111
Communications
Fall 2008
NCTU EE
Tzu-Hsien Sang
22
Outlines
• Linear Modulation
• Angle Modulation
• Interference
• Feedback Demodulators
• Analog Pulse Modulation
• Delta Modulation and PCM
• Multiplexing
2
3
Phase-Lock Loops (PLL) for FM Demodulation
• Tracks the instantaneous angle (phase and frequency) of the input signal.
(1) phase detector (comparator)
(2) loop filter
(3) loop amplifier
(4) VCO (voltage-controlled oscillator)
4
)).()(sin(2
)( :Example
sawtooth :Ideal
function. sticcharacteri theis function The
)).()(()( :Detector Phase
)()( :goalOur
)](sin[)( :ouput VCO The
)](cos[)( :input The
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te
g
ttgte
tt
ttAte
ttAtx
dVCd
d
matches
cVo
cCr
5
VCO
)(teV )](sin[)( ttAte cVo
.)()(
constant) VCO theis ( rad/s )()(
age.input volt the
on dependingfrequency with oscillatoran :VCO
t
VV
VVV
deKt
KteKdt
td
6
• Analysis of PLL: first, simplification, of course. Assume that the frequency matches, look at the phase difference.
(1) Non-linear Model:
7
).()())()(sin( ,)()( If
:ModelLinear )2(
tttttt
8
• Now we will present classical PLL analysis with classification on different loop filters.
<Case 1> Loop filter = 1
)).()(sin()(
))()(sin()()(
))()(sin(2
)(
modelNonlinear (i)
ttKdt
td
dKdeKt
ttKAA
te
t
t
tVV
dVCV
9
page)next (seeplot plane-Phase :tionrepresenta Graphical
PLL. theofbehavior theus tells(t) ofsolution The
.)(sin)(
)(sin)()()()(
then
),()()(Let
message)function step a with (FM
input.at jumpfrequency a Assume :Example
tKdt
td
tKdt
td
dt
td
dt
td
dt
td
ttt
t
t
10point. stablelocally a isA Point
positive becomes )(
increases )(
decreases (t)sin decreases )( 0)(
(2)
Apoint 0)(
negative becomes )(
decreases )(
increases (t)sin increases )( 0)(
(1)
)( :BPoint
dt
td
dt
td
tdt
tddt
tddt
td
dt
td
tdt
tddt
td
11
axis. 0)(
with theintersect not doesplot plane-phase
The .0)(
, If range.lock theis
. ifA Point toconverges system This :rangeLock (2)
exists).error (phase 0)( , As error).frequency (no
0)(
A,Point at case, In this :error stateSteady (1)
:Remarks
dt
td
Kdt
tdKK
K
ttdt
td
ttt
t
ss
12
13.
)()()(
1
)( 1
)(
)()(
jumpfrequency a :Example
).()( )(
)()(
))()(()( )()(()(
)()(()(
)()()]()(sin[
analysis) detailed more a (allows modelLinear (ii)
2
2
t
tf
t
t
ff
f
tKt
t
t
tt
t
t
Kss
KAKs
Ks
Ks
sAKs
sAKss
tAuKdt
td
tueKthKs
K
s
ssH
ssKssttKdt
td
dKt
tttt
t
14
better. theis, larger the:Note
.0)(
, As ).()(
.)1
()(:Frequency
).()( , As )).()(()(
).11
()1
()1(
)()()( :Phase
).()()(Let error?about How
2
t
tKf
t
f
t
f
t
ftK
t
f
tt
f
t
f
t
tf
Kdt
tdttueAK
dt
td
Ks
AK
Kss
sAKss
tuK
AKtttuetu
K
AKt
KssK
AK
Kss
AK
Ks
K
s
AK
sss
ttt
t
t
15
• First-order PLL summary
1.Limited lock range
2.Nonzero steady state error
3.The complete system loop gain is
4.Kt also controls the bandwidth of PLL
5.A large Kt is impractical since (a) hardware implementation issues and (b) noise increases due to the wide bandwidth.
To overcome some of the drawbacks, move to higher-order PLL.
VdCt KkAAK v2
1
t
t
Ks
KsH
)(
16
<Case 2> Perfect 2nd-order PLL
Use the linear model to analyze.
)].()()[()(
./)()(filter loop The
sssFKss
sassF
t
17
function.sfer order tran 2nd typicala of form in the is This
factor). (damping 2
1
frequency) (natural where
2)()(1
)(
)(
))(1)(()()()()()()(
output. tracking theandinput ebetween th difference out the figure Then,
.)(
)(
)(
)(
)()(
function. transfer loop-close thefind First,
22
2
2
2
2
a
Kς
aK
ss
s
aKsKs
s
sFKs
ssH
s
s
sHsssHssss
aKsKs
asK
sFKs
sFK
s
ssH
t
tn
nnttt
tt
t
t
t
18(rad). 2 iserror phase statesteady the:slipping-Cycle
.phenomenon slipping"-cycle" has PLL But the
unlimited! is rangelock The
:Remarks
error).frequency statesteady (no 0 as 0)(
.1for )1sin(1
)(
.22
)(
domain) (in .)(
domain) (in time ).()(
input frequency step of Analysis
2
2
22222
2
2
m
tt
tet
sssss
ss
ss
s
tudt
td
ntw
n
nnnn
n
19
20
• Applications of PLL
(1) Frequency multiplier: Generate the harmonics of the input and the VCO tracks one of the harmonics.
21
(2) Frequency divider: Generate the harmonics of the VCO output. One of the harmonics tracks the input.
22
(3) FM demodulator
Implementation of the phase detector:
Phase
detector Loop filter & amplifier
VCO
xr(t) ed(t)
eo(t)
eV(t) Demodulated
output
)()(
)( tmdt
tdteV
LPF xr(t)=ACcos[ct+(t)]
y(t) ed(t)
eo(t)=AVsin(ct+(t))
).()()]()(sin[ small, is )]()([When
)]()(sin[2
)(
)]()(sin[2
)]()(2sin[2
)()()(
tttttt
ttAA
te
ttAA
tttAA
tetxty
VCd
VCc
VCor
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