© 2010 the mcgraw-hill companies communication systems, 5e chapter 4: linear cw modulation a. bruce...

© 2010 The McGraw-Hill Companies

Communication Systems, 5e

Chapter 4: Linear CW Modulation

A. Bruce CarlsonPaul B. Crilly

(W.J. Song and J. H. Cho)

Why modulation?

1. Antenna size2. Fractional Bandwidth < 10%3. Wideband noise reduction4. Freq. Assignment5. Multiplexing

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Chapter 4: Linear CW Modulation

Bandpass signals and systems Double-sideband amplitude modulation (DSB) Modulation and transmitters Single-sideband (SSB) amplitude modulation Frequency conversion and demodulation

cf. Nonlinear modulation in Ch. 5

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Bandpass signals and systems

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Bandpass signal (a) Spectrum; Waveform

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Bandpass signals

( ) Definition: ( )

0 c c

bpc c

X f f W f f WV f

f W f f W

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(a)Rotating phasor; (b) Phasor diagram with rotation suppressed

Figure 4.1-3

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Quadrature-carrier representation:

( ) ( )cos2 ( )sin 2

where: ( ) ( )cos ( ) in-phase component ( ) ( )sin ( ) quadrature component

bp i c q c

i

q

v t v t f t v t f t

v t A t tv t A t t

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2 2 1

( ) ( )cos 2 ( )

where( )

( ) ( ) ( ) and ( ) tan( )

bp c

qi q

i

v t A t f t t

v tA t v t v t t

v t

Envelope-phase representation

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Modulation to create a BP signal

Modulation is the translation of a band limited LP signal toa band pass signal with some center frequency cf

message spectrum

bandpass spectrum

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Analog message conventions

0

2 2

0

2

Message signal: ( )

Amplitude: ( ) 1

1Power: ( ) ( ) 1

Thus with a single tone message ( ) cos21

1 2 2

Message bandwidth =

x

T

m m

mm x

m

x t

x t

S x t x t dtT

x t A f tA

A S

W f W

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Bandwidth

Message bandwidth: Transmission bandwidth:

W

TB

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Fractional bandwidth

(a) Relevant to band pass signals

(b) fractional bandwidth defined as T

c

B

f

(c) For practical systems we require 0.01 0.1T

c

B

f

(d) Upper limit 10 prevents spillover into negative frequencies

(e) Lower limit 100 economics

c T

c T

f B

f B

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How is bandwidth defined?

Absolute bandwidth: 100% of energy is within some frequency range

3 dB, or half power bandwidth: frequency range where magnitude reduction is less than -3 dB

Noise equivalent bandwidth (see chapter 9) Occupied bandwidth: FCC definition where frequency range that

contains 99% of energy Relative power bandwidth: frequency range where magnitude

rolloff is less than a given level of dB (e.g. -40 dB)

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Types of linear CW modulation

Conventional/Standard Amplitude Modulation (AM)

Suppressed carrier double sideband (SC-DSB, DSB-SC,or DSB)

Single sideband (USSB and LSSB) Vestigial sideband (VSB)

Vestigial 퇴화한 , 흔적으로 남아 있는

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AM, DSB, SSB, and VSB are subclasses of amplitude modulation because the

message alters the carrier’s amplitude.

However, ‘AM’ quite often means conventional/standard AM = DSB-WC.

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4.2 Double-sideband amplitude modulation

Conventional AM Suppressed carrier DSB, (SCDSB) or simply DSB

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Conventional AM, or simply AM

( ) [1 ( )]cos2

where

carrier amplitude ( ) message, and ( ) 1 modulation index, 1 and =1 100% modulation carrier frequency, Hz

c c c

c

c

x t A x t f t

Ax t x t

f

1 1( ) ( ) ( ) ( )

2 2c c c c c cx t X f A f f A X f f

Overmodulation: phase reversal & envelop distortion

bandwidth for

(Baseband cut-off Freq.)

wf

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AM waveforms (a) Message; (b) AM wave with < 1; (c) AM wave with > 1 (overmodulation)

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Spectrum of AM signals

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AM Spectrum

Note:(a) carrier impulse at this impulse carries no informationcf

(b) redundant sidebands: the lower and upper sidebands carry the same information increased bandwidth

2TB W

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AM Power

2

2 2

Output power: carrier power + sideband power

2where

1

21

2

Peak envelope power:

T c sb

c c

sb c x

peak envel

S P P

P A

P A S

P

22 2max max

1 ( )ope cA A u x t

4

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AM Systems Relatively simple transmitter and receiver hardware The first voice modulation system More than half power goes into carrier, but carrier

carries no information inefficient Not suited for messages with low frequency content

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Suppressed Carrier DSB (DSB-SC) Signals

2

22 2max max

1( ) ( )cos2 ( )

2

Output power:

1 2

2

Peak envelope power

( )

c c c c c c

T sb c x

peak envelope c

x t A x t f t X f A X f f

S P A S

P A A x t

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DSB waveforms

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DSB systems

Suppressed carrier: typically -40→ -60 dB All power goes into sidebands more efficient than

AM Demodulation is more complicated than AM; requires

synchronization Transmitter hardware is more complex than AM. Well suited to transmission of messages with low

frequency or DC content

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4.3 Modulation and transmitters

AM (DSB-WC)

DSB (DSB-SC)

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AM transmitters

Implemented using a nonlinear element or some nonlinear portion of a circuit.

Often done where the message is superimposed on one of the active device’s terminals (i.e. the base/gate or collector/drain)

Because of nonlinear elements, may require a tank circuit to remove other of band components

Multiplication ?

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2

21 ininout vavav outv

inv

)(tx

inv outv)(tv

twccos

filter

Nonlinear Device

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tattxaa

atxatxaa

tattxaa

atxatxa

tattxatxatatxav

cc

cc

cccout

2cos21

cos)](21[)()(21

]2cos1[21

cos)](21[)()(

coscos)(2)(cos)(

21

21

2212

21

21

221

222

2211

ttxv cin cos)(

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)(2

12 fa

)(1 fXa )()(2 fXfXa

)(2

11 cffa

)(2 cffXa

wfc cf wfc

)2(2

12 cffa

cf2 f

)( fH

f

w2

?

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AM modulator example

(a) the concept, (b) practical circuit.

Note in (b) how the message and carrier source are superimposedonto the gate circuitry.

tank circuit

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DSB transmitters

Due to technological limitations, practical DSB systems are rarely implemented via ordinary multiplers.

Balanced modulators Ring modulators Other nonlinear devices

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Balanced modulator concept for DSB generation*

*Only for purposes of illustrating the balanced modulator concept. Practical DSB modulators are implemented using nonlinear devices such as diode arrays

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Ring modulator for DSB generation

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4.4 Single-sideband (SSB) modulation

If we have a DSB signal with symmetrical sidebands, we can suppress one of the sidebands without loss of information.

Therefore, we reduce transmission bandwidth from

Double the number of users on a channel

2DSB SSBT TB W B W

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Types of SSB

Lower sideband: LSSB or LSB

Upper sideband: USSB or USB

The decision to choose one over the other is dictated

by: Convention or prior assignment

Technological considerations

Neither USSB or LSSB is inherently better than the

other

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SSB signals

1ˆ( ) ( )cos ( )sin

2

ˆwhere ( ) is the Hilbert transform of the message

The in-phase and quadrature components are:1

ˆ ( ) ( ) and ( ) ( )2

1and the envelope is ( )

2

c c c c

ci c cq c

x t A x t t x t t

x t

x t A x t x t A x t

A t A

2 2ˆ( ) ( )c x t x t

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SSB spectra

(a) Generation of SSB from DSB using filter method, (b) USSB, (c) LSSB

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SSB generation

Filter method: use a high-Q filter to suppress one of

the sidebands.

Phase methods: shift sidebands using a phase shift

method to cancel one of them out

Phase shift

Weavers, weaver modulator

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Weaver’s SSB modulator

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VSB

SSB method but with a trace of the other sideband left

Practical SSB systems with imperfect filters are VSB

VSB allows for messages with low frequency or DC

content

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4.5 Frequency conversion and demodulation

Modulation: translate message to some carrier frequency

Frequency translation: move a signal from one carrier frequency to another

Demodulation: move modulated signal back to baseband Synchronous or product detectors: phase recovery Envelope detectors : no phase recovery

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Basic hetrodyne frequency converter

Frequency converson via hetrodyning takes advantage of the property of the product of 2 cosine functions sum and difference

1 1 cos cos cos( ) cos( )

2 2

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Frequency conversion via hetrodyning (multiplication)

1 2 1 2 1 2

1 2 1 2

1 1( )cos2 cos2 ( )cos2 ( ) ( )cos2 ( )

2 21 1

( ) ( )2 2 sum and the difference of 2 the frequencies

x t f t f t x t f f t t x t f f t t

X f f X f f

We use a filter to select a particular component

cf. homodyne receiver, super heterodyne receiver

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Frequency translation example

Q. Convert 7 MHz USSB signal into a 50 MHz LSSB signal via hetrodyning.

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Synchronous detection example

~ cos2 ( )LO cf f t

LPF( )cx t ( )x t

cf

( )cX f

( )X f

f

f

Demodulation bytranslation to baseband

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~ cos2 ( )cf f t

LPF( )cx t ( )x t

cf

( )cX f

( )X ff

f

Synchronous detection when there is an error in the local oscillator (LO)

f

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Detector output single tone at , and message is translated to a center frequency of distorted messageand obnoxious background tone

f ff

Mandatory that the local oscillator and its phasematch the carrier frequency

Synchronization error continued

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Envelope detection

Suitable for AM signals or signals with a carrier

Does not require synchronization

Simple hardware: diode, resistor, capacitor

Will work with suppressed carrier modulation systems

if the receiver inserts a carrier

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Envelope detection (a) Circuit; (b) Waveforms

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)(tm

.1)(

and1)(

Thus

.)(then,)(If

)](1

)(1

)(2

1[

)]()()(2[)(

2

2

2

2

2

12

2

2

2

2

1222

A

tx

Atx

AtxAtx

txA

txA

txA

A

txtxtAxAtm

h

h

h

h

Envelope

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)(

)](1

1[

)](2

1[)( 2

1

txA

txA

A

txA

Atm

.efficientnot!)(thatnoteBut Atx

Therefore

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© 2010 The McGraw-Hill Companies

© 2010 The McGraw-Hill Companies

ttxttx

ttxtxttx

tdfefXfHj

ttxttx

cqc

chc

cftj

chc

sin)(cos)(

sin)]()([cos)(

sin])()(2[

sin)(cos)(

2

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)}(cos{)(

]sin)(cos)}(1[{

]}sin)(cos)([{cos)(

tttm

ttxttxA

ttxttxtAtv

c

cqcc

cqccc

VSB+C

possible! is detecton Envelope

)](1[)(

Thus

.1)(,1)(Since

)](1[

])([1)](1[)(

where

22

21

2

2

txAtm

txtx

tx

txtxAtm

c

qq

qc

용어정리 AM

Verbatimly, it can be any amplitude modulation scheme.

However, by convention, it means DSB-WC (with carrier), a subclass of amplitude modulation

Often called ‘standard AM’.

DSB It is an amplitude modulation. DSB-SC (suppressed carrier)

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