introduction to communication system-lecture3

7/23/2019 Introduction to Communication System-lecture3

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Dar es Salaam institute of Technology(DIT)

ETU 07123

Introduction to Communication System

Ally, J

jumannea!mail"com


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Angle Modulation


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An!le modulation o#er#ie$

In t%e last su&to'ic, $e in#esti!ated t%e e((ect o( slo$ly #aryin! t%e

am'litude o( a sinusoidal carrier $a#e in accordance $it% t%e&ase&and si!nal" T%ere is anot%er $ay o( modulatin! a sinusoidal carrier $a#e,

namely, An!le )odulation in $%ic% t%e an!le o( t%e carrier $a#e is#aried accordin! to t%e &ase&and si!nal"

In t%is met%od o( modulation, t%e am'litude o( t%e carrier $a#e is

maintained constant An im'ortant (eature o( an!le modulation is t%at it can 'ro#ide &etter

discrimination a!ainst noise and inter(erence t%an am'litudemodulation"

*o$e#er, t%is im'ro#ement in 'er(ormance is ac%ie#ed at t%e

e+'ense o( increased transmission &and$idt% t%at is, an!lemodulation 'ro#ides us $it% a 'ractical means o( e+c%an!in! c%annel&and$idt% (or im'ro#ed noise 'er(ormance" Suc% a tradeo((

is not 'ossi&le $it% am'litude modulation, re!ardless o( its (orm"


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-asic de(initions .et denote t%e an!le o( a modulated sinusoidal carrier, assumed to

&e a (unction o( t%e messa!e si!nal" /e e+'ress t%e resultin! an!le

modulated $a#e as

T%ere are an in(inite num&er o( $ays in $%ic% t%e an!le may &e

#aried in some manner $it% t%e messa!e &ase&and si!nal" *o$e#er,$e s%all consider only t$o commonly used met%ods, '%ase modulation

and (reuency modulation, de(ined as (ollo$s4

1 5%ase modulation 5) is t%at (orm o( an!le modulation in $%ic% t%e

an!le is #aried linearly $it% t%e messa!e si!nal mt, as s%o$n as

T%e term re'resents t%e an!le o( t%e unmodulated carrier and t%e

constant re'resents t%e '%ase sensiti#ity o( t%e modulator, e+'ressed

in radians 'er #olt on t%e assum'tion t%at mt is a #olta!e $a#e(orm"


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-asic de(initions2T%e '%asemodulated si!nal st in t%e time domain is !i#en &y

2 6reuency modulation 6) is t%at (orm o( an!le modulation in $%ic%

t%e instantaneous (reuency is #aried linearly $it% t%e messa!e

si!nal mt, as s%o$n &y

T%e term fcre'resents t%e (reuency o( t%e unmodulated carrier, andt%e constant (re'resents t%e (reuency sensiti#ity o( t%e modulator,

Inte!ratin! a&o#e euation

$it% res'ect to time and multi'lyin! t%e

result &y 28,

$e !et

$%ere, (or con#enience, $e %a#e assumed t%at t%e an!le o( t%eunmodulated carrier $a#e is 9ero at t : 0" T%e (reuencymodulated

si!nal in t%e time domain is !i#en &y


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6reuency )odulation

T%e 6) si!nal st

is a nonlinear (unction o( t%e modulatin! si!nal mt,

$%ic% maes (reuency modulation a nonlinear modulation 'rocess"

Consider t%en a sinusoidal modulatin! si!nal de(ined &y

T%e instantaneous (reuency o( t%e resultin! 6) si!nal euals

$%ere

T%e uantity is called t%e (reuency de#iation, re'resentin! t%e

ma+imum de'arture o( t%e instantaneous (reuency o( t%e 6) si!nal

(rom t%e carrier (reuency A (undamental c%aracteristic o( an 6) si!nal is t%at t%e (reuency

de#iation is 'ro'ortional to t%e am'litude o( t%e modulatin! si!nal

and is inde'endent o( t%e modulation (reuency"


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6reuency )odulation2

T%e an!le o( t%e 6) si!nal is o&tained as

T%e ratio o( t%e (reuency de#iation to t%e modulation (reuency

is commonly called t%e modulation inde+ o( t%e 6) si!nal" /e

denote it &y and so $rite and

T%e 6) si!nal itsel( is !i#en &y

De'endin! on t%e #alue o( t%e modulation inde+ , $e may distin!uis%t$o cases o( (reuency modulation4

;arro$&and 6), (or $%ic% is small com'ared to one radian"

/ide&and 6), (or $%ic% is lar!e com'ared to one radian"


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6) -and$idt% and Carsonmt>

)a+imum de#iation o( (i(rom (c4 (i:(c?(mt

an a''ro+imate rule (or t%e transmission &and$idt% o( an 6) si!nal

!enerated &y a sin!letone modulatin! si!nal o( (reuency (m, as

(ollo$s4

T%e ralation is no$ as Carson


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E+am'le 1

In ;ort% America, t%e ma+imum #alue o( (reuency de#iation is

(i+ed at 7B*9 (or commercial 6) &roadcastin! &y radio" I($e taet%e modulation (reuency / : 1B *9,$%ic% is ty'ically t%ema+imum audio (reuency o( interest in 6) transmission, $e (ind

t%at t%e corres'ondin! #alue o( t%e de#iation ratio is

usin! carlson rule &y re'lacin! &y D, and re'lacin! (m &y /, t%ea''ro+imate #alue o( t%e transmission &and$idt% o( t%e 6) $a#e is


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E+am'le 2Determine t%e 'ercent modulation o( an 6) si!nal $%ic% is

&ein! &roadcast in t%e 10 )*9 &and %a#in! a carriers$in! o( 12B*9"

Solution4


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;arro$&and 6) E+'andin! t%e relation 6) si!nal resultin! (rom t%e use o( a sinusoidal

modulatin! si!nal, $e !et

Assumin! t%at t%e modulation inde+ is small com'ared to one

radian, $e may use t%e (ollo$in! a''ro+imations4

and

%ence

A&o#e euation de(ines t%e a''ro+imate (orm o( a narro$&and 6)

si!nal 'roduced &y a sinusoidal modulatin! si!nal


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;arro$&and 6)2 T%e euation (or narro$&and 6) si!nal can &e e+'anded as

T%is e+'ression is some$%at similar to t%e corres'ondin!one de(inin! an A) si!nal, $%ic% is as (ollo$s4

$%ere is t%e modulation (actor o( t%e A) si!nal" /e see t%at in t%e case o( sinusoidal modulation, t%e &asic

di((erence &et$een an A) si!nal and a narro$&and 6)

si!nal is t%at t%e al!e&raic si!n o( t%e lo$er side (reuency int%e narro$&and 6) is re#ersed"

T%us, a narro$&and 6) si!nal reuires essentially t%e sametransmission &and$idt% i"e", 2(m as t%e A) si!nal"


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Feneration o( narro$&and 6) si!nal T%is modulator in#ol#es s'littin! t%e carrier $a#e into t$o 'at%s"

Gne 'at% is direct t%e ot%er 'at% contains a H0 de!ree '%ases%i(tin! net$or

and a 'roduct modulator, t%e com&ination o( $%ic% !enerates a DS-SCmodulated si!nal"

T%e di((erence &et$een t%ese t$o si!nals 'roduces a narro$&and 6) si!nal,

&ut $it% some distortion"


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Feneration o( $ide&and 6) si!nal

T%ere are t$o &asic met%ods o( !eneratin! (reuencymodulated

si!nals &y usin! Direct met%od and Indirect met%od

In t%e direct met%od t%e carrier (reuency is directly #aried in

accordance $it% t%e in'ut &ase&and si!nal, $%ic% is readily

accom'lis%ed usin! a #olta!econtrolled oscillator CG"

In t%e indirect met%od, t%e modulatin! si!nal is (irst used to 'roduce a

narro$&and 6) si!nal, and (reuency multi'lication is ne+t used to

increase t%e (reuency de#iation to t%e desired le#el"

T%e indirect met%od is t%e 're(erred c%oice (or (reuency modulation

$%en t%e sta&ility o( carrier (reuency is o( major concern as in

commercial radio &roadcastin!"


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Feneration o( $ide&and 6) si!nal &y

Indirect met%od

A(ter &and'ass (ilterin! o( t%e nonlinear de#ices out'ut #t, $e %a#e a ne$ 6)

si!nal de(ined &y

$%ose instantaneous (reuency is


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6) Detection

In t%eory just need di((erentiator and en#elo'e detection (or 6)")any tec%niues used in 'ractice mostly CG"

Di((erentiator and En#elo'e Detector

Kero Crossin! Detector

Uses rate o( 9ero crossin!s to estimate (i

5%ase .oc .oo' 5..

Uses olta!e Controlled Gscillator CG and (eed&ac to e+tractmt

++=t

fcfcc dmktftmkfAts0

])(22sin[)](22[)(


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6) Demodulation &y CG

5%ase

Detector

.oo' Am'li(ier and

.o$ 5ass 6ilter

CG

s(mt mt


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Noise in AnalogueModulation To undertae suc% a study $e (ollo$ t%e customary 'ractice &y

(ormulatin! t$o models4 C%annel model, $%ic% assumes a communication c%annel t%at is

distortionless &ut 'ertur&ed &y additi#e $%ite Faussian noise

A/F;"

=ecei#er model, $%ic% assumes a recei#er consistin! o( an ideal

&and'ass (ilter (ollo$ed &y an ideal demodulator a''ro'riate (or t%e

a''lication at %and t%e &and'ass (ilter is used to minimi9e t%e

e((ect o( c%annel noise"

6i!ure $%ic% s%o$s t%e noisy recei#er model t%at com&ines t%e

a&o#e t$o assum'tions"


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AM Signal Noise Analysis T%e c%annel si!naltonoise ratio (or A)

T%e out'ut S;= o( an A) recei#er usin! an en#elo'e detector is

T%e (i!ure o( merit (or A) is

Consider modulatin! $a#e

T%e corres'ondin! A) $a#e is

$%ere L:aAmis t%e modulation (actor" 6or a load resistor o( 1M,

$%en L:1 i"e" 100N modulation, $e !et t%e (i!ure o( merit eual to 1O3"


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FM Signal Noise Analysis C%annel si!naltonoise ratio

Gut'ut si!naltonoise ratio

6i!ure o( merit (or 6)

T%e modulated 6) si!nal is

6or a load resistor o( 1M,

T%e out'ut si!naltonoise ratio is $%ere :P(O/ is t%e modulation inde+, t%e (i!ure o( merit (or 6) is

6) o((ers t%e 'ossi&ility o( im'ro#ed noise

'er(ormance o#er A) $%en

t%at is,


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Thanks!

Technology changesbut communication lasts.

introduction to communication system-lecture3

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