chapter 2 principle am (1)

7/28/2019 Chapter 2 Principle Am (1)

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Chapter 2: Amplitude Modulation (AM) Transmission and Reception

BENT 3113: Communication Principles

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2.1 Introduction

Information signals are transported between a transmitter and receiver over some form of

transmission medium. However, original signals are seldom in a form that is suitable fortransmission. Therefore, they must be transformed into a form that is more suitable for

transmission. The process of impressing low-frequency information signals onto a high-frequency carrier signal is calledmodulation.Demodulation is the reverse process where

the received signals are transformed back to their original form. In this chapter, the

student is first introduced to the fundamental concepts of amplitude modulation (AM)

before looking at the practical modulator and demodulator circuits used for AMmodulation.

2.2 Principles of AM

Amplitude modulation is the process of changing the amplitude of a relatively highfrequency carrier signal in proportion with the instantaneous value of the modulating

signal (information signal)

There are 2 inputs to the modulation device (often calledmodulator):1. A single, high-frequency RF carrier signal of constant amplitude2. Low-frequency information signals that maybe a single frequency or a

complex waveform made up of many frequencies

In the modulator, the information modulates the RF carrier producing a modulatedwaveform, often called an AM envelope

2.2.1 The AM Envelope

There are several types of amplitude modulation and the most commonly used is AMdouble-sideband full carrier (DSBFC) scheme. It is also called conventional AM. Thefollowing figure illustrates the relationship among the carrier, the modulating signal and

the modulated signal for conventional AM.

Signal representation:Carrier signal = ]2sin[ tfV cc

Modulating signal = ]2sin[ tfV mm

Modulated wave = ][tVam

When a modulating signal is applied to the carrier signal, the amplitude of theoutput wave varies in accordance with the modulating signal


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Figure 2.1: AM Generation

2.2.2 AM Frequency Spectrum and Bandwidth

The output envelope is a complex wave made up of a DC voltage, the carrier frequency,

and the sum )(mc

ff + and difference )(mc

ff frequencies. These sum and difference

frequencies are displaced from carrier frequency by an amount equal to modulating

frequency. I.e., an AM signal spectrum contains frequency components spaced mf Hz on

either side of the carrier as shown in Figure 2.2:

Figure 2.2: Frequency spectrum of an AM DSBFC wave

The AM spectrum ranges from (max)mc ff to (max)mc ff +


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Parameters:Lower sideband(LSB) = band of frequencies between (max)mc ff and cf

Lower side frequency (LSF) = any frequency within LSB

Upper sideband(USB) = band of frequencies between cf and (max)mc ff +

Upper side frequency (USF) = any frequency within USB

Bandwidth = twice the highest modulating signal frequency(max)2 mf=

2.2.3 Coefficient of Modulation and Percent Modulation

Coefficient of modulation is a term used to describe the amount of amplitude change

present in an AM waveform

Percent modulation is the coefficient of modulation stated as a percentage

Mathematical representation:c

m

E

Em = (2.1)

100=c

m

E

EM (2.2)

where m = modulation coefficient where usually 1m M =percent modulation

mE = peak change in the amplitude of the output waveform

cE = peak amplitude of the unmodulated carrier

Graphical representation of the relationship among m, mE and cE :

Figure 2.3: Modulation coefficient, mE and cE


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Based from Figure 2.3:

)(2

1minmax VVEm = (2.3)

)(2

1minmax VVEc += (2.4)

Thus 100)(

)(

minmax

minmax +=

VV

VVM (2.5)

mE is also defined as the sum of the voltages from upper and lower sidefrequencies

lsfusfm EEE +=

Also, lsfusf EE =

Therefore )(4

1

2

)(2/1

2minmax

minmax VVVVE

EE mlsfusf =

=== (2.6)

2.2.4 AM Voltage Distribution and Analysis

From previous section, we know that amplitude of the AM wave varies proportional to

the amplitude of the modulating signal and the maximum amplitude of the AM wave

is mc EE + . Given an unmodulated carrier and a modulating signal as,

)2sin()( tfEtv ccc = (2.7)

)2sin()( tfEtv mmm = (2.8)

The modulated wave can be expressed as:

)]2)][sin(2sin([)( tftfEEtv cmmcam += (2.9)

where cE = peak carrier amplitude

cf = carrier frequency, mf = modulating frequency,

mE = peak modulating amplitude / peak change in the amplitude of the envelope

Substituting Equation (2.1) into Equation (2.9), we get)]2)][sin(2sin([)( tftfmEEtv cmccam += (2.10)

Rearranging Equation (2.10) )]2sin()][2sin(1[)( tfEtfmtv ccmam += (2.11)I.e. it can seen that the modulating signal contains a constant component and asinusoidal component at the modulating signal frequency


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Next, expanding Equation (2.11) yields)]2)][sin(2sin([)2sin()( tftfmEtfEtv cmcccam +=

Using trigonometric function, above equation can be represented as:

])(2cos[2

])(2cos[2

)2sin()( tffmE

tffmE

tfEtv mcc

mc

c

ccam ++= (2.12)

Voltage spectrum for representing AM DSBFC wave (Equation (2.12)) :

Figure 2.4: Voltage spectrum for AM DSBFC wave

From Equation (2.12), there are few characteristics of AM DSBFC can be deduced:

1. The amplitude of carrier is unaffected by the modulation process2. The amplitude of USF and LSF depends on both the carrier amplitude and the

coefficient of modulation3. For 100 % modulation (m = 1) and from previous section

c

cc

clsfusfcmc EEE

EEEEEEV 222

(max) =++=++=+=

022

(min) ====cc

clsfusfcmc

EEEEEEEEV

I.e. the maximum peak amplitude of an AM envelope is cEV 2(max) = and the

minimum peak amplitude of the envelope is 0(min) =V .


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2.2.5 AM Power Distribution

The average power dissipated in a load by an unmodulated carrier is equal to therms carrier voltage divided by the load resistance

RE

REP ccc

2)()707.0(

22

== (2.13)

Besides that, the upper and lower sideband powers, usbP and lsbP respectively, aregiven as

R

mEPP clsbusb

2

)2/( 2==

Rearranging this equation

==R

EmPP clsbusb

24

22

(2.14)

Substituting Equation (2.13) into Equation (2.14) gives

4

2

c

lsbusb

PmPP == (2.15)

Total power in an amplitude-modulated wave is equal to the sum of the powers ofthe carrier, the upper sideband and the lower sideband. I.e. the total power in an

AM DSBFC wave:

lsbusbct PPPP ++=

2

2c

ct

PmPP += (2.16)

Note that the total power in an AM envelope increases with modulation

Figure 2.5: Power spectrum for an AM DSBFC wave


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2.2.6 Modulation by a Complex Information Signal

In previous section, coefficient of modulation, voltage and power distribution for AM

DSBFC wave were analyzed for a single frequency modulating signal. In practice, the

modulating signal is often a complex waveform made up of many sine waves with

different amplitudes and frequencies.

Consider a modulating signal containing two frequencies, 1mf and 2mf . Themodulated wave obtained will contain the carrier and two sets of side frequencies

spaced symmetrically about the carrier

])(2cos[2

1])(2cos[

2

1)2sin()( 11 tfftfftftv mcmccam ++=

])(2cos[2

1])(2cos[

2

122 tfftff mcmc ++ (2.17)

For coefficient of modulation for a case involving several modulating frequencies:22

3

2

2

2

1 .... nt mmmmm ++++= (2.18)

Consequently, the combined coefficient of modulation, tm , can be used todetermine the total sideband and total transmitted powers

24

22

tc

sbt

ct

lsbtusbt

mPP

PmPP === (2.19)

Thus2

2

tcct

mPPP += (2.20)

Where usbtP = total upper sideband power

lsbtP = total lower sideband power

sbtP = total sideband power

tP = total transmitted power

chapter 2 principle am (1)

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