Lecture 6 Modulation Processsloyka/elg3175/Lec_6_ELG3175.pdf · · 2018-01-091.Find time-domain...

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 ∫

1(25)


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

2(25)


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

3(25)


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

4(25)


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 =

+

5(25)


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?

6(25)


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= = = =

7(25)


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

8(25)


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

9(25)


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.

10(25)


Examples of Modulators for Conventional AMLecture 6

adopted from Electronics World,

July 1998.

11(25)


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 = <<

12(25)


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 ≠

13(25)


Multiplier ImplementationLecture 6

simplified

more realistic

Adopted from “Considering Multipliers ” by B. Gilbert

AD534: A Four-Quadrant Translinear Multiplier

14(25)


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?

15(25)


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

16(25)


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

17(25)


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?

18(25)


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 =

19(25)


Demodulation of DSB-SC

Why will the envelope detector not work?

Lecture 6

( ) ( ) ( )cos 2in cx t m t f t= π ( ) ?

outx t =

20(25)



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?

21(25)



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

22(25)



Using a pilot tone:modulation

demodulation

J.Proakis, M.Salehi, Communications Systems Engineering, Prentice Hall, 2002

Lecture 6

23(25)


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

24(25)


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

25(25)

Lecture 6 Modulation Processsloyka/elg3175/Lec_6_ELG3175.pdf · · 2018-01-091.Find time-domain...

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