amplitude modulation slides by (2003/04): eryk schiller, daniel starnowski modulation &...
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Amplitude Modulation
Slides by (2003/04): Eryk Schiller, Daniel Starnowski „Modulation & Detection” Zdzisław Papir
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Amplitude Modulation• DSB Double Sideband
Modulacja dwuwstęgowa
• AM Amplitude Modulation
Modulacja amplitudy
• SSB Single Sideband
Modulacja jednowstęgowa
• VSB Vestigal Sideband
Modulacja z częściowostłumiona wstęgą boczną
„Modulation & Detection” Zdzisław Papir
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DSB-SC Modulation
Carrier: A0cos0t
k – modulator constant
tAtkxt 00DSB cos
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DSB-SC Modulator
x
kx(t) ttxkAt 00DSB cos)()(
tA 00 cos„Modulation & Detection” Zdzisław Papir
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DSB-SC Modulation
x(t)
tAtkxt 00DSB cos
-x(t)
t
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DSB-SC Modulation
000DSB 2
1 XXkA
tAtkxt 00DSB cos
X()
DSB() g
0-g 0 0+g
g
WDSB = 2g
=2
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DSB-SC Detection
Two possible detection techniques:
• Envelope detection (Detekcja obwiedni)
• Coherent (synchronous) detection
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Envelope DSB-SC Detection
x(t) e(t) !
t
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g0
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Coherent DSB-SC Detection
x
cos0t
Predetection
Filter
Lowpass
Filter
~x(t)
tDSB
txttxtx
ttxtt
~2cos~
~cos~cos
filter lowpass
0
02
0DSB
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X()
½X()
DSB()
0-g 0 0+g
20g-g
g-g
Coherent DSB-SC Detection
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Transmitter: cos0t
Receiver: cos[(0+)t + ]
In most cases: = 0 and variable in time
Receiver: cos(0t + )
Coherent DSB-SC DetectionErrors
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Coherent detection:[x(t) cos(0t)]cos(0t + )
Detected signal: x(t) cos()
Synchronous operation of both transmitter
and receiver is necessary.
Coherent DSB-SC DetectionPhase Errors
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AM Modulation
tAttxkA 0000AM coscos
ttkxA 00AM cos1
01 tkx
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Single tone modulation: x(t) = acosmt
AM=A0(1 + ka cosmt) cos0t
ka = m – modulation index
AM=A0(1 + m cosmt) cos0t
AM Modulation
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A0(1+m)
A0(1-m)
ttmA m 00AM coscos1
t
mA0
AM Modulation
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0-m 0+m
0
0A
20mA
20mA
AM Modulation
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AM Phasor Diagram tjtjtj
m
eeemAt
ttmAt0mm
21
0AM
00AM
1
coscos1
Re
Re
Im 0
A0
m
m
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2
2
T
SAM 2 m
m
P
P
%333
10 AM
PS – sidelobe power
PT – total power
AM Modulation
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X()
~X()
SSB()
0-g 0 0+g
20g-g
g-g
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00
SSB-SC Modulation
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? ttxttxt 00SSB sinˆcos
tx tx̂2
X() SSB()
SSB-SC Modulation
quadrature (Hilbert’s) filter
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2
x
x
+
x(t)
cos0t
sin0t
SSB-SC+(t)
-
)(ˆ tx
+
SSB-SC Modulation
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Quadrature (Hilbert’s) Filter
0,
0,2sgn
j
jeeAH jj
A()
()
12
2
XHX ˆ
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Analytic Signal
0,
0,ˆ
jX
jXX
txjtxtx ˆ
0,
0,
X
XXX
0,0
0,2
X
X
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SSB-SC Modulation
tjetxjtxt 0ˆReSSB
2
Re*
VV
tv
00 sidebandupper
0*
sidebandupper
0SSB 2
1
2
1
XX
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Coherent SSB-SC Detection
x
cos0t
Predetection
Filter
Lowpass
Filter
~x(t)
tSC-SSB
txttxttxtx
tttxttxtt
~2sinˆ2cos~
~cossinˆcos~cos
filter lowpass
0
filter lowpass
0
0002
0SC-SSB
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ttxttxt 00SSB sinˆcos
txtxte 22SSB ˆ
txte SSB
Envelope SSB-SC Detection
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Envelope SSB-SC Detection
Re
Ime
xxjˆ
)exp(ˆ jexjxx
22 x̂xe
tjetetxjtxtx SSBˆ
tte SSBln H
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ttetx cosSSB
te ln2
cos
tSSB
x
tx
Envelope SSB-SC Detection
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tte SSBln H
tjetetxjtxtx SSBˆ
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Nyquist FilterVSB-SC Concept
H()
Nyquist filter
SCDSB
HSCDSB
SSB-SC VSB-SC
Vestigal SideBand„Modulation & Detection” Zdzisław Papir
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VSB-SC Modulation
H ttxt 0DSB cos)(
DSBVSB
tVSB
H
Nyquist filter
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VSB-SC Modulation
ttttt 0
quadrature
Q0
inphase
ISC-VSB sincos
Lowpass I & Q representation
of a bandpass VSB-SC signal
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Coherent VSB-SC Detection
filter lowpass
0Q0II
0SC-VSB
2sin2cos~
~cos
ttttt
tt
Requirement for a coherent VSB-S.C. detection
txt I
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VSB-SC Modulation
thH
ttxtht 0VSB cos
tthtthth 0Q0I sin2cos2
ttxthttxtht QI 00VSB sin)]()([cos)]()([)(
)(tI )(tQ
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VSB-SC Modulation
x
x
+x(t) cos0t
sin0t
-
)(Q H
tVSB
txt ~I)(I H
+
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VSB-SC Modulation
00I HHH
00Q HHjH
const~ II Htxt
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const00I HHH
H()
const
0
0
H
H
VSB-SC Modulation
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VSB-SC Modulation
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0
Nyquist filter, 50%
const00
I
HH
H
00
Q
HHj
H
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ttttxt 0Q0VSB sincos
componet enabling vestigal sideband filtering
component
enabling
coherent detection
VSB-SC Modulation
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Amplitude Modulation- different schemes
DSB
AM
SSB
VSB„Modulation & Detection” Zdzisław Papir