principles of communications lecture 3: analog modulation...
TRANSCRIPT
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Principles of CommunicationsLecture 3: Analog Modulation Techniques (1)
Chih-Wei Liu 劉志尉National Chiao Tung [email protected]
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Outlines
Linear Modulation
Angle Modulation
Interference
Feedback Demodulators
Analog Pulse Modulation
Delta Modulation and PCM
Multiplexing
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Types of Modulation
Analog modulation and Digital modulationA process to translate the information data to a new spectral location depending on the intended frequency for transmission.
Modulation, historically, is done on the RF transmission system. Thus, the conversion from message signals to RF signals is called modulation.
Analog modulation: continuous-wave modulation and pulse modulation (sampled data)
Continuous-wave modulation: linear modulation (AM) and angle modulation (FM)
m(t) xc(t)
modulated carrier
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Linear Modulation
General form:
Ac(t): 1-to-1 correspondence to the message m(t)
cos(ωct): carrier (ωct is fixed)
DSB (Double-Sideband) Suppressed Carrier (SC)
ttAtx ccc ωcos)()( =
)(21)(
21)(X
cos)()(
C CCCC
cCc
ffMAffMAf
ttmAtx
−++=⇔
= ω
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DSB-SC
Upper sideband (USB)
Lower sideband (LSB)
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DSB-SC
Coherent (Synchronous) Demodulator (Detector): The receiver knows exactly the phase and frequency of the carrier in the received signal.
ttmAtmAtttmAttxtd
cCC
ccCcc
ωωωω
2cos)()( cos2]cos)([cos2)()(
+=⋅=⋅=
Message m(t) is recovered!
desired part High freq. noise
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What if the receiver reference is not coherent? -- A phase error occurs (θ(t), unknown, random, time-varying, …)
2cos(ωct+θ(t))
xc(t) d(t)
))(2cos()()(cos)( ))(cos(cos)(2)(
tttmAttmAttttmAtd
cCC
ccC
θωθθωω
++=+⋅=
1)(cos1 ),(cos)()( ≤≤−= tttmtyD θθIt is time-varying !!
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Carrier Recovery
Carrier recovery: Regenerate the carrier (fc and θ(t)) at the receiver site
Example: Square circuit
( )2 NarrowbandBPF at 2fc 2÷fxr(t)
cos2ωct cosωct
ttmAtmAttmAtx cCCcCr ωω cos2)(21)(
21cos)()( 22222222 +==
Carrier (2xf)!DC
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Carrier Recover (2)
How to extract the carrier? It becomes clearer when we examine it in the frequency domain.FT of xr2(t):
0 2fc-2fc
FT(m2(t))
Narrow BPF
f
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Remarks
The spectrum of DSB signal does not contain a discrete spectral component at the carrier frequency unless m(t) has a DC component.DSB systems with no carrier frequency component present are often referred to as suppressed carrier (SC) systems.If the carrier frequency is transmitted along with DSB signal, the demodulation process can be rather simplified. Alternatively, let’s see the following amplitude modulation (AM) scheme.
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Amplitude Modulation
A DC bias A is added to m(t) prior to the modulation process
The result is that a carrier component is present in the transmitted signal
DefinitionttamA
tAtmAtx
cnc
ccc
ωω
cos)](1[ cos)]([)(
+=
′+=
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Amplitude Modulation (AM): DSB with carrier
Normalized message 1+mn(t)>=0
AM
mn(t): the normalized message
A
tma t
)(min= a: the modulation index (had better be less than 1)
ttamAtx cnCc ωcos)](1[)( +=
,)(min
)()(tm
tmtmt
n =m(t): the original message
A: the DC bias
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Envelope Detection
The modulation index is defined such that if a=1, the minimum value of Ac[1+amn(t)] is zero
a 0 for all tIn AM, all the information is just the envelop.The envelop detection is a simple and straightforward technique
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Over-modulation: modulation index a > 1DC bias: the shifted level of the zero-value message
AM (2)
mn(t)m(t)
mmin
mn(t)+1/am(t)+A
-1
A
mmax
1/a
x 1/mmin→
↓ dc bias ↓ dc bias
x 1/mmin→
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-fc fc0 0
AM
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AM Demodulation
Coherent detection: precise but requires carrier recovery circuit.
Incoherent detection, envelope detection: simple receiver (LPF) but requires sufficient carrier power (a < 1) and fc >> W. (In theory, fc>W is sufficient, but a “good”LPF is needed.)
Impulse response of RC circuit:
1( ) ( )tRCh t e u t
RC−=
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Remarks
The time constant RC of the envelop detector is an important design parameter.The appropriate RC time constant is related to the carrier frequency fc and to the bandwidth W of the original signal m(t)
1/fc
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Power Efficiency of AM
Suppose that m(t) has zero mean, then the total power contained in the AM modulator output is
The power efficiency : the power ratio of the input information to the transmitted signal
])([21
])()(2[21
2cos)()]([21)()]([
21
cos)()]([)(
222
222
2222
2222
tmAA
tmtmAAA
tAtmAAtmA
tAtmAtx
C
C
cCC
cCc
+′=
++′=
′++′+=
′+=
ω
ω
%100)(1
)(%100
)(
)(Efficiency
22
22
22
2
×+
=×+
≡≡tma
tma
tmA
tmE
n
n
〈⋅〉 denotes the time average value
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Power Efficiency Example
If the signal has symmetrical value, i.e. |minm(t)|=|maxm(t)|,then |mn(t)|≤1 and hence 〈mn2(t)〉≤1.
If a≤1, the maximum efficiency is 50%, e.g. the square wave-type
For a sine wave, 〈mn2(t)〉=1/2, for a=1, the efficiency is 33.3%If we allow a>1,
Efficiency can exceed 50%, (a→∞, the efficiency=100%)
But, the envelope detector is precluded.
%)100()(1
)(%)100(
)(
)(22
22
22
2
tma
tma
tmA
tmEfficiencyE
n
n
+=
+≡≡
,)(min
)()(tm
tmtmt
n =
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Remarks
The main advantage of AM:A coherent reference is not necessary for demodulation as long as a≤1
The disadvantage of AM:The power efficiency The DC value of the message signal m(t) cannot be accurately recovered. (mixed with carrier)
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Single Sideband (SSB) Modulation
Why SSB? In DSB, either the USB and the LSB have equal amplitude and odd phase symmetry about the carrier frequency
Send only “half” signal (USB & LSB symmetric);Good power efficiency; Good bandwidth utilizationBasis of more advanced modulations
Methods to generate SSB signalsMethod 1: Sideband (BPF) filtering Easy to understand, but difficult to implement. Method 2: Phase-shift modulation
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Sideband Filtering
Sideband filtering
An ideal passband filter is necessaryThe (very) low frequency component will be encapulated
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SSB Modulation
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DSB signal: ( ) ( ) ( )2 2
1LPF: ( ) [sgn( ) sgn( )]2
( ) ( ) ( )1 [ ( )sgn( ) ( )sgn( )]41 [ ( )sgn( ) ( )sgn( )]4
C CDSB c c
L c c
c DSB L
C c c c c
C c c c c
A AX f M f f M f f
H f f f f f
X f X f H f
A M f f f f M f f f f
A M f f f f M f f f f
= + + −
= + − −
= ⋅
= + + + − +
− + − + − −
[ ( ) ( )] part-A4
[ ( )sgn( ) ( )sgn( )] part-B4
Cc c
Cc c c c
A M f f M f f
A M f f f f M f f f f
= − + +
+ + + − − −
SSB Signal Generation
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2 21
2 2
ˆ ˆ{part-B} [ ( ) ( ) ]4
1ˆ ˆ ( )[ ( )] ( )sin2 2 2
c c
c c
j f t j f tC
j f t j f tC Cc
A jm t e jm t e
A Am t j e e m t t
π π
π π ω
−−
−
ℑ = −
= − =
SSB Signal Generation (2)
1
Part-A (FT of) DSB signal: ( )cos2
ˆPart-B: Let ( ) { sgn( ) ( )}
Cc
A m t t
m t j f M f
ω
−
↔
≡ ℑ − ⋅
-jsgn(f)( )m t ˆ ( )m t
ˆThus, ( ) sgn( ) ( )M f j f M f= − ⋅2ˆ ˆ( ) ( ) cj f tcM f f m t eπ− ↔
Define Hilbert Transform:
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Phase-shift SSB Modulator
ˆLower-Side Band: ( ) ( )cos ( )sin2 2C C
c c cA Ax t m t t m t tω ω= +
ttmAttmAtx cCcCc ωω sin)(ˆ2cos)(
2)( +=
ttmAttmAtx cCcCc ωω sin)(ˆ2cos)(
2)( −=
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Phase-shift SSB Modulator (2)
ˆUpper-Side Band: ( ) ( )cos ( )sin2 2C C
c c cA Ax t m t t m t tω ω= −