comm 03 amplitude modulation

8/2/2019 Comm 03 Amplitude Modulation

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Chapter 3Chapter 3Amplitude ModulationAmplitude Modulation

Wireless Information Transmission System Lab.ireless Information Transmission System Lab.Institute of Communications EngineeringInstitute of Communications Engineering

National SunNational Sun YatYat--sensen UniversityUniversity


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OutlineOutline

3.1 Introduction

3.2 Amplitude Modulation

3.3 Double Sideband-Suppressed Carrier Modulation

3.4 Quadrature-Carrier Multiplexing

3.5 Sin le-Sideband and Vesti ial-Sideband Methods of Modulation

3.7 Frequency Translation

2


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Chapter 3.1Chapter 3.1IntroductionIntroduction




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3.1 Introduction3.1 Introduction

Purpose of a communication system: convey information through a

.

The information is often represented as a baseband signal(, . .

frequency.

shift of the range of baseband frequencies into other frequencyranges suitable for transmission, and a corresponding shift back to

the original frequency range after reception.

A shift of the range of frequencies in a signal is accomplished byus ng mo u ation, w c s e ne as t e process y w ic some

characteristic of a carrier is varied in accordance with a

4

.


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3.1 Introduction3.1 Introduction

A common form of the carrier is asinusoidal wave, in which case

- .

The baseband signal is referred to as the modulating wave, and theresult of the modulation process is referred to as the modulated wave.

.

At the receiving end, we require the original baseband signal to be

restored. This is accomplished by using a process known as

demodulation, which is the reverse of the modulation process.

CW: continuous-wave.

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Chapter 3.2Chapter 3.2Amplitude ModulationAmplitude Modulation




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3.2 Amplitude Modulation3.2 Amplitude Modulation

Asinusoidal carrier wave:Ac is the carrier amplitude

fc is the carrier frequency

Phase is assumed to be 0.

AM is defined as a process in which the amplitude of the carrier

cos 2 3.1c cc t A t =

wave c s var e a ou a mean va ue, near y w ase an

signal m(t).

,

( ) ( ) ( )1 cos 2c a cs t A k m t f t = + (3.2), c

measured in volts, in which case the ka is measured in volt-1.

-1a .

m(t): modulating wave; the baseband signal that carries the message.

7

.

m(t) and Ac are measured in volts.


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The envelope ofs(t) has essentially the same shape as the

baseband signal m(t) provided that two requirements are satisfied:

1. The amplitude ofkam(t) is always less than unity, that is,

( ) ( )1 for all 3.3ak m t t 1 for any tthe carrier wave becomes

overmodulated resultin in carrier hase reversals wheneverthe factor 1+ kam(t) crosses zero. (envelope distortion)

The absolute maximum value ofk m(t) multiplied by 100 is

8

referred to as thepercentage modulation.


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Baseband signal m(t)

9

AM wave for |kam(t)|1 or some t

Envelope distortion


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2. The carrier frequencyfc is much greater than the highest

frequency component Wof the message signal m(t), that is

( )3.4cf W e ca t e message an w t . t e con t on o q. .

is not satisfied, an envelope can not be visualized satisfactorily.

. . ,

s(t) is given byA k A

( ) ( ) ( ) ( )1 cos 2 3.2c a cs t A k m t f t = + ( ) ( ) ( )1

cos 22

c c cf t f f f f + +

.2 2

c c c c=

10


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From the spectrum ofS(f), we note the following:

. ,

m(t) for negative frequencies extending from Wto 0 becomes completely

visible for positive frequencies, provided that the carrier frequency satisfies thecon on c .

2. For positive frequencies: The spectrum of an AM wave above fc is referred

to as t e upper si e an , e ow fc

s re erre to as t e ower si e an . For

negative frequencies: The upper sidebandis below fc and the lower sideband

is above fc. The condition fc >Wensures that the sidebands do not overlap.

3. For positive frequencies, the highest frequency component of the AM wave

equals fc +W, and the lowest frequency component equals fcW. Thedifference between these two frequencies defines the transmission bandwidth

BT for an AM wave.2 3.6TB W=

11


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Example 3.1 Single-Tone Modulation (1/3)

m m carrier wave: c(t) = Accos(2fct)

.

where

c m c

a mk A= :modulation factor(or percentage modulation)

To avoid overmodulation

||


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. .

( ) ( ) ( ) ( )

1 1cos 2 cos 2 cos 2

2 2c c c c m c c ms t A f t A f f t A f f t = + + +

cos cos cos cos2

B A B A B= + +

( ) ( ) ( ) ( ) ( )2 4

1

c c c c c m c mS f A f f f f A f f f f f f = + + + + + +

4c c m c m

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2

2 2

Carrier power2

1- =

cA=

2 2

8

1Lower side-frequency power=

c

cA

In any case, the ratio of the total sideband power to the total

( )2 2 2 +.

If=1, the total power in the two side frequencies of the resulting AM

wave is only one-third of the total power in the modulated wave.

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When the percentage modulation is less than 20 percent, the power in one

side frequency is less than 1 percent of the total power in the AM wave.


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Switching Modulator (1/4)

One way to generate an AM wave: witc ing Mo u ator.

Assume carrier wave c(t) is large in amplitude and the diode acts as an.

( ) ( ) ( ) ( )1 cos 2 3.8

0

c cv t A f t m t

v t c t

= +

>

( )23.9

0, 0v t

c t


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. . ,

values v1(t) and zeros at a rate equal to the carrier frequency fc.

B assumin a modulatin wave that is weak com ared with the

carrier wave, we have effectively replace the nonlinear behavior

of the diode by an approximately equivalent piecewise-linear

time-varying operation. We may express Eq. (3.9) mathematically as

( ) ( ) ( ) ( ) ( )02

cos 2 3.10c c Tv t A f t m t g t +

period0= c

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01 1T


0

0

0

1 0 0

2

cos 2 sin 2

1

T n n

n

T

g t a a t b tT T=

= + +

=

0

0

0

0 4

4

2

sin2

T

T

aT

n t

= =

( )

00

0

0

02

0

22cos 2

T

T

n T

T

na g t t dt

=

0

0

04

0 4 0 0

04

cos2

2Tn

T

na tdt

nT T T

T

= =

( )0

00

0 0

2

20 0

2sin 2

T

n TT

nb g t t dt

T T

=

1 2 sin sin sin 2 2 2

n n nn n

= =

0

cos 22 2T

nt

Tn

0

4

T ( )

( )

sin2 1 2

2cos

m

m

=

= 0

4

0 0 04

sin 2

2Tn

t tnT T T

T

= =

00 T

( )( )

( )( )

1

2 21 1

2 1 2 1

m m

m

m m

+

= =

17

1 cos cos 0 2 2

n nn

= =

( ) ( )

12

12 1

m

m

=


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Switching Modulator (4/4)1n

( ) ( ) ( )0

1

cos 2 2 1 3.11

2 2 1

T c

n

g t f t n

n=

= +

Substituting Eq. (3.11) in (3.10), v2(t) consists of two component

A desired AM wave: ( ) ( ) ( ) ( ) ( )02

cos 2 3.10c c Tv t A f t m t g t +

( ) ( )4 41 cos 2 ,2

cc a

c c

A m t f t k A A

+ =

Unwanted component, the spectrum of which contains

Delta function at 0, 2fc, 4fc and so on. Occupy frequency intervals of width 2Wcentered at 0, 3fc, 5fc and so

on, where Wis the message bandwidth.

18

- - c

bandwidth 2W, provide that fc >2W.


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Envelope Detector (1/2)

The process ofdemodulation is used to recover the original

modulating wave from the incoming modulated wave. ne way o emo u a e an wave: enve ope e ec or.

Consist of a diode and a resistor-capacitor (RC) filter. (see next page)

On a positive half-cycle of the input signal, the diode is forward-biased

and the capacitorCcharges up rapidly to the peak value of the input signal.

When the input signal falls below this value, the diode becomes reverse-

biased and the capacitorCdischarges slowly through the load resistorRl.

- .

When the input signal becomes greater than the voltage across the

capacitor, the diode conducts again and the process is repeated.

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Envelope detector circuit diagram, Envelope Detector (2/2)

assuming the diode is ideal, having a

constant resistance rf when forward

biased and infinite resistance when

reverse-biased.

s nuso a wave w percen

modulation.

Envelope detector output contains a

small amount of ripple at the carrier

frequency; this ripple is easily

20

removed by the low-pass filter.


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Virtues,Virtues, Limitations,Limitations, andand ModulationsModulations ofof

AM is the oldest method of performing modulation.

.

In the transmitter: a switching modulator or a square-law modulator (Problem 3.4).

In the receiver: an envelope detector or a square-law detector (Problem 3.6). ts system s re at ve y c eap to u .

The reason that AM radio broadcasting has been popular for so long.

communication resources. Using Eq. (3.2) suffers form limitations. AM is wasteful of power: The carrier wave c(t) and baseband signal m(t) are

independent. The carrier wave represents a waste of power, which means that

in AM only a fraction of the total transmitted power is actually affect by m(t).

are uniquely related to each other by virtue of their symmetry about the carrier

frequency.

21

.c a c=


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Virtues,Virtues, Limitations,Limitations, andand ModulationsModulations ofof

To overcome these limitations, we trade off system complexity for improved

utilization of communication resources.

Three modified forms of amplitude modulation:

Double sideband-suppressed carrier(DSB-SC) modulation, in which the.

Transmitted power is saved through the suppression of the carrier. The channel bandwidth

requirement is 2W.

es g a s e an mo u a on,

completely and just a trace, orvestige, of the other sideband is retained. The required channel bandwidth is in excess of the message bandwidth by an amount equal

o e w o e ves g a s e an .

Suited for the transmission of wideband signals such as television signals.

Single sideband(SSB) modulation, in which the modulated wave consists onlyof the upper sideband or the lower sideband.

Suited for the transmission of voice signals by virtue of the energy gap that exists in the

spectrum of voice signals between zero and a few hundred hertz.

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The minimum transmitted power and minimum channel bandwidth: its principal

disadvantage is increased cost and complexity.


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Spectra of the various modulated signalsSpectra of the various modulated signals

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..

--Carrier ModulationCarrier Modulation




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3.3 Double Sideband3.3 Double Sideband--Suppressed Carrier ModulationSuppressed Carrier Modulation

Double sideband-suppressed carrier(DSB-SC) modulation.

( ) ( ) ( ) ( ) ( ) ( )cos 2 3.14c cs t c t m t A f t m t= = The modulated signals(t) undergoes aphase reversalwhenever the message signal m(t)

crosses zero.F - .

( ) ( ) ( ) ( )1

3.15c c cS f A M f f M f f = + +

Bandwidth:

2W

limited to the interval

-Wf W

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Ring Modulator (1/4)Four diodes

orm a r ng

26


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Ring Modulator (2/4)

ng mo u ator s one o t e most use u pro uct mo u ator, we

suited for generating a DSB-SC wave.

- c,

which is applied longitudinally by means of two center-tapped transformers.

If the transformers are perfectly balanced and the diodes are identical, there

is no leakage of the modulation frequency into the modulation output .

The operation of the circuit.

ssum ng a e o es ave a cons an orwar res s ance rf w en

switched on and a constant backward resistance rb when switched off. And

they switch as the carrier wave c(t) goes through zero. On one half-cycle of the carrier wave, the outer diodes are switched to their

forward resistance rf and the inner diodes are switched to their backward

-

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in the opposite condition.


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Ring Modulator (3/4) e ou pu vo age as e same magn u e as e ou pu vo age, u ey

have opposite polarity.

In fact, the ring modulator acts as a commutator.

Square-wave carrierc(t) can be represented by a Fourier series:1

1n

The rin modulator out ut is therefore1

cos 2 2 1 3.16 2 1 cn

c t f t nn=

=

( ) ( ) ( )

( )

( ) ( ) ( )

114

cos 2 2 1 3.17

n

cs t c t m t f t n m t

= = It is sometimes referred to as a double-balanced modulator,

1n n=

28

ecause s a ance w respec o o e ase an s gna

and the square-wave carrier.


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Ring Modulator (4/4) Assumin that m t is limited to the fre uenc band -W W

the spectrum of the modulator output consists of sidebands

around each of the odd harmonics of the square-wave carrierm(t). To prevent sideband overlapfc >W.

We can use a band-pass filter of mid-band frequency fc and

bandwidth 2Wto select the desired pair of sidebands around thecarrier frequencyfc.

e c rcu ry nee e or e genera on o a - mo u a e wave

consists of a ring modulator followed by a band-pass filter.

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Coherent Detection (1/4)

It is assumed that the local oscillator signal is exactly coherent or

, ,used in the product modulator to generates(t). This method of

demodulation is known as coherent detection orsynchronous

30

demodulation.


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' cos 2t A f t s t = + ( ) ( ) ( )cos 2c cs t A f t m t=

For a more general demodulation process, we assume is a arbitrary phase difference.

( ) ( ) ( ) ( )' cos 2 cos 2 3.18c c c cA A f t f t m t= +

( ) ( ) ( )' '

cos 4 cos2 2c c c c cA A f t m t A A m t = + +

31


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e rst term n q. . s remove y ow-pass ter,

provided that the cut-off frequency of this filter is greater than W

c . c .

Therefore:( ) ( ) ( )'

1cos 3.19o c ct A A m t =

vo(t) is proportional to m(t) when the phase error is a constant.Attenuated by a factor equal to cos.

( )'_ max1

,when =02

o c cv A A m t

=

_ mim 0, when =2

ov

=

(quadrature null effect)

32

,

version of the original baseband signal m(t).


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Coherent Detection (4/4) In practice, we usually find that the phase error varies randomly with

time, due to random variations in communication channel. The result is

that at the detector output, the multiplying factor cos also variesrandomly with time, which is obviously undesired.

Prov s on must e ma e n t e system to ma nta n t e oca

oscillator in the receiver inperfect synchronism, in both

,

DSB-SC modulated signal in the transmitter.

The resulting system complexity is the price that must be paid for

su ressin the carrier wave to save transmitter ower.

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Costas Receiver (1/2)

,

suitable for demodulating DSB-SC waves.

A multiplier

followed by a

low-pass filter.

34


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Costas Receiver (2/2)

e requency o t e oca osc ator s a uste to e t e same as

the carrier frequency fc, which is assumed known a prior.

n e upper pa s re erre o as e n-p ase co eren e ec or

orI-channel, and that in the lower path is referred to as the

- -

detectors are coupled together to from a negative feedbacksystem designed in such a way as to maintain the local oscillator

synchronous with the carrier wave.

By combining theI- and Q-channel outputs inphase

iscriminator w c cons sts o a mu tip ier o owe y a ow-

pass filter), a dc control signal is obtained that automatically

35

-

(VCO).


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Outputs of Product Modulator1

-

-Channel

cos cos cos cos2

c c c c ct m t t m t t + = + +

1=

Outputs of Low-Pass Filter

2c c c c c

I-Channel ( )1

cos2cA m t

- anne ( )sin2

cA m t

221 1 1cos sin sin 2A m t A m t A m t

=

36

2 2 8c c c


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Chapter 3.4Chapter 3.4

QuadratureQuadrature--Carrier MultiplexingCarrier Multiplexing




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3.4 Quadrature3.4 Quadrature--Carrier Multi lexinCarrier Multi lexin

Enable two DSB-SC modulated waves to occupy the same channel

. - .

( ) ( ) ( ) ( ) ( ) ( )1 2cos 2 sin 2 3.20c c c cs t A m t f t A m t f t= +

in-phase component quadrature-phase component

38

It is important to maintain the correct phase frequency relationship between the

local oscillators used in the transmitter and receiver parts of the system.


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..

-- --Sideband Methods of ModulationSideband Methods of Modulation



3 5 Single3 5 Single--Sideband and VestigialSideband and Vestigial--


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3.5 Single3.5 Single Sideband and VestigialSideband and Vestigial

With double-sideband modulation, we are transmitting only one

-

pass bandwidth of 2Wis actually required.

In actual fact, it can be shown that due to the symmetry of the DSB

signal about the carrier frequency, the same information is

transmitted in the upperand lower sidebands, and only one of thesidebands needs to be transmitted.

There are two bandwidth conservation methods:

Single-sideband(SSB) modulation .

Vestigial sideband(VSB) modulation.

40

SingleSingle sideband modulationsideband modulation


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SingleSingle--sideband modulationsideband modulation

The generation of a SSB signal is straightforward.

rs , genera e a ou e-s e an s gna

Then apply an ideal pass-band filter to the result with cutoff frequencies of

fc and fc +W(orfcW) for the upper sideband (or lower sideband).

Practically, the approximate construction of an ideal filter is very difficult.

Voice Signal

41

VSB Modulation(1/3)VSB Modulation(1/3)


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A vestigial-sideband system is a compromise between DSB and

.

disadvantages.

B si nals are relativel eas to enerate an their ban wi th isonly slightly (typically 25 percent) greater than that of SSB signals.

In VSB, instead of re ectin one sideband com letel as in SSB, a

gradual cutoff of one sideband is accepted. All of the one sidebandis transmitted and a small amount (vestige) of the other sideband is

transm tte as we .

The filter is allowed to have a nonzero transition band.

The roll-off characteristic of the filter is such that the partial

suppression of the transmitted sideband in the neighborhood of the

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corresponding part of the suppressed sideband.



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Our goal is to determine the particularH( f) required to produce a

,

that the original baseband signal m(t) may be recovered froms(t)

by coherent detection.( ) ( ) ( )

3.21c

S f U f H f

AM H

=

= + +

m(t) M(f) , u(t) U(f)

2

c c

F F

43

Figure 3.18:Amplitude response of VSB filter;

only positive-frequency portion is shown.fv: the width of the vestigial sideband



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( ) ( ) ( )' cos 2c cv t A f t s t ='

F

( ) ( ) ( ) ( )3.222

cc cV f S f f S f f = + +

'A ACombine Eq. (3.21) and (3.22)

'

4

2 2 3.23

c c

c cA A H M H

= + +

+ + + +4

c c c c

'

0 3.24c c

c c

A AV f M f H f f H f f = + +

Low-pass filter

To obtain baseband signal m(t) at coherent detector output, we

require Vo(f) to be a scaled version ofM(f). Therefore, we canchoose:( ) ( ) ( )1, 3.26c cH f f H f f W f W + + =

'

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Eq. (3.24) becomes ( ) ( )04

c ct m t = basebandM( f) interval:

-Wf W


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Chapter 3.7Chapter 3.7Frequency TranslationFrequency Translation



3 7 Frequency Translation3 7 Frequency Translation


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3.7 Frequency Translation3.7 Frequency Translation

The basic operation involved in single-sideband modulation is in fact

.

SSB modulation is sometimes referred to asfrequency changing, mixing, or

heterodyning. The mixerconsists a product modulator followed by a band-pass

filter.

Band-pass filter bandwidth: equal to that of the modulated signals1(t) used as

input.

46

carrier frequency f1 carrier frequency f2

3 7 Frequency Translation3 7 Frequency Translation


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3.7 Frequency Translation3.7 Frequency Translation

Due to frequency translation performed by the mixer: We may set

2 1 lf f f= +

=

assume f2 >f1

translated upward

2 1 lf f f= or

assume f1 >f2

1 2l =

( ) ( )( ) ( )( )

1 1

1 1

1cos 2 cos 2

2

l l l l

l l lA m t f f t f f t = + +

The band-pass filter rejects the unwanted frequency and keeps the desired one.

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.

comm 03 amplitude modulation

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