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© 2010 The McGraw-Hill Companies
Communication Systems, 5e
Chapter 4: Linear CW Modulation
A. Bruce CarlsonPaul B. Crilly
(W.J. Song and J. H. Cho)
Why modulation?
1. Antenna size2. Fractional Bandwidth < 10%3. Wideband noise reduction4. Freq. Assignment5. Multiplexing
© 2010 The McGraw-Hill Companies
© 2010 The McGraw-Hill Companies
Chapter 4: Linear CW Modulation
Bandpass signals and systems Double-sideband amplitude modulation (DSB) Modulation and transmitters Single-sideband (SSB) amplitude modulation Frequency conversion and demodulation
cf. Nonlinear modulation in Ch. 5
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Bandpass signals and systems
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Bandpass signal (a) Spectrum; Waveform
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Bandpass signals
( ) Definition: ( )
0 c c
bpc c
X f f W f f WV f
f W f f W
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(a)Rotating phasor; (b) Phasor diagram with rotation suppressed
Figure 4.1-3
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Quadrature-carrier representation:
( ) ( )cos2 ( )sin 2
where: ( ) ( )cos ( ) in-phase component ( ) ( )sin ( ) quadrature component
bp i c q c
i
q
v t v t f t v t f t
v t A t tv t A t t
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2 2 1
( ) ( )cos 2 ( )
where( )
( ) ( ) ( ) and ( ) tan( )
bp c
qi q
i
v t A t f t t
v tA t v t v t t
v t
Envelope-phase representation
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Modulation to create a BP signal
Modulation is the translation of a band limited LP signal toa band pass signal with some center frequency cf
message spectrum
bandpass spectrum
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Analog message conventions
0
2 2
0
2
Message signal: ( )
Amplitude: ( ) 1
1Power: ( ) ( ) 1
Thus with a single tone message ( ) cos21
1 2 2
Message bandwidth =
x
T
m m
mm x
m
x t
x t
S x t x t dtT
x t A f tA
A S
W f W
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Bandwidth
Message bandwidth: Transmission bandwidth:
W
TB
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Fractional bandwidth
(a) Relevant to band pass signals
(b) fractional bandwidth defined as T
c
B
f
(c) For practical systems we require 0.01 0.1T
c
B
f
(d) Upper limit 10 prevents spillover into negative frequencies
(e) Lower limit 100 economics
c T
c T
f B
f B
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© 2010 The McGraw-Hill Companies
© 2010 The McGraw-Hill Companies
How is bandwidth defined?
Absolute bandwidth: 100% of energy is within some frequency range
3 dB, or half power bandwidth: frequency range where magnitude reduction is less than -3 dB
Noise equivalent bandwidth (see chapter 9) Occupied bandwidth: FCC definition where frequency range that
contains 99% of energy Relative power bandwidth: frequency range where magnitude
rolloff is less than a given level of dB (e.g. -40 dB)
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Types of linear CW modulation
Conventional/Standard Amplitude Modulation (AM)
Suppressed carrier double sideband (SC-DSB, DSB-SC,or DSB)
Single sideband (USSB and LSSB) Vestigial sideband (VSB)
Vestigial 퇴화한 , 흔적으로 남아 있는
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AM, DSB, SSB, and VSB are subclasses of amplitude modulation because the
message alters the carrier’s amplitude.
However, ‘AM’ quite often means conventional/standard AM = DSB-WC.
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4.2 Double-sideband amplitude modulation
Conventional AM Suppressed carrier DSB, (SCDSB) or simply DSB
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Conventional AM, or simply AM
( ) [1 ( )]cos2
where
carrier amplitude ( ) message, and ( ) 1 modulation index, 1 and =1 100% modulation carrier frequency, Hz
c c c
c
c
x t A x t f t
Ax t x t
f
1 1( ) ( ) ( ) ( )
2 2c c c c c cx t X f A f f A X f f
Overmodulation: phase reversal & envelop distortion
bandwidth for
(Baseband cut-off Freq.)
wf
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AM waveforms (a) Message; (b) AM wave with < 1; (c) AM wave with > 1 (overmodulation)
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Spectrum of AM signals
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AM Spectrum
Note:(a) carrier impulse at this impulse carries no informationcf
(b) redundant sidebands: the lower and upper sidebands carry the same information increased bandwidth
2TB W
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AM Power
2
2 2
Output power: carrier power + sideband power
2where
1
21
2
Peak envelope power:
T c sb
c c
sb c x
peak envel
S P P
P A
P A S
P
22 2max max
1 ( )ope cA A u x t
4
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AM Systems Relatively simple transmitter and receiver hardware The first voice modulation system More than half power goes into carrier, but carrier
carries no information inefficient Not suited for messages with low frequency content
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Suppressed Carrier DSB (DSB-SC) Signals
2
22 2max max
1( ) ( )cos2 ( )
2
Output power:
1 2
2
Peak envelope power
( )
c c c c c c
T sb c x
peak envelope c
x t A x t f t X f A X f f
S P A S
P A A x t
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DSB waveforms
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DSB systems
Suppressed carrier: typically -40→ -60 dB All power goes into sidebands more efficient than
AM Demodulation is more complicated than AM; requires
synchronization Transmitter hardware is more complex than AM. Well suited to transmission of messages with low
frequency or DC content
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4.3 Modulation and transmitters
AM (DSB-WC)
DSB (DSB-SC)
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AM transmitters
Implemented using a nonlinear element or some nonlinear portion of a circuit.
Often done where the message is superimposed on one of the active device’s terminals (i.e. the base/gate or collector/drain)
Because of nonlinear elements, may require a tank circuit to remove other of band components
Multiplication ?
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2
21 ininout vavav outv
inv
)(tx
inv outv)(tv
twccos
filter
Nonlinear Device
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tattxaa
atxatxaa
tattxaa
atxatxa
tattxatxatatxav
cc
cc
cccout
2cos21
cos)](21[)()(21
]2cos1[21
cos)](21[)()(
coscos)(2)(cos)(
21
21
2212
21
21
221
222
2211
ttxv cin cos)(
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)(2
12 fa
)(1 fXa )()(2 fXfXa
)(2
11 cffa
)(2 cffXa
wfc cf wfc
)2(2
12 cffa
cf2 f
)( fH
f
w2
?
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AM modulator example
(a) the concept, (b) practical circuit.
Note in (b) how the message and carrier source are superimposedonto the gate circuitry.
tank circuit
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DSB transmitters
Due to technological limitations, practical DSB systems are rarely implemented via ordinary multiplers.
Balanced modulators Ring modulators Other nonlinear devices
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Balanced modulator concept for DSB generation*
*Only for purposes of illustrating the balanced modulator concept. Practical DSB modulators are implemented using nonlinear devices such as diode arrays
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Ring modulator for DSB generation
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© 2010 The McGraw-Hill Companies
4.4 Single-sideband (SSB) modulation
If we have a DSB signal with symmetrical sidebands, we can suppress one of the sidebands without loss of information.
Therefore, we reduce transmission bandwidth from
Double the number of users on a channel
2DSB SSBT TB W B W
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Types of SSB
Lower sideband: LSSB or LSB
Upper sideband: USSB or USB
The decision to choose one over the other is dictated
by: Convention or prior assignment
Technological considerations
Neither USSB or LSSB is inherently better than the
other
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SSB signals
1ˆ( ) ( )cos ( )sin
2
ˆwhere ( ) is the Hilbert transform of the message
The in-phase and quadrature components are:1
ˆ ( ) ( ) and ( ) ( )2
1and the envelope is ( )
2
c c c c
ci c cq c
x t A x t t x t t
x t
x t A x t x t A x t
A t A
2 2ˆ( ) ( )c x t x t
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SSB spectra
(a) Generation of SSB from DSB using filter method, (b) USSB, (c) LSSB
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SSB generation
Filter method: use a high-Q filter to suppress one of
the sidebands.
Phase methods: shift sidebands using a phase shift
method to cancel one of them out
Phase shift
Weavers, weaver modulator
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Weaver’s SSB modulator
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VSB
SSB method but with a trace of the other sideband left
Practical SSB systems with imperfect filters are VSB
VSB allows for messages with low frequency or DC
content
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4.5 Frequency conversion and demodulation
Modulation: translate message to some carrier frequency
Frequency translation: move a signal from one carrier frequency to another
Demodulation: move modulated signal back to baseband Synchronous or product detectors: phase recovery Envelope detectors : no phase recovery
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Basic hetrodyne frequency converter
Frequency converson via hetrodyning takes advantage of the property of the product of 2 cosine functions sum and difference
1 1 cos cos cos( ) cos( )
2 2
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© 2010 The McGraw-Hill Companies
Frequency conversion via hetrodyning (multiplication)
1 2 1 2 1 2
1 2 1 2
1 1( )cos2 cos2 ( )cos2 ( ) ( )cos2 ( )
2 21 1
( ) ( )2 2 sum and the difference of 2 the frequencies
x t f t f t x t f f t t x t f f t t
X f f X f f
We use a filter to select a particular component
cf. homodyne receiver, super heterodyne receiver
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Frequency translation example
Q. Convert 7 MHz USSB signal into a 50 MHz LSSB signal via hetrodyning.
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Synchronous detection example
~ cos2 ( )LO cf f t
LPF( )cx t ( )x t
cf
( )cX f
( )X f
f
f
Demodulation bytranslation to baseband
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~ cos2 ( )cf f t
LPF( )cx t ( )x t
cf
( )cX f
( )X ff
f
Synchronous detection when there is an error in the local oscillator (LO)
f
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© 2010 The McGraw-Hill Companies
© 2010 The McGraw-Hill Companies
© 2010 The McGraw-Hill Companies
Detector output single tone at , and message is translated to a center frequency of distorted messageand obnoxious background tone
f ff
Mandatory that the local oscillator and its phasematch the carrier frequency
Synchronization error continued
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Envelope detection
Suitable for AM signals or signals with a carrier
Does not require synchronization
Simple hardware: diode, resistor, capacitor
Will work with suppressed carrier modulation systems
if the receiver inserts a carrier
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Envelope detection (a) Circuit; (b) Waveforms
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© 2010 The McGraw-Hill Companies
)(tm
.1)(
and1)(
Thus
.)(then,)(If
)](1
)(1
)(2
1[
)]()()(2[)(
2
2
2
2
2
12
2
2
2
2
1222
A
tx
Atx
AtxAtx
txA
txA
txA
A
txtxtAxAtm
h
h
h
h
Envelope
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)(
)](1
1[
)](2
1[)( 2
1
txA
txA
A
txA
Atm
.efficientnot!)(thatnoteBut Atx
Therefore
© 2010 The McGraw-Hill Companies
© 2010 The McGraw-Hill Companies
© 2010 The McGraw-Hill Companies
ttxttx
ttxtxttx
tdfefXfHj
ttxttx
cqc
chc
cftj
chc
sin)(cos)(
sin)]()([cos)(
sin])()(2[
sin)(cos)(
2
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)}(cos{)(
]sin)(cos)}(1[{
]}sin)(cos)([{cos)(
tttm
ttxttxA
ttxttxtAtv
c
cqcc
cqccc
VSB+C
possible! is detecton Envelope
)](1[)(
Thus
.1)(,1)(Since
)](1[
])([1)](1[)(
where
22
21
2
2
txAtm
txtx
tx
txtxAtm
c
qc
용어정리 AM
Verbatimly, it can be any amplitude modulation scheme.
However, by convention, it means DSB-WC (with carrier), a subclass of amplitude modulation
Often called ‘standard AM’.
DSB It is an amplitude modulation. DSB-SC (suppressed carrier)
© 2010 The McGraw-Hill Companies