Chapter 3. Amplitude Modulation

Essentials of Communication Systems Engineering

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Amplitude Modulation Speech, music, images, and video are examples of analog

signals Speech and audio signals :

The signal has just one component, which measures air pressure Speech: Bandwidth of up to 4 kHz Music signal : Bandwidth of 20 kHz

Color video The signal has four components, namely, the red, green, and blue color

components, plus a fourth component for the intensity Video signals have a much higher bandwidth, about 6 MHz

The general trend is the digital transmission of analog signals We still have a significant amount of analog signal transmission,

especially in audio and video broadcast In this chapter, we study amplitude-modulation systems, where

the message signals change the amplitude of the carrier

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INTRODUCTION TO MODULATION Assume that the analog signal m(t) is denoted as follows

A lowpass signal of bandwidth W, that is, M(f) = 0, for |f| > W The power content of this signal is denoted by

The message signal m(t) is transmitted through the channel by impressing it on a carrier signal of the form

A, fc, c : Carrier amplitude, Carrier frequency, Carrier phase , respectively

c depends on the choice of the time origin. we assume that the time origin is chosen such that c = 0

Modulation converts m(t) from lowpass signal to bandpass signal, in the neighborhood of the carrier frequency fc

2/

2/

2)(

1lim

T

TTm dttm

TP

)2cos()( ccc tfAtc

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INTRODUCTION TO MODULATION Modulation of the carrier c(t) by the message signal m(t) is perfo

rmed to achieve the following objectives Match the passband characteristics of the channel

To translate the lowpass signal to the passband of the channel so that the spectrum of the transmitted bandpass signal will match the passband characteristics of the channel

Simplify the structure of the transmitter For instance, in the wireless communications, transmission of the signal at lo

w frequencies requires huge antennas Modulation helps translate the frequency band to higher frequencies, thus req

uiring smaller antennas This simplifies the structure of the transmitter (and the receiver)

Frequency-division multiplexing (FDM) To accommodate for the simultaneous transmission of signals from se

veral message sources, by means of FDM (See Section 3.4.)

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AMPLITUDE MODULATION (AM) In amplitude modulation, the message signal m(t) is impresse

d on the amplitude of the carrier signal c(t) = Accos(2fct)

This results in a sinusoidal signal whose amplitude is a function of the message signal m(t)

There are several different ways of amplitude modulating the carrier signal by m(t)(a) Double sideband, suppressed-carrier AM (DSB-SC A

M)(b) Conventional double-sideband AM(c) Single-sideband AM (SSB AM)(d) Vestigial-sideband AM (VSB AM)

Each results in different spectral characteristics for the transmitted signal

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Double-Sideband Suppressed-Carrier AM

A double-sideband, suppressed-carrier (DSB-SC) AM signal is obtai

ned by multiplying the message signal m(t) with the carrier c(t)

Amplitude-modulated signal

An example of the message signal m(t), the carrier c(t), and the modulated sign

al u (t) are shown in Figure 3.1

This figure shows that a relatively slowly varying message signal m(t) is chang

ed into a rapidly varying modulated signal u(t), and due to its rapid changes wit

h time, it contains higher frequency components

At the same time, the modulated signal retains the main characteristics of the m

essage signal, and it can be used to retrieve the message signal at the receiver

)2cos()()()()( tftmAtctmtu cc

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Double-Sideband Suppressed-Carrier AM

Figure 3.1 An example of message, carrier, and DSB-SC modulated signals

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Spectrum of the DSB-SC AM Signal Spectrum of the modulated signal can be obtained by taking th

e FT of u(t)

The magnitude of the spectrum of the message signal m(t) has been translated or shifted in frequency by an amount fc

The bandwidth occupancy, of the amplitude-modulated signal is 2W, whereas the bandwidth of the message signal m(t) is W

The channel bandwidth required to transmit the modulated signal u(t) is Bc = 2W

)]()([2

)( ccc ffMffM

AfU Magnitude spectra of

the message signal m(t) and the DSB-AM signal u(t)

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Spectrum of the DSB-SC AM Signal The frequency content of the modulated signal u(t) in

the frequency band | f | > fc is called the upper sideband of U(f)

The frequency content in the frequency band | f | < fc is called the lower sideband of U(f)

Either one of the sidebands of U(f) contains all the frequencies that are in M(f)

Since U(f) contains both the upper and the lower sidebands, it is called a double-sideband (DSB) AM signal

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Spectrum of the DSB-SC AM Signal

The other characteristic of the modulated signa

l u(t) is that it does not contain a carrier compo

nentThat is, all the transmitted power is contained in th

e modulating (message) signal m(t)

For this reason, u(t) is called a suppressed-carrier

signal

Therefore, u(t) is a DSB-SC AM signal.

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Power Content of DSB-SC Signals The power content of the DSB-SC signal

Pm indicates the power in the message signal m(t)

Since the envelope of m2(t)cos(4fct) is slowly varying, the positive and the negative halves of each cycle have almost the same amplitude

Thus, the overall integral of m2(t)cos(4fct) is almost zero

mc

T

T cT

c

T

T ccT

T

TTx

PA

dttftmT

A

dttftmAdttuT

P

2)4cos(1)(

1lim

2

)2(cos)(lim)(1

lim

22/

2/

22

2/

2/

2222/

2/

2

Plot of m2(t)cos(4fct)