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Chapter 5AM, 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
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The modulated bandpass signal can be described by
cc ffGffGfV *
21)(
cgcgv ffPffPfP 41)(
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
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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)AtmAAtmAA
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 A m tA
The percentage of negative modulation on an AM signal is
max min max ( ) min ( )% Modulation 100 100
2 2c
m t m tA AA
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
21
21
2121
121
21
21
21 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
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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
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Example 5-1. Power of an AM signalSuppose 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
15.12
modulation 100%for
212 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
142
The modulation efficiency would be 33% since < m2(t) >=1/2
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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 21
21 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 ffMffMAfS
2)(
Power 21 222 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
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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
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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.
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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
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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
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Single Sideband SignalSingle Sideband Signal
0 ,00 ,2
fffMA
fG c
cc
cc
c
ccc ffffM
ffA
ffffffM
AfS,
,0 ,0
,
Proof: Fourier transform of the complex envelope
fjHfMAfG c 1Using thtmtm ˆ
Recall from Chapter 4 )]([*)(21)( 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
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Single Sideband SignalSingle Sideband Signal
0 ,00 ,2
fffMA
fG c
,
0,
0,
,
c cc
c
cc
c c
M f f f fS f A
f f
f fA
M f f f f
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SSB - PowerThe normalized average power of the SSB signal
22222 ˆ21)(
21 tmtmAtgts c
tmtm 22ˆ Hilbert transform does not change power.
SSB signal power is: tmAts c222
2222 ˆ21)(max
21 tmtmAtg c
The normalized peak envelope (PEP) power is:
Power gain factor Power of the modulating signal
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Generation of SSB
22 ˆ tmtmAtgtR c
tmtmtgt
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
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Generation of SSBGeneration of SSB SSB Can be generated using two techniquesSSB Can be generated using two techniques
1.1. Phasing methodPhasing method2.2. 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
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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.
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Frequency Divison Multiplexing
