03-Amplitude Modulation Transmission

11/5/20101

ELECTRONIC COMMUNICATIONSSYSTEMS

Chapter 3

Amplitude Modulation Transmission

11/5/20102

• BASEBAND COMMUNICATION: COMMUNICATION THATDOES NOT USE MODULATION (TRANSMIT INFORMATIONIN ITS ORIGINAL FORM) - NO SHIFT IN THERANGE OF FREQUENCIES OF THE SIGNAL.(NO FREQUENCY TRANSLATION)

• CARRIER COMMUNICATION: COMMUNICATION THATUSES MODULATION - SHIFTING OF THE RANGE OFFREQUENCIES IN THE SIGNAL.(FREQUENCY TRANSLATION)

• (AM, FM, PM, FSK, PSK, QAM, ……)

BASEBAND AND CARRIER COMMUNICATION

11/5/20103

• THE TERM BASEBAND IS USED TO DESIGNATE THEBAND OF FREQUENCIES OF THE SIGNAL DELIVEREDBY THE SOURCE

• TELEPHONY: BASEBAND IS THE AUDIO BAND (BAND OFVOICE SIGNALS) OCCUPYING 0 - 4000 Hz

• TELEVISION: BASEBAND IS THE VIDEO BAND (BAND OFVIDEO SIGNALS) OCCUPYING 0 - 6 MHz

• DIGITAL DATA/PCM (A-TO-D CONVERTION):USING BIPOLAR SIGNALING AT A RATE OF BITS/SEC,THE BASEBAND IS 0 - Hz

BASEBAND COMMUNICATION

0f0f

11/5/20104

• PULSE MODULATED SIGNALS SUCH AS:

• PAM (PULSE AMPLITUDE MODULATION)• PWM (PULSE WIDTH MODULATION)• PPM (PULSE POSITION MODULATION)• PCM (PULSE CODE MODULATION)

• DESPITE THE TERM MODULATION, THE ABOVE SIGNALSARE BASEBAND CODING SCHEMES AND THEY YIELDBASEBAND SIGNALS


11/5/20105

• BASEBAND SIGNALS HAVE SIZABLE POWER AT LOWFREQUENCIES

• BASEBAND SIGNALS CANNOT BE TRANSMITTEDOVER A RADIO LINK (FREE SPACE)

• BASEBAND SIGNALS ARE SUITABLE FOR TRANSMISSIONOVER COPPER (PAIR OF WIRES, COAXIAL CABLE) ORGLASS (FIBER). EXAMPLES:

• LOCAL TELEPHONE COMMUNICATION• SHORT-HAUL PCM COMMUNICATION (BETWEEN

LOCAL EXCHANGES)


11/5/20106

• MODULATION IS USED WHEN IT IS IMPRACTICAL TOPROPAGATE LOW-FREQUENCY BASEBAND SIGNALSOVER FREE SPACE

• MODULATION USES HIGH FREQUENCY CARRIERS TOACHIEVE SIMULTANEOUS TRANSMISSION WITH NOINTERFERENCE (MULTIPLEXING OF VARIOUSSIGNALS)

• MODULATION ALLOWS CONSTRUCTION OF SMALLANTENNAS (i.e. 1/4 WAVELENGTH)

MODULATION COMMUNICATION

11/5/20107

IN AMPLITUDE MODULATION, THE AMPLITUDE OF THEHIGH FREQUENCY CARRIER SIGNAL(UNMODULATED WAVE) IS MODULATED (VARIED)PROPORTIONAL TO THE INSTANTANEOUS AMPLITUDEOF THE MESSAGE BEARING SIGNAL (MODULATING WAVE) SUCH AS TO GENERATING AN ENVELOPE(MODULATED WAVE) WHICH CARRIES THEINFORMATION.

THE REPETITION RATE OF THE AM ENVELOPE EQUALSTHE FREQUENCY OF THE MODULATING SIGNAL.

AMPLITUDE MODULATIONAMPLITUDE MODULATION

11/5/20108

AM MODULATORS: NONLINEAR DEVICES (MIXER)WITH: TWO INPUTS, ONE OUTPUT


AM MODULATOR(NON LINEAR

DEVICE, MIXER,MULTIPLIER)

HIGH FREQUENCYCARRIER SIGNAL(UNMODULATED WAVE)

LOW FREQUENCYINFORMATION SIGNAL(MODULATING WAVE)

• SINGLE FREQUENCY WAVE (TONE)OR

• COMPLEX WAVE (MULTIPLE FREQENCIES) - VOICE (SPEECH): 0 Hz - 4000 Hz

AM MODULATED WAVE

AM BROADCAST RADIO(550 kHz - 1600 kHz)

11/5/20109

• AMPLITUDE MODULATION IS RELATIVELYINEXPENSIVE

• AMPLITUDE MODULATION PROVIDES A LOW QUALITYFORM OF MODULATION (POOR PERFORMANCE INNOISY ENVIRONMENTS)

• AMPLITUDE MODULATION IS USED FOR COMMERCIALBROADCASTING (AM RADIO)

• AMPLITUDE MODULATION IS USED FOR TWO-WAYMOBILE RADIO COMMUNICATIONS (CB RADIO)


11/5/201010

• THERE ARE SEVERAL TYPES OF AMPLITUDEMODULATION SCHEMES

• DSB-SC (DOUBLE SIDEBAND SUPPRESS CARRIER)• DSB-FC (DOUBLE SIDEBAND FULL CARRIER)• SSB-SC (SINGLE SIDEBAND SUPPRESS CARRIER)

(ALSO KNOWN AS: USBAM OR LSBAM)• SSB-FC (SINGLE SIDEBAND FULL CARRIER)• VSB (VESTIGIAL SIDEBAND)

DSB-FC IS THE MOST COMMONLY USED SCHEME.IT IS ALSO CALLED CONVENTIONAL AM OR SIMPLY AM

AMPLITUDE MODULATION TYPESAMPLITUDE MODULATION TYPES

11/5/201011


DSB-FC AM(AM)

11/5/201012

[ ] ttmEtV ccam ωcos)()( +=

AMPLITUDE MODULATION (DSBAMPLITUDE MODULATION (DSB--FC)FC)

AMAM

MODULATING THE AMPLITUDE OF THE CARRIER WITHTHE MODULATING SIGNAL

11/5/201013

( ) ( )( ) ( )

[ ]tfftffEtfEtV

givesWhichtftfEtfEtVgetWe

YXYXYXGiven

tftfEtVtftfEEtVSignalModulated

mcmcc

ccam

mccccam

cmcam

cmmcam

)(2cos)(2cos2

2cos)(

:2cos2cos2cos)(:

)cos(21)cos(

21))(cos(cos:

2cos2cos1)(2cos2cos)(:

++−+=

+=

++−=

+=+=

ππβπ

ππβπ

ππβππ

tfEtEFor ccc π2cos)( = tfEtE mmm π2cos)( =


AND

c

m

EE

=β

11/5/201014


tEtE mmm ωcos)( =

MULTIPLIERMODULATOR

tcωcos

∑

SUMMER

cE

[ ]tfftffEtfE mcmcc

cc )(2cos)(2cos2

2cos ++−+ ππβπ

• THE AMPLITUDE OF THECARRIER IS UNAFFECTED BYTHE AM PROCESS

11/5/201015

DOUBLEDOUBLE--SIDEBAND FULL CARRIER (DSBSIDEBAND FULL CARRIER (DSB--FC)FC))(ωMMESSAGE

)(ωϑDSB

MODULATED SIGNAL(DSB-FC AM)

BANDWITH:

mmf ωπ =2mω−

mm fB =

cω mc ωω +mc ωω −

USBLSB

mB0

0

mBmB

mBB 2=BW OF THE MODULATED SIGNAL IS:

CARRIER

11/5/201016

DOUBLEDOUBLE--SIDEBAND FULL CARRIER (DSBSIDEBAND FULL CARRIER (DSB--FC)FC)THE MODULATED CARRIER SPECTRUM CENTEREDAT fc IS COMPOSED OF AN UPPER SIDEBAND ABOVEfc, (USB), AND A LOWER SIDEBAND BELOW fc, (LSB).

USBLSB

2 fmMODULATED SIGNAL COMPRISES A COMPONENT AT fc, INTHIS CASE THE SCHEME IS CALLED DSB-FC MODULATION

[ ]tfftffEtfE mcmcc

cc )(2cos)(2cos2


11/5/201017

DOUBLEDOUBLE--SIDEBAND FULL CARRIER (DSBSIDEBAND FULL CARRIER (DSB--FC)FC)

[ ]tfftffEtfE mcmcc

cc )(2cos)(2cos2


β=mlet

11/5/201018

AMPLITUDE MODULATION (DSB-FC)

11/5/201019


UNMODULATED CARRIER:

MODULATING SIGNAL:

MODULATION INDEX:

PERCENT MODULATION:

tfEORtfEtV cccc c ππ 2cos2sin)( =

tfEORtfEtV mmmmm ππ 2cos2sin)( =

{c

m

EE

=β

%100xEEM

c

m=

RANGE OF M: 0% 100% WHERE:

M < 100%, UNDERMODULATIONM = 100%, 100% MODULATIONM > 100%, OVERMODULATION (i.e. DISTORTION)

• Modulation Coefficient• Modulation Factor• Modulation Index

11/5/201020

PERCENT MODULATION (M)

PERCENT MODULATION GIVES THE PERCENTAGE CHANGE IN THE AMPLITUDEOF THE OUTPUT WAVE WHEN THE CARRIER IS ACTED ON BY A MODULATINGSIGNAL.

%100xEEM

c

m=

11/5/201021


MODULATED CARRIER AMPLITUDE: { mmc EEEV ±+=

mcmc EEVEEV −=+= minmax ;

WE KNOW: cmc

m EEEE ββ =∴=

ccc

ccc

EEEVEEEV

)1()1(

min

max

ββββ

−=−=+=+=THUS:

WITH:

100% MODULATION:

50% MODULATION:

0% MODULATION

0;2;1 minmax === VEV cβcc EVEV 5.;5.1;5.0 minmax ===β

cc EVEV === minmax ;;0β

11/5/201022

AMPLITUDE MODULATION

11/5/201023

AMPLITUDE MODULATION (DSB_FC)

minmax

minmax

VVVV

EE

c

m

+−

==β

)(21

minmax VVE m −=

)(21

minmax VVE c +=

)(41

2minmax VVEEE m

lsfusf −===

EUSF = PEAK AMPLITUDE OF THE UPPER SIDE FREQUENCY

ELSF = PEAK AMPLITUDE OF THE LOWER SIDE FREQUENCY

mcmc EEVEEV −=+= minmax ;

ASSUMPTIONS:• MODULATING SIGNAL IS A TONE• MODULATING PROCESS IS SYMMETRICAL

(EQUAL + and – ENVELOPE EXCURCIONS)

11/5/201024


Modulating Signal

Unmodulated Carrier

50% Modulation

100% Modulation

11/5/201025

DSB-FC EXAMPLE 1FOR AN AM DSB-FC MODULATOR, WITH CARRIER FREQUENCYOF 100 kHz, AND A MAXIMUM MODULATING SIGNAL OF 5 kHz,DETERMINE:

(100 - 5) kHz TO 100 kHz = 95 kHz TO 100 kHz = LSB100 kHz TO (100 + 5) kHz = 100 kHz TO 105 kHz = USB

BANDWITH OF THE MODULATED SIGNAL

B = 2 fm = 2 x 5 kHz = 10 kHz

FREQUENCY LIMITS FOR THE UPPER AND LOWER SIDEBANDS

UPPER AND LOWER SIDE FREQUENCIES WHEN MODULATING SIGNALIS A 3 kHz TONE

(100 - 3) kHz = 97 kHz = LSF(100 + 3) kHz = 103 kHz = USF

11/5/201026

DSB-FC EXAMPLE 2FOR THE AM WAVEFORM BELOW:

DETERMINE:

11/5/201027

DSB-FC EXAMPLE 2PEAK AMPLITUDE OF THE UPPER AND LOWER SIDE FREQUENCIES

)(41

2minmax VVEEE m

lsfusf −===

VEE lsfusf 4)218(41

=−==

PEAK AMPLITUDE OF THE UNMODULATED CARRIER

VVVE c 10)218(21)(

21

minmax =+=+=

PEAK CHANGE IN THE AMPLITUDE OF THE ENVELOPE

VVVE m 8)218(21)(

21

minmax =−=−=

11/5/201028

DSB-FC EXAMPLE 2COEFFICIENT INDEX

8.0108

minmax

minmax==

+−

==VVVV

EE

c

mβ

PERCENT MODULATION

%80%1008.0%100 === xxEEM

c

m

%80%100218218%100

minmax

minmax=

+−

=+−

= xxVVVVM

11/5/201029

DSB-FC EXAMPLE 3ONE INPUT TO A CONVENTIONAL MODULATOR IS A 500 kHzCARRIER WITH AN AMPLITUDE OF 20 Vp. THE SECOND INPUTIS A 10 kHz MODULATING SIGNAL THAT IS OF SUFFICIENT AMPLITUDE TO CAUSE A CHANGE IN THE OUTPUT WAVEOF . DETERMINE:

UPPER AND LOWER SIDE FREQUENCIES

MODULATION COEFFICIENT AND PERCENT MODULATION

(500 + 10) kHz = 510 kHz = USF(500 - 10) kHz = 490 kHz = LSF

Vp5.7±

375.020

5.7==β

%5.37%10020

5.7== xM

11/5/201030

DSB-FC EXAMPLE 3PEAK AMPLITUDE OF THE MODULATED CARRIER

UPPER AND LOWER SIDE FREQUENCY VOLTAGES

Ec (MODULATED) = Ec (UNMODULATED) = 20 Vp

VpEEEE cmlsfusf 75.3

2)20(375.0

22=====

β

MAXIMUM AND MINIMUM AMPLITUDES OF THE ENVELOPE

mcmc EEVEEV −=+= minmax ;VpV 5.275.720max =+=VpV 5.125.720min =−=

11/5/201031

DSB-FC POWER DISTRIBUTION

22cm

lsfusfEEEE β

===

THE POWER DISSIPATION OF AN UNMODULATED CARRIERIN LOAD RESISTANCE R:

RE

REP cc

c2

)707.0( 22

==

FROM:

cc

lsbusb PREPP

48

22 2 ββ===

THE TOTAL POWER IN AN AM DSB-FC ENVELOPE IS:

lsbusbct PPPP ++=

11/5/201032

DSB-FC POWER DISTRIBUTIONFOR A DSB-FC MODULATED WAVE, THE TOTAL POWER INAN AM DSB-FC ENVELOPE IS:

lsbusbct PPPP ++=

244

222c

ccc

ctPPPPPP βββ

+=++=

)2

1(2β

+= ct PP

MODULATED WAVE CARRIER POWER = UNMODULATED WAVE CARRIER POWER(POWER OF THE CARRIER IS UNAFFECTED BY THE MODULATION PROCESS)

11/5/201033


)2

1(2β

+= ct PP

THE TOTAL POWER IN AN AM DSB-FC ENVELOPE INCREASES WITHMODULATION

tP↑↑ β

cc

lsbusb PREPP

48

22 2 ββ===

11/5/201034

DSB-FC POWER DISTRIBUTION)

21(

2β+= ct PP clsbusb PPP

4

2β==

β=mlet

11/5/201035


)2

1(2β

+= ct PP clsbusb PPP4

2β==

WITH 100% MODULATION, :

clsbusb PPP41

== clsbusb PPP21

=+

cct PPP 5.1)211( =+=

DSB-FC DISADVANTAGE: THE INFORMATION IS CONTAINED INTHE SIDEBANDS ALTHOUGH MOST OF THE POWER IS WASTEDIN THE CARRIER (DSB-SC ELIMINATES THIS DISADVANTAGE)

1=β

11/5/201036


THE ADVANTAGE OF ENVELOPE DETECTION IN AMHAS ITS PRICE.

IN AM, THE CARRIER COMPONENT DOES NOT CARRYANY INFORMATION,HENCE, THE CARRIER POWERIS WASTED.

11/5/201037

DSB-FC EXAMPLEFOR AN AM DSB-FC WAVE WITH A PEAK UNMODULATEDCARRIER VOLTAGE Vc = 10 Vp, A LOAD RESISTANCE OFRL = 10 Ohms, AND A MODULATION INDEX OF 1, DETERMINE:

CARRIER POWER

UPPER AND LOWER SIDEBAND POWER

WR

EP cc 5

)10(210

2

22

===

WPPP clsbusb 25.14

)5(14

2

====β

TOTAL SIDEBAND POWER

WPPP clsbusb 5.22

)5(12

2

===+β

11/5/201038

DSB-FC EXAMPLEFOR AN AM DSB-FC WAVE WITH A PEAK UNMODULATEDCARRIER VOLTAGE Vc = 10 Vp, A LOAD RESIATANCE OFRL = 10 Ohms, AND A MODULATION INDEX OF 1, DETERMINE:

TOTAL POWER IN THE MODULATED WAVE

WPP ct 5.7)2

11(5)2

1(22

=+=+=β

POWER SPECTRUM:

11/5/201039

MODULATION BY A COMPLEX SIGNALMODULATION BY A COMPLEX SIGNAL

IN ALL THE ANALYSIS PRESENTED SO FAR FOR AM, WE ASSUMED A SINGLE_FREQUENCY MODULATINGSIGNAL (TONE).

IN PRACTICE, THE MODULATING SIGNAL IS OFTENA COMPLEX WAVEFORM (IT CONSISTS OF MANYFREQUENCY COMPONENTS WITH ASSOCIATED AMPLITUDES)

11/5/201040

IF A MODULATING SIGNAL CONTAINS TWOFREQUENCIES, THEN, THE MODULATED WAVE WILL CONTAIN THE CARRIER AND 2 SETS OF SIDE FREQUENCIES:

[ ]

[ ]tfftffEtfE

tfftffEtfE

mcmcc

cc

mcmcc

cc

)(2cos)(2cos2

2cos

)(2cos)(2cos2

2cos

222

111

++−+

+

++−+

ππβπ

ππβπ


11/5/201041

WE LEAVE IT TO THE IMAGINATION OF THEREADER TO TAKE THIS FURTHER WHEN MORE THAN TWO FREQUENCIES ARE PRESENT. WHEN SEVERAL FREQUENCIES ARE USED TO MODULATETHE CARRIER, THE TOTAL MODULATION INDEX ISGIVEN AS FOLLOWS:

2222121 nt βββββ ++++= L


11/5/201042

DSB-FC POWER DISTRIBUTIONTHE POWER DISSIPATION OF AN UNMODULATED CARRIERBECOMES:

ctct

lsbtusbt PREPP

48

22 2 ββ===

THE TOTAL SIDEBAND POWER IS:

22cm

lsfusfEEEE β

===

RE

REP cc

c2

)707.0( 22

==REMEMBERING:

THEN:

ct

sbt PP2

2β=

11/5/201043

DSB-FC POWER DISTRIBUTIONTHE TOTAL POWER IS:

sbtct PPP +=

)2

1(2

tct PP β

+=

CARE MUST BE TAKEN TO INSURE THAT THE COMBINEDVOLTAGES OF ALL THE MODULATING SIGNALS DO NOTOVERMODULATE THE CARRIER !!

11/5/201044

DSB-FC EXAMPLEFOR AN AM DSB-FC TRANSMITTER WITH AN UNMODULATEDCARRIER POWER Pc = 100 W, THAT IS MODULATEDSIMULTANEOUSLY BY 3 MODULATING SIGNALS WITH

DETERMINE:

TOTAL COEFFICENT OF MODULATION:

TOTAL SIDEBAND POWER:

WPP ct

sbt 445.222

)100(67.02

2

===β

5.0,4.0,2.0 321 === βββ

67.05.04.02.0 222 =++=tβ

TOTAL TRANSMITTED POWER:

WP t 445.122)267.01(100

2

=+=

11/5/201045

GENERATION OF AM SIGNALSONE CAN GENERATE AN AM SIGNAL (DSB-FC) USINGANY DSB-SC GENERATOR IF THE MODULATING SIGNAL IS:

[ ] )()( tmofinsteadtmE c +

)(tmEc +

ttC cωcos)( =

)()( tCtm MULTIPLIERMODULATOR

11/5/201046

GENERATION OF AM SIGNALSHOWEVER, AM CAN BE GENERATED IN SIMPLERWAYS …………

BAND-PASS

FILTERRm(t)

+

+tcωcos

E1

I1

)(tVo+

AM MODULATOR: USE ONLY THE UPPER BRANCH OF THEDSB-SC BALANCED MODULATOR

cω±

11/5/201047

DSBDSB--SC NONLINEAR MODULATORSC NONLINEAR MODULATOR

)(cos1 tmtE c += ω 2111 EbEaI +=

[ ] [ ]21 )(cos)(cos tmtbtmtaI cc +++= ωω

SUPPRESSED USING BP FILTER TUNED TO cω±

[ ] [ ] =+++= 21 )(cos)(cos tmtRbtmtRaRI cc ωω

tbRtbRmtaRmttbRmtaR ccc ωωω 22 cos)()(cos)(2cos ++++

Vo(t)=AM SIGNAL

11/5/201048

GENERATION OF AM SIGNALSHOWEVER, AM CAN BE GENERATED IN SIMPLERWAYS ………

BAND-PASS

FILTERR

m(t)+

+tc cωcos

)(tVo+

AM MODULATOR: USE SWITCHING MODULATOR

DIODE ACTS AS ASWITCH

cω±

11/5/201049

GENERATION OF AM SIGNALS• THE DIODE ACTS A SWITCH THAT TURNS ON/OFF.

• THE INPUT SIGNAL IS:

)()(cos tmcwithtmtc c >>+ωSO THAT THE SWITCHING ACTION OF THE DIODE ISCONTROLLED BY:

tc cωcos• THE DIODE SHORTS & OPENS PERIODICALLY IN EFFECT

MULTIPLYING THE INPUT SIGNAL BY S(t)

11/5/201050

GENERATION OF AM SIGNALS• THE SIGNAL ACROSS R IS:

[ ] )()(cos tstmtcV cR += ω

⎥⎦⎤

⎢⎣⎡ ++++= LtttVVts ccc ωωω

π5sin

513sin

31sin2

2)(WITH:

GIVING:

termsotherttmtcV ccR ++= ωπ

ω cos)(2cos2

SUPPRESSED BY BP FILTER

Vo(t)=AM SIGNAL

11/5/201051

GENERATION OF AM SIGNALS• LOW-LEVEL MODULATION: IT TAKES PLACE

PRIOR TO THE OUTPUT ELEMENT OF THE FINAL STAGE(ANTENNA IS NEXT STAGE) OF THE TRANSMITTER(i.e. EMITTER IN A TRANSISTORIZED XMITTER)

• ADVANTAGE: LESS MODULATING SIGNAL POWERIS REQUIRED TO ACHIEVE HIGH PERCENTAGE OFMODULATION:

tm PE ↑↑↑ β• DISADVANTAGE: AMPLIFIER AFTER MODULATOR

STAGE MUST BE LINEAR

11/5/201052

GENERATION OF AM SIGNALS• HIGH-LEVEL MODULATION: IT TAKES PLACE

IN THE FINAL ELEMENT OF THE FINAL STAGEOF THE TRANSMITTER (i.e. COLLECTOR OUTPUT)( CARRIER SIGNAL IS AT ITS MAXIMUM AMPLITUDE)

• REQUIRES A MUCH HIGHER AMPLITUDE MODULATINGSIGNAL TO ACHIEVE A REASONABLE M

• THE FINAL MODULATING SIGNAL AMPLIFIER MUSTSUPPLY ALL THE SIDEBAND POWER – BUT CAN BE ANON-LINEAR AMPLIFIER (PROVIDES MODULATION)

100xEEM

c

m=

11/5/201053

LOW-LEVEL MODULATOR

CARRIER SIGNAL

MODULATING SIGNALVARIES THE GAIN OF THEAMPLIFIER AT A RATE EQUALTO THAT OF THE FREQUENCYOF THE MODULATING SIGNALCOLLECTOR VOLTAGE

AM DSBFC ENVELOPE

EMITTER MODULATOR

MODULATING SIGNAL

COUPLING CAPACITORREMOVES COMPONENT mf

DISADVANTAGES:• CLASS A AMPLIFIER

(NOT EFFICIENT)• LOW POWER OUTPUT

COLLECTOR: OUTPUT ELEMENT

11/5/201054

EMITTER MODULATOR

[ ]tAA cqV ωβ sin1+=

VOLTAGE GAIN IS GIVEN BY:

GAIN WITH MODULATION

GAIN WITHOUT MODULATION (QUIESCENT)

[ ]β±= 1qV AATHUS:

⎩⎨⎧

==

=02

1v

qv

AAA

FOR β

11/5/201055

EXAMPLEFOR THE AM EMITTER MODULATOR WITH MODULATIONINDEX OF 0.8, QUIESCIENT VOLTAGE GAIN OF 100, INPUTCARRIER FREQUENCY OF 500 kHz WITH AMPLITUDE OF 5 mVAND A 1000 Hz MODULATING SIGNAL, DETERMINE:

MAXIMUM & MINIMUM VOLTAGE GAINS:

180)8.01(100max =+=A20)8.01(100min =−=A

MAXIMUM & MINIMUM Vout AMPLITUDES:

VV out 9.0)005.0(180(max) ==

VV out 1.0)005.0(20(min) ==

11/5/201056

MEDIUM LEVEL MODULATORMEDIUM POWERAM MODULATOR

MODULATION AT Q OUTPUT ELEMENT(COLLECTOR MODULATOR)

MODULATING SIGNAL

CLASS C AMPLIFIER• HIGHER POWER EFFICIENCY

CARRIER SIGNAL

REQUIRES HIGHERAMPLITUDES

DISADVANTAGE:• M < 100%

11/5/201057

LINEAR IC MODULATOR

RCfc

1=

MODULATINGSIGNAL

MODULATEDSIGNAL

LOW POWEROUTPUT

FUNCTION GENERATOR

11/5/201058

LINEAR IC MODULATOR - EXAMPLE

kHzuFk

fc 100)001(.10

1==

11/5/201059


DSB-SC AM

11/5/201060

• MESSAGE SIGNAL =

• CARRIER SIGNAL =

• MODULATED SIGNAL =

AMPLITUDE MODULATION (DSBAMPLITUDE MODULATION (DSB--SC)SC)

)(cos)( ωω MtEtm mm ↔=

)(cos)( ωω CtEtC cc ↔=

ttEEtCtm cmcm ωω coscos)()( =

[ ]ttEEmcmc

cm )cos()cos(2

ωωωω −++

[ ])()(2

cos)( mcmccm

cEEttm ωωϑωωϑω −++↔

fπω 2= )cos(21)cos(

21))(cos(cos YXYXYX −++=

11/5/201061

AMPLITUDE MODULATION (DSBAMPLITUDE MODULATION (DSB--SC)SC)

ttm mωcos)( =

ttC cωcos)( =

)()( tCtm

[ ]ttEEmcmc

cm )cos()cos(2

ωωωω −++

MULTIPLIERMODULATOR

11/5/201062

DOUBLEDOUBLE--SIDEBAND SUPPRESS CARRIER (DSBSIDEBAND SUPPRESS CARRIER (DSB--SC)SC)

)(ωMMESSAGE

)(ωϑDSB

MODULATED SIGNAL(DSB-SC AM)

BANDWITH:

mmf ωπ =2mω−

mm fB =

cω mc ωω +mc ωω −cω mc ωω +mc ωω −

USBLSB

mB0

0

mBmB

mBB 2=BW OF THE MODULATED SIGNAL IS:

11/5/201063


THE MODULATED CARRIER SPECTRUM CENTEREDAT fc IS COMPOSED OF AN UPPER SIDEBAND ABOVEfc, (USB), AND A LOWER SIDEBAND BELOW fc, (LSB).

USBLSB

2 fm

[ ]ttEEmcmc

cm )cos()cos(2

ωωωω −++

MODULATED SIGNAL DOES NOT HAVE A COMPONENT AT fc, INTHIS CASE THE SCHEME IS CALLED DSB-SC MODULATION

11/5/201064

DSB-SC MODULATORS• MULTIPLIER MODULATORS

• ANALOG MULTIPLIERS (i.e. VARIABLE GAINAMPLIFIER USING OP-AMPS OR TRANSISTORS,WHEREBY THE GAIN PARAMETER IS CONTROLLEDBY ONE OF THE SIGNALS (i.e. S1(t) )

VARIABLE GAINK S1(t)

S1(t)

S2(t)

K S1(t) S2(t)

LINEAR TIME-VARYING MODULATOR

11/5/201065

DSB-SC MODULATORS• NONLINEAR MODULATORS

MODULATION CAN BE ACHIEVED BY USINGNONLINEAR DEVICES (SQUARE LAW DEVICE = DIODE,TRANSISTOR)

I

V

2bVaVI +≈

11/5/201066

DSB-SC NONLINEAR MODULATOR

BAND-PASS

FILTER

R

R

m(t)

m(t)

+

+

+tcωcos

E1

E2

I1

I2

V

cω±ttKm

tVocωcos)(

)( =

+

+

11/5/201067

DSBDSB--SC NONLINEAR MODULATORSC NONLINEAR MODULATOR

)(cos1 tmtE c += ω )(cos2 tmtE c −= ω

2111 EbEaI += 2

222 EbEaI +=

[ ] [ ]21 )(cos)(cos tmtbtmtaI cc +++= ωω

[ ] [ ]22 )(cos)(cos tmtbtmtaI cc −+−= ωω

RIRIV 21 −=

[ ])(cos)(22 tmattmbRV c += ω

[ ] ttKmttmbRV cco ωω cos)(cos)(22 ==

FILTER USING BP FILTERTUNED TO cω±

11/5/201068


MODULATED SIGNAL(DSB-SC AM)

cω mc ωω +mc ωω −cω mc ωω +mc ωω − 0

BP FILTER

11/5/201069

DSB-SC MODULATORS• SWITCHING MODULATOR

A MODULATED SIGNAL CAN BE REALIZED BYMULTIPLYING m(t) BY ANY PERIODIC SIGNAL OF THEFUNDAMENTAL FREQUENCY (i.e. SQUARE PULSETRAIN)

cω

VV

00 T/2T/2 TT timetime

S(t)S(t)

⎩⎨⎧

<<−<<+

=02/,02/0,

)(tTTtV

ts

SQUARE WAVE: 50% DUTY CYCLESQUARE WAVE: 50% DUTY CYCLE

--T/2T/2

NEITHER FUNCTION

11/5/201070

FOURIER SERIES OF THE SQUARE WAVEFOURIER SERIES OF THE SQUARE WAVE

VV


S(t)S(t)

⎩⎨⎧

<<−<<+

=02/,02/0,

)(tTTtV

ts

SQUARE WAVE: 50% DUTY CYCLESQUARE WAVE: 50% DUTY CYCLE

∑∞

=

++=1

sincos)(n

cncno tnBtnAAts ωω

∫=T

cn dttntsT

B0

sin)(2 ω

--T/2T/2

∫=T

o dttsT

A0

)(1

∫=T

cn dttntsT

A0

cos)(2 ω

NEITHER FUNCTION

11/5/201071


VV


S(t)S(t) SQUARE WAVE: 50% DUTY CYCLESQUARE WAVE: 50% DUTY CYCLE

⎥⎦⎤

⎢⎣⎡= ∫ 2

0sin2 T

cn dttnVT

B ω

dtndutnuuduu oob

a

ba ωω ==−=∫ ;;cossin

--T/2T/2

22111 2/

02

0

VTVT

VtT

dtVT

A TTo ===⎥⎦

⎤⎢⎣⎡= ∫

⎥⎦⎤

⎢⎣⎡−= 2

0cos2 Tc

cn tn

TnVB ωω

11/5/201072


timetime

⎪⎩

⎪⎨⎧

=

++===

0;0

;22

t

nTtT

tntn cππω

[ ])0coscos( +−= ππ

nn

VBn

[ ]ππ

nn

VBn cos1−=

⎥⎦⎤

⎢⎣⎡−= 2

0cos2 Tc

cn tn

TnVB ωω

VV

00 T/2T/2 TT


--T/2T/2

⎩⎨⎧ −

=1;

1;cos

evennoddn

nπ

⎪⎩

⎪⎨⎧

0;

2;

evennnVoddnπ

11/5/201073


VV



⎥⎦⎤

⎢⎣⎡= ∫ 2

0cos2 T

cn dttnVT

A ω

dtndutnuuduu oob

a

ba ωω ===∫ ;;sincos

--T/2T/2

⎥⎦⎤

⎢⎣⎡= 2

0sin2 Tc

cn tn

TnVA ωω

11/5/201074


timetime

⎪⎩

⎪⎨⎧

=

++===

0;0

;22

t

nTtT

tntn cππω

[ ])0sin(sin −= ππ

nn

VAn

[ ] 0sin == ππ

nn

VAn

VV

00 T/2T/2 TT


--T/2T/2

⎥⎦⎤

⎢⎣⎡= 2

0sin2 Tc

cn tn

TnVA ωω

11/5/201075


timetime

VV

00 T/2T/2 TT


--T/2T/2

2VAo =

∑∞

=

++=1

sincos)(n

cncno tnBtnAAts ωω

0=nA

∑∞

=

+=oddn

c tnnVVts ωπ

sin22

)(

⎪⎩

⎪⎨⎧

=0;

2;

evennnVoddn

Bn π

11/5/201076

⎥⎦⎤

⎢⎣⎡ ++++= LtttVVts ccc ωωω

π5sin

513sin

31sin2

2)(


timetime

VV

00 T/2T/2 TT


--T/2T/2

∑∞

=

+=oddn

c tnnVVts ωπ

sin22

)(

11/5/201077

∑∞

=

+=oddn

c tntmnVtVmtstm ωπ

sin)(22

)()()(

)()( tstmTHE SPECTRUM OF THE PRODUCT :

)()(22

)()()( cmcnodd

mm nMnM

nVVMtstm ωωωωπ

ω−+++↔ ∑

∞

IS:

SWITCHING MODULATORS

MULTIPLICATION OF TWO WAVES

IF THIS SIGNAL IS PASSED THROUGH A BANDPASS FILTEROF BANDWITH 2B AND TUNED TO THEN WE GETTHE DESIRED MODULATED SIGNAL:

cω

)()( tstKmV o =

11/5/201078

SUPPRESS CARRIER SYSTEMCHARACTERISTICS

• SC SYSTEMS NEED SOPHISTICATED CIRCUITRYAT THE RECEIVER SO TO GENERATE A LOCAL CARRIEROF EXACTLY THE RIGHT FREQUENCY AND PHASE FOR SYNCHRONOUS DEMODULATION (NEED TOSUPPRESS THE CARRIER FREQUENCY AT THETRANSMITTER)

• SC SYSTEMS ARE VERY EFFICIENT FROM THE POINTOF VIEW OF POWER REQUIREMENTS AT THETRANSMITTER (COMPARED TO DSB-FC/SSB-FC)

11/5/201079

SUPPRESS CARRIER SYSTEMCHARACTERISTICS

• SC SYSTEMS ARE JUSTIFIED IN POINT-TO-POINT COMMUNICATIONS (ONE RECEIVER FOR EACH TRANSMITTER)

• FOR BROADCAST SYSTEMS WITH A MULTITUDE OFRECEIVERS FOR EACH TRANSMITTER, IT IS MOREECONOMICAL TO HAVE SIMPLER, LESS EXPENSIVERECEIVERS (INEXPENSIVE DEMODULATOR), THUS

FULL CARRIER SYSTEMS (i.e. DSB-FC)

03-Amplitude Modulation Transmission

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