Analog Signal Modulation AM & FM Feb 5, 2002

Announcement Class Test Out option available Email: Homework: Test: Feb 23, 2002 Contact Dr. Jeremy Allnutt, jallnutt@gmu.edu Email: ebonilla@gmu.edu Homework: Chapter 3: 4, 6, 12, 16, 18 Chapter 4: 6, 8, 12, 14

Class Objectives AM Modulation FM Modulation

Modulation What is modulation? Why modulate? 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 Amplitude = volts t = milliseconds

40 kHz Carrier Amplitude = volts t = milliseconds

40 kHz Carrier Modulated by 3 kHz Signal 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 Hioki Telecommunications, 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. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

AM Signal in Time Domain Carrier frequency LSB USB (lower side-band) (upper side-band)

FIGURE 3-6 The AM waveform: (a) time domain; (b) frequency domain. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FIGURE 3-7 Power distribution for the AM wave with sine-wave modulation. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FIGURE 3-8 The AM waveform with 100% modulation (m = 1): (a) time domain; (b) frequency domain. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FIGURE 3-9 The resulting AM waveforms for various modulating voltages: (a) triangle wave; (b) pulse train; (c) voice. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FIGURE 3-10 Double-sideband suppressed carrier (DSBSC) with sine-wave modulation: (a) time domain; (b) frequency domain. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FIGURE 3-11 Block diagram of a balanced modulator. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FIGURE 3-15 In an SSBSC or SSB system, the LSB or USB is selected for transmission. Here, the USB is selected. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

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. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FIGURE 3-17 (a) Standard FCC channel format for monochrome and color picture transmissions in the United States; (b) channel 2 frequency assignment. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

Class Exercises and Demo

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).

Frequency and Phase Modulation 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)

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

FM Signal in Time Domain We can see that having a sine function within another sine function is much more complex to evaluate 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

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.) Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

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.) Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

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. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

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. Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

Warren Hioki Telecommunications, Fourth Edition Copyright ©2001 by Prentice-Hall, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FM – MathCad® Example

Bandwidth Requirement for FM Bessel Functions: Carson’s Rule: Bessel Function is slightly more conservative that Carson’s Rule

Example of FM Systems Commercial FM Broadcast Narrowband 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 and Demo