Amplitude Modulation DSB-SCihayee/Teaching/ee5765/ece5765_chapter_4_5.pdfAmplitude Modulation Formats • Vestigial Side Band (VSB) increases almost 50% effective bandwidth used in

Department of Electrical and Computer Engineering

Amplitude Modulation – DSB-SC

Modulation: )()( Mtm

)]()([2

1)cos()()(mod ccc MMttmtS

)(tm

)cos( tc

)cos()( ttm c

Modulating signalModulated Signal

Modulating carrier


)(M

BB

c


)]()([2


)(mod S

c

2

1

1

Bc Bc Bc Bc


Demodulation: )(cos)()( 2 ttmtS cdem

)]2cos()()([2

1ttmtm c

)]2()2([4

1)(

2

1)( ccdem MMMS

Amplitude Demodulation – DSB-SC

)cos( tc

)cos()( ttm c

Modulated signalDemodulated Signal

Modulating carrier

)(tSdem

Lowpass Filter

1. Upper and Lower

Sidebands

2. Relationship of carrier

freq and signal bandwidth


c

)(mod S

c

2

1

Bc Bc Bc Bc

Demodulation: )(cos)()( 2 ttmtS cdem

)]2cos()()([2

1ttmtm c

)]2()2([4

1)(

2

1)( ccdem MMMS

)(mod S

c2

2

1

Bc 2Bc 2Bc 2c2BB Bc 2

Lowpass Filter


Example of DSB-SC Modulation

Let )cos()( ttm m

)]()([)( mmM

)cos()()(mod ttmtS c

)cos()cos( tt cm

])cos()[cos(2

1tt mcmc

then


)(cos)()( 2 ttmtS cdem

)(cos)cos( 2 tt cm

))2cos(1)(cos(2

1tt cm

)2cos()cos(2

1)cos(

2

1ttt cmm

Example of DSB-SC Demodulation


Frequency Conversion or Mixing

How to change carrier frequency from one frequency to another?

)()( Mtm

)]()([2


c

)(mod S

c

2

1

Bc Bc Bc Bc

The Goal is to change toc I

)cos()( ttm c )cos()( ttm I

conversionupif cI

conversiondownif cI


tIc )cos(2

)cos()( ttm c

Signal with a carrier frequencyFrequency Converted Signal

Bandpass FilterOption 1

tttmtx Icc )cos(2)cos()()(

])cos()cos(2)[( tttm Icc

])2cos())[cos(( tttm IcI

)(tx

I

)(X

I

1

Ic 2Ic 2

Bandpass Filter


tIc )cos(2

)cos()( ttm c

Signal with a carrier frequencyFrequency Converted Signal

Bandpass FilterOption 2

tttmtx Icc )cos(2)cos()()(

])cos()cos(2)[( tttm Icc

])2cos())[cos(( tttm IcI

)(tx

I

)(X

I

1

Ic 2Ic 2

Bandpass Filter


Switching Modulators

AM modulation can be obtained by not only multiplying with pure sinosoidal signal

but by any periodic signal with fundamental frequency c. Any periodic signal can

be represented as:

)cos()(0

nc

n

n tnCt

)cos()()()(0

nc

n

n tntmCttm

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

10 nc

n

nnc tntmCtCtmtmCttm

Need a Bandpass Filter


t

w(t)

....]5cos5

13cos

3

1[cos

2

2

1)( ttttw ccc

.....]5cos)(5

13cos)(

3

1cos)([

2)(

2

1)()( ttmttmttmtmtwtm ccc

)]()([1

)(2

1)(mod cc MMMS

)]3()3([3

1cc MM

)].....5()5([5

1cc MM


Modulating Signal Modulated Signal

BPF

Switch

Can be realized with a diode (a basic

switching element) or combination of diodes

Demodulation still needs to be synchronous

~

tccos


)cos()()cos()()mod( ttmtAtS ccAM

Regular Amplitude Modulation without carrier suppression

)cos()]([ ttmA c

)]()([)]()([2

1)()( ccccAMdem AMMS

Important condition for envelop detection

A+m(t) ≥ 0 for all t


Let mp is the maximum peak value of m(t), then

pmA

A

mp

10

Let’s define modulation index


Power of Carrier vs. Power in Sidebands


2

2APc )(

2

1 2 tmPs

)(

)(22

2

tmA

tm

PP

P

P

P

sc

s

total

useful

and

Power Efficiency



)cos()( tBtm m

)cos()cos()cos()()mod( ttBtAtS cmcAM

)cos()]cos([ ttBA cm

Let

ABA

B

A

mp

)cos()]cos([)()mod( ttAAtS cmAM

)cos()]cos(1[ ttA cm


Example of Tone modulation => max efficiency = 33%

2

2APc )(

2

1 2 tmPs and

2

2APc

22

1 22 APs

2

2

222

22

22

AA

A

PP

P

P

P

sc

s

total

useful

1%3333.012

1

for


Generation of AM signals

Generation of AM signals is the same as generation f AM-SC

signals, the only difference is that m(t) is replaced by [A+m(t)]

Demodulation of AM signals

Two commonly used methods are:

1. Rectifier Detection – synchronous demodulation

2. Envelop Detection – very simple detection


Rectifier Detector

)cos()]([1 ttmAv c+

-)()}cos()]({[2 twttmAv c

2v

1v

....]5cos5

23cos

3

2cos

2

2

1)[cos()]([ tttttmA cccc

termsfrequencyhighertmA )]([1

LPF

3v

)]([1

3 tmAv

4v

)(1

4 tmv

....]5cos5

23cos

3

2

2

1)[cos()]([cos

2*)cos()]([ ttttmAtttmA ccccc



Envelop Detector

+

-

1vCharges Discharge

CR

Time Constant = RC

c

RC

1

BRC

2

1

3v 4v



Frequency Division Multiplexing

1c

SingnalFDM

1c

1

2c 3c 4c2c3c4c

Ch. 1 Ch. 2 Ch. 3 Ch. 4

Bandwidth/Channel needed = 2B

(where B is the bandwidth of the signal)

Superheterodyne AM Receiver?


Amplitude Modulation – SSB-SC


)]()([2

1)cos()()(mod cccDSB MMttmtS

)]()()()([2

1mod ccccSSB MMMMS

c c

2

1

Bc Bc Bc Bc

)(M

BB

)(mod DSBS

1

)( cM

)( cM )( cM

)( cM

same for real signals

=> waste of bandwidth


c c

2

1

Bc Bc Bc Bc

)(mod DSBS

)( cM

)( cM )( cM

)( cM

c c

2

1

Bc Bc Bc Bc

)(mod SSBS

)( cM )( cM

c c

2

1

Bc Bc Bc Bc

)(mod SSBS )( cM )( cM

AM-SSB can potentially double the useable channel bandwidth

What we need to accomplish this?


)(tm

)cos( tc

Modulating signalSSB Signal

Modulating carrier

Sharp cut-off BPF

c c

2

1

Bc Bc Bc Bc

)(mod DSBS

A sharp cut-off bandpass filter!

Not practical to make!


More Practical Bandwidth Saving

Amplitude Modulation Formats

• Vestigial Side Band (VSB)

increases almost 50% effective bandwidth

used in TV

Same as SSB but uses a practical bandpass filter

• Quadrature Amplitude Modulation (QAM)

Doubles the effective bandwidth

Uses in limited bandwidth channel applications


c c

2

1

Bc Bc Bc Bc

)(mod SSBS

c c

2

1

Bc Bc Bc Bc

)(mod VSBS

c c

2

1

Bc Bc Bc Bc

c c

2

1

Bc Bc Bc Bc

AM-Single Side Band

Bandwidth needed = B

AM-Vestigial Side Band

Bandwidth needed ~ 1.5B


Quadrature Amplitude Modulation

)sin()()cos()()( 21 ttmttmtS ccQAM

2

~

)(1 tm

)(2 tm

tccos

)(tSQAM


Quadrature Amplitude Demodulation


2

~ tccos

LPF )(1 tx

)(2 tx

)(tSQAM

LPF


)cos()]sin()()cos()([)( 211 tttmttmtx ccc


)cos()sin()()(cos)( 2

2

1 tttmttm ccc

)cos()sin()()2cos()(2

1)(

2

1211 tttmttmtm ccc

will be filtered by lowpass filter


)sin()]sin()()cos()([)( 212 tttmttmtx ccc


)(sin)()sin()cos()( 2

21 ttmtttm ccc

)2cos()(2

1)(

2

1)sin()cos()( 221 ttmtmtttm ccc

will be filtered by lowpass filter

)(2

1)2cos()(

2

1)sin()cos()( 221 tmttmtttm ccc


Concept of Generalized Angle

)(cos)( tAt

)cos()( 0 tAt cSpecial Case

dt

dti

)(

t

i dxxt )()(

Instantaneous Frequency


Phase Modulation

)cos()( tAt c

)()( tmktt pc

)](cos[)( tmktAt pcPM

)()( tmkdt

dt pci


Frequency Modulation

)cos()( tAt c

)()( tmkt fci

t

fc dxxmkt )]([)(

t

fc dxxmkt )(

])(cos[)(

t

fcFM dxxmktAt


PM and FM - Inseparable

PM)(tm dxxm )(

)(tFM

FM)(tm

)(tm

dt

d )(tPM


Example 1

)(tm

)(tm

1

-1

2x10-4

t

t

20,000

-20,000

5102 fk

10pk

MHzfc 100


Example 2

)(tm

t

1

-1

5102 fk

2

pk

)(tm

t

)(2 t

)(2 t

MHzfc 100


Bandwidth of FM Signal

])(cos[)(

t

fcFM dxxmktAt

])()(

t

dxxmta

)]([)(ˆ taktj

FMfcAet

)(tajktj fc eAe

Let’s define

and

then )](ˆRe[)( tt FMFM


)()(ˆ tajktj

FMfc eAet

)](!

...)(!2

)(1[ 2

2

tan

kjta

ktajkAe n

n

fnf

f

tj c

]sin)][cos(!

...)(!2

)(1[ 2

2

tjttan

kjta

ktajkA cc

n

n

fnf

f

)](ˆRe[)( tt FMFM

...]sin)(!3

cos)(!2

sin)([cos 3

3

2

2

ttak

ttak

ttaktA c

f

c

f

cfc

If m(t) is band limited to B, then Bandwidth of an(t) is nB


...]sin)(!3

cos)(!2

sin)([cos)( 3

3

2

2

ttak

ttak

ttaktAt c

f

c

f

cfcFM

0.1)( tak fif

]sin)([cos)( ttaktAt cfcFM then

]sin)([cos)( ttmktAt cpcPM Similarly

Narrow Band FM and PM (NBFM or NWPM)

Bandwidth of narrowband FM or PM is 2B


Generation of NBFM or NBPM

]sin)([cos)( ttaktAt cfcFM

]sin)([cos)( ttmktAt cpcPM

tA ccos

NBPM)(tm

~

2/

DSB-SC

Modulator

tA csin

tA ccos

NBFM)(tm

~

2/

DSB-SC

Modulator

tA csin


]sin)([cos)( ttaktAt cfcFM

Distortion Estimate in NBFM Signals

)](cos[)( tttAE c

)(1)( 22 taktE f

)]([tan)( 1 takt f

where

Amplitude distortion can be

minimized by bandbass limiter


Phase Distortion

)]([tan)( 1 takt f

)(1

)()()(

22 tak

taktt

f

f

i

)(1

)(22 tak

tmk

f

f

...])()(1)[( 4422 taktaktmk fff


Example of Tone Modulation

...])()(1)[()( 4422 taktaktmkt fffi

ttm m cos)(

m

mtta

sin)(

m

fk

...]sinsin1(cos 4422 ttt mmmm

)sin1(cos)( 22 ttt mmmi

)2

]2cos1[1(cos 2 t

t mmm

B

FLet’s define


tt mm

mm

3cos4

cos)4

1(32

)2

]2cos1[1(cos 2 t

t mmm

)2

2cos

21(cos

22 tt m

mm

2

2coscoscos

2cos

33 tttt mmm

mm

mm

4

)3cos(coscos

2cos

33 tttt mmm

mm

mm

13cos4

cos3

fortt mm

mm


B4 B4

pfc mk pfc mk)( kfc tmk

)( ktmpm

pm

t

)(tm

pf mk2

B2

1

t

Wide Band FM (WBFM)

c


Wide Band FM (WBFM)

)2(2 BfBFM

2

pf mkf

Bf BBFM 4if then

This bandwidth is slightly more than the actual because this

corresponds to the staircase approximation of the signal

Let’s make the adjustment, we know that

Which is not right from our NBFW analysis,

we know that

BBFM 2


Wide Band FM (WBFM)

Bf fBFM 2

B

f )1(2 BBFMif we define then

)(2 BfBFM

Now, if then

)2(2 BfBFM Therefore,

Should change to

And if Bf BBFM 2then

WBFM

NBFM


Wide Band PM (WBPM)

)(2 BfBPM

2

ppmkf

)1(2 BBPM

)()( tmkt pci

B

f


Example 1

)(tm

)(tm

1

-1

2x10-4

t

t

20,000

-20,000

5102 fk

10pk

1. What is the bandwidth of

corresponding FM or PM

signals ?

2. What if m(t) is doubled in

magnitude?

3. What if the period is doubled?


Understanding the Spectrum of FM

)]([)(ˆ taktj

FMfcAet

We previously defined

Also, we know

ttm m cos)(

m

mtta

sin)(

)]sin([

)(ˆt

ktj

FM

mm

fc

Aet

fpf kmk

m

fk

B

fNow

Let’s use the example of tone modulation


)]sin([)(ˆ ttj

FMmcAet

][)sin( tjtj mc eAe

n

tj

n

tj mm eCe sin

Now

Where )(2

/

/

sin

n

tjntmn JdteeC

m

m

mm

tjn

n

n

tj

FMmc eJAet

)()(ˆ

Bessel Function


tjn

n

n

tj

FMmc eJAet

)()(ˆ

)()(

tntj

n

nmceJA

)](ˆRe[)( tt FMFM

Remember we were interested in

)cos()()( tntJAt mc

n

nFM


Bessel Function


tA ccos

)(tm

2/

DSB-SC

Modulator

tA csin

OSC

200kHz

Frequency

Multiplier

x64

Frequency

Multiplier

x48

Frequency

Converter

Power

Amplifier

OSC

10.9MHz

Hzf

kHzfc

25

2001

kHzf

MHzfc

6.1

8.121

kHzf

MHzfc

6.1

9.11

kHzf

MHzfc

8.76

2.911

Wideband FM Generation - Indirect

NBFMFrequency

MultiplierWBFM

)(tm


Wideband FM Generation - Direct

Voltage Controlled Oscillator

LC

10

can be varied with bias voltage

can be varied with current through coil


Demodulation of FM

])(cos[)(

t

fcFM dxxmktAt

]})(cos[{)(

t

fcFM dxxmktAdt

dt

])(sin[)]([

t

fcfc dxxmkttmkA

Envelope

Detection

)(tFM

dt

d )]([ tmkA fc


Demodulation of PM

)](cos[)( tmktAt pcPM

)]}(cos[{)( tmktAdt

dt pcPM

)](sin[)]([ tmkttmkA pcpc

Envelope

Detection

)(tFM

dt

d

)]([ tmkA pc

)(tmAk p

)(tmAk pC


Demodulation of FM – Phase Lock Loop

VCO

)(H)(tx

)()(0 tmte )](sin[ ttA ic

)](cos[ 0 ttB c

)(0 tcecVCO

)](cos[)](sin[)( 0 ttttABtx cic

)]}()(2sin[)]()({sin[2

00 tttttAB

ici

t

fi dmkt )()(

Suppressed by loop filter, )(H

)()(0 tcet o


So the effective input to the loop filter will be

))]()(sin[2

)( 0 ttAB

tx i

)()()( 0 ttt ie where

)](sin[2

tAB

e

)()()(0 ttt ei


)]()([ 0 tcet o

)()()(0 ttt ei

])()([

t

fi dmkt )()()( tdmkt e

t

fo

)()( tmkt fo

For small error

Now

)()( tmc

kte

f

o

For FM Signal

t

fo dmkt )()(

Taking derivative on both sides


)]()([ 0 tcet o

)]()([ tmkt pi )()()( ttmkt epo

)()( tmkt po

For small error

Now

)()( tmc

kte

p

o

For PM Signal

You need an integrator after PLL for PM demodulation

)()( tmkt po


Interference in Angle Modulated Signals

tItAtr cc )cos(cos)(

Desired signal Interfering signal

ttIttItA ccc sinsincoscoscos

)](cos[)( tttE dcr

ttIttIA cc sinsincos)cos(

22 )sin()cos()( tItIAtEr

tIA

tItd

cos

sintan)( 1

where


tA

It

A

Itd sinsintan)( 1

tIA

tItd

cos

sintan)( 1

When I<<A

)](cos[)()( tttEtr dcr

Remember original signal

tA

Ityd sin)(

tA

Ityd

cos)(

For PM

For FM

After passing through PM or FM demodulator


Pre-emphasis and De-emphasis in FM


Stereo FM

Receiver

Amplitude Modulation DSB-SCihayee/Teaching/ee5765/ece5765_chapter_4_5.pdfAmplitude Modulation Formats • Vestigial Side Band (VSB) increases almost 50% effective bandwidth used in

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