05 - amplitude modulation techniques

8/14/2019 05 - Amplitude Modulation Techniques

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Phasor Analysis of Bandpass Signals

Background: Phasors for Monochromatic Signals

1

cos 2 ox t A f t


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Phasor Analysis of Bandpass Signals

Narrowband Signals:Define:

2

x t 2Z f u t X f


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Narrowband Signals: Continued

3


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Phasor Equivalent for Narrowband

4


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Transmitting Bandpass Signals

through Bandpass Systems

5

: 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)

7


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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

8


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Amplitude Modulation

9

( ) 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:

10

( ) 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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11


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Example

Message signal

AM Wave

Time Domain:

Frequency Domain:

12

( ) ( ) ( )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

13

( ) ( ) ( )2

1( ) ( )

41( ) ( )

4

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

14


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Conclusions on AM

Power

Channel Bandwidth

Complexity

15


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Double Sideband-Suppressed

Carrier Modulation (DSB-SC)

Message signal:

Carrier Wave:Transmit Signal:

16

( )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?

17

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

18

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:

21

( ) ( )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

22

( ) 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:

23

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

12

24

24

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

4

cc c

AV f M f H f f H f f


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Vestigial Sideband Filter

05 - amplitude modulation techniques

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