos)( :signal modulating tone-Multi

2

2

2

1

2211

2211

2211

2211

avg

avg

mama

cmmammac

cmmmmac

cac

mmmm

AkAk

tftfAktfAkA

tftfAtfAkA

tftmkAs(t)

tfAtfAtm

Proof is not required

]2

1[2

22avgc

avg

AP

22

]1[2

avgc

PEP

AP

2

2

2 avg

avg

1thatsuch avg

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Example: Conventional AM

is the modulation

index

1, mA

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Example: Conventional AM (cont.)

tt

tftfAs(t)

AkAk

tfAtm

cmc

m

ama

mm

5102cos]20002cos5.01[5

2cos2cos1

5.0

)2cos()(

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Example: Conventional AM (cont.)

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Example: Conventional AM (cont.)

14)625.0(4)5.2(2)( 222

fSPavg

)( fS

f

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Example: Conventional AM (cont.)

22

]1[2

cPEP

AP

]2

1[2

22 c

avg

AP

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Appendix:

Power Calculations

The following formulas are valid for

all types of modulations

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Appendix: Power CalculationsNormalized average power: (using complex envelope C(t))

2

)(2

1tCPavg

Peak envelope power: (using complex envelope C(t))

Modulation Efficiency:

100powerTotal

power band side

2)(max2

1tCPPEP

Dr. Ahmed El-Mahdy COMM 601: Modulation I

Appendix: Power CalculationsTime average:

For Non-periodic signal:

2/

2/

)(1

lim

T

TT

dttxT

x

0

00

)(1

T

dttxT

x

When x(t) is periodic with period To:

signalrealais)(tx

periodsignaltheis0T