Chapter 2 Fm

8/10/2019 Chapter 2 Fm

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Analog Modulation The purpose of a communication system is to transmit information signals

(baseband signals) through a communication channel

The term basebandis used to designate the band of frequencies representing the

original signal as delivered by the input transducer

For example, the voice signal from a microphone is a baseband signal, and

contains frequencies in the range of 0-3000 Hz The hello wave is a baseband signal:


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Since this basebandsignal must be transmitted through a communication channel(such as air or cable) using electromagnetic waves, a procedure is needed to shift therange of basebandfrequencies to other frequency ranges suitable for transmission;and, a corresponding shift back to the original frequency range after reception. This iscalled the process of modulationand demodulation

Remember the radio spectrum:

For example, an AM radio system transmits electromagnetic waves with frequencies ofaround a few hundred kHz (MF band)

The FM radio system operates with frequencies in the range of 88-108 MHz (VHFband)

AM radio FM radio/TV


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Since the basebandsignal contains frequencies in the audio frequencyrange (3 kHz), some form of frequency-band shifting must beemployed for the radio system to operate properly

This process is accomplished by a device called a modulator

The transmitterblock in any communications system contains themodulatordevice

The receiverblock in any communications system contains thedemodulatordevice

The modulator modulatesa carrier wave(the electromagnetic wave)which has a frequency that is selected from an appropriate band inthe radio spectrum

For example, the frequency of a carrier wave for FM can bechosen from the VHF band of the radio spectrum

For AM, the frequency of the carrier wave may be chosen to bearound a few hundred kHz (from the MF band of the radiospectrum)

The demodulator extracts the original basebandsignal from thereceived modulated signal

In Summary:

Modulation is the process of impressing a low-frequency informationsignal (baseband signal) onto a higher frequency carrier signal


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FREQUENCY MODULATION


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FREQUENCY MODULATION


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FIGURE 7-20 LIC direct FM modulator--simplified block diagram

Tomasi

Electronic Communications Systems, 5eCopyright 2004 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

All rights reserved.


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8

Frequency Modulation

Carrier wave

Baseband signal

Modulated waveFrequency varying-

amplitude constant

Large amplitude:

high frequencySmall amplitude:

low frequency


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FM (frequency modulation) signal0

( ) cos 2 2 ( )t

c c fs t A f t k m d

0

0

: frequency sensitivity

instantanous frequency ( ) ( )

angle ( ) 2 ( )

2 2 ( )

f

i c f

t

i i

t

c f

k

f t f k m t

t f d

f t k m d

(Assume zero initial phase)


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FM Characteristics

Characteristics of FM signals

Zero-crossings are not regular Envelope is constant

FM and PM signals are similar


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FM (frequency modulation) signal0

( ) cos 2 2 ( )t

c c fs t A f t k m d

0

0

: frequency sensitivity

instantanous frequency ( ) ( )

angle ( ) 2 ( )

2 2 ( )

f

i c f

t

i i

t

c f

k

f t f k m t

t f d

f t k m d

(Assume zero initial phase)

( ) cos(2 )m m

m t A f t cos(2 )i c f m m

f f k A f t

0

Let

2 cos(2 )21 1 1

2 2 2

1 2 cos(2 )

2

t

f m mc

i

c f m m t

d k A f d d f tdf

dt dt dt

f k A f


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Example

m(t)

0 T 2T t

kandk

.Ttfork)t(and

t0fork)t(mk)t(isfrequencyousinstantaneThe

t.-T)-(t-d)m(d)m(d)m(,1-m(t)Ttfor

andtd)m(,1m(t)t0For0.tatstartsm(t)Assume

).d)m(ktcos(A)t(

fcminifcmaxi

2T

fci

2T

fcfci

2T

2T

t

0

t

02T

t

02T

t

-

fcFM

2

T

2

T

t

)t(FM

Consider m(t)- a square wave- as shown. The FM wave for this m(t) is

shown below.


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TABLE 7-3 Bessel Functions of the First Kind,Jn(m)

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FIGURE 7-6 Frequency spectrum for Example 6-2

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FIGURE 7-7 Frequency spectrum for Example 7-3

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FIGURE 7-8A Output frequency spectrums for Example 7-

5: (a) frequency spectrums for FM and PM

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FIGURE 7-8B Output frequency spectrums for Example 7-

5: (b) frequency spectrums for FM and PM;

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FIGURE 7-8C Output frequency spectrums for Example 7-

5: (c) frequency spectrum for FM

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FIGURE 7-8D Output frequency spectrums for Example 7-

5: (d) frequency spectrum for PM

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Modulation Index

Indicate by how much the modulated variable

(instantaneous frequency) varies around its

unmodulated level (message frequency)

Bandwidth

max | ( ) |AM (envelope): ,

1max | ( ) |

FM (frequency):

a

f

m

k m t

k m t

f

A

t

dmta )()(

...sin)(

!3cos)(

!2sin)(cos))(Re()(

3

2

2

2

twtak

twtak

twtaktwAtt cf

c

f

cfc


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Bandwidth of FM

Facts

FM has side frequencies extending to infinite frequency

theoretically infinite bandwidth

But side frequencies become negligibly small beyond apointpractically finite bandwidth

FM signal bandwidth equals the required transmission

(channel) bandwidth

Bandwidth of FM signal is approximately by

Carsons Rule (which gives lower-bound)


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Carsons Rule

Nearly all power lies within a bandwidth of

For single-tone message signal with frequency fm

For general message signal m(t) with bandwidth (or highest

frequency) W

2 2 2( 1)T m m

B f f f

2 2 2( 1)T

B f W D W

where is deviation ratio (equivalent to ),

max ( )f

fD

W

f k m t


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AM vs. FM

AM requires a simple circuit, and is very easy to generate.

It is simple to tune, and is used in almost all short wave broadcasting.

The area of coverage of AM is greater than FM (longer wavelengths(lower frequencies) are utilized-remember property of HF waves?)

However, it is quite inefficient, and is susceptible to static and otherforms of electrical noise.

The main advantage of FM is its audio quality and immunity to noise.Most forms of static and electrical noise are naturally AM, and an FMreceiver will not respond to AM signals.

The audio quality of a FM signal increases as the frequency deviation

increases (deviation from the center frequency), which is why FMbroadcast stations use such large deviation.

The main disadvantage of FM is the larger bandwidth it requires


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Comparison between PM and FM


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Relations between FM and PM

0FM of ( ) PM of ( )

t

m t m d

( )PM of ( ) FM of

dm tm t

dt


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FM/PM Example (Time)

FIGURE 7-3 Phase and frequency modulation of a sine-wave carrier by a sine-


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FIGURE 7 3 Phase and frequency modulation of a sine wave carrier by a sine

wave signal: (a) unmodulated carrier; (b) modulating signal; (c) frequency-

modulated wave; (d) phase-modulated wave

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FM/PM Example (Frequency)


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TABLE 7-2 Angle Modulation Summary

Tomasi Copyright 2004 by Pearson Education, Inc.

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