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Chapter 5 AM, FM, and Digital Modulated Systems Amplitude Modulation (AM) Double Sideband Suppressed carrier (DSSC) Assymetric Sideband Signals Single sideband signals (SSB) Frequency Division Multiplexing (FDM). Huseyin Bilgekul Eeng360 Communication Systems I - PowerPoint PPT Presentation
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Eeng 360 1
Chapter 5
AM, FM, and Digital Modulated Systems
Amplitude Modulation (AM) Double Sideband Suppressed carrier (DSSC) Assymetric Sideband Signals Single sideband signals (SSB) Frequency Division Multiplexing (FDM)
Huseyin BilgekulEeng360 Communication Systems I
Department of Electrical and Electronic Engineering Eastern Mediterranean University
Eeng 360 2
The modulated bandpass signal can be described by
cc ffGffGfV *
2
1)(
cgcgv ffPffPfP 4
1)(
Bandpass Signaling Review
The voltage spectrum of the bandpass signal is
The PSD of the bandpass signal is
; tgFfG g(t); envelopecomplex theof PSD -fPgWhere
})(Re{)( tj Cetgts FrequencyCarier - ;2 cffcc Where
Modulation Mapping function: Convert m(t) →g(t) Ref : Table 4-1
Eeng 360 3
Amplitude Modulation
)](1[)( tmAtg c
The Complex Envelope of an AM signal is given by
Ac indicates the power level of AM and m(t) is the Modulating Signal
Ac[1+m(t)] In-phase component x(t)
If m(t) has a peak positive values of +1 and a peak negative value of -1
AM signal 100% modulated
Representation of an AM signal is given by
( ) [1 ( )]cosc cs t A m t t
Envelope detection can be used if % modulation is less than 100%.
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An Example of a message signal m(t)
Waveform for Amplitude modulation of the message signal m(t)
Amplitude Modulation
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Amplitude Modulation
An Example of message energy spectral density.
Energy spectrum of the AM modulated message signal.
B
2BCarrier component together
with the message
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]0 [i.e., modulation of absence in the envelope AM of Level -
)](1[ of valueMinimum -
)](1[ of valueMaximum -
min
max
m(t)A
tmAA
tmAA
c
c
c
Definition: The percentage of positive modulation on an AM signal is
max% Positive Modulation 100 max ( ) 100c
c
A Am t
A
min 100 min ( ) 100c
c
A Am t
A
The percentage of negative modulation on an AM signal is
max minmax ( ) min ( )
% Modulation 100 1002 2c
m t m tA A
A
The percentage of overall modulation is
AM – Percentage Modulation
If m(t) has a peak positive values of +1 and a peak negative value of -1
AM signal 100% modulated
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AM Signal Waveform
Amax = 1.5Ac
Amin = 0.5 Ac
% Positive modulation= 50%% Negative modulation =50%Overall Modulation = 50%
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AM – Percentage Modulation
Under modulated (<100%) 100% modulated
Envelope Detector
Can be used
Envelope Detector
Gives Distorted signal
Over Modulated (>100%)
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tmAtmAA
tmtmA
tmAtgts
ccc
c
c
2222
22
2222
2
1
2
1
212
1
12
1
2
1
2
1
2
1 2222 tmAAts cc
AM – Normalized Average Power
The normalized average power of the AM signal is
If the modulation contains no dc level, then 0tm
The normalized power of the AM signal is
Discrete Carrier Power Sideband power
Eeng 360 10
AM – Modulation Efficiency
Translated Message Signal
Definition : The Modulation Efficiency is the percentage of the total power of the modulated signal that conveys information.
Only “Sideband Components” – Convey information
Modulation Efficiency:
2
2100
1
m tE
m t
Highest efficiency for a 100% AM signal : 50% - square wave modulation
Normalized Peak Envelope Power (PEP) of the AM signal:
22
max12
tmA
P cPEP
Voltage Spectrum of the AM signal:
ccccc ffMffffMff
AfS
2)(
Unmodulated Carrier Spectral Component
Eeng 360 11
Example 5-1. Power of an AM signal
Suppose that a 5000-W AM transmitter is connected to a 50 ohm load;
V 707000,5502
1 2
cc A
AThen the constant Ac is given by Without
Modulation
If the transmitter is then 100% modulated by a 1000-Hz test tone , the total (carrier + sideband) average power will be
WAc 500,750005.1502
15.1
2
modulation 100%for
2
12 tm
The peak voltage (100% modulation) is (2)(707) = 1414 V across the 50 ohm load.
The peak envelope power (PEP) is WAc 000,2050004502
14
2
The modulation efficiency would be 33% since < m2(t) >=1/2
Eeng 360 12
Double Side Band Suppressed Carrier Double Side Band Suppressed Carrier (DSBSC)(DSBSC)
Power in a AM signal is given byPower in a AM signal is given by 2
1
2
1 2222 tmAAts cc
Carrier Power Sideband power
DSBSC is obtained by eliminating carrier component If m(t) is assumed to have a zero DC level, then ttmAts cc cos)()(
Spectrum ccc ffMffM
AfS
2)(
Power 2
1 222 tmAts c
Disadvantages of DSBSC:• Less information about the carrier will be delivered to the receiver.• Needs a coherent carrier detector at receiver
%1001002
2
tm
tmEModulation Efficiency
Eeng 360 13
DSBSC Modulation
An Example of message energy spectral density.
Energy spectrum of the DSBSC modulated message signal.
No Extra Carrier component
ttmAts cc cos)()( B
2B
Eeng 360 14
Carrier Recovery for DSBSC DemodulationCarrier Recovery for DSBSC Demodulation Coherent reference for product detection of DSBSC can not be obtained by the use of ordinary PLL because there are no spectral line components at fc.
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Carrier Recovery for DSBSC DemodulationCarrier Recovery for DSBSC Demodulation A squaring loop can also be used to obtain coherent reference carrier for product detection of DSBSC. A frequency divider is needed to bring the double carrier frequency to fc.
Eeng 360 16
Single Sideband (SSB) ModulationSingle Sideband (SSB) Modulation
An upper single sideband (USSB) signal has a zero-valued spectrum for cff
A lower single sideband (LSSB) signal has a zero-valued spectrum for cff
SSB-AM – popular method ~ BW is same as that of the modulating signal.
Note: Normally SSB refers to SSB-AM type of signal
USSB LSSB
Eeng 360 17
Single Sideband SignalSingle Sideband Signal
Theorem : A SSB signal has Complex Envelope and bandpass form as:
tmjtmAtg c ˆ
ttmttmAts ccc sin )(ˆ cos Upper sign (-) USSB
Lower sign (+) LSSB
)(ˆ tm – Hilbert transform of m(t) thtmtm ˆ Where t
th1
thfH 0 ,
0 ,
f j
fjfH
and
Hilbert Transform corresponds to a -900 phase shift
H(f)
f-j
j
Eeng 360 18
Single Sideband SignalSingle Sideband Signal
0 ,0
0 ,2
f
ffMAfG c
cc
cc
c
ccc ffffM
ffA
ff
ffffMAfS
,
,0
,0
,
Proof: Fourier transform of the complex envelope
fjHfMAfG c 1Using thtmtm ˆ
Recall from Chapter 4 )]([*)(2
1)( cc ffGffGfV
If lower signs were used LSSB signal would have been obtained
Upper sign USSBLower sign LSSB
Upper sign USSB
ˆˆ ( )c cG f A M f j m t A M f jM f
Eeng 360 19
Single Sideband SignalSingle Sideband Signal
0 ,0
0 ,2
f
ffMAfG c
,
0,
0,
,
c cc
c
c
cc c
M f f f fS f A
f f
f fA
M f f f f
Eeng 360 20
SSB - Power
The normalized average power of the SSB signal
22222 ˆ2
1)(
2
1tmtmAtgts c
tmtm 22ˆ Hilbert transform does not change power.
SSB signal power is: tmAts c222
2222ˆ
2
1)(max
2
1tmtmAtg c
The normalized peak envelope (PEP) power is:
Power gain factor Power of the modulating signal
Eeng 360 21
Generation of SSB
22 ˆ tmtmAtgtR c
tm
tmtgt
ˆtan 1
SSB signals have both AM and PM.
tmjtmAtg c ˆThe complex envelope of SSB:
For the AM component,
For the PM component,
Advantages of SSB
• Superior detected signal-to-noise ratio compared to that of AM
• SSB has one-half the bandwidth of AM or DSB-SC signals
Eeng 360 22
Generation of SSBGeneration of SSB SSB Can be generated using two techniquesSSB Can be generated using two techniques
1.1. Phasing methodPhasing method
2.2. Filter MethodFilter Method
Phasing methodPhasing methodThis method is a special modulation type of IQ canonical formThis method is a special modulation type of IQ canonical form
of Generalized transmitters discussed in Chapter 4 ( Fig 4.28)of Generalized transmitters discussed in Chapter 4 ( Fig 4.28)
tmjtmAtg c ˆ
Eeng 360 23
Generation of SSBGeneration of SSB Filter MethodFilter Method
The filtering method is a special case in which RF processing (with aThe filtering method is a special case in which RF processing (with asideband filter) is used to form the equivalent sideband filter) is used to form the equivalent g(t)g(t), instead of using, instead of usingbaseband processing to generate baseband processing to generate g(m)g(m) directly. The filter method is the directly. The filter method is themost popular method because excellent sideband suppression can bemost popular method because excellent sideband suppression can beobtained when a crystal oscillator is used for the sideband filter. obtained when a crystal oscillator is used for the sideband filter. Crystal filters are relatively inexpensive when produced in quantity atCrystal filters are relatively inexpensive when produced in quantity at standard IF frequencies.standard IF frequencies.
Eeng 360 24
Weaver’s Weaver’s MMethod for ethod for GGenerating SSB.enerating SSB.
Eeng 360 25
Generation of Generation of VSBVSB
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Frequency Divison Multiplexing