chapter 4

Chapter 4

Amplitude (Linear) Modulation

2

Outlines• Introduction• Base-band and Carrier Communication• Amplitude Modulation (AM):DSB-Large Carrier• Amplitude Modulation: Double sideband- Suppressed

Carrier (DSBSC)• Quadrature amplitude Modulation (QAM)• Single Sideband Modulation (SSB)• Vestigial Sideband (VSB)• Frequency mixing• Superhetrodyne AM radio.• Frequency division multilplexing (FDM).

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Introduction• Modulation is a process that causes a shift in

the range of frequencies of a message signal.

• A communication that does not use modulation is called baseband communication

• A communication that uses modulation is called Carrier communication

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Example of AM transmitter

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Example of AM (radio) Receiver

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Baseband and Carrier Communication

• Baseband signal: is message signal (information bearing signal) delivered by the information source or the input transducer .it is usually low frequency signal.

• Communication that uses modulation to shift the frequency spectrum of message signal is known as carrier communication.

– Amplitude modulation (AM),

– Frequency modulation (FM)

– Phase modulation (PM)

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Amplitude Modulation (AM) Double Sideband Large Carrier (DSB-LC)

( ) ( ) cos 2 cos 2AM c cs t m t f t A f t

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Another example of AM Waveform

( ) sin 2

( ) sin 2c

m

c t Ec f t

m t Em f t

( ) ( ( ))sin 2 cS t Ec m t f t

( ) sin 2

( ) sin 2c

m

c t Ec f t

m t Em f t

( ) ( ( ))sin 2 cs t Ec m t f t

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Modulation Index

• The amount of modulation in AM signal is given by its modulation index:

max min

max min

, min ( )pp

m E Eor m m t

A E E

When mp = A , =1 or 100% modulation.

Over-modulation, i.e. mOver-modulation, i.e. mpp >A >A , should be avoided, should be avoided

because it will create distortions.because it will create distortions.

max min,p pE A m E A m

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Effect of Modulation Index

<1

12

>1

=1

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Effects of Modulation Index

= 1 > 1

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Sideband and Carrier Power

• Carrier Power

• Sideband Power • Total power

• Power efficiency

• For single tone modulation

2

2c

AP

sc

s

PP

P

22

22100%, [1 ]

2 tot cP P

2m

s

PP

tot c sp P P

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Modulation index

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Example• Conventional AM signal with a sinusoidal

message has the following parameters:

A=10, =0.5, fc= 1MHz, and fm= 1kHz

1. Find time-domain expression

2. Find its Fourier transform

3. Sketch its spectrum

4. Find the signal power, carrier power and the power efficiency

5. Find the AM signal bandwidth

( )Ams t

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Example• A given AM (DSB-LC) broadcast station

transmits an average carrier power output of 40kW and uses a modulation index of 0.707 for sine-wave modulation. Calculate

a) the total output power

b) the power efficiency

c) the peak amplitude of the output if the antenna is represented by a 50- resistance load.

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Generation of AM Signalsdiode as NLE or as switch

Square-law modulator

2( ) ( ) ( )o i iv t av t bv t

' ( ) [ 2 ( )]cos 2o cv t aA Abm t f t

3cf B To avoid overlap the spectrum of

2 ( ) and ( )cm t M f f

Switching modulator

• Assume

1

1

'

( ) ( ) ( ),

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

2 2 1

2( ) [ ( )]cos 2

2

o i

n

cn

o c

v t v t w t where

w t f n tn

Av t m t f t

( ) ,and diode an ideal switchm t A

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Demodulation of AM signals

• AM signals can be demodulated by

– Envelope detector

– Rectifier detector

– Coherent (synchronous) detector.

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Envelope Detector

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Envelope Detector (Cont.)

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Rectifier Detector

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Coherent detector

cos(2 )cA f t

LPFV(t)

Local oscillator

2 ( ) cosA m t

( )Ams t

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Advantages/Disadvantages of Conventional AM (DSB-LC)

• Advantages– Very simple demodulation (envelope detector)– “Linear” modulation

• Disadvantages– Low power efficiency– Transmission bandwidth twice the message

bandwidth.

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Double-sideband suppressed carrier DSBSC

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The modulating signal m(t)

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DSBSC signal: m(t) cos(ct)

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Modulated signal m(t) cos(ct)

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Example.

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DSBSC Modulators

• DSBSC signal can be generated using several types of modulators:– Multiplier Modulators

– Nonlinear Modulators

– Switching Modulators

Multiplier modulator

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Nonlinear Modulators

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Switching Modulators

( ) cos 2 ckm t f t

a b

BPFM(t)

+

-

v2

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Switching Modulators

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40

Diode-bridge electronic switch

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Series-bridge diode modulator

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Shunt-bridge diode modulator

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Ring Modulator

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Ring modulator

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Demodulation of DSBSC

( ) cos(2 )cm t f t

cos(2 )cA f t

LPFV(t)

Local oscillator

2 ( ) cosA m t

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Quadrature Amplitude Modulation (QAM)

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Transmitter

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Receiver

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QAM cont.

• Quadrature multiplexing is used in color television to multiplex the signals which carry the information about colors.

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Single Sideband (SSB)

SSB time representation

ˆ( ) ( ) cos 2 ( )sin 2 ,

:

:

1ˆ ( ) ( ) Hilpert transform of ( )

SSB c cS t m t f t m t f t

USB

LSB

m t m t m tt

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Selective filtering method

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Selective filtering method (Cont.)

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Phase–Shift Method

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Phase–Shift Method

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Hilbert transform

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Phase–Shift Method (Cont.)

• Advantages:

– Does not deploy bandpass filter.

– Suitable for message signals with frequency content down to dc.

• Disadvantage:

– Practical realization of a wideband 90o phase shift circuit is difficult.

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Demodulation of SSB Signals• Demodulation of SSB signals can be accomplished

by using a synchronous detector as used in the demodulation of normal AM and DSBSC signals.

• If we want to use an envelope detector, it can be shown that we must insert a pilot carrier signal Acos(2 fct) to the SSB signal,

where A >> m(t) and A >> m^(t).

• The pilot signal carries most of the transmission power which becomes inefficient.

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Example

• A DSB-LC signal is generated using a 1-kHz carrier and the input is m(t)= cos(200t). The modulation index is 80%. The lower sideband is attenuated (assume ideal filter). Find an expression for the resulting SSB-LC signal if it develops 0.58 W across a one-Ohm resistive load.

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Vestigial-Sideband Modulation (VSB)

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VSB modulator

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Demodulation of VSB• Demodulation of VSB signals can be

accomplished by using a synchronous detector.

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Vestigial-Sideband Modulation (VSB)

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VSB modulator

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Demodulation of VSB• Demodulation of VSB signals can be

accomplished by using a synchronous detector.

Transfer function of LPF in VSB receiver

1( ) ,

( ) ( )LPFBPF c BPF c

H f f BH f f H f f

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68

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VSB+C

• VSB modulated signals can also be detected by an envelope detector.

• As in the demodulation of a SSB signal, we need to send a pilot carrier signal, resulting an inefficient use of available transmitted power.

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Comparison of conventional AM, DSB-SC, SSB and VSB.

• Conventional AM: simple to modulate and to demodulate, but low power efficiency (50% max) and double the bandwidth

• DSB-SC: high power efficiency, more complex to modulate & demodulate, double the bandwidth

• SSB: high power efficiency, the same (message) bandwidth, more difficult to modulate & demodulate.

• VSB: lower power efficiency & larger bandwidth but easier to implement.

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Multiplexing• Multiplexing: combining a number of message

signals into a composite signal to transmit them simultaneously over a wideband channel.

• Two commonly-used types: time-division multiplexing (TDM) and frequency division multiplexing (FDM).

• TDM: transmit different message signals in different time slots (mostly digital).

• FDM: transmit different message signals in different frequency slots (bands) using different carrier frequencies.

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FDM

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Time Division Multiplexing

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TDM

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AM receiver for many radio stations ?

Frequency mixing

• It is desired in communication system to translate the spectrum of the modulated signal up word or down word in frequency to be centered around desired frequency

0

0

: up conversio

: down conversio

l c

l c

c l

f f f

f f nf

f f n

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Superheterodyne AM Receiver

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• The RF amplifier amplifies the incoming signal and start the process of selecting the wanted station and rejecting the unwanted ones.

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The Mixer and the IF Amplifier

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84

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Introduction to Carrier Acquisition

• Consider a DSB-SC demodulator where a received signal is m(t) cos(ct) and the local carrier is 2 cos[(c+) t+] . Find the LPF output if

a) =0, and

b) =0

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Carrier Acquisition• To ensure identical carrier frequencies at the

transmitter and the receiver, we can use quartz crystal oscillators, which are generally very stable.

• At very high carrier frequencies, the quartz- crystal performance may not be adequate, we can use the phased-locked loop (PLL)

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Phased-Locked Loop (PLL)

• Phase-locked loop is one of the most commonly used circuit in both telecommunication and measurement engineering.

• PLL can be used to track the phase and the frequency of the carrier component of an incoming signal.

88

• A PLL has three basic components:

1. A voltage controlled oscillator

2. A multiplier

3. A loop filter H(s)

recovered carrier signal

vout(t)

vin(t) e0(t)x(t) Loop Filter

H(s)

Voltage-Controlled Oscillator (VCO)

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• In every application, the PLL tracks the frequency and the phase of the input signal. However, before a PLL can track, it must first reach the phase-locked condition.

• In general, the VCO center frequency differs from the frequency of the input signal.

• First the VCO frequency has to be tuned to the input frequency by the loop. This process is called frequency pull-in.

• Then the VCO phase has to be adjusted according to the input phase. This process is known as phase lock-in.

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How the PLL works?

)sin()( icin tAtv

)cos()( ocout tBtv

vout(t)

vin(t) e0(t)x(t) Loop Filter

H(s)

Voltage-Controlled Oscillator (VCO)

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Signal Squaring Method

( )2BPF

@ 2 c

PLL

2:1 Frequency divider

m(t) cos(c t)

k cos(c t)

c cos(2c t)

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Suggested Problems

• 4.2-1  4.2-2  4.2-3  4.2-4  4.2-6, 4.2-8 

• 4.3-1 4.3-2  4.3-3  4.3-4  4.3-7 4.3-8  

• 4.5-1  4.5-2  4.5-3  4.5-5, 4.5-6

• 4.6-1

• 4.8-1  4.8-2

• Read Section 4.9 (Television)