Electronic Communications Systems Fundamentals Through Advanced PDF

Electronic i n i in linear i FUNDAMENTALS THROUGH ADVANCED WAYNE TOM ASI M lid, MM ELECTRONIC COMMUNICATIONS SYSTEMS Fundamentals Through Advanced Wayne Tomasi Mesa Community College PRENTICE H...

Electronic i n i in linear i FUNDAMENTALS THROUGH ADVANCED WAYNE TOM ASI M lid, MM ELECTRONIC COMMUNICATIONS SYSTEMS Fundamentals Through Advanced Wayne Tomasi Mesa Community College PRENTICE HALL, Englewood Cliffs, New Jersey 07632 Library of Congress Cataloging-in-Publication Data Tomasi, Wayne. Electronic communications systems. Includes index. 1. Telecommunication systems. I. Title. TK5101.T625 1988 62 1.38 '04 13 87-7205 ISBN 0-13-250804-^ Chapters 1 through 12 are published a Fundamentals of Electronic Communications Systenu by Wayne Tomasi (© 1988) chapters 13 through 22 are published as Advanced Electronic Communications Systenu /Hen County Pubk Uhm by Wayne Tomasi (© 1987] " Wayne, Indiana Editorial/production supervision an interior design: Kathryn Pavele Cover design: Diane Sax Cover photo: Courtesy of Sperry Corporatio Manufacturing buyer: Margaret Rizzi/Lorraine Fumqs © 1988 by Prentice-Hall, Inc. = A Division of Simon & Schuster => Englewood Cliffs, New Jersey 07632 All rights reserved. No part of this book may i reproduced, in any form or by any mean without permission in writing from the publish* Printed in the United States of Ameri 10 9 8 7 6 5 ISBN D-13-2SDflDt Prentice-Hall International (UK) Limited, Lo< Prentice-Hall of Australia Pty. Limited,.S Prentice-Hall Canada Inc., To Prentice-Hall Hispanoamericana, S.A.. M Prentice-Hall ok India Private Limited. New Prentice-Hall of Japan, Inc.. Ti Simon & Schuster Asia Pte. Ltd.. Singo\ Editora Prentice-Hall do Brasil. Ltda., Rio dc Jan  To my loving and very patient wife, Cheryl  CONTENTS PREFACE xi Chapter 7 INTRODUCTION TO ELECTRONIC COMMUNICATIONS 1 Introduction 1 Signal Analysis 5 Electrical Noise 18 Multiplexing 29 Questions 32 Problems 33 Chapter 2 FREQUENCY GENERATION 35 Introduction 35 Oscillators 35 Frequency Multipliers 70 Mixing 70 Questions 78 Problems 78  1 vi Contents Chapter 3 AMPLITUDE MODULATION TRANSMISSION 81 Introduction 8 Mathematical Analysis of AM Double-Sideband Full Carrier 89 Circuits for Generating AM Double-Sideband Full Carrier 98 AM Double-Sideband Full-Carrier Transmitters 113 Trapezoidal Patterns 117 Carrier Shift 120 Questions 122 Problems 122 Chapter 4 AMPLITUDE MODULATION RECEPTION 126 Introduction 1 26 AM Receivers 130 AM Receiver Circuits 145 Automatic Gain Control and Squelch 163 Double-Conversion AM Receivers 168 Questions 169 Problems 170 Chapter 5 PHASE-LOCKED LOOPS AND FREQUENCY SYNTHESIZERS 1 72 Introduction 172 Phase-Locked Loop 172 Frequency Synthesizers 187 Large-Scale Integration Programmable Timers 205 Questions 214 Problems 214 Chapter 6 SINGLE-SIDEBAND COMMUNICATIONS SYSTEMS 217 Introduction 217 Single-Sideband Systems 217 Circuits for Generating Single-Sideband 224 Single-Sideband Transmitters 232  8 Contents vii Single-Sideband Receivers 254 Questions 261 Problems 262 Chapter 7 ANGLE MODULATION TRANSMISSION 264 Introduction 264 Angle Modulation 264 Frequency Modulation Transmission 290 Questions 314 Problems 315 Chapter 8 ANGLE MODULATION RECEIVERS AND SYSTEMS 318 Introduction 31 FM Receivers 319 FM Systems 340 Questions 358 Problems 358 Chapter 9 TRANSMISSION LINES 360 Introduction 360 Transverse Electromagnetic Waves 360 Types of Transmission Lines 363 Transmission-Line Equivalent Circuit 367 Transmission-Line Wave Propagation 373 Transmission-Line Losses 376 Incident and Reflected Waves 378 Standing Waves 380 Transmission-Line Input Impedance 387 Questions 395 Problems 396 Chapter W WAVE PROPAGATION 398 Introduction 398 Rays and Wavefronts 398 viii Contents Electromagnetic Radiation 400 Spherical Wavefront and the Inverse Square Law 401 Wave Attenuation and Absorption 403 Optical Properties of Radio Waves 405 Propagation of Waves 412 Propagation Terms and Definitions 418 Questions 421 Problems 421 Chapter 11 ANTENNAS 423 Introduction 423 Terms and Definitions 424 Basic Antennas 433 Antenna Arrays 442 Special-Purpose Antennas 445 Questions 449 Problems 450 Chapter 12 BASIC TELEVISION PRINCIPLES 452 Introduction 452 History of Television 452 Monochrome Television Transmission 454 The Composite Video Signal 456 Monochrome Television Reception 467 Color Television Transmission and Reception 475 Questions 483 Problems 484 Chapter 13 DIGITAL COMMUNICATIONS 487 Introduction 487 Information Capacity 489 Digital Radio 490 Frequency Shift Keying (FSK) 490 Phase Shift Keying (PSK) 496 Binary Phase Shift Keying (BPSK) 496 Quaternary Phase Shift Keying (QPSK) 502 Contents jx Eight-Phase PSK 510 Sixteen-Phase PSK 518 Quadrature Amplitude Modulation (QAM) 518 Eight QAM 518 Sixteen QAM 522 Bandwidth Efficiency 527 PSK and QAM Summary 528 Carrier Recovery 529 Differential Phase Shift Keying 530 Differential BPSK 530 Clock Recovery 532 Probability of Error and Bit Error Rate 533 Applications for Digital Modulation 533 Questions 534 Problems 535 Chapter 14 DATA COMMUNICATIONS 536 Introduction 536 History of Data Communications 536 Data Communications Circuits 537 Data Communications Codes 540 Error Control 547 Synchronization 557 Data Communications Hardware 559 Serial Interfaces 568 Transmission Media and Data Modems 575 Questions 581 Problems 583 Chapter 15 DATA COMMUNICATIONS PROTOCOLS 584 Introduction 584 Public Data Network 609 ISO Protocol Hierarchy 612 CCITT X.25 User-to-Network Interface Protocol 614 Local Area Networks 617 Questions 620 Problems 622  1 x Contents Chapter 16 DIGITAL TRANSMISSION 623 Introduction 623 Pulse Modulation 624 Pulse Code Modulation (PCM) 625 PCM Codes 630 Delta Modulation PCM 650 Adaptive Delta Modulation PCM 653 Differential Pulse Code Modulation 653 Questions 654 Problems 655 Chapter 17 DIGITAL MULTIPLEXING 657 Introduction 657 Time-Division Multiplexing 657 Tl Digital Carrier System 658 CCITT Time-Division-Multiplexed Carrier System 663 CODECS 665 2913/14 Combo Chip 666 North American Digital Hierarchy 680 Line Encoding 685 T Carriers 688 Frame Synchronization 692 Bit Interleaving Versus Word Interleaving 695 Questions 695 Problems 696 Chapter 18 FREQUENCY-DIVISION MULTIPLEXING 697 Introduction 697 AT&T'S FDM Hierarchy 698 Composite Baseband Signal 700 L Carriers 71 Hybrid Data 714 Questions 720 Problems 720  1 Contents x j Chapter 19 MICROWAVE COMMUNICATIONS AND SYSTEM GAIN 722 Introduction 722 Microwave System Simplified 722 Microwave Repeaters 724 Diversity 725 Protection Switching 729 Microwave Radio Stations 732 System Gain 738 Questions 750 Problems 75 Chapter 20 SATELLITE COMMUNICATIONS 752 Introduction 752 History of Satellites 753 Orbital Satellites 754 Geostationary Satellites 755 Orbital Patterns 756 Summary 758 Look Angles 758 Orbital Spacing and Frequency Allocation 761 Radiation Patterns: Footprints 763 Satellite System Link Models 766 Satellite System Parameters 769 Satellite System Link Equations 780 Link Equations 781 Link Budget 782 Nonideal System Parameters 788 Questions 788 Problems 789 Chapter 2 7 SATELLITE MULTIPLE-ACCESS ARRANGEMENTS 791 FDM/FM Satellite Systems 791 Multiple Accessing 793 Frequency Hopping 805 Channel Capacity 805  1 1 xii Contents Questions 807 Problems 808 Chapter 22 FIBER OPTICS COMMUNICATIONS 809 Introduction 809 History of Fiber Optics 810 Fiber Optic Versus Metallic Cable Facilities 81 Electromagnetic Spectrum 812 Fiber Optic Communications System 814 Optical Fibers 815 Light Propagation 817 Propagation of Light through an Optical Fiber 822 Optical Fiber Configurations 823 Comparison of the Three Types of Optical Fibers 827 Acceptance Angle and Acceptance Cone 828 Losses in Optical Fiber Cables 83 Light Sources 838 Light Detectors 845 Questions 848 Problems 848 Appendix A THE SMITH CHART 850 SOLUTIONS TO ODD-NUMBERED PROBLEMS 872 INDEX 880  PREFACE During the past two decades, the electronic communications industry has undergone some remarkable technological changes, primarily in the form of miniaturization. In the late 1950s and early 1960s, vacuum tubes were replaced with transistors. More recently, transistors are being replaced with multipurpose large-scale integrated circuits. The development of large-scale digital and linear integrated circuits has paved the way for many new and innovative approaches to electronic communications. Also, digital electronics principles are being implemented into electronic communications circuits and systems more and more each year. The need for these changes is attrributed to the continuing increase in the number of digital and data communications systems. The purpose of this book is to introduce basic electronic communications fundamen- tals to expand the knowledge of the reader to more modern digital and data communi- and cations systems. The book was written so that a reader with previous knowledge in basic electronic principles and an understanding of mathematics through trigonometry will have little trouble grasping the concepts presented. An understanding of calculus principles (i.e., differentiation and integration) would be helpful but is not a prerequisite. Within the text, there are numerous examples that emphasize the important concepts, and questions and problems are included at the end of each chapter. Also, answers to the odd-numbered problems are given at the end of the book. Chapter 1 is an introduction to electronic communications. Fundamental communi- cations terms and concepts such as modulation, demodulation, bandwidth, and informa- tion capacity are explained. Signal analysis using both frequency and time domain is discussed. Nonsinusoidal periodic waves are examined using fourier analysis, and the effects of bandlimiting on signals is discussed. Electrical noise, signal-to-noise ratio, and noise figure are explained and discussed. The basic principles of frequency and XIII  1 xiv Preface time division multiplexing are also explained in Chapter 1. Chapter 2 covers frequency generation. The basic requirements for oscillations to occur are outlined and discussed. Standard LC, crystal, and negative resistance oscillator configurations are explained. The basic concepts of frequency multiplication are discussed. Linear and nonlinear mixing with single and multiple frequency input signals are analyzed. Chapter 3 defines and explains the basic concepts of amplitude modulation transmission. A detailed analysis is presented on the voltage, power, and bandwidth considerations of amplitude modulation in both the frequency and time domain. Circuits for generating amplitude modulation are explained. High and low level transmitters are discussed. Chapter 4 introduces the basic concepts of radio receivers including a detailed analysis of tuned radio frequency and superheterodyne receivers. The primary functions of each receiver stage are ex- plained. Amplitude modulation receivers and the detection of amplitude modulated signals are explained. The basic concepts of automatic gain control and squelch are discussed and double conversion receivers are introduced. Chapter 5 is dedicated to the analysis of phase-locked loops and frequency synthesizers. Basic phase-locked loop concepts are introduced and a detailed explanation of the operation of a phase-locked loop is given. Both direct and indirect frequency synthesizers with single and multiple crystals are discussed. Chapter 6 extends the coverage of amplitude modulation given in Chapters 3 and 4 to single sideband transmission. The various types of sideband transmission are explained and contrasted. Circuits for generating single sideband waveforms are explained. Several types of single sideband receivers are discussed in Chapter 6. Chapter 7 introduces the basic concepts of angle modulation. Frequency and phase modulation are explained and contrasted. The amplitude, power, and frequency characteristic of an angle modulated wave are explained in detail. Both direct and indirect frequency and phase modulation transmitters are shown and discussed in detail. Chapter 8 extends the coverage of angle modulation to receivers. Several types of angle modulation demodula- tors are introduced and discussed. Frequency modulation stereo transmission, two-way frequency modulation communications, and mobile telephone communications including cellular radio are discussed. Chapter 9 explains the characteristics of an electromagnetic wave and wave propagation on a metallic transmission line. Several basic transmission line configurations are discussed and contrasted. Incident and reflected energy and the concept of standing waves are discussed in Chapter 9. Transmission line characteristic impedance and input impedance are also introduced. The concept of a matched line is explained and the consequences of a mismatched line are discussed. Chapter 10 extends the coverage of wave propagation to free space. Electromagnetic radiation concepts are explained. Spherical wavefronts are analyzed and the inverse square law is derived. Wave attenuation and absorption are covered. Chapter 10 gives a complete explanation of the optical properties of electromagnetic waves: refraction, reflection, diffraction, and interference. Ground, space, and sky wave propagation are discussed, and the funda- mental limits for free space wave propagation are defined and explained. Chapter 1 introduces the antenna and describes basic antenna operation. Fundamental antenna terms are defined and explained. Radiation patterns are explained. The most basic antenna, Preface xv the elementary doublet, is explained. The basic half- and quarter- wave antenna are explained along with the effects of the ground on the wave, and several antenna-loading techniques are described. Some of the more common antenna arrays and special-purpose configurations are explained including the following: folded dipole, log-periodic and loop antennas. Chapter 12 introduces the basic concepts of television broadcasting. Both monochrome and color television transmission and reception are explained. Genera- tion of the composite video signal is explained. Basic transmitter and receiver circuits are explained. The basic concepts of scanning, blanking, and synchronization are dis- cussed. Chapter 13 introduces the concepts of digital transmission and digital modulation. In this chapter the most common modulation schemes used in modern digital radio systems —FSK, PSK, and QAM— are described. The concepts of information capacity and bandwidth efficiency are explained. Chapter 14 introduces the field of data communi- cations. Detailed explanations are given for numerous data communications concepts, including transmission methods, circuit configurations, topologies, character codes, error control mechanisms, data formats, and data modems. Chapter 15 describes data communi- cations protocols. Synchronous and asynchronous data protocols are first defined, then explicit examples are given for each. The most popular character- and bit-oriented proto- cols are described. In Chapter 15 the basic concepts of a public data network and a local area network are outlined, and the international user-to-network packet switching protocol, X.25, is explained. Chapter 16 introduces digital transmission techniques. This includes a detailed explanation of pulse code modulation. The concepts of sampling, encoding, and companding (both analog and digital) are explained. Chapter 16 also includes descriptions of two lesser-known digital transmission techniques: adaptive delta modulation PCM and differential PCM. Chapter 17 explains the multiplexing of digital signals. Time-division multiplexing is discussed in detail and the operation of a modern LSI combo chip is explained. The North American Digital Hierarchy for digital transmis- sion is outlined, including explanations of line encoding schemes, error detection/correc- tion methods, and synchronization techniques. In Chapter 18 analog multiplexing is explained and AT&T's North American frequency-division-multiplexing hierarchy is described. Several methods are explained in which digital information can be transmitted with analog signals over the same communications medium. Chapter 19 introduces microwave radio communications and the concept of system gain. A block diagram approach to the operation of a microwave radio system is presented and numerous examples are included. In Chapter 20 satellite communications is introduced and the basic concepts of orbital patterns, radiation patterns, geosynchronous, and nonsynchro- nous systems are covered. System parameters and link equations are discussed and a detailed explanation of a satellite link budget is given. Chapter 21 extends the coverage of satellite systems to methods of multiple accessing. The three predominant methods for multiple accessing — frequency-division, time-division, and code-division multiple accessing — are explained. Chapter 22 covers the basic concepts of a fiber optic communi- cations system. A detailed explanation is given for light- wave propagation through a xvi Preface guided fiber. Also, several light sources and light detectors are discussed, contrasting their advantages and disadvantages. Appendix A describes the Smith chart and how it is used for transmission line calculations. Examples are given for calculating input impedance, quarter- wave transformer matching, and shorted stub matching. Wayne Tomasi ACKNOWLEDGMENTS I would like to acknowledge the following individuals for their contributions to this book: Gregory Burnell, Executive Editor and Assistant Vice President, Electronic Tech- nology, for giving me the opportunity to write this book; Kathryn Pavelec, Production Editor, for deciphering my manuscript, and providing a pleasant and professional working environment; and the two reviewers of my manuscript who corrected several of my mathematical errors and provided invaluable constructive criticism —Robert E. Green- wood, Ryerson Poly technical Institute; and James W. Stewart, DeVry, Woodbridge.  Chapter 1 INTRODUCTION TO ELECTRONIC COMMUNICATIONS INTRODUCTION In essence, electronic communications is the transmission, reception, and processing of information with the use of electronic circuits. The basic concepts involved in electronic communications have not changed much since their inception, although the methods by which these concepts are implemented have undergone dramatic changes. Figure 1-1 shows a communications system in its simplest form, which comprises three primary sections: a source (transmitter), a destination (receiver), and a transmission medium (wire pair, coaxial cable, fiber link, or free space). The information that is propagated through a communications system can be analog (proportional), such as the human voice, video picture information, or music; or it can be digital pulses, such as binary-coded numbers, alpha/numeric codes, graphic symbols, microprocessor op-codes, or data base information. However, very often the source information is unsuitable for transmission in its original form and therefore must be converted to a more suitable form prior to transmission. For example, with digital communications systems, analog information is converted to digital form prior to trans- mission, and with analog communications systems, digital data are converted to analog signals prior to transmission. This book is concerned with the basic concepts of conven- tional analog radio communications and the concepts of digital radio communications. Modulation and Demodulation For reasons that are explained in Chapter 10, it is impractical to propagate low-frequency electromagnetic energy through the earth's atmosphere. Therefore, with radio communi-  Introduction to Electronic Communications Chap. 1 Source Transmission medium Destination (transmitter) (receiver) FIGURE 1-1 Block diagram of a com- munications system in its simplest form. cations, it is necessary to superimpose a relatively low-frequency intelligence signal onto a relatively high-frequency signal for transmission. In electronic communications systems, the source information (intelligence signal) acts upon or modulates a single- frequency sinusoidal signal. Modulate simply means to vary or change. Therefore, the source information is called the modulating signal, the signal that is acted upon (modu- lated) is called the carrier, and the resultant signal is called the modulated wave. In essence, the source information is transported through the system on the carrier. With analog communications systems, modulation is the process of changing some property of an analog carrier in accordance with the original source information and then transmitting the modulated carrier. Conversely, demodulation is the process of converting the changes in the analog carrier back to the original source information. The total or composite information signal that modulates the main carrier is called baseband. The baseband is converted from its original frequency band to a band more suitable for transmission through the communications system. Baseband signals are up- converted at the transmitter and down-converted at the receiver. Frequency translation is the process of converting a frequency or band of frequencies to another location in the total frequency spectrum. Equation 1-1 is the general expression for a time varying sine wave of voltage such as an analog carrier. There are three properties of a sine wave that can be varied: the amplitude (V), the frequency (F), or the phase (0). If the amplitude of the carrier is varied proportional to the source information, amplitude modulation (AM) results. If the frequency of the carrier is varied proportional to the source information, frequency modulation (FM) results. If the phase of the carrier is varied proportional to the source information, phase modulation (PM) results. v(t) = V sin (litFt + 0) (1-D where v(f) = time-varying sine wave of voltage V = peak amplitude (Volts) Modulated wave Modulating (transmission medium) Demodulator Information signal Modulator Amplifier (information receiver (information) - i detector) - * System noise car rier FIGURE 1-2 Communications system block diagram. Introduction 3 F= frequency (Hz) = phase (deg) Figure 1-2 is a simplified block diagram for a communications system showing the relationships among the modulating signal (information), the modulated signal (car- rier), the modulated wave (resultant), and the system noise. Again, the frequency of the carrier is relatively high as compared to the frequency of the intelligence signal. Transmission Frequencies In the United States, frequency assignments for free-space radio propagation are assigned by the Federal Communications Commission (FCC). The exact frequencies assigned specific transmitters operating in the various classes of service are constantly being updated and altered to meet the nation's communications needs. However, the general division of the total usable frequency spectrum is decided at the International Telecommu- nications Conventions, which are held approximately once every 10 years. The usable radio-frequency (RF) spectrum is divided into narrower frequency bands which are given descriptive names and band numbers. The International Radio Consultative Committee' s (CCIR) designations are listed in Table 1-1. Several of these bands are further broken down into various services, which include shipboard search, microwave, satellite, mobile land-based search, shipboard navigation, aircraft approach, airport surface detection, airborne weather, mobile telephone, and many more. TABLE 1-1 CCIR BAND DESIGNATIONS Band number Frequency range 3 Designation 2 30-300 Hz ELF (extremely low frequencies) 3 0.3-3 kHz VF (voice frequencies) 4 3-30 kHz VLF (very low frequencies) 5 30-300 kHz LF (low frequencies) 6 0.3-3MHz MF (medium frequencies) 7 3-30 MHz HF (high frequencies) 8 30-300 MHz VHF (very high frequencies) 9 0.3-3 GHz UHF (ultra high frequencies) 10 3-30 GHz SHF (super high frequencies) 11 30-300 GHz EHF (extremely high frequencies) 12 0.3-3 THz Infrared light 13 3-30 THz Unassigned 14 30-300 THz Visible-light spectrum 15 0.3-3 PHz Ultraviolet light 16 3-30 PHz X-ray 17 30-300 PHz Unassigned 18 0.3-3 EHz Gamma rays 19 3-30 EHz Cosmic rays a 10°, hertz (Hz); 10 3 , kilohertz (kHz); 10 6 , megahertz (MHz); 10 9 , gigahertz 12 15 18 (GHz); 10 , terahertz (THz); 10 , petahertz (PHz); 10 , exahertz (EHz).  Introduction to Electronic Communications Chap. 1 TABLE 1-2 EMISSION CLASSIFICATIONS Type of modulation Supplementary or emission Type of information characters A Amplitude Carrier on only None Double sideband, full car- F Frequency 1 Carrier on-off rier P Pulse 2 Carrier on, keyed tone —on-off a Single sideband 3 Telephony, voice, or music b Two independent sidebands 4 Facsimile, nonmoving or slow- c Vestigal sideband scan TV d Pulse amplitude modulation 5 Vestigal sideband, commercial (PAM) TV e Pulse width modulation 6 Four-frequency diplex telephony (PWM) 7 Multiple sidebands f Pulse position modulation 8 Unassigned g Digital video 9 General, all others h Single sideband, full carrier i Single sideband, no carrier Classification of Transmitters For licensing purposes in the United States, radio transmitters are classified according to their bandwidth, type of modulation, and type of intelligence information. The emission classification is identified by combinations of letters and numbers as shown in Table 1- 2. Emission designations include an uppercase letter which identifies the type of modula- tion, a number which identifies the type of emission, and a lowercase subscript which further defines the emission characteristics. For example, the designation A3 a describes a single-sideband, reduced-carrier, amplitude-modulated signal carrying voice or music information. Bandwidth and Information Capacity The two most significant limitations on system performance are noise and bandwidth. The significance of noise is discussed later in this chapter. The bandwidth of a communica- tions system is the minimum passband required to propagate the source information through the system. The bandwidth of a communications system must be sufficiently large to pass all significant information frequencies. The information capacity of a communications system is a measure of how much source information can be carried through the system in a given period of time. The amount of information that can be propagated through a transmission system is propor- tional to the product of the system bandwidth and the time of transmission. The relation- ship among bandwidth, transmission time, and information capacity was developed by R. Hartley of Bell Telephone Laboratories in 1928. Simply stated. Hartley's law is C oc B x T (1-2)  Signal Analysis 5 where C= information capacity B = bandwidth (Hz) T= transmission time (s) Equation 1-2 shows that information capacity is a linear function and is directly propor- tional to both the system bandwidth and the transmission time. If either the bandwidth or the transmission time changes, the information capacity changes by the same propor- tion. Approximately 3 kHz of bandwidth is required to transmit basic voice-quality telephone signals. Approximately 200 kHz of bandwidth is required for FM transmission of high-fidelity music, and almost 6 MHz of bandwidth is required for broadcast-quality television signals (i.e., the more information per unit time, the more bandwidth required). SIGNAL ANALYSIS When designing electronic communications' circuits, it is often necessary to analyze and predict the performance of the circuit based on the power distribution and frequency composition of the information signal. This is done with mathematical signal analysis. Although all signals in electronic communications are not single-frequency sine or cosine waves, many of them are, and the signals that are not can be represented by a series of sine and cosine functions. Sinusoidal Signals In essence, signal analysis is the mathematical analysis of the frequency, bandwidth, and voltage level of a signal. Electrical signals are voltage- or current-time variations that can be represented by a series of sine or cosine waves. Mathematically, a single- frequency voltage or current waveform is v(t) = V sin (2-nFt + 9) or v(t) = V cos (2-nFt + 6) i(t) = I sin (2irFt + 0) or i(r) = / cos (2irFf + 0) where v(i) = time-varying voltage wave V = peak voltage (Volts) i(t) = time-varying current wave / = peak current (Amps) F= frequency (Hz) = phase (deg) Whether a is used to represent a signal is purely arbitrary sine or a cosine function and depends on which chosen as the reference (however, it should be noted that sin is = cos - 90°). Therefore, the following relationships hold true: 6 Introduction to Electronic Communications Chap. 1 v(t) = V sin (2>nFt + 6) = V cos (2irfY + - 90°) v(i) = V cos (2>nFt + 0) = V sin (ZirFt + + 90°) The preceding formulas are for a single-frequency, repetitive waveform. Such a waveform is called a periodic wave because it repeats at a uniform rate (i.e., each successive cycle of the signal takes exactly the same length of time and has exactly the same amplitude variations as every other cycle — each cycle has exactly the same shape). A series of sine waves is an example of a periodic wave. Periodic waves can be analyzed in either the time or the frequency domain. In fact, it is often necessary when analyzing system performance to switch from the time domain to the frequency domain, and vice versa. Time domain. A standard oscilloscope is a time-domain instrument. The display on the CRT is an amplitude-versus-time representation of the input signal and is commonly called a signal waveform. Essentially, a signal waveform shows the shape and the instantaneous value of the signal but is not necessarily indicative of its frequency content. With an oscilloscope, the vertical deflection is proportional to the instantaneous amplitude of the total input signal, and the horizontal deflection is a function of time (sweep rate). Figure 1-3 shows the signal waveform for a single-frequency sinusoidal signal with a peak amplitude of V volts and a frequency of F Hertz. Frequency domain. A spectrum analyzer is a frequency-domain instrument. Essentially, there is no waveform displayed on the CRT. Instead, an amplitude- versus- frequency plot is shown (this is called a frequency spectrum). With a spectrum analyzer, 0.707 v peak l\ 1 1 \\ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1/F Time 1/2 f\ -0-707 V pea > v peak -V FIGURE 1-3 Time-domain representation (signal waveform) for a single-frequency sinusoidal wave. Signal Analysis -- FIGURE 1-4 Frequency-domain ^presentation (spectrum) for a single- Frequency (Hz) frequency sinusoidal wave. the horizontal axis represents frequency and the vertical axis amplitude. Therefore, there is a vertical deflection for each input frequency. Effectively, the input waveform is swept with a variable-frequency, high-g bandpass filter whose center frequency is synchronized to the horizontal sweep rate of the CRT. Each frequency present in the input waveform produces a vertical line on the CRT (these are called spectral compo- nents). The height of each line is proportional to the amplitude of that frequency. A frequency-domain representation of a wave shows the frequency content but is not neces- sarily indicative of the shape of the waveform or the instantaneous amplitude. Figure 1-4 shows the spectrum for a single-frequency sinusoidal signal with a peak amplitude of V volts and a frequency of F Hertz. Nonsinusoidal Periodic Waves (Complex Waves) Essentially, any repetitive waveform that comprises more than one sine or cosine wave is a nonsinusoidal or complex periodic wave. To analyze a complex periodic waveform, it is necessary to use a mathematical series developed in 1826 by the French physicist and mathematician Baron Jean Fourier. This series is appropriately called the Fourier series. The Fourier series. The Fourier series is used in signal analysis to represent the sinusoidal components of a nonsinusoidal periodic waveform. In general, a Fourier series can be written for any series of terms that include trigonometric functions with the following mathematical expression: f{t) =A 4- A x cos a + A2 cos 2a + A 3 cos 3a + + AN cos Na (1-3) +B x sin p + B2 sin 2p + B 3 sin 30 + + BN sin N$ Equation 1-3 states that the waveform /(r) comprises an average value (A ), a series of cosine functions in which each successive term has a frequency that is an integer multiple of the frequency of the first cosine term in the series, and a series of sine functions in which each successive term has a frequency that is an integer multiple of the frequency of the first sine term in the series. There are no restrictions on the values or relative values of the amplitudes for the sine or cosine terms. Equation 1-3 is stated in words as follows: Any periodic waveform comprises an average component and a series of 8 Introduction to Electronic Communications Chap. 1 harmonically related sine and cosine waves. A harmonic is an integral multiple of the fundamental frequency. The fundamental frequency is the first harmonic, the second multiple of the fundamental is called the second harmonic, the third multiple is called the third harmonic, and so on. The fundamental frequency is the minimum frequency necessary to represent a waveform and is also the frequency of the waveform (i.e., the repetition rate). Therefore, Equation 1-3 can be rewritten as f{t) = dc + fundamental + 2nd harmonic + 3rd harmonic + + nth harmonic Wave symmetry Even symmetry. If a periodic voltage waveform is symmetric about the vertical (amplitude) axis, it is said to have axes or mirror symmetry and is called an even function. For all even functions, the B coefficients in Equation 1-3 are zero. Therefore, the signal simply contains a dc component and the cosine terms (note that a cosine wave is itself an even function). The sum of a series of even functions is an even function. Even functions satisfy the condition f(t)=f(-t) (1-4) Equation 1-4 states that the magnitude of the function at +t is equal to the magnitude at —t. A waveform that contains only the even functions isshown in Figure l-5a. Odd symmetry. If a periodic voltage waveform is symmetric about a line midway between the vertical and horizontal axes and passing through the coordinate origin, it is said to have point or skew symmetry and is called an odd function. For all odd functions, the A coefficients in Equation 1-3 are zero. Therefore, the signal simply contains a dc component and the sine terms (note that a sine wave is itself an odd function). The sum of a series of odd functions is an odd function. This form must be mirrored first in the Y axis, then in the X axis for superposition. Thus f(t)=-f(-t) (1-5) Equation 1-5 states that the magnitude of the function at +t is equal to the negative of the magnitude at -t. A periodic waveform that contains only the odd functions is shown in Figure l-5b. Half-wave symmetry. If a periodic voltage waveform is such that the waveform for the first half cycle (t = to 772) repeats itself except with the opposite sign for the second half cycle (/ = 772 to T), it is said to have half-wave symmetry. For all waveforms with half- wave symmetry, the even harmonics in the series for both the sine and cosine terms are zero. Therefore, half- wave functions satisfy the condition f(t) = -fiTIl + t) (1-6) A periodic waveform that exhibits half- wave symmetry is shown in Figure l-5c. The coefficients A , B x to B N and A, , to AN can be evaluated using the following integral formulas: Signal Analysis 9 T 1 f K) =- f(t)dt (1-7) 1 J f(t) cos Nut dt (1-8) f(t) sin Nut dt (1-9) Solving Equations 1-7, 1-8, and 1-9 requires integral calculus, which is beyond the intent of this book. Therefore, in subsequent discussions, the appropriate solutions are given. Symmetry about vertical axis Time Time Positive half-cycle mirror image of negative half-cycle Time FIGURE 1-5 Wave symmetries: (a) even symmetry; (b) odd symmetry; (c) half- wave symmetry.  Introduction to Electronic Communications Chap. 1 10 EXAMPLE 1-1 train of square waves shown in Figure 1-6: For the (a) Determine the coefficients for the first 9 harmonics. (b) Draw the frequency spectrum. Sketch the time-domain signal for frequency components up to the ninth harmonic (c) FIGURE 1-6 Waveform for Example 1-1. it can be seen that the average dc component Solution (a) From inspection of the waveform, half-wave symmetry. Evaluating Equations 1-7, 1-8, and 1-9 is V and the waveform has yields the following Fourier series for a square wave: 4V- — / (COS OJ/ - cos 3a>f + - cos 5t - - cos lut + (1 Nit 3 5 7 From Equation 1-10 the following frequencies and coefficients are derived: 4V v »=^ (odd) where N= Nth harmonic (odd harmonics only) V= peak amplitude of the complex waveform N Harmonic Frequency (kHz) Voltage (V) dc 1 1st 1 5.09 2 2nd 2 3rd 3 1.69 3 4 4th 4 5th 5 1.02 5 6 6th 6 7 7th 7 0.728 8 8th 8 9 9th 9 0.566 (b) The spectrum is shown in Figure 1-7. (Note that although both + and - com] nents are included in the waveform, all magnitudes are shown in the + direction on a waveform spectrum.) (c) The time-domain signal for the first nine harmonics is shown in Figure 1-8. closely resemble one. Although the waveform shown is not an exact square wave, it docs Signal Analysis 11 5h 4 3 - o > 2 1 - 3 4 J_^i 5 6 7 8 9 FIGURE 1-7 Voltage spectrum Frequency, F (kHz) for Example 1-1. f(t) 0.125 ms 0.25 ms 0.5 ms -0.5 0.0625 ms -1 -1.5 -2 -2. 5 -3 -3 5 -4 -4.5 -4. h -5 FIGURE 1-8 Time-domain signal for Example 1-1. Table 1-3 is a summary of the Fourier series for several of the more common nonsinusoidal periodic waveforms. Fourier Series for a Rectangular Waveform When analyzing electronic communications circuits, it is often necessary to use rectangu- lar pulses. A waveform for a string of rectangular pulses is shown in Figure 1-9. The  — 12 Introduction to Electronic Communications Chap. 1 TABLE 1-3 FOURIER SERIES SUMMARY Waveform Fourier series v(t) = - + V — sin cot 2V - — — - cos 2cot - 2V cos 4cot + 2 3tt 15tt N] « Y + Y + 2 V[1 +( v(t) sin cot V cos Ncot T/2 T IT 2 N = 2 7T(1-N 2 ) , rt v(t) = — 2V 4V + —— , cos cot ,4V - —— cos 2cot. ^+ /W\ s*\- v(t) = — 2V 7T * a + n 37T ? 2 = i tt[1-(2N) 2 N 4V(-1)'——- 1 157T ] cos XT Ncot. 1 » +V/2 v(t) = — 2V IT sin cot + 2V -— 37T sin 3cot + u v(t) = 2 |Y Si n Ncot T N = odd NTT -V/2 i +V/2 v(t) = — 2V it cos cot - 2V 3tt cos 3cot 4- 2V 5tt cos 5cot + 1 1 ,., = ~ 2 V sin —I— N7r/2 X7. v(t) cos Ncot T n = l Ntt/2 -VII H +V »m- — Vt a v f2Vt — sinN7rt/T, — E v(t)= T + n 2 = V Ti ; N7rt/T cos Ncot +V V duty cycle (DS) for the period of the waveform waveform v(t) v(t) is = = 4V — N - tt 2 = (T). Mathematically, the duty cycle 2 odd cos cot (NTT) 4V the ratio of the active time of the pulse + 2 4V (3tt) cos Ncot 2 cos 3cot is + 4V (5tt) 2 cos 5 cot + (f) to the DS (11 la) DS (%) = - x 100 (1-llb) T Signal Analysis 13 FIGURE 1-9 Rectangular pulse waveform. Regardless of the duty cycle, a rectangular waveform is made up of a series of harmonically related sine waves. However, the amplitude of the spectrum components are dependent on the duty cycle. The Fourier series for a rectangular voltage waveform is v =—+ Vt T — 2Vt T sin* (cos o>f) + sin 2x 2x (1-12) sin 3* Nx sin (cos ojf) -1- + (cos u>0 3jc Nx where X = TTt/T N= Nth harmonic and can be any value integer From Equation 1-12 it can be seen that a rectangular waveform has a O-Hz (dc) component equal to V x - or V x duty cycle (1-13) The narrower the pulse width, the smaller the dc component. Also, from Equation 1 12, the amplitude of the Nth harmonic is 2Vt sin Nx Vm = (1-14) T Nx The (sin x)lx function is used to describe repetitive pulse waveforms. Sin x is simply a sinusoidal waveform whose instantaneous amplitude depends on x. With only x in the denominator, the denominator increases with x. Therefore, a (sin x)lx function is simply a damped sine wave. A (sin x)lx function is shown in Figure 1-10. (sin x)/x FIGURE 1-10 (sin x)lx function.. 14 Introduction to Electronic Communications Chap. 1 T to * * t = 0.1T (a) * 1st lobe *--« 2nd lobe -« 3rd lobe > 1st null 2nd null 3rd null I ±_L J_L j_lH Frequency F 5F 10F 15F 20F 25F 30F (b) FIGURE 1-11 (sin x)lx function: (a) rectangular pulse waveform; (b) frequency spectrum. Figure 1-11 shows the frequency spectrum for a rectangular pulse with a pulse width-to-period ratio of 0.1. It can be seen that the amplitudes of the harmonics follow a damped sinusoidal shape. The frequency whose period equals \lt (i.e., at frequency 10F Hz), there is a 0-V component. A second null occurs at 20F Hz (period = lit), a third at 30F Hz (period = 3/r), and so on. All harmonics between Hz and the first null frequency are considered in the first lobe of the frequency spectrum. All spectrum components between the first and second null frequencies are in the second lobe, frequen- cies between the second and third nulls are in the third lobe, and so on. The following characteristics are true for all repetitive rectangular waveforms: 1 The dc component is equal to the pulse amplitude times the duty cycle. 2. There are 0-V components at frequency lit Hz and all integer multiples of that frequency. 3. The amplitude-versus-frequency time envelope of the spectrum components take on the shape of a damped sine wave. EXAMPLE 1-2. For the pulse waveform shown in Figure 1-12: (a) Determine the dc component. (b) Determine the peak amplitudes of the first 10 harmonics. (c) Plot the (sin x)lx function. (d) Sketch the frequency spectru Signal Analysis 15 t - 0.4 ms T = 2ms- FIGURE 1-12 Pulse waveform for Example 1-2. Solution (a) From Equation 1-13 the dc component is V(0 Hz) = iiM^ = o.2 v 2 ms (b) The amplitudes of the first 10 harmonics are determined from Equation 1-14: ! ).4 ms\ "sin W 1 80(0.4 ms/2ms)] 2(1) ( 2 ms ) /V(3. 14)(0.4 ms/2 ms) N Frequency (Hz) Amplitude 0.2 1 500 0.374 2 1000 0.303 3 1500 0.202 4 2000 0.094 5 2500 6 3000 -0.063 7 3500 -0.087 8 4000 -0.076 9 4500 -0.042 10 5000 (c) The (sin x)lx function is shown in Figure 1-13. 0.5 1 1.5 2 2.5 3 3.5 4.5 FIGURE 1-13 (sin x)lx Frequency, F (kHz) function for Example 1-2.  16 Introduction to Electronic Communications Chap. 1 0.4 0.3 fS 0.2 a 0.1 J JL_L FIGURE 1-14 Voltage 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 spectrum for Example Frequency, F (kHz) 1-2. (d) The frequency spectrum is shown in Figure 1-14. Although the frequency components in the second lobe are negative, it is customary to plot all voltages in the positive direction on the frequency spectrum. Figure 1-15 shows the effect that reducing the duty cycle (i.e., reducing the t/T ratio) has on the frequency spectrum for a nonsinusoidal waveform. It can be seen that narrowing the pulse width produces a frequency spectrum with a more uniform amplitude. In fact, for infinitely narrow pulses, the frequency spectrum comprises an infinite number of frequencies of equal amplitude. Increasing the period of a rectangular waveform while keeping the pulse width constant has the same effect on the frequency spectrum. t/T = 0.25 sin x/x Jtl — — — —i— — — — — -1 ' | | ' ' I ' Frequency j t/T = 0.125 m il sin x/x 1 I | I Frequency t/T = 0.03125 rh sin x/x | I I I |.. FIGURE 1-15 Effects of reducing the I I ' * ' I ' ' ' » I 1 I I I I Frequency tIT ratio (either decreasing / or increasing T). Signal Analysis 17 Effects of Band limiting on Signals Every communications channel has a limited bandwidth and therefore has a limiting effect on signals that are propagated through them. We can consider a communications channel to be equivalent to an ideal linear phase filter with a finite bandwidth. If a (a) Time (b) Time (c) Time (d) Time (e) Time FIGURE 1-16 Bandlimiting signals: (a) 1-kHz square wave; (b) 1-kHz square wave bandlimited to 8 kHz; (c) 1-kHz square wave bandlimited to 6 kHz; (d) 1-kHz square wave bandlimited to 4 kHz; (e) 1-kHz square wave bandlimited to 2 kHz.  18 Introduction to Electronic Communications Chap. 1 nonsinusoidal repetitive waveform passes through an ideal low-pass filter, the harmonic frequency components that are higher in frequency than the upper cutoff frequency for the filter are removed. Consequently, the shape of the waveform is changed. Figure 1- 16a shows the time-domain waveform for the square wave used in Example 1-1. If thiswaveform is passed through a low-pass filter with an upper cutoff frequency of 8 kHz, frequencies above the eighth harmonic (9 kHz and above) are cut off and the waveform shown in Figure l-16b results. Figures l-16c, d, and e show the waveforms produced when low-pass filters with upper cutoff frequencies of 6, 4, and 2 kHz are used, respectively. It can be seen from Figure 1-16 that bandlimiting a signal changes the frequency content and thus the shape of its waveform and, if sufficient bandlimiting is imposed, the waveform eventually comprises only the fundamental frequency. In a communications system, bandlimiting reduces the information capacity of the system and, if excessive bandlimiting is imposed, a portion of the information signal can be removed from the composite waveform. ELECTRICAL NOISE In general terms, electrical noise is defined as any unwanted electrical energy present in the usable passband of a communications circuit. For instance, in audio recording any undesired signals that fall into the band to 15 kHz are audible and will interfere with the audio information. Consequently, for audio circuits, any unwanted electrical energy in the band to 15 kHz is considered noise. Essentially, noise can be divided into two general categories: correlated and uncorre- cted. Correlation implies a relationship between the signal and the noise. Uncorrected noise is noise that is present in the absence of any signal. Correlated Noise Correlated noise is unwanted electrical energy that is present as a direct result of a signal such as harmonic and intermodulation distortion. Harmonic and intermodulation distortion are both forms of nonlinear distortion; they are produced from nonlinear amplifi- cation. Correlated noise can not be present in a circuit unless there is an input signal. Simply stated, no signal, no noise! Both harmonic and intermodulation distortion change the shape of the wave in the time domain and the spectral content in the frequency domain. Harmonic Harmonic distortion is the generation of unwanted multi- distortion. ples of a single-frequency sine wave when the sine wave is amplified in a nonlinear device such as a large-signal amplifier. Amplitude distortion is another name for harmonic distortion. Generally, the term "amplitude distortion" is used for analyzing a waveform in the time domain, and the term "harmonic distortion" is used for analyzing a waveform Electrical Noise 19 in the frequency domain. The original input frequency is the first harmonic and, as stated previously, is called the fundamental frequency. There are various degrees or orders of harmonic distortion. Second-order harmonic distortion is the ratio of the amplitude of the second harmonic to the amplitude of the fundamental frequency. Third-order harmonic distortion is the ratio of the amplitude of the third harmonic to the amplitude of the fundamental frequency, and so on. The ratio of the combined amplitudes of the higher harmonics to the amplitude of the funda- mental frequency is called total harmonic distortion (THD). Mathematically, total har- monic distortion is higher THD x 100 (1-15) fundamental where % THD = percent total harmonic distortion ^higher = quadratic sum of the root-mean-square (rms) voltages of the higher harmonics ^fundamental = rms voltage of the fundamental frequency E 4MPLE 1-3 Determine the percent second-order, third-order, and total harmonic distortion for the output spectrum shown in Figure 1-17. 6 V, 1st V, 2nd harmonic harmonic harmonic FIGURE 1-17 Harmonic distortion for Frequency, F (kHz)