05 - amplitude modulation techniques
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Phasor Analysis of Bandpass Signals
Background: Phasors for Monochromatic Signals
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cos 2 ox t A f t
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Phasor Analysis of Bandpass Signals
Narrowband Signals:Define:
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x t 2Z f u t X f
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Narrowband Signals: Continued
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Phasor Equivalent for Narrowband
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Transmitting Bandpass Signals
through Bandpass Systems
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: bandpass signal with center frequency
: impulse response of LTI system
- narrowband
- centered on frequency
Find :
o
o
x t f
h t
f
y t
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Amplitude Modulation
ECE460
Spring, 2012
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Analog Modulation Techniques
Modulation: The process by which somecharacteristic of a carrier wave is
varied in accordance with an
information-bearing signal
Amplitude modulation
1. Amplitude modulation (AM)
2. Double sideband-suppressed carrier (DSB-SC)
3. Single sideband (SSB)
4. Vestigial sideband (VSB)
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Amplitude Modulation (AM)
AM is formally defined as a process in which the
amplitude of the carrier wave c(t)is variedabout a mean value linearly with a message
signal m(t).
Message Signal:
Sinusoidal Carrier:
AM Wave:
( )m t
( ) cos(2 )c cc t A f t
( ) 1 ( ) cos(2 )c a cs t A k m t f t
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Amplitude Modulation
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( ) 1ak m t t
( ) 1 for someak m t t
Message signal ( )m t
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Frequency Domain
Message signal: Band-limited to W
AM wave:
Time Domain:
Frequency Domain:
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( ) 1 ( ) cos(2 )c a cs t A k m t f t
( ) ( )m t M f
( ) ( ) ( ) ( ) ( )2 2
c a cc c c c
A k AS f f f f f M f f M f f
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Example
Message signal
AM Wave
Time Domain:
Frequency Domain:
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( ) ( ) ( )2
1( ) ( )
41
( ) ( )4
cc c
c c m c m
c c m c m
AS f f f f f
A f f f f f f
A f f f f f f
( ) cos(2 )m m
m t A f t
wherea c
k A
1 1
cos(2 ) cos 2 cos 22 2c c c c m c c mA f t A f f t A f f t
( ) 1 cos(2 ) cos(2 )c m cs t A f t f t
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Varying m
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( ) ( ) ( )2
1( ) ( )
41( ) ( )
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cc c
c c m c m
c c m c m
A f f f f f
A f f f f f f
A f f f f f f
0.5
1.0
2.0
1
0.4
0.05
c
c
m
A
f Hz
f Hz
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Envelope Detection
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Conclusions on AM
Power
Channel Bandwidth
Complexity
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Double Sideband-Suppressed
Carrier Modulation (DSB-SC)
Message signal:
Carrier Wave:Transmit Signal:
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( )m t
( )c t( ) ( ) ( )
cos(2 ) ( )c c
s t c t m t
A f t m t
( )S f
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Why Coherent Detection?
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Local
Oscillator
Product
modulator
Low-pass
filter
( )v t( )s t( )
ov t
cos(2 )c cA f t
( ) cos 2
cos 2 cos 2
1 1cos 4 cos
2 2
c c
c c c c
c c c c c
v t A f t s t
A A f t f t m t
A A f t m t A A m t
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Costas Receiver
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Voltage Controlled
Oscillator
Product
modulator
Low-pass
filter
cos(2 )cf t
Productmodulator Low-passfilter
-90
Phase Shifter
Phase
discriminator
sin(2 )cf t
1
cos2
cA m t
1
sin2
cA m t
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Conclusions on DSB-SC
Power
Channel Bandwidth
Complexity
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Single Modulation (SSB)
1. Creating an SSB signal via a Hilbert Transform
2. Filtering a DSBSC signal
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Filtering DSB-SC signal for SSB
DSB-SC Signal:
Filter:
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( ) ( )cos(2 )DSB c cs t A m t f t
1,( )
0, otherwise
cf fH f
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Find SSB Transmission Signal
Message Signal:
Begin by finding
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( ) cos(2 ),c m m c
m t A f t f f
( )m t
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Demodulation of an SSB signal
Requires a phase coherent demodulator like a
DSB-SC demodulation
Low-pass filtering leaves:
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cos 2 cos 2
1 1cos sin double frequency terms
2 2
c c
c c
r t f t s t f t
A m t A m t
1 1
cos 2 cos sin2 2
c c cr t f t A m t A m t
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Conclusions on SSB
Power
Channel Bandwidth
Complexity
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Vestigial Sideband Modulation
Compromise between DSB-SC and SSB:
Keeps a trace, or vestige, of the other sideband A portion of the other sideband is transmitted
Transmitted Signal:
Received Signal:
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( ) cos 2
c c
s t A m t f t h t
cos 2 cv t s t f t
( )2
cc c
AS f M f f M f f H f
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c c
cc c
cc c
V f S f f S f f
AM f f M f H f f
AM f M f f H f f
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cc c
AV f M f H f f H f f
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Vestigial Sideband Filter
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