Communications P3 2

Fall 2001 ENZO PATERNOENZO PATERNO 1

ELECTRONIC

COMMUNICATIONS

SYSTEMS

PART 3-2


AMPLITUDE

MODULATION

TRANSMISSION


AMPLITUDE MODULATIONAMPLITUDE MODULATION

DSB-FC AM (AM)


ttmEtV ccam cos)()(

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

AMAM

MODULATING THE AMPLITUDE OF THE CARRIER WITHTHE MODULATING SIGNAL


tfftffE

tfEtV

givesWhich

tftfEtfEtVgetWe

YXYXYXGiven

tftfEtV

tftfEEtVSignalModulated

mcmcc

ccam

mccccam

cmcam

cmmcam

)(2cos)(2cos2

2cos)(

:

2cos2cos2cos)(:

)cos(2

1)cos(

2

1))(cos(cos:

2cos2cos1)(

2cos2cos)(:

tfEtEFor ccc 2cos)( tfEtE mmm 2cos)(


AND

c

m

E

E



tEtE mmm cos)(

MULTIPLIERMODULATOR

tccos

SUMMER

cE

tfftffE

tfE mcmcc

cc )(2cos)(2cos2

2cos

• THE AMPLITUDE OF THECARRIER IS UNAFFECTED BYTHE AM PROCESS


DOUBLE-SIDEBAND FULL CARRIER (DSB-FC)DOUBLE-SIDEBAND FULL CARRIER (DSB-FC)

)(MMESSAGE

)(DSB

MODULATED SIGNAL(DSB-SC AM)

BANDWITH:

mmf 2m

mm fB

c mc mc c mc mc

USBLSB

mB0

0

mBmB

mBB 2BW OF THE MODULATED SIGNAL IS:

CARRIER



THE MODULATED CARRIER SPECTRUM CENTERED

AT fc IS COMPOSED OF AN UPPER SIDEBAND ABOVE

fc, (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

tfftffE

tfE mcmcc

cc )(2cos)(2cos2

2cos



tfftffE

tfE mcmcc

cc )(2cos)(2cos2

2cos

mlet


AMPLITUDE MODULATION (DSB-FC)



UNMODULATED CARRIER:

MODULATING SIGNAL:

MODULATION INDEX:

PERCENT MODULATION:

tfEORtfEtV cccc c 2cos2sin)(

tfEORtfEtV mmmmm 2cos2sin)(

c

m

E

E

%100xE

EM

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


PERCENT MODULATION (M)

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

%100xE

EM

c

m



MODULATED CARRIER AMPLITUDE: mmc EEEV

mcmc EEVEEV minmax ;

WE KNOW: cmc

mEE

E

E

ccc

ccc

EEEV

EEEV

)1(

)1(

min

max

THUS:

WITH:

100% MODULATION:

50% MODULATION:

0% MODULATION

0;2;1 minmax VEVB c

cc EVEVB 5.;5.1;5.0 minmax cc EVEVB minmax ;;0


AMPLITUDE MODULATION


AMPLITUDE MODULATION (DSB_FC)

minmax

minmax

VV

VV

E

E

c

m

)(2

1minmax VVEm

)(2

1minmax VVEc

)(4

1

2minmax VV

EEE

mlsfusf

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)



Modulating Signal

Unmodulated Carrier

50% Modulation

100% Modulation


DSB-FC EXAMPLEFOR 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


DSB-FC EXAMPLEFOR THE AM WAVEFORM BELOW:

DETERMINE:


DSB-FC EXAMPLEPEAK AMPLITUDE OF THE UPPER AND LOWER SIDE FREQUENCIES

)(4

1

2minmax VV

EEE

mlsfusf

VEE lsfusf 4)218(4

1

PEAK AMPLITUDE OF THE UNMODULATED CARRIER

VVVEc 10)218(2

1)(

2

1minmax

PEAK CHANGE IN THE AMPLITUDE OF THE ENVELOPE

VVVEm 8)218(2

1)(

2

1minmax


DSB-FC EXAMPLECOEFFICIENT INDEX

8.010

8

minmax

minmax

VV

VV

E

E

c

m

PERCENT MODULATION

%80%1008.0%100 xxE

EM

c

m

%80%100218

218%100

minmax

minmax

xxVV

VVM


DSB-FC EXAMPLEONE 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

%5.37%10020

5.7 xM


DSB-FC EXAMPLE

PEAK AMPLITUDE OF THE MODULATED CARRIER

UPPER AND LOWER SIDE FREQUENCY VOLTAGES

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

VpEE

EEcm

lsfusf 75.32

)20(375.0

22

MAXIMUM AND MINIMUM AMPLITUDES OF THE ENVELOPE

mcmc EEVEEV minmax ;VpV 5.275.720max VpV 5.125.720min


DSB-FC POWER DISTRIBUTION

22

cmlsfusf

EEEE

THE POWER DISSIPATION OF AN UNMODULATED CARRIER IN LOAD RESISTANCE R:

R

E

R

EP

ccc

2

)707.0( 22

FROM:

cc

lsbusb PR

EPP

48

22 2

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

lsbusbct PPPP


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

lsbusbct PPPP

244

222c

ccc

ctP

PPP

PP

)2

1(2

ct PP

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



)2

1(2

ct PP

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

tP

cc

lsbusb PR

EPP

48

22 2



)2

1(2

ct PP clsbusb PPP4

2

mlet



)2

1(2

ct PP clsbusb PPP4

2

WITH 100% MODULATION, :

clsbusb PPP4

1 clsbusb PPP

2

1

cct PPP 5.1)2

11(

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

1



THE ADVANTAGE OF ENVELOPE DETECTION IN AMHAS ITS PRICE.

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


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(2

10

2

22

WPPP clsbusb 25.14

)5(1

4

2

TOTAL SIDEBAND POWER

WPPP clsbusb 5.22

)5(1

2

2


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)

21(

22

POWER SPECTRUM:

Communications P3 2

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