Amplitude Modulation (AM) by Erol Seke For the course Communications - - PowerPoint PPT Presentation

SLIDE 1

Amplitude Modulation (AM)

by Erol Seke For the course “Communications”

OSMANGAZI UNIVERSITY

SLIDE 2

Initial Problem : Carry voice signal over distances without using cable The Problem : Human ear can only hear sounds in the frequency range of 20Hz

• 20kHz approximately†. We would need a veerrrrry looonnnng antenna to

efficiently radiate such low frequency signals into air

† : Various sources give different ranges depending on some parameters (age, health etc) but we are not interested in an exact number here anyway.

The Solution : Use RF which radiates in air and carry voice with it. The Question : How? The Solution : Radiate its electromagnetic wave through air. The Answer : Modulate RF with voice signal.

SLIDE 3

RF Converter? Transmitter RF Receiver Converter?

Radio Frequency Radiating Antenna RF Receiving Antenna Message signal Message signal RF signal Electromagnetic Wave in media (air) RF signal LF signal LF signal air

Summary of Radio Transmission

air air

SLIDE 4

Modulation property of Fourier Transform

) ( ) ( ) cos( ) (

2 1 2 1

• X

X t t x ω ω ω ω ω + + − ⇔ ) ( ) ( ω X t x ⇔

1

ω ω >

• is called the carrier signal or carrier. is called carrier frequency

) cos( t

• ω
• ω

1

ω is presumed to be cutoff freq. of ) (t x

SLIDE 5

Voice signal Carrier signal Multiplied signal (modulated signal) In time domain

) cos( t

c

ω ) cos( ) ( t t x

c

ω ) (t x t t t

180º phase shift at zero crossings envelope

SLIDE 6

Example : Find/Draw for

where

) sin( ) ( t t x

m

ω =

m c

ω ω >>

{ }

) cos( ) ( t t x

c

ω

F { }

)) ( ) ( ( ) sin( ) (

m m m

j t X ω ω δ ω ω δ π ω ω − − + = = F

{ }

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

c c c

X X t t x Y ω ω ω ω ω ω + + − = = F ) ( 2 ) ( 2 ) ( 2 ) ( 2

m c m c m c m c

j j j j ω ω ω δ π ω ω ω δ π ω ω ω δ π ω ω ω δ π − + − + + + − − − + − =

II I III IV

( )

) ) sin(( 2 1 )) ( ( )) ( ( 2 IV I t j

m c m c m c

ω ω ω ω ω δ ω ω ω δ π − − ⇔ − + − − − = +

( )

) ) sin(( 2 1 )) ( ( )) ( ( 2 III II t j

m c m c m c

ω ω ω ω ω δ ω ω ω δ π + ⇔ + − − + + = +

lower frequency components

Solution

upper frequency components

SLIDE 7

) ) sin(( 2 1 ) ) sin(( 2 1 ) ( t t t y

m c m c

ω ω ω ω − − + =

Entire signal

II I III IV

Lower Side Band Upper Side Band

SLIDE 8

Homework : Find the modulated signal m(t) and its Fourier spectrum for

) cos( ) cos( ) (

2 2 1 1

φ ω ω + + = t A t A t x ) cos( ) ( t A t c

c c

ω =

and

SLIDE 9

Let us apply the same multiplication operation on the modulated signal m(t)

) (t x ) (t c ) (t m ) (t y ) ( ) ( ) ( t c t x t m = ) ( ) ( ) ( t c t m t y ′ = ) cos( ) ( t A t c

c c

ω = ) cos( ) ( t A t c

c c

ω ′ = ′ ) (t c′

if and

) ( cos ) ( ) (

2

t A A t x t y

c c c

ω ′ =

then

( )

) 2 cos( ) ( ) ( 2 1 t t x t x A A

c c c

ω + ′ = 2 / )) 2 cos( 1 ( ) ( cos2 x x + =

use

SLIDE 10

) (t x ) cos( t

c

ω

baseband signal

) cos( t

c

ω

Transmitter LPF Receiver

) ( ˆ t x

Basic AM Modulator, Transmitter and Synchronous Receiver typical Low Pass Filter freq. response

) ( ˆ ω X

Problem is : how to create at the receiver in phase with the transmitter oscillator

) cos( t

c

ω

removed by LPF removed by LPF

SLIDE 11

) cos( ) ( t t x

c

ω ) cos( ) ) ( ( t m t x

c c

ω +

Let us use instead of at the transmitter where

)} ( min{ t x mc >

c

m t x + ) ( ) cos( ) ) ( ( t m t x

c c

ω + ) cos( t

c

ω

no zero crossing no phase inversion

Synchronous demodulation is easier now since we have a carrier signal to extract from input and use

SLIDE 12

LPF

Notch filter to extract carrier

Synchronous demodulation is easier now since we have a carrier signal to extract and use

SLIDE 13

Upper Side Band = USB Lower Side Band = LSB

Carrier Double Side Band, Suppressed Carrier = DSB-SC AM Conventional Amplitude Modulation

Can we have single?

)} ( min{ t x mc <

SLIDE 14

Another Way to Demodulate Conventional AM Signal

Half-Wave rectifier RC-discharge circuit (a LPF) better LPF DC blocking capacitor

Note : Better LPF may not be enough. Much higher carrier frequency than illustrated would clearly improve the performance

SLIDE 15

In general

) cos( )) ( 1 ( ) ( φ ω + + = t t x a A t y

c n m

modulation index normalized signal

) ( max ) ( ) ( t x t x t xn =

so that

1 ) ( 1 < < − t xn ) cos( )) ( ( ) ( φ ω + + = t t x m K t y

c c

• r

in order for

) ( > +

c

m t x

{ }

) ( min t x mc >

{ }

c m

m t x a ) ( min =

larger smaller carrier power per signal power

m

a

SLIDE 16

Carrier Power

2 ) cos(

2 c c c

m t m = ω =

c

P

mean square of Sideband Power

= ) cos( ) ( t t x

c

ω =

s

P

mean square of

½ mean square of

) ( 2 1 ) (

2 t

x t x =

Power of a single sideband Total Power

( )

) ( 2 1

2 2

t x m P P P

c c s T

+ = + = ) ( 4 1

2 t

x P P

L u

= = ) 100 ( ) ( ) ( ) 100 (

2 2 2

× + = × + = t x m t x P P P

c c s s

η

as efficiency define for pure sinusoidal message signal

) cos( ) ( t m a t x

m c m

ω = 2 ) ( ) (

2 2 c mm

a t x =

and

1 , ) 100 ( 2

2 2

≤ × + =

m m m

a a a η

at

1 =

m

a % 33

max =

=η η

(best case) For conventional AM two thirds of power is wasted at

• best. That is, if we want to send 1 then we have to spend

additional 2. So, why do we use conventional AM instead

• f other versions of AM (DSB-SC for example)?

SLIDE 17

USB LSB Notice that information within USB and LSB are identical

for real signals

Then, is it enough to transmit only one side to save power (and have the info transmitted of course)? Question : Why do we use conventional AM instead of other versions of AM (DSB-SC for example) even though we know the power disadvantage ? Simple Answer : Receiver is easier and cheaper (explain)

SLIDE 18

Single Side Band Suppressed Carrier AM USB LSB The power advantages are obvious. The question is; how do we generate these SSB-SC AM signals?

SLIDE 19

Let us assume that

) ( ) ( ) ( t x t x t x

+ −

+ =

so that

) ( ) ( t x t x

∗ + −

=

It can be written that

[ ]

) ( ) ( ) (

2 1

t jx t x t x

h

+ =

+

[ ]

) ( ) ( ) (

2 1

t jx t x t x

h

− =

−

and

) ( ) ( ) ( ω ω ω U X X =

+

) sgn( ) ( ) ( ) (

2 1 2 1

ω ω ω ω X X X + =

+

) sgn( ) ( ) ( ω ω X t jxh ⇔ ) sgn( ) ( ) ( ω ω ω jX X h − =

• r

We know that (from tables)

) sgn(ω π ⇔ t j

{ }

) ( ) ( ) ( ) ( ω ω Y X t y t x = ∗

F

and (convolution)

{ }

∫

∞ ∞ −

− = − = α α α π ω ω d t x jX

• t

xh ) ( 1 ) sgn( ) ( 1 ) (

F

Hilbert Transform

) sin( ) ( ˆ ) cos( ) ( ) (

USB

t t x A t t x A t y

c c c c

ω ω − = ) sin( ) ( ˆ ) cos( ) ( ) (

LSB

t t x A t t x A t y

c c c c

ω ω + =

ideal phase shift

2 π

SLIDE 20

Example : Find

) cos( ) ( t t x

x

ω =

x c

ω ω >> ) (t yUSB

for where

) sin( ) sin( ) cos( ) cos( ) (

USB

t t A t t A t y

c x c c x c

ω ω ω ω − =

Solution

) ( ˆ t x

is 90 degrees phase shifted version of

) sin( ) ( ˆ t t x

x

ω = ) ) cos(( ) (

USB

t A t y

x c c

ω ω + = ) ) cos(( ) (

LSB

t A t y

x c c

ω ω − =

and Homework How can we demodulate SSB-AM signals?

? ) (

USB t

y ? ? ) (t x ) (t x

So

SLIDE 21

USB Another way to generate SSB Very sharp filter We need to have very sharp filters to achieve this.!

SLIDE 22

Instead we can allow a little bit of other sideband to pass; which means a relaxed version of the filter (cheaper)

) (t x ) cos( t A

c c

ω

BPF DSB VSB

VSB : Vestigial Side Band VSB – AM is used in modulation of television picture signals

SLIDE 23

Use of Nonlinear Circuits to Realize Multiplication

) (

2 t

x ) (

1 t

x ) log(x ) log(x ) exp(x ) ( ) (

2 1

t x t x

×

• 90

phase delay

• 90

phase delay

) (t x ) cos( t

c

ω ) sin( t

c

ω ) cos( ) ( t t x

c

ω ) (t xh ) sin( ) ( t t x

c h

ω

SSB Generation of SSB

SLIDE 24

Example : Draw

) cos( ) ) ( ( ) ( t a t x t y

c m

ω + =

for if the binary message signal is given as shown below.

=

m

a 2 =

m

a 1 =

m

a

and , Assume that carrier has high enough frequency that at least 3 cycles fit into a binary period.

=

m

a 2 =

m

a 1 =

m

a

SLIDE 25

In general

) cos( ) ( φ ω + = t A t y

c Vary this with the message, you get Amplitude Modulation (AM) If there are finite number of amplitude values, it is called Amplitude Shift Keying (ASK) Vary this with the message signal, you get Phase Modulation (FM) Vary this with the message signal, you get Frequency Modulation (FM) If there are finite number of phase values, it is called Phase Shift Keying (PSK) If there are finite number of frequency values, it is called Frequency Shift Keying (FSK) If both amplitude and phase modulation are used at the same time and there are finite number of amplitude and phase values, it is called Quadrature Amplitude Modulation (QAM) In AM, amount of carrier and sidebands in the frequency spectrum determines the modulation type : SSB, SSB-SC, DSB, DSB-SC, Conventional AM, VSB and their sub-types.

SLIDE 26

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