1-11 Ch4-Amplitude Modulation 2

8/3/2019 1-11 Ch4-Amplitude Modulation 2

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Chapter 4

Amplitude Modulation


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Baseband vs Passband Transmission

Baseband signals:

Voice (0-4kHz)

TV (0-6 MHz)

A signal may be sent inits baseband format

when a dedicated wired

channel is available.

Otherwise, it must be

converted to passband.


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Modulation: What and Why?

The process of shifting the baseband signal topassband range is calledModulation.

The process of shifting the passband signal to

baseband frequency range is calledDemodulation.

Reasons for modulation:

Simultaneous transmission of several signals

Practical Design of Antennas

Exchange of power and bandwidth


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Types of (Carrier) Modulation

In modulation, one characteristic of a signal(generally a sinusoidal wave) known as thecarrieris changed based on the information

signal that we wish to transmit (modulatingsignal).

That could be the amplitude, phase, or frequency,which result in Amplitude modulation (AM),

Phase modulation (PM), or Frequencymodulation (FM). The last two are combined asAngle Modulation


5/57

Types of Amplitude Modulation (AM)

Double Sideband with carrier (we will call it AM):This is the most widely used type of AM modulation.In fact, all radio channels in the AM band use this typeof modulation.

Double Sideband Suppressed Carrier (DSBSC):This is the same as the AM modulation above butwithout the carrier.

Single Sideband (SSB): In this modulation, only halfof the signal of the DSBSC is used.

Vestigial Sideband (VSB): This is a modification ofthe SSB to ease the generation and reception of thesignal.


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Double Sideband Suppressed Carrier (DSBSC)

Assume that we have a message signal m(t) withbandwidth 2B rad/s (orB Hz). m(t) M().

Let c(t) be a carrier signal, c(t) = cos(c

t), c

>> 2B

gDSBSC(t) = m(t)cos(ct)

(1/2) [M(c) +M(+ c)].

Xm(t)

c(t)

gDSBSC

(t)

DSBSC Modulator (transmitter)


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Time and Frequency Representation of DSBSC

Modulation Process


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DSBSC Demodulation

e (t)=gDSBSC(t)cos(ct)= m(t)cos2(ct)

= (1/2) m(t) [1 + cos(2ct)]

= (1/2) m(t) + (1/2) m(t) cos(2 ct)

E() (1/2)M() + (1/4) [M(

2 c) +M(+ 2 c)].

The output signalf(t) of the LPF will be

f(t) = (1/2) m(t) (1/2)M().

X

c(t)

gDSBSC

(t)e(t)

HLPF

()

BW = 2Bf(t)

DSBSC Demodulator (receiver)


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Time and Frequency Representation of DSBSC

Demodulation Process


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Modulator Circuits


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Switching Modulators

Any periodic function can be expressed as a

series of cosines (Fourier Series).

The information signal, m(t), can therefore be,equivalently, multiplied by any periodic

function, and followed by BPF.

Let this periodic function be a train of pulses.

Multiplication by a train of pulses can be

realized by simple switching.


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Switching Modulator Illustration


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Switching Modulator: Diode Bridge


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Switching Modulator: Ring


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Demodulation of DSBSC

The modulator circuits can be used for demodulation, but

replacing the BPF by a LPF of bandwidthB Hz.

The receiver must generate a carrier frequency in phase

and frequency synchronization with the incoming carrier.

This type of demodulation is therefore called coherent

demodulation (or detection).

X

c(t)

gDSBSC

(t)e(t)

HLPF

()

BW = 2B

f(t)

DSBSC Demodulator (receiver)


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From DSBSC to DSBWC (AM)

Carrier recovery circuits, which are required forthe operation of coherent demodulation, aresophisticated and could be quite costly.

If we can let m(t) be the envelope of themodulated signal, then a much simpler circuit,the envelope detector, can be used fordemodulation (non-coherent demodulation).

How can we make m(t) be the envelope of themodulated signal?


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Definition of AM

Shift m(t) by some DC value A

such thatA+m(t) 0. OrA mpeak

Called DSBWC. Here will refer to

it as Full AM, or simply AM

Modulation index m= mp/A.

0 m 1

)cos()()cos(

)cos()]([)(

ttmtA

ttmAtg

CC

CAM


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Spectrum of AM

)()(2

1)()()( CCCCAM MMAtg


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The Buy and Price of AM

Buy: Simplicity in demodulation.

Price: Waste in Power

gAM(t) =Acosct + m(t) cosct

Carrier Power Pc =A2/2 (carries no information)

Sideband Power Ps

= m2(t) /2=Pm

/2 (useful)

Power efficiency = h= Ps/(Pc + Ps)= Pm/(A2 +Pm)


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Tone Modulation

m(t) = mcos(mt) and m2(t) = (mA)2/2

g(t)=[A+Bcos(mt)] cosct=A[1+mcos(mt)] cosct

h= m2/(2+m2) 100%

Under best conditions, m=1hmax =1/3 =33%

For m= 0.5, h= 11.11%

For practical signals, h< 25%

? Would you use AM or DSBSC?


21/57

Generation of AM

AM signals can be generated by any DSBSC

modulator, by usingA+m(t) as input instead of

m(t).

In fact, the presence of the carrier term can

make it even simpler. We can use it for

switching instead of generating a local carrier.

The switching action can be made by a single

diode instead of a diode bridge.


22/57

AM Generator

A >> m(t)(to ensure switchingat every period).

vR=[cosct+m(t)][1/2 + 2/(cosct-1/3cos3ct+ )]

=(1/2)cosct+(2/)m(t) cosct+ other terms (suppressed by BPF)

vo(t) = (1/2)cosct+(2/)m(t) cosct

cos(ct)

m(t)

R BPF vo(t)

A


23/57

AM Modulation Process (Frequency)


24/57

AM Demodulation: Rectifier Detector

Because of the presence of a carrier term in the

received signal, switching can be performed in

the same way we did in the modulator.

[A+m(t)]cos(ct)

LPF m(t)

C

R


25/57

Rectifier Detector: Time Domain


26/57

Rectifier Detector (Frequency Domain)


27/57

Envelope Detector

When D is forward-biased, the capacitor charges andfollows input.

When D is reverse-biased, the capacitor dischargesthroughR.

[A+m(t)]cos(ct)

vo(t)RC


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Envelope Detection

The operations of the circuit requires

careful selection of t=RC

IfRCis too large, discharging will be

slow and the circuit cannot follow a

decreasing envelope.

WhenRCis too small the ripples will

be high.

1/(2B)


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Quadrature Amplitude Modulation (QAM)

In DSBSC or AM the modulated signal

occupies double the bandwidth of the baseband

signal.

It is possible to send two signals over the same

band, one modulated with a cosine and one

with sine.

Interesting enough, the two signals can bereceived separately after demodulation.


30/57

m1(t)cos(ct) HLPF

()

BW = 2BXm1(t)

cos(ct)

QAM Modulator/Demodulator

m2(t)sin(

ct)

Xm2(t)

sin(ct) Phase Shifter/2

m1(t)cos(ct) + m2(t)sin(ct)

X m1(t)/2

cos(ct)

X m2(t)/2

sin(ct) Phase Shifter/2

m1(t)cos2(

ct) + m

2(t)sin(

ct)cos(

ct)

=m1(t)/2+m

1(t) cos(2

ct)/2 + m

2(t)sin(2

ct)/2

HLPF

()

BW = 2B

Baseband Around c Around c

m1

(t)sin(c

t)cos(c

t) + m2

(t)sin2(c

t)

=m1(t)sin(2

ct)/2 + m

2(t)/2 m

2(t)cos(2

ct)/2

BasebandAround c Around c

QUADRATURE

modulator branch

IN-PHASE

modulator branch

QUADRATUREdemodulator branch

IN-PHASE

demodulator branch


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m1(t)cos(

ct)

HLPF

()

BW = 2BXm1(t)

cos(ct)

QAM Modulator/Demodulator with Demodulator Carrier Phase and/or Frequency Error

m2(t)sin(

ct)

Xm2(t)

sin(ct)

Phase Shifter

/2

m1(t)cos(ct) + m2(t)sin(ct)

X (1/2)[m1(t)cos(t+)m2(t)sin(t+)]

cos[(c+)t+

X (1/2)[m1(t)sin(t+) + m2(t)cos(t+)]

sin[(c+)t+

Phase Shifter

/2

m1(t)cos(

ct)cos[(

c+)t+ + m

2(t)sin(

ct)cos[(

c+)t+

=(1/2)[m1(t)cos(t+) + m

1(t) cos(2

ct+t+) m

2(t)sin(t+) + m

2(t)sin(2

ct+t+)]

HLPF

()

BW = 2B

Baseband Around c Around c

BasebandAround c Around c

Baseband

m1(t)cos(ct)sin[(c+)t+ + m2(t)sin(ct)sin[(c+)t+=(1/2)[m

1(t)sin(t+) + m

1(t) sin(2

ct+t+) + m

2(t)cos(t+) m

2(t)cos(2

ct+t+)]

Baseband


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Single-Side Band (SSB) Modulation

DSBSC (as well as AM) occupies double the

bandwidth of the baseband signal, although the two

sides carry the same information.

Why not send only one side, the upper or the lower? Modulation: similar to DSBSC. Only change the

settings of the BPF (center frequency, bandwidth).

Demodulation: similar to DSBSC (coherent)


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SSB Representation

How would we

represent the SSB signal

in the time domain?

gUSB(t) = ?gLSB(t) = ?


34/57

Time-Domain Representation of SSB (1/2)

M() =M+() +M-()

Let m+(t)M+() and m-(t)M-()

Then: m(t) = m+(t) + m-(t) [linearity]

Because M+

(),M-

() are not even

m+(t), m-(t) are complex.

Since their sum is real they must be

conjugates.

m+(t) = [m(t) +jmh(t)]

m-(t) = [m(t) -jmh(t)]

What is mh(t) ?


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Time-Domain Representation of SSB (2/2)

M() =M+() +M-()

M+() =M()u();M-() =M()u(-)

sgn()=2u() -1u()= + sgn(); u(-) = - sgn()

M+() = [M() +M()sgn()]M-() = [M() - M()sgn()]

Comparing to:

m+(t) = [m(t) +jmh(t)] [M() +j Mh()]

m-(t) = [m(t) -jmh(t)] [M() - jMh()]We find

Mh() = - j M()sgn() where mh(t)Mh()


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Hilbert Transform

mh(t) is known as the Hilbert Transform (HT) ofm(t).

The transfer function of this transform is given by:H() = -j sgn()

It is basically a /2 phase shifter

H() = jsgn()

j

j

|H()| = 1

1

/2

/2

) ) sgn)


37/57

Hilbert Transform of cos(ct)

cos(ct) (c) + (+ c)]

HT[cos(ct)] -j sgn() (c) + (+ c)]= j sgn() (c) (+ c)]

= j (c) + (+ c)]

= j (+ c) - (- c)] sin(ct)

Which is expected since:

cos(ct-/2) = sin(ct)


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Time-Domain Operation for Hilbert

Transformation

For Hilbert Transformation H() = -j sgn().

What is h(t)?

sgn(t) 2/(j) [From FT table]

2/(jt) 2sgn(-) [symmetry]

1/(t) -j sgn()

SinceMh() = - j M()sgn() =H() M()

Then

dt

m

tmt

tmh

)(1

)(*1

)(


39/57

)sin()()cos()(

)(2

1)(

2

1

)(2

1)(

2

1)(

)sin()()cos()(

)(2

1)(

2

1

)(2

1)(

2

1)(

ttmttm

etjmetm

etjmetmtg

ttmttm

etjmetm

etjmetmtg

ChC

tj

h

tj

tj

h

tj

LSB

ChC

tj

h

tj

tj

h

tj

USB

CC

CC

CC

CC

)()()(

)()()(

CCLSB

CCUSB

MMG

MMG

tjtj

LSB

tjtj

USB

CC

CC

etmetmtg

etmetmtg

)()()(

)()()(

Finally


40/57

Generation of SSB

Selective Filtering Method

Realization based on spectrum analysis

Phase-Shift Method

Realization based on time-domain expression

of the modulated signal


41/57

Selective Filtering

GDSBSC

()

C+2B

C2B

C

C

C+2B

C2B

USBLSBLSBUSB

M()

+2B

2B CC

GUSB

()

C+2B

C

C

C2B

USBUSB

GLSB

()

C2B CC C+2B

LSBLSB

HUSB

()

C+2B

C2B

C

C

C+2B

C2B

HLSB

()

C+2B

C2B

C

C

C+2B

C2B

BW = 2B (B Hz)

Center Freq = c+B

BW = 2B (B Hz)

Center Freq = cB

M() (an example of an

audio signal)

5000 Hz 300 Hz 300 Hz 5000 Hz

Guard Band

of 600 Hz


42/57

Phase Shifting

X

cos(ct)

SSB Modulator

X

sin(ct)

Phase Shifter

/2

Phase Shifter

/2

m(t)

mh(t)

mh(t)sin(

ct)

m(t)cos(ct)

gSSB

(t)

gUSB

(t) if

gLSB

(t) if ++ or

(a)

(b) (c)

(d)

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

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

ttmttmtg

ttmttmtg

ChCLSB

ChCUSB


43/57

Phase-shifting Method:

Frequency-Domain Illustration


44/57

SSB Demodulation (Coherent)

X

cos(ct)

gSSB

(t)

(Upper or Lower

Side bands)

HLPF

()

BW = 2Bm(t)

SSB Demodulator (receiver)

)(21OutputLPF

)2sin()(2

1)]2cos(1)[(

2

1)cos()(

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

tm

ttmttmttg

ttmttmtg

ChCCSSB

ChCSSB


45/57

FDM in Telephony

FDM is done in stages

Reduce number of carrier frequencies

More practical realization of filters

Group: 12 voice channels 4 kHz = 48 kHzoccupy the band 60-108 kHz

Supergroup: 5 groups 48 kHz = 240 kHzoccupy the band 312-552

Mastergroup: 10 S-G 240 kHz = 2400 kHzoccupy the band 564-3084 kHz


46/57

FDM Hierarchy

4

0

54

321

109

876

5432

1

1112

60 k

108 k

312 k

552 k

Group

Supergroup


47/57

Vestigial Side Band Modulation (VSB)

What if we want to generate SSB using

selective filtering but there is no guard band

between the two sides?

We will filter-in a vestige of the other band.

Can we still recover our message, without

distortion, after demodulation?

Yes. If we use a proper LPF.


48/57

Filtering Condition of VSB

X

2cos(ct)

m(t)H

VSB()

(BPF)g

VSB(t)

VSB Modulator (transmitter)

gDSBSC

(t)

X

2cos(ct)

gVSB

(t)H

LPF()

BW = 2Bm(t)

VSB Demodulator (receiver)

x(t)

)cos()(2)( ttmtg CDSBSC

)()()( CCDSBSC MMG

)()()()( CCVSBVSB MMHG

C

C

at

C

baseband

CVSB

Basebandat

CCVSB

MMH

MMHX

2

2

)2()()(

)()2()()(

)()()()()( MHHHZ CVSBCVSBLPF

)()(

1)(

CVSBCVSB

LPFHH

H

; || 2 B


49/57

VSB FilteringH

VSB()

C

C

HVSB

(c)+H

VSB(

c)

Shifted filter

components

Band of Signal

HVSB

(c) = 1/[H

VSB(

c)+H

VSB(

c)]

over the band of the signal only

Band of Signal

What happens outside the

band of the demodulated

signal is not important . So,

the LPF does not have to

inverse this part.


50/57

VSB Filter: Special Case

Condition For distortionless demodulation:

If we impose the condition on the filter at the modulator:

HVSB(c) +HVSB(c) = 1 ; || 2 B

Then HLPF

= 1 for|| 2 B (Ideal LPF)

HVSB() will then have odd symmetry around c over thetransition period.

)()(

1)(

CVSBCVSB

LPFHH

H

; || 2 B

M()


51/57

GDSBSC

()

C

C

+2B

2B C

C

HVSB

()

2B (B Hz) < BW < 4B (2B Hz)

C

C

GVSB

()

C

C

X()

C

C

C

M()

C

C

HLPF

()

C

C

C


52/57

AM Broadcasting

Allocated the band 530 kHz1600 kHz (with

minor variations)

10 kHz per channel. (9 kHz in some countries)

More that 100 stations can be licensed in the

same geographical area.

Uses AM modulation (DSB + C)


53/57

AM station Reception

In theory, any station can be extracted from the stream of spectra by

tuning the receiver BPF to its center frequency. Then demodulated.

Impracticalities:

Requires a BPF with very high Q-factor (Q =fc/B).

Particularly difficult if the filter is to be tunable.


54/57

Solution: Superheterodyne receiver

Step 1: Frequency Translation from RF to IF

Shift the desired station to another fixed pass band

(called Intermediate Frequency IF = 455 kHz)

Step 2: Bandpass Filtering at IFBuild a good BPF around IF to extract the desired

station. It is more practical now, because IF is

relatively low (reasonable Q) and the filter is not

tunable. Step 3: Demodulation

Use Envelope Detector


55/57

The Local Oscillator

What should be the frequency of the local

oscillator used for translation from RF to IF?

fLO =fc +fIF (up-conversion)

or fLO =fcfIF (down-conversion)

Tuning ratio =fLO, max /fLO, min

Up-Conversion: (1600 + 455) / (530+455) 2

Down-Conversion: (1600455) / (530455) 12

Easier to design oscillator with small tuning ratio.


56/57

Image Station Problem

While up-converting the desired station to IF, we are,at the same time, down-converting another station to IFas well.

These two stations are called image stations, and theyare spaced by 2x455=910kHz.

Solution:Before conversion, use a BPF (at RF) centered atfc ofthe desired station.

The purpose of the filter is NOT to extract the desiredstation, but to suppress its image. Hence, it does nothave to be very sharp.


57/57

Superheterodyne Receiver Block Diagram

Antenna

IF Stage(intermediate frequency)

IF Amplifier

& IF BPF

X

Converter

(Multiplier)

a(t) b(t) d(t)

c(t)

Envelope Detector

Diode, Capacitor,

Resistor, & DC blocker

Audio Stage

Power amplifier

d(t) e(t) f(t) g(t)

Ganged RFBPF and

Oscillator

RF Stage(radio frequency)

RF Amplifier

& RF BPF

Local

Oscillator

cos[(c+

IF)t]

Notes:

With one knob, we are tuning the RF Filter

and the local oscillator.

The filter are designed with high gain

to provide amplification as well.

1-11 Ch4-Amplitude Modulation 2

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