amplitude modulation slides by (2003/04): eryk schiller, daniel starnowski modulation &...

Amplitude Modulation

Slides by (2003/04): Eryk Schiller, Daniel Starnowski „Modulation & Detection” Zdzisław Papir

Amplitude Modulation• DSB Double Sideband

Modulacja dwuwstęgowa

• AM Amplitude Modulation

Modulacja amplitudy

• SSB Single Sideband

Modulacja jednowstęgowa

• VSB Vestigal Sideband

Modulacja z częściowostłumiona wstęgą boczną

„Modulation & Detection” Zdzisław Papir

DSB-SC Modulation

Carrier: A0cos0t

k – modulator constant

tAtkxt 00DSB cos


DSB-SC Modulator

x

kx(t) ttxkAt 00DSB cos)()(

tA 00 cos„Modulation & Detection” Zdzisław Papir

DSB-SC Modulation

x(t)

tAtkxt 00DSB cos

-x(t)

t


DSB-SC Modulation

000DSB 2

1 XXkA

tAtkxt 00DSB cos

X()

DSB() g

0-g 0 0+g

g

WDSB = 2g

=2


DSB-SC Detection

Two possible detection techniques:

• Envelope detection (Detekcja obwiedni)

• Coherent (synchronous) detection


Envelope DSB-SC Detection

x(t) e(t) !

t


g0

Coherent DSB-SC Detection

x

cos0t

Predetection

Filter

Lowpass

Filter

~x(t)

tDSB

txttxtx

ttxtt

~2cos~

~cos~cos

filter lowpass

0

02

0DSB


X()

½X()

DSB()

0-g 0 0+g

20g-g

g-g

Coherent DSB-SC Detection


Transmitter: cos0t

Receiver: cos[(0+)t + ]

In most cases: = 0 and variable in time

Receiver: cos(0t + )

Coherent DSB-SC DetectionErrors


Coherent detection:[x(t) cos(0t)]cos(0t + )

Detected signal: x(t) cos()

Synchronous operation of both transmitter

and receiver is necessary.

Coherent DSB-SC DetectionPhase Errors


AM Modulation

tAttxkA 0000AM coscos

ttkxA 00AM cos1

01 tkx


Single tone modulation: x(t) = acosmt

AM=A0(1 + ka cosmt) cos0t

ka = m – modulation index

AM=A0(1 + m cosmt) cos0t

AM Modulation


A0(1+m)

A0(1-m)

ttmA m 00AM coscos1

t

mA0

AM Modulation


0-m 0+m

0

0A

20mA

20mA

AM Modulation


AM Phasor Diagram tjtjtj

m

eeemAt

ttmAt0mm

21

0AM

00AM

1

coscos1

Re

Re

Im 0

A0

m

m


2

2

T

SAM 2 m

m

P

P

%333

10 AM

PS – sidelobe power

PT – total power

AM Modulation


X()

~X()

SSB()

0-g 0 0+g

20g-g

g-g


00

SSB-SC Modulation

? ttxttxt 00SSB sinˆcos

tx tx̂2

X() SSB()

SSB-SC Modulation

quadrature (Hilbert’s) filter


2

x

x

+

x(t)

cos0t

sin0t

SSB-SC+(t)

-

)(ˆ tx

+

SSB-SC Modulation


Quadrature (Hilbert’s) Filter

0,

0,2sgn

j

jeeAH jj

A()

()

12

2

XHX ˆ


Analytic Signal

0,

0,ˆ

jX

jXX

txjtxtx ˆ

0,

0,

X

XXX

0,0

0,2

X

X


SSB-SC Modulation

tjetxjtxt 0ˆReSSB

2

Re*

VV

tv

00 sidebandupper

0*

sidebandupper

0SSB 2

1

2

1

XX


Coherent SSB-SC Detection

x

cos0t

Predetection

Filter

Lowpass

Filter

~x(t)

tSC-SSB

txttxttxtx

tttxttxtt

~2sinˆ2cos~

~cossinˆcos~cos

filter lowpass

0

filter lowpass

0

0002

0SC-SSB


ttxttxt 00SSB sinˆcos

txtxte 22SSB ˆ

txte SSB

Envelope SSB-SC Detection



Re

Ime

xxjˆ

)exp(ˆ jexjxx

22 x̂xe

tjetetxjtxtx SSBˆ

tte SSBln H


ttetx cosSSB

te ln2

cos

tSSB

x

tx



tte SSBln H

tjetetxjtxtx SSBˆ

Nyquist FilterVSB-SC Concept

H()

Nyquist filter

SCDSB

HSCDSB

SSB-SC VSB-SC

Vestigal SideBand„Modulation & Detection” Zdzisław Papir

VSB-SC Modulation

H ttxt 0DSB cos)(

DSBVSB

tVSB

H

Nyquist filter


VSB-SC Modulation

ttttt 0

quadrature

Q0

inphase

ISC-VSB sincos

Lowpass I & Q representation

of a bandpass VSB-SC signal


Coherent VSB-SC Detection

filter lowpass

0Q0II

0SC-VSB

2sin2cos~

~cos

ttttt

tt

Requirement for a coherent VSB-S.C. detection

txt I


VSB-SC Modulation

thH

ttxtht 0VSB cos

tthtthth 0Q0I sin2cos2

ttxthttxtht QI 00VSB sin)]()([cos)]()([)(

)(tI )(tQ


VSB-SC Modulation

x

x

+x(t) cos0t

sin0t

-

)(Q H

tVSB

txt ~I)(I H

+


VSB-SC Modulation

00I HHH

00Q HHjH

const~ II Htxt


const00I HHH

H()

const

0

0

H

H

VSB-SC Modulation


VSB-SC Modulation


0

Nyquist filter, 50%

const00

I

HH

H

00

Q

HHj

H

ttttxt 0Q0VSB sincos

componet enabling vestigal sideband filtering

component

enabling

coherent detection

VSB-SC Modulation


Amplitude Modulation- different schemes

DSB

AM

SSB

VSB„Modulation & Detection” Zdzisław Papir

amplitude modulation slides by (2003/04): eryk schiller, daniel starnowski modulation &...

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