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Lecture 6 Modulation Processsloyka/elg3175/Lec_6_ELG3175.pdf · · 2018-01-091.Find time-domain...
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Modulation Process
Modulation: transforming an information-carrying signal m(t)
(lowpass) into a narrowband signal x(t). m(t) is also called the
modulating signal or message.
Start with a sinusoidal signal (carrier)
Varying according to m(t) – amplitude modulation (AM)
Varying according to m(t) – phase modulation (PM)
Varying according to m(t) – frequency modulation
(FM)
FM and PM can be viewed as angle modulation.
General form of a modulated signal:
Lecture 6
( )0( ) cos 2x t A ft= π +ϕ
( )A A t=
( )tϕ = ϕ
( )f f t=
0( ) ( )cos ( ) ( )
t
cx t A t t d t
= ω + ∆ω τ τ + ϕ ∫
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Amplitude Modulation (AM)
Information-bearing signal m(t) is impressed onto the
carrier amplitude.
Four types of AM:
– conventional,
– double sideband suppressed carrier (DSB-SC)
– single sideband (SSB); can be lower or upper (LSB/USB)
– vestigial sideband (VSB)
Spectral characteristics & bandwidth
Modulation index
Power efficiency
Lecture 6
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Conventional AM
General form:
m(t) must be constrained:
( ) ( ) ( )( )
1 cos 2c c c
A t
x t A m t f t= + π +φ
( )1 m t− ≤
( )1c
A m t+
( ) ( )cosm t a t= Ω
Ac– carrier amplitude
without modulation;
- time-varying
(modulated) carrier
amplitude.
Example: sinusoidal
modulating signal: ( )x t
L.W
. C
ouch II,
Dig
ital and A
nalo
g C
om
munic
ation S
yste
ms, P
rentice H
all, 2001.
Lecture 6
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Conventional AM: Sinusoidal Modulation
Modulated signal:
Minimum & maximum carrier amplitudes:
Modulation index:
% mod.=M*100%
x(t) spectrum:
( ) [ ] ( )1 cos(2 ) cos 2c c c
x t A a Ft f t= + π π + φ
[ ]
[ ]
min
max
1
1
c
c
A A a
A A a
= −
= +max min1
2c
A AM
A
−= ≤
[ ] ( )
( )
( ) cos 2 cos 22
cos 22
c
c c c c c
c
c c
A ax t A f t f F t
A af F t
= π + φ + π − + φ
+ π + + φ 2 ( )x
S f+
f
cf( )
cf F− ( )
cf F+
2
cA a
2
cA a
cA
2
cA a
2
cA a
cA
ctω
tΩ
tΩGeometrical
representation
Bandwidth?
Lecture 6
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Conventional AM: Sinusoidal Modulation
Signal power
(average):
Power efficiency:
Bandwidth:
Peak power:
In general:
(no DC in m(t))
( ) ( )2 2 2
2 21lim
2 2 4
T
c c
xT
T
A a AP x t dt x t
T→∞
−
= = = +∫
2
22
SB
tot
P a
P aη= =
+
carrier sidebands
2f F∆ =
0 0.2 0.4 0.6 0.8 10
10
20
30
40
.
Power efficiency of AM
a
effic
ien
cy,
%
Lecture 6
[ ]2
(1 )
2
cpeak
A aP
+
=
What is the best power efficiency?
1
m
m
P
Pη =
+
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Conventional AM: General Case
General form:
Modulated signal spectrum:
Measured by spectrum analyzer: no inf. height for delta function in practice,
( ) ( ) ( )1 cos 2c c c
x t A m t f t= + π + φ
( ) ( ) ( ) ( ) ( )2
c c c cj j j jc
x c c m c m c
AS f f f e f f e S f f e S f f e
φ − φ φ − φ = δ − + δ + + − + +
( )2 ( ) ( )x c c m c
S f A f f S f f+ = δ − + −
f
( )m
S f
cf0
f
( )x
S f
cf
cf−
2
c
m
AS2
c
m
AS
0
Bandwidth???
Lecture 6
( ) ( )c c
f f f fδ − ↔ ∆ −
Power ?
Power efficiency?
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Example
• Conventional AM signal with a sinusoidal message has
the following parameters:
1. Find time-domain expression x(t) of the signal
2. Find its Fourier transform
3. Sketch its spectrum as it appears on the spectrum
analyzer
4. Find the signal power, peak power and the power
efficiency
5. Find the signal bandwidth
10, 0.5, 1 , 1c c
A M f MHz F kHz= = = =
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Generation of Conventional AM
Power-law modulator:
Using variable-gain amplifier (modulator):
( ) 2
1 2( ) ( )
out in inv t a v t a v t= +
( )inv t
variable gain
amplifier
( )m t
cos( )c
A tω
~
( ) ( ) ( )( )
1 cosc c
g t
x t A m t t= + ω
( ) ( )2
1
1
21 cos2
c c
ax t A a m t f t
a
= + π
Lecture 6
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Generation of Conventional AM
Switching modulator:
( ) 1 1
2
1
( ), ( ) 0
0, ( ) 0
v t v t
v t
v t
≥=
<
+ BPF
at fc
( )( )
( )1
1
11 2cos 2 2 1
2 2 1
n
c
n
s t f t nn
−∞
=
−= + π − π −
∑
( ) ( )
( )
BPF ( ) cos2 ( )
41 cos2
2
c c
c
c
c
x t m t A f t s t
Am t f t
A
= + π
= + π
π
cT
cT−
Lecture 6
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Examples of Modulators for Conventional AMLecture 6
For more info, see e.g.
B. Razavi, RF Microelectronics, Prentice Hall, 2012.
U.L. Rohde, D.P. Newkirk, RF/Microwave Circuit Design for Wireless Applications, Wiley, 2000.
B. Leung, VLSI for Wireless Communications, Prentice Hall, 2002.
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Examples of Modulators for Conventional AMLecture 6
adopted from Electronics World,
July 1998.
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Demodulation of Conventional AM
Envelope detector
1
2c
f fRC
∆ << <<π
RC – lowpass filter
Attenuates carrier, passes modulating signal
cA
( )outv t
Lecture 6
c mT RC T<< τ = <<
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Demodulation of Conventional AM
• Product detector:
( ) ( ) ( )1 cos 2c c
x t A m t f t= + π
( ) ( )cos 2o cv t f t= π
( ) ( )1
2out cv t A m t=
Lecture 6
0θ =
carrier recovery
What happens if ?0θ ≠
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Multiplier ImplementationLecture 6
simplified
more realistic
Adopted from “Considering Multipliers ” by B. Gilbert
AD534: A Four-Quadrant Translinear Multiplier
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Advantages/Disadvantages of
Conventional AM
Advantages
– Very simple demodulation (envelope detector)
– “Linear” modulation*
Disadvantages
– Low power efficiency
– Doubles the baseband bandwidth
*Q.: is the conventional AM modulator an LTI system?
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Double-Sided AM: Suppressed Carrier
(DSB-SC)
How to increase power efficiency?
DSB-SC signal:
Example: sinusoidal modulation,
Spectrum:
( ) ( ) ( )cos 2c c
x t A m t f t= π
( ) ( )cos(2 )cos 2c c
x t A a Ft f t= π π
( ) ( ) ( )cos 2 ( ) cos 2 ( )2
c
c c
aAx t f F t f F t= π − + π +
2 ( )x
S f+
f
cf( )
cf F− ( )
cf F+
2
cA a
2
cA a
Bandwidth???
Geometrical representation???
Power efficiency???
Modulation index???
Lecture 6
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
DSB-SC: General Case
DSB-SC signal:
Spectrum:
What do you see on a spectrum analyzer?
Bandwidth ? Power efficiency? PSD?
( ) ( ) ( )2
c
x m c m c
AS f S f f S f f= − + +
( ) ( ) ( )cos 2c c
x t A m t f t= π
f
( )m
S f
cf0
f
( )x
S f
cf
cf−
2
c
m
AS
2
c
m
AS
0
Lecture 6
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Generation of DSB-SC Generation:
Mixer. Not practical in many cases.
Filtered conventional AM. Not practical.
Balanced modulator:
J.Proakis, M.Salehi, Communications Systems Engineering, Prentice Hall, 2002
Lecture 6
Q: what if misbalanced?
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Generation of DSB-SCRing modulator
D1
D2
D3
D4
Large-amplitude sinusoidal signal may be used instead of the square wave
+ BPF at fc
Carrier is
suppressed here
( )( )
( )1
1
12cos 2 2 1
2 1
n
c c
n
s t A f t nn
−∞
=
−= π − π −
∑( )
( )
BPF ( ) ( )
2cos2
out
c
c
v t m t s t
Am t f t
=
= π
π
( ) 0DC m t =
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Demodulation of DSB-SC
Why will the envelope detector not work?
Lecture 6
( ) ( ) ( )cos 2in cx t m t f t= π ( ) ?
outx t =
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Demodulation of DSB-SC
Demodulation - Costas loop:
Lecture 6
L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.
Details: Couch,
Sec. 4.14, 5.4
0?
/ 2?
?
θ =
= π
= π
Why 2 channels?
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Demodulation of DSB-SC
Product detector + squaring carrier recovery loop:
L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.
Lecture 6
+ BPF at 2fc
+ BPF at fc
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Demodulation of DSB-SC
Using a pilot tone:modulation
demodulation
J.Proakis, M.Salehi, Communications Systems Engineering, Prentice Hall, 2002
Lecture 6
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Advantages/Disadvantages of DSB-SC
• Advantages
– High power efficiency
– If message m(t)>0, envelope detection is possible
• Disadvantages
– Doubles the baseband bandwidth
– Complex modulation/demodulation (some form of
carrier recovery is required)
– Pilot tone may be required to simplify demodulation
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10-Feb-16 Lecture 6, ELG3175 : Introduction to Communication Systems © S. Loyka
Summary
Modulation process. Types of analog modulation.
Conventional AM. Time-domain & frequency-domain
representations. Power efficiency & bandwidth.
Generation (modulation) & demodulation of conv. AM.
Double sideband suppressed carrier (DSB-SC). Spectrum.
Bandwidth. Generation & demodulation of DSB-SC.
Advantages/disadvantages of conventional & DSB-SC AM.
• Homework: Reading: Couch, 5.1-5.4, 4.4., 4.11-4.13. Study
carefully all the examples, make sure you understand and
can solve them with the book closed.
• Do some end-of-chapter problems. Students’ solution
manual provides solutions for many of them.
Lecture 6
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