Analog Signal Modulation AM & FM Sept 12, 2002. Announcements Homework: –Chapter 3: 4, 6, 12, 16,...

Analog Signal ModulationAM & FM

Sept 12, 2002

Announcements

• Homework:– Chapter 3: 4, 6, 12, 16, 18

– Chapter 4: 6, 8, 12, 14

• Class URL:http://teal.gmu.edu/ececourses/tcom500_2/lectures.html

• Test #1– Sept 26, 7:30-8:30 PM

– Closed book, closed notes, formulas will be provided. Bring calculator.

Class Objectives

• AM Modulation

• FM Modulation

Modulation

• What is modulation?– Modulation is to vary a carrying signal’s

amplitude, frequency or phase in order to convey information.

• Why modulate?– Avoid interference by efficient use of spectrum– Propagation characteristics– Antenna constraints based on wavelength

AM - Amplitude Modulation

• Technique which varies the amplitude of a carrier signal in proportion to the instantaneous amplitude of the modulating signal

• Mostly used in commercial AM band as well as shortwave radio stations, maritime, aviation, military, and amateur operators.

• The most common modulating signal is the human voice, although can transmit music as well.

3 kHz Signal

0 200 400 600 800 10001

0

1

sine1 t( )

t

Amplitude = volts

t = milliseconds

40 kHz Carrier

Amplitude = volts

t = milliseconds

0 200 400 600 800 10001

0

1

carrier t( )

t

40 kHz Carrier Modulated by 3 kHz Signal

0 200 400 600 800 10002

1

0

1

2

AM_Signal t( )

t

Amplitude = volts

t = milliseconds

FIGURE 3-4 The AM waveform with sine wave modulation shown in the time domain: (a) modulating voltage; (b) carrier frequency; (c) resulting AM waveform.

Warren HiokiTelecommunications, Fourth Edition

Copyright ©2001 by Prentice-Hall, Inc.Upper Saddle River, New Jersey 07458

All rights reserved.

FIGURE 3-5 Measuring the modulation index, m, using: (a) peak values; (b) peak-to-peak values.




AM Signal in Time Domain

Carrier frequency LSB USB

(lower side-band) (upper side-band)

tmV

tmV

tVV mcc

mcc

ccAM )cos(2

)cos(2

sin

FIGURE 3-6 The AM waveform: (a) time domain; (b) frequency domain.




FIGURE 3-7 Power distribution for the AM wave with sine-wave modulation.




FIGURE 3-8 The AM waveform with 100% modulation (m = 1): (a) time domain; (b) frequency domain.




FIGURE 3-9 The resulting AM waveforms for various modulating voltages: (a) triangle wave; (b) pulse train; (c) voice.




FIGURE 3-10 Double-sideband suppressed carrier (DSBSC) with sine-wave modulation: (a) time domain; (b) frequency domain.




FIGURE 3-11 Block diagram of a balanced modulator.




FIGURE 3-15 In an SSBSC or SSB system, the LSB or USB is selected for transmission. Here, the USB is selected.




FIGURE 3-16 (a) Block diagram of an SSB dual-conversion filter system; (b) frequency response depicting the increased frequency separation between the LSB and USB because of dual conversion.




FIGURE 3-17 (a) Standard FCC channel format for monochrome and color picture transmissions in the United States; (b) channel 2 frequency assignment.




Class Exercise

Principal AM Characteristics• The frequency power spectrum has a dominant

carrier and two sidebands called the upper and lower sidebands (USB/LSB).

• USB and LSB components are mirror images of each other and contain the same information.

• The transmit power varies continuously as a function of the modulation index.

• The carrier can be suppressed in order to lower transmit power requirement. (DSBSC)

• SSB is produced when one of the sidebands is filtered (USB or LSB).

Frequency and Phase Modulation

• When the frequency of a carrier is varied in accordance to the instantaneous amplitude of the modulating signal, the result is frequency modulation (FM).

• When the phase of a carrier is varied in accordance to the instantaneous amplitude of the modulating signal, the result is phase modulation (PM).

• FM and PM techniques are very similar mathematically.

• In practice:– FM is more common in analog modulation

(handheld radios, commercial FM radio)– PM is more common in digital modulation

(spread spectrum, microwave point-to-point)

Frequency and Phase Modulation

Key FM Characteristics

• FM is more immune to noise that AM– Noise effects are less on frequency than

amplitude

• FM requires more bandwidth than AM– Allows higher fidelity for voice and music

• Mathematical description is more complicated than AM

)sinsin( tmtAV mfccFM

FM Signal in Time Domain

We can see that having a sine function within another sine function is much more complex toevaluate than the additive terms of AM.

Modulation index

• Modulation index m is the ratio of the maximum frequency carrier deviation and the frequency of the modulating signal

mff

m

mf

ffc

m

FIGURE 4-1 The FM and PM waveforms for sine-wave modulation: (a) carrier wave; (b) modulation wave; (c) FM wave; (d) PM wave. (Note: The derivative of the modulating sine wave is the cosine wave shown by the dotted lines. The PM wave appears to be frequency modulated by the cosine wave.)




FIGURE 4-3 Spectral components of a carrier of frequency, fc, frequency modulated by a sine wave with frequency fm. (Source: James Martin, Telecommunications and the Computer, 2nd ed. [Englewood Cliffs, N.J.: Prentice-Hall, 1976], p. 218. Reprinted with permission from the publisher.)







FIGURE 4-4 Frequency spectrum of an FM signal with a modulation index, mf, of 2.4 (first carrier null or eigenvalue). Note that the carrier amplitude goes to zero. Relative amplitudes are approximated from Table 4-1 using mf = 2.5.




FIGURE 4-5 Amplitude versus frequency spectrum for various modulation indices (fm fixed, & varying): (a) mf = 0.25; (b) mf = 1; (c) mf = 2; (d) mf = 5; (e) mf = 10.







0 200 400 600 800 10001

0

11

1

sine1 t( )

1 1031 t

FM – MathCad® Example

0 200 400 600 800 100010

0

109.98

9.98

carrier t( )

1 1031 t

0 200 400 600 800 100010

5

0

5

1010

10

FM_Signal t( )

1 1031 t

Bandwidth Requirement for FM

• Bessel Functions:

• Carson’s Rule:

• Bessel Function is slightly more conservative that Carson’s Rule

B W f m 2 ( )

B W n f m 2 ( )

Example of FM Systems

• Commercial FM Broadcast– δ is 75kHz

– Modulation frequencies 100Hz and 15 kHz (much better than AM)

– Each channel has a 200 kHz width

• Narrowband– Mostly used in handheld radio applications and first generation cell

phones (AMPS)

– Channel widths could range from 6.25 kHz to 30 kHz

– Low modulation index

FM Highlights

• FM signal has constant power level

• Has much higher SNR than AM

• Signal quality improves with greater modulation index– The price to pay for this feature is the need for

more bandwidth

Class Exercises

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Analog Signal Modulation AM & FM Sept 12, 2002. Announcements Homework: –Chapter 3: 4, 6, 12, 16,...

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