Post on 10-Apr-2015
Fall 2001 ENZO PATERNOENZO PATERNO 1
ELECTRONIC
COMMUNICATIONS
SYSTEMS
PART 3-2
Fall 2001 ENZO PATERNOENZO PATERNO 2
AMPLITUDE
MODULATION
TRANSMISSION
Fall 2001 ENZO PATERNOENZO PATERNO 3
AMPLITUDE MODULATIONAMPLITUDE MODULATION
DSB-FC AM (AM)
Fall 2001 ENZO PATERNOENZO PATERNO 4
ttmEtV ccam cos)()(
AMPLITUDE MODULATION (DSB-FC)AMPLITUDE MODULATION (DSB-FC)
AMAM
MODULATING THE AMPLITUDE OF THE CARRIER WITHTHE MODULATING SIGNAL
Fall 2001 ENZO PATERNOENZO PATERNO 5
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)(
AMPLITUDE MODULATION (DSB-FC)AMPLITUDE MODULATION (DSB-FC)
AND
c
m
E
E
Fall 2001 ENZO PATERNOENZO PATERNO 6
AMPLITUDE MODULATION (DSB-FC)AMPLITUDE MODULATION (DSB-FC)
tEtE mmm cos)(
MULTIPLIERMODULATOR
tccos
SUMMER
cE
tfftffE
tfE mcmcc
cc )(2cos)(2cos2
2cos
• THE AMPLITUDE OF THECARRIER IS UNAFFECTED BYTHE AM PROCESS
Fall 2001 ENZO PATERNOENZO PATERNO 7
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
Fall 2001 ENZO PATERNOENZO PATERNO 8
DOUBLE-SIDEBAND FULL CARRIER (DSB-FC)DOUBLE-SIDEBAND FULL CARRIER (DSB-FC)
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
Fall 2001 ENZO PATERNOENZO PATERNO 9
DOUBLE-SIDEBAND FULL CARRIER (DSB-FC)DOUBLE-SIDEBAND FULL CARRIER (DSB-FC)
tfftffE
tfE mcmcc
cc )(2cos)(2cos2
2cos
mlet
Fall 2001 ENZO PATERNOENZO PATERNO 10
AMPLITUDE MODULATION (DSB-FC)
Fall 2001 ENZO PATERNOENZO PATERNO 11
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
Fall 2001 ENZO PATERNOENZO PATERNO 12
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
Fall 2001 ENZO PATERNOENZO PATERNO 13
AMPLITUDE MODULATION (DSB-FC)
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
Fall 2001 ENZO PATERNOENZO PATERNO 14
AMPLITUDE MODULATION
Fall 2001 ENZO PATERNOENZO PATERNO 15
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)
Fall 2001 ENZO PATERNOENZO PATERNO 16
AMPLITUDE MODULATION (DSB-FC)
Modulating Signal
Unmodulated Carrier
50% Modulation
100% Modulation
Fall 2001 ENZO PATERNOENZO PATERNO 17
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
Fall 2001 ENZO PATERNOENZO PATERNO 18
DSB-FC EXAMPLEFOR THE AM WAVEFORM BELOW:
DETERMINE:
Fall 2001 ENZO PATERNOENZO PATERNO 19
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
Fall 2001 ENZO PATERNOENZO PATERNO 20
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
Fall 2001 ENZO PATERNOENZO PATERNO 21
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
Fall 2001 ENZO PATERNOENZO PATERNO 22
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
Fall 2001 ENZO PATERNOENZO PATERNO 23
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
Fall 2001 ENZO PATERNOENZO PATERNO 24
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)
Fall 2001 ENZO PATERNOENZO PATERNO 25
DSB-FC POWER DISTRIBUTION
)2
1(2
ct PP
THE TOTAL POWER IN AN AM DSB-FC ENVELOPE INCREASES WITHMODULATION
tP
cc
lsbusb PR
EPP
48
22 2
Fall 2001 ENZO PATERNOENZO PATERNO 26
DSB-FC POWER DISTRIBUTION
)2
1(2
ct PP clsbusb PPP4
2
mlet
Fall 2001 ENZO PATERNOENZO PATERNO 27
DSB-FC POWER DISTRIBUTION
)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
Fall 2001 ENZO PATERNOENZO PATERNO 28
DSB-FC POWER DISTRIBUTION
THE ADVANTAGE OF ENVELOPE DETECTION IN AMHAS ITS PRICE.
IN AM, THE CARRIER COMPONENT DOES NOT CARRYANY INFORMATION,HENCE, THE CARRIER POWERIS WASTED.
Fall 2001 ENZO PATERNOENZO PATERNO 29
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
Fall 2001 ENZO PATERNOENZO PATERNO 30
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: