Modern Electronic Communication: Pearson New International Edition [Ninth new international edition] 1292025476, 9781292025476, 9781299960251, 1299960251

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Modern Electronic Communication Jeffrey S. Beasley Gary M. Miller Ninth Edition

Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk © Pearson Education Limited 2014 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS. All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners.

ISBN 10: 1-292-02547-6 ISBN 13: 978-1-292-02547-6

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Printed in the United States of America

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Table of Contents

1. Introductory Topics Jeffrey S. Beasley/Gary M. Miller

1

2. Amplitude Modulation: Transmission Jeffrey S. Beasley/Gary M. Miller

67

3. Amplitude Modulation: Reception Jeffrey S. Beasley/Gary M. Miller

115

4. Single-Sideband Communications Jeffrey S. Beasley/Gary M. Miller

163

5. Frequency Modulation: Transmission Jeffrey S. Beasley/Gary M. Miller

203

6. Frequency Modulation: Reception Jeffrey S. Beasley/Gary M. Miller

257

7. Communications Techniques Jeffrey S. Beasley/Gary M. Miller

297

8. Digital Communications: Coding Techniques Jeffrey S. Beasley/Gary M. Miller

347

9. Wired Digital Communications Jeffrey S. Beasley/Gary M. Miller

403

10. Wireless Digital Communications Jeffrey S. Beasley/Gary M. Miller

457

11. Transmission Lines Jeffrey S. Beasley/Gary M. Miller

501

12. Wave Propagation Jeffrey S. Beasley/Gary M. Miller

559

13. Antennas Jeffrey S. Beasley/Gary M. Miller

607

I

14. Waveguides and Radar

II

Jeffrey S. Beasley/Gary M. Miller

651

Glossary Jeffrey S. Beasley/Gary M. Miller

695

Index

715

INTRODUCTORY TOPICS

From Modern Electronic Communication, Ninth Edition, Jeffrey S. Beasley, Gary M. Miller. Copyright © 2008 by Pearson Education, Inc. Published by Prentice Hall. All rights reserved.

1

Chapter Outline 1 2 3 4 5 6 7 8 9 10

Introduction The dB in Communications Noise Noise Designation and Calculation Noise Measurement Information and Bandwidth LC Circuits Oscillators Troubleshooting Troubleshooting with Electronics Workbench™ Multisim

Objectives • • • • • • • • • •

2

Describe a basic communication system and explain the concept of modulation Develop an understanding of the use of the decibel (dB) in communications systems Define electrical noise and explain its effect at the first stages of a receiver Calculate the thermal noise generated by a resistor Calculate the signal-to-noise ratio and noise figure for an amplifier Describe several techniques for making noise measurements Explain the relationship among information, bandwidth, and time of transmission Analyze nonsinusoidal repetitive waveforms via Fourier analysis Analyze the operation of various RLC circuits Describe the operation of common LC and crystal oscillators

INTRODUCTORY TOPICS

Tektronix’s digital oscilloscopes include easy-to-use features, high bandwidth, MegaZoom rates, and integrated logic timing channels. (Courtesy of Tektronix, Inc.)

Key Terms modulation intelligence signal intelligence demodulation transducer dB dBm 0 dBm dBm(600) dBm(75) dBm(50) dBW dBmV electrical noise static

external noise internal noise wave propagation atmospheric noise space noise solar noise cosmic noise Johnson noise thermal noise white noise low-noise resistor shot noise excess noise transit-time noise signal-to-noise ratio

noise figure noise ratio octave Friiss’s formula device under test tangential method information theory channel Hartley’s law Fourier analysis FFT frequency domain record aliasing quality leakage

dissipation resonance tank circuit poles constant-k filter m-derived filter roll-off stray capacitance oscillator flywheel effect damped continuous wave Barkhausen criteria frequency synthesizer

3

1

Modulation process of putting information onto a highfrequency carrier for transmission

Intelligence Signal the low frequency information that modulates the carrier

Intelligence low-frequency information modulated onto a highfrequency carrier in a transmitter

Demodulation process of removing intelligence from the highfrequency carrier in a receiver

I NTRODUCTION

We will provide an introduction to all relevant aspects of communications systems. These systems had their beginning with the discovery of various electrical, magnetic, and electrostatic phenomena prior to the twentieth century. Starting with Samuel Morse’s invention of the telegraph in 1837, a truly remarkable rate of progress has occurred. The telephone, thanks to Alexander Graham Bell, came along in 1876. The first complete system of wireless communication was provided by Guglielmo Marconi in 1894. Lee DeForest’s invention of the triode vacuum tube in 1908 allowed the first form of practical electronic amplification and really opened the door to wireless communication. In 1948 another major discovery in the history of electronics occurred with the development of the transistor by Shockley, Brattain, and Bardeen. The more recent developments, such as integrated circuits, very large-scale integration, and computers on a single silicon chip, are probably familiar to you. The rapid transfer of these developments into practical communications systems linking the entire globe (and now into outer space) has stimulated a bursting growth of complex social and economic activities. This growth has subsequently had a snowballing effect on the growth of the communication industry with no end in sight for the foreseeable future. Some people refer to this as the age of communications. The function of a communication system is to transfer information from one point to another via some communication link. The very first form of “information” electrically transferred was the human voice in the form of a code (i.e., the Morse code), which was then converted back to words at the receiving site. People had a natural desire and need to communicate rapidly between distant points on the earth, and that was the major concern of these developments. As that goal became a reality, and with the evolution of new technology following the invention of the triode vacuum tube, new and less basic applications were also realized, such as entertainment (radio and television), radar, and telemetry. The field of communications is still a highly dynamic one, with advancing technology constantly making new equipment possible or allowing improvement of the old systems. Communications was the basic origin of the electronics field, and no other major branch of electronics developed until the transistor made modern digital computers a reality.

Modulation Basic to the field of communications is the concept of modulation. Modulation is the process of putting information onto a high-frequency carrier for transmission. In essence, then, the transmission takes place at the high frequency (the carrier) which has been modified to “carry” the lower-frequency information. The low-frequency information is often called the intelligence signal or, simply, the intelligence. It follows that once this information is received, the intelligence must be removed from the high-frequency carrier—a process known as demodulation. At this point you may be thinking, why bother to go through this modulation/demodulation process? Why not just transmit the information directly? The problem is that the frequency of the human voice ranges from about 20 to 3000 Hz. If everyone transmitted those frequencies directly as radio waves, interference would cause them all to be ineffective. Another limitation of equal importance is the virtual impossibility of transmitting

Introductory Topics

4

such low frequencies since the required antennas for efficient propagation would be miles in length. The solution is modulation, which allows propagation of the low-frequency intelligence with a high-frequency carrier. The high-frequency carriers are chosen such that only one transmitter in an area operates at the same frequency to minimize interference, and that frequency is high enough so that efficient antenna sizes are manageable. There are three basic methods of putting lowfrequency information onto a higher frequency. Equation (1) is the mathematical representation of a sine wave, which we shall assume to be the high-frequency carrier. v  VP sin 1vt  £2

(1)

where v  instantaneous value VP  peak value v  angular velocity  2pf £  phase angle Any one of the last three terms could be varied in accordance with the low-frequency information signal to produce a modulated signal that contains the intelligence. If the amplitude term, VP, is the parameter varied, it is called amplitude modulation (AM). If the frequency is varied, it is frequency modulation (FM). Varying the phase angle, £ , results in phase modulation (PM). In subsequent chapters we shall study these systems in detail.

Communications Systems Communications systems are often categorized by the frequency of the carrier. Table 1 provides the names for various frequency ranges in the radio spectrum. The extra-high-frequency range begins at the starting point of infrared frequencies, but the infrareds extend considerably beyond 300 GHz (300  109 Hz). After the infrareds in the electromagnetic spectrum (of which the radio waves are a very small portion) come light waves, ultraviolet rays, X rays, gamma rays, and cosmic rays.

Table 1

Radio-Frequency Spectrum

Frequency

Designation

Abbreviation

30 –300 Hz 300–3000 Hz 3–30 kHz 30–300 kHz 300 kHz–3 MHz 3–30 MHz 30–300 MHz 300 MHz–3 GHz 3–30 GHz 30–300 GHz

Extremely low frequency Voice frequency Very low frequency Low frequency Medium frequency High frequency Very high frequency Ultra high frequency Super high frequency Extra high frequency

ELF VF VLF LF MF HF VHF UHF SHF EHF

Introductory Topics

5

Transducer device that converts energy from one form to another

Figure 1 represents a simple communication system in block diagram form. Notice that the modulated stage accepts two inputs, the carrier and the information (intelligence) signal. It produces the modulated signal, which is subsequently amplified before transmission. Transmission of the modulated signal can take place by any one of four means: antennas, waveguides, optical fibers, or transmission lines. These four modes of propagation will be studied in subsequent chapters. The receiving unit of the system picks up the transmitted signal but must reamplify it to compensate for attenuation that occurred during transmission. Once suitably amplified, it is fed to the demodulator (often referred to as the detector), where the information signal is extracted from the high-frequency carrier. The demodulated signal (intelligence) is then fed to the amplifier and raised to a level enabling it to drive a speaker or any other output transducer. A transducer is a device that converts energy from one form to another. Many of the performance measurements in communication systems are specified in dB (decibels). Section 2 introduces the use of this very important concept in communication systems. This is followed by two basic limitations on the performance of a communications systems: (1) electrical noise and (2) the bandwidth of frequencies allocated for the transmitted signal. Sections 3 to 6 are devoted to these topics because of their extreme importance. Transmitter

Low-frequency information (intelligence)

Modulated signal

Modulated stage

Amplifier

Highfrequency carrier

Transmitting medium

Antennas Transmission lines Waveguides Optical fibers

Receiver

Amplifier

Demodulator (detector)

Amplifier

Intelligence signal

FIGURE 1

A communication system block diagram.

Introductory Topics

6

Output transducer

2

T HE dB

IN

C OMMUNICATIONS

Decibels (dBs) are used to specify measured and calculated values in noise analysis, audio systems, microwave system gain calculations, satellite system link-budget analysis, antenna power gain, light-budget calculations, and many other communications system measurements. In each case, the dB value is calculated with respect to a standard or specified reference. The dB value is calculated by taking the log of the ratio of the measured or calculated power (P2) with respect to a reference power (P1) level. This result is then multiplied by 10 to obtain the value in dB. The formula for calculating the dB value of two ratios is shown in Equation (2). Equation (2) is commonly referred to as the power ratio form for dB. dB  10 log10

P2 P1

dB (decibel) relative unit of measurement used frequently in electronic communications to describe power gain or loss

(2)

By using the power relationship P  V 2 R, the relationship shown in Equation (3) is obtained: dB  10 log10 a

V 22 R2 V 21 R1

b

Let R1  R2: dB  10 log10

V 22 V 21

(3)

Note that we have assumed that the resistances (R1 and R2) are equivalent; therefore, these terms can be ignored in the dB power equation. This is a reasonable assumption in most communication systems since maximum power transfer (a desirable characteristic) is obtained when the input and output impedances are matched. Equation (3) can be modified (using a property of logarithms) to provide a relationship for decibels in terms of the voltage ratios instead of power ratios. This is called the voltage gain equation and is shown in Equation (4). dB  20 log10 a

V2 b V1

(4)

Applying the dB Value The dB unit is often used in specifying input- and output-signal-level requirements for many communication systems. When making dB measurements, a reference level is specified or implied for that particular application. An example is found in audio consoles in broadcast systems, where a 0-dBm input level is usually specified as the required input- and output-audio level for 100% modulation. Notice that a lowercase m has been attached to the dB unit. This indicates that the specified dB level is relative to a 1-mW reference. In standard audio systems 0 dBm is defined as 0.001 W measured with respect to a load termination of 600  . A 600-  balanced audio line is the

dBm dB level using a 1-mW reference

0 dBm 1 mW measured relative to a 1-mW reference

Introductory Topics

7

standard for professional audio, broadcast, and telecommunications systems. However, 0 dBm is not exclusive to a 600- impedance.

Example 1 Show that when making a dBm measurement, a measured value of 1 mW will result in a 0 dBm power level.

Solution dB  10 log10

P2 1 mW  0 dB  10 log10 P1 1 mW

or

0 dBm

(2)

This result, 0 dB, is expressed as 0 dBm to indicate that the result was obtained relative to a 1-mW reference. It can be shown that the voltage measured across a 600- load for a 0-dBm level is 0.775 V. This value can be obtained by first modifying Equation (2) by inserting the 1 mW value for P1, as shown. dB  10 log10 a

P2 b P1

V 22 600 P1  0.001 W

where P2 

Since 1 mW is the specified reference for dBm, the voltage reference for 0 dBm can be developed as follows: 0 dBm  10 log 0 dBm  log log1 10 dBm2 

V 22 600 0.001

V22600 0.001

V 22600 0.001

V 22 600 0.001 0.6  V 22 V2  0.77459 1

dBm(600) decibel measurement using a 1-mW reference with respect to a 600- load

The voltage value 0.77459 (0.775 V) is the reference for 0 dB with respect to a 600- load when a voltage measurement is used to calculate the dBm(600) value. The dBm(600) term indicates that this measurement or calculation is made using a 1-mW reference with respect to a 600- load. dBm16002  20 log10 a

Introductory Topics

8

V2 b 0.775

(5)

Example 2 demonstrates how to solve for the voltage value (V2) if a 8-dBm level is specified.

Example 2 A microwave system requires a 8-dBm audio level to provide 100% modulation. Determine the voltage level required to produce a 8-dBm level. Assume a 600- audio system.

Solution Since this is a 600- system, use the 0.775-V reference shown in Equation (5). dBm16002  20 log10 a 8 dBm  20 log 0.4  log

V2 b 0.775

(5)

V2 0.775

V2 0.775

log1 10.42 

V2 0.775 V2  1.947 V

Thus, to verify that a 8-dBm level is being provided to the input of the microwave transmitter, approximately 1.95 V must be measured across the 600- input. The term dBm also applies to communication systems that have a standard termination impedance other than 600 . For example, many communication systems are terminated with 75 . The 0-dBm value is still defined as 1 mW, but it is measured with respect to a 75- termination instead of 600 . Therefore, the voltage reference for a 0-dBm system with respect to 75  is obtained by solving for V in the expression P  V 2R as shown: V  1PR  110.0012 1752  0.274 V ˛

To calculate the voltage gain or loss with respect to a 75- load, use Equation (6). This value is specified as dBm(75) to indicate that this measure was made or calculated using a 1-mW reference relative to a 75- load. dBm1752  20 log10

V 0.274

(6)

dBm(75) a measurement made using a 1-mW reference with respect to a 75- load

Fifty-ohm systems are usually used in radio communications. The dBm voltage reference for a 50- system is V  1PR  110.0012 1502  0.2236 V ˛

Introductory Topics

9

dBm(50) a measurement made using a 1-mW reference with respect to a 50- load

dBW a measurement made using a 1-W reference

To calculate the voltage gain or loss expressed in dB for a 50- system [dBm(50)], use Equation (4) with V1  0.2236. This relationship is shown in Equation (7). dBm1502  20 log10

V 0.2236

(7)

It is common for power to be expressed in watts instead of milliwatts. In this case the dB unit is obtained with respect to 1 W and the dB values are expressed as dBW. 0 dBW is defined as 1 W measured with respect to a 1-W reference. Remember, dB is a relative measurement. As shown by Equations (1) and (3), both power and voltage gains can be expressed in dB relative to a reference value. In the case of dBW, the reference is 1 W; therefore, Equation (1) is written with 1 W replacing the reference P1. This gives Equation (8). dBW  10 log10

P2 1W

(8)

In some applications, it may be necessary to convert from one reference dB to another. Example 3 demonstrates how to convert from dBm to dBW.

Example 3 A laser diode outputs 10 dBm. Convert this value to (a) watts. (b) dBW.

Solution (a) Convert 10 dBm to watts. Substitute and solve for P2: 10 dBm  10 log log1 112 

P2 0.001

P2 P2 1 10  0.001 0.001

(2)

P2  0.01 W (b) Convert 10 dBm to dBW. dBW  10 log

dBV a measurement made using a 1-mV reference

0.01 W  20 dBW 1W

It is common with communication receivers to express voltage measurements in terms of dBV, dB-microvolts. For voltage gain calculations involving dBV, use Equation (4) and specify 1 V as the reference (V1) in the calculations, as shown in Equation (9). dBmV  20 log10

Introductory Topics

10

(8)

V2 1 mV

(9)

Conversion Table for Common dBm Values

Table 2

Common dBm Values 38 30 20 15 10 8 6 2 1 0 1 2 6 10 15 20 35 50 70

Equivalent Voltage Level (600 )

Equivalent Voltage 75 

Equivalent Voltage 50 

Watts

dBW

61.560 V 24.508 V 7.750 V 4.358 V 2.451 V 1.947 V 1.546 V 0.976 V 0.870 V 0.775 V 0.691 V 0.616 V 0.388 V 0.245 V 0.138 V 77.5 mV 13.78 mV 2.45 mV 0.2451 mV

21.765 V 8.665 V 2.740 V 1.541 V 0.866 V 0.688 V 0.547 V 0.345 V 0.307 V 0.274 V 0.244 V 0.218 V 0.137 V 86.65 mV 48.72 mV 27.40 mV 4.872 mV 866.5 V 86.65 V

17.761 V 7.071 V 2.236 V 1.257 V 0.7071 V 0.5617 V 0.4461 V 0.2815 V 0.2509 V 0.2236 V 0.1993 V 0.1776 V 0.1121 V 70.7 mV 39.8 mV 22.4 mV 3.98 mV 0.707 mV 70.7 V

6.3 1.0 1.00  101 3.16  102 1.00  102 6.31  103 3.98  103 1.58  103 1.26  103 1.00  103 7.94  104 6.31  104 2.51  104 1.00  104 3.16  105 1.00  105 3.16  107 1.00  108 1.00  1010

8 0 10 15 20 22 24 28 29 30 31 32 36 40 45 50 65 80 100

There are many applications using decibels in calculations involving relative values. The important thing to remember is that a relative reference is typically specified or understood when calculating or measuring a decibel value. Table 2 is a conversion table for many common dBm values. A conversion table is provided for dBm, voltage, and watts for 600-, 75-, and 50- systems. Additionally, a list of common decibel terms is provided in Table 3.

3

N OISE

Electrical noise may be defined as any undesired voltages or currents that ultimately end up appearing in the receiver output. To the listener this electrical noise often manifests itself as static. It may only be annoying, such as an occasional burst of static, or continuous and of such amplitude that the desired information is obliterated. Noise signals at their point of origin are generally very small, for example, at the microvolt level. You may be wondering, therefore, why they create so much trouble. Well, a communications receiver is a very sensitive instrument that is given a very small signal at its input that must be greatly amplified before it can possibly drive a speaker. Consider the receiver block diagram shown in Figure 1 to be representative of a standard FM radio (receiver). The first amplifier block, which forms the “front end” of the radio, is required to amplify a received signal from the radio’s antenna that is often less than 10 mV. It does not take a very large dose of undesired signal (noise) to ruin reception. This is true even though the transmitter output may be many thousands of watts because, when received, it is severely attenuated. Therefore, if the desired signal received is of the same order of magnitude as the

Electrical Noise any undesired voltages or currents that end up appearing in a circuit

Static electrical noise that may occur in the output of a receiver

Introductory Topics

11

Table 3 dBm dBm(600)

dBm(50) dBm(75) dBmW dBW dBV dBV dBVRMS dB/bit dBi dB/Hz

dBc dBmV

External Noise noise in a received radio signal that has been introduced by the transmitting medium

Internal Noise noise in a radio signal that has been introduced by the receiver

Wave Propagation movement of radio signals through the atmosphere from transmitter to receiver

dB Reference Table The dB using a 1-mW (0.001-W) reference, which is the typical measurement for audio input/output specifications. This measurement is also used in low-power optical transmitter specifications. The standard audio reference power level defined by 1 mW measured with respect to a 600- load. This measurement is commonly used in broadcasting and professional audio applications and is a common telephone communications standard. The standard defined by 1 mW measured with respect to a 50- load. This measurement is commonly used in radio-frequency transmission/ receiving systems. The standard defined by 1 mW measured with respect to a 75- load. The generic form for a 1-mW reference, also written as dBm. This term usually has an inferred load reference, depending on the application. A common form for power amplification relative to a 1-W reference (usually 50 ). Typical applications are found in specifications for radio-frequency power amplifiers and high-power audio amplifiers. A common form for specifying input radio-frequency levels to a communications receiver. This is called a decibel-microvolt, where 1 mV  1  10 6 V. The decibel value is obtained with respect to 1 V. A dB value measured relative to 1 VRMS, where 0 dB  1 VRMS. This value is sometimes used to define measurements in FFT frequency analysis, as described later in this chapter. A common term used for specifying the dynamic range or resolution for a pulse-code modulation (PCM) system such as a CD player. This reference is defined by 20/log122/bit  6.02 dB/bit. Decibel isotropic, or gain relative to an isotropic radiator. It is used as the reference when defining antenna gain. Relative noise power in a 1-Hz bandwidth. This term is used often in digital communications and in defining a laser’s relative intensity noise (RIN). For a laser system, this is an electrical, not an optical, measurement. A typical RIN for a semiconductor laser is 150 dB/Hz. The dB measurement relative to the carrier power. This measurement is used in 8 VSB digital television. A cable TV standard that uses a reference of 1 mV across 75  and is used to provide a measurement of the RF level in digital television systems.

undesired noise signal, it will probably be unintelligible. This situation is made even worse because the receiver itself introduces additional noise. The noise present in a received radio signal that has been introduced in the transmitting medium is termed external noise. The noise introduced by the receiver is termed internal noise. The important implications of noise considerations in the study of communications systems cannot be overemphasized.

External Noise Human-Made Noise The most troublesome form of external noise is usually the human-made variety. It is often produced by spark-producing mechanisms such as engine ignition systems, fluorescent lights, and commutators in electric motors. This noise is actually “radiated” or transmitted from its generating sources through the atmosphere in the same fashion that a transmitting antenna radiates desirable electrical signals to a receiving antenna. This process is called wave propagation. If the human-made noise exists in the vicinity of the transmitted radio signal and is

Introductory Topics

12

within its frequency range, these two signals will “add” together. This is obviously an undesirable phenomenon. Human-made noise occurs randomly at frequencies up to around 500 MHz. Another common source of human-made noise is contained in the power lines that supply the energy for most electronic systems. In this context the ac ripple in the dc power supply output of a receiver can be classified as noise (an unwanted electrical signal) and must be minimized in receivers that are accepting extremely small intelligence signals. Additionally, ac power lines contain surges of voltage caused by the switching on and off of highly inductive loads such as electrical motors. It is certainly ill-advised to operate sensitive electrical equipment in close proximity to an elevator! Human-made noise is weakest in sparsely populated areas, which explains the location of extremely sensitive communications equipment, such as satellite tracking stations, in desert-type locations.

Atmospheric Noise Atmospheric noise is caused by naturally occurring disturbances

Atmospheric Noise

in the earth’s atmosphere, with lightning discharges being the most prominent contributors. The frequency content is spread over the entire radio spectrum, but its intensity is inversely related to frequency. It is therefore most troublesome at the lower frequencies. It manifests itself in the static noise that you hear on standard AM radio receivers. Its amplitude is greatest from a storm near the receiver, but the additive effect of distant disturbances is also a factor. This is often apparent when listening to a distant station at night on an AM receiver. It is not a significant factor for frequencies exceeding about 20 MHz.

external noise caused by naturally occurring disturbances in the earth’s atmosphere

Space Noise The other form of external noise arrives from outer space and is called space noise. It is pretty evenly divided in origin between the sun and all the other stars. That originating from our star (the sun) is termed solar noise. Solar noise is cyclical and reaches very annoying peaks about every eleven years. All the other stars also generate this space noise, and their contribution is termed cosmic noise. Since they are much farther away than the sun, their individual effects are small, but they make up for this by their countless numbers and their additive effects. Space noise occurs at frequencies from about 8 MHz up to 1.5 GHz 11.5  109 Hz2 . While it contains energy at less than 8 MHz, these components are absorbed by the earth’s ionosphere before they can reach the atmosphere. The ionosphere is a region above the atmosphere where free ions and electrons exist in sufficient quantity to have an appreciable effect on wave travel. It includes the area from about sixty to several hundred miles above the earth.

Space Noise external noise produced outside the earth’s atmosphere

Solar Noise space noise originating from the sun

Cosmic Noise space noise originating from stars other than the sun

Internal Noise As stated previously, internal noise is introduced by the receiver itself. Thus, the noise already present at the receiving antenna (external noise) has another component added to it before it reaches the output. The receiver’s major noise contribution occurs in its very first stage of amplification, where the desired signal is at its lowest level, and noise injected at that point will be at its largest value in proportion to the intelligence signal. A glance at Figure 2 should help clarify this point. Even though all following stages also introduce noise, their effect is usually negligible with respect to the very first stage because of their much higher signal level. Note that the noise injected between amplifiers 1 and 2 has not appreciably increased the noise on

Introductory Topics

13

Received signal

Amplifier 1 output

Amplifier 1 Noise Noise

Amplifier 2

FIGURE 2

Output

Noise effect on a receiver’s first and second amplifier stages.

the desired signal, even though it is of the same magnitude as the noise injected into amplifier 1. For this reason, the first receiver stage must be carefully designed to have low noise characteristics, with the following stages being decreasingly important as the desired signal gets larger and larger.

Johnson Noise another name for thermal noise, first studied by J. B. Johnson

Thermal Noise internal noise caused by thermal interaction between free electrons and vibrating ions in a conductor

White Noise another name for thermal noise because its frequency content is uniform across the spectrum

Thermal Noise There are two basic types of noise generated by electronic circuits. The first one to consider is due to thermal interaction between the free electrons and vibrating ions in a conductor. It causes the rate of arrival of electrons at either end of a resistor to vary randomly, and thereby varies the resistor’s potential difference. Resistors and the resistance within all electronic devices are constantly producing a noise voltage. This form of noise was first thoroughly studied by J. B. Johnson in 1928 and is often termed Johnson noise. Since it is dependent on temperature, it is also referred to as thermal noise. Its frequency content is spread equally throughout the usable spectrum, which leads to a third designator: white noise (from optics, where white light contains all frequencies or colors). The terms Johnson, thermal, and white noise may be used interchangeably. Johnson was able to show that the power of this generated noise is given by Pn  kT ¢f where k  Boltzmann’s constant (1.38  1023 J/K) T  resistor temperature in kelvin (K) ¢f  frequency bandwidth of the system being considered Since this noise power is directly proportional to the bandwidth involved, it is advisable to limit a receiver to the smallest bandwidth possible. You may be wondering how the bandwidth figures into this. The noise is an ac voltage that has random instantaneous amplitude but a predictable rms value. The frequency of this noise voltage is just as random as the voltage peaks. The more frequencies allowed

Introductory Topics

14

(10)

R en 2

RL

en

Noise-generating resistance Maximum noise power voltage value when R = RL

FIGURE 3

Resistance noise generator.

into the measurement (i.e., greater bandwidth), the greater the noise voltage. This means that the rms noise voltage measured across a resistor is a function of the bandwidth of frequencies included. Since P  E2R, it is possible to rewrite Equation (10) to determine the noise voltage (en) generated by a resistor. Assuming maximum power transfer of the noise source, the noise voltage is split between the load and itself, as shown in Figure 3. 1en 22 2 Pn   kT ¢f R Therefore, e2n  kT ¢f R 4 en  14kT¢f R

(11)

where en is the rms noise voltage and R is the resistance generating the noise. The instantaneous value of thermal noise is not predictable but has peak values generally less than 10 times the rms value from Equation (11). The thermal noise associated with all nonresistor devices is a direct result of their inherent resistance and, to a much lesser extent, their composition. This applies to capacitors, inductors, and all electronic devices. Equation (11) applies to copper wire-wound resistors, with all other types exhibiting slightly greater noise voltages. Thus, dissimilar resistors of equal value exhibit different noise levels, which gives rise to the term low-noise resistor; you may have heard this term before but not understood it. Standard carbon resistors are the least expensive variety, but unfortunately they also tend to be the noisiest. Metal film resistors offer a good compromise in the cost/performance comparison and can be used in all but the most demanding lownoise designs. The ultimate noise performance (lowest noise generated, that is) is obtained with the most expensive and bulkiest variety: the wire-wound resistor. We use Equation (11) as a reasonable approximation for all calculations in spite of these variations.

Low-Noise Resistor a resistor that exhibits low levels of thermal noise

Introductory Topics

15

Example 4 Determine the noise voltage produced by a 1-M resistor at room temperature (17°C) over a 1-MHz bandwidth.

Solution It is helpful to know that 4kT at room temperature (17°C) is 1.60  10 20 Joules. en  14kT ¢f R 1  3 11.6  10201 211  106 211  106 2 4 2 8 2  11.6  10 2  126 V rms

(11)

From the preceding example we can deduce that an ac voltmeter with an input resistance of 1 M and a 1-MHz bandwidth generates 126 V of noise (rms). Signals of about 500 V or less would certainly not be measured with any accuracy. A 50- resistor under the same conditions would generate only about 0.9 V of noise. This explains why low impedances are desirable in low-noise circuits.

Example 5 An amplifier operating over a 4-MHz bandwidth has a 100- source resistance. It is operating at 27°C, has a voltage gain of 200, and has an input signal of 5 V rms. Determine the rms output signals (desired and noise), assuming external noise can be disregarded.

Solution To convert °C to kelvin, simply add 273°, so that K  27°C  273°  300 K. Therefore en  14kT ¢f R

(11) 23

 24  1.38  10  2.57 V rms

J/K  300 K  4 MHz  100 

After multiplying the input signal es (5 V) and noise signal by the voltage gain of 200, the output signal consists of a 1-mV rms signal and 0.514-mV rms noise. This is not normally an acceptable situation. The intelligence would probably be unintelligible!

Transistor Noise In Example 5, the noise introduced by the transistor, other than Shot Noise noise introduced by carriers in the pn junctions of semiconductors

its thermal noise, was not considered. The major contributor of transistor noise is called shot noise. It is due to the discrete-particle nature of the current carriers in all forms of semiconductors. These current carriers, even under dc conditions, are not moving in an exactly steady continuous flow since the distance they travel varies due to random paths of motion. The name shot noise is derived from the fact that when amplified into a speaker, it sounds like a shower of lead shot falling on a metallic surface. Shot noise and thermal noise are additive. Unfortunately, there is no valid formula to calculate its value for a complete transistor where the sources of shot noise are the currents within the emitter–base and collector–base diodes. Hence, the device user must refer to the manufacturer’s

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data sheet for an indication of shot noise characteristics. The methods of dealing with these data are covered in Section 5. Shot noise generally increases proportionally with dc bias currents except in MOSFETs, where shot noise seems to be relatively independent of dc current levels.

Frequency Noise Effects Two little-understood forms of device noise occur at the opposite extremes of frequency. The low-frequency effect is called excess noise and occurs at frequencies below about 1 kHz. It is inversely proportional to frequency and directly proportional to temperature and dc current levels. It is thought to be caused by crystal surface defects in semiconductors that vary at an inverse rate with frequency. Excess noise is often referred to as flicker noise, pink noise, or 1f noise. It is present in both bipolar junction transistors (BJTs) and field-effect transistors (FETs). At high frequencies, device noise starts to increase rapidly in the vicinity of the device’s high-frequency cutoff. When the transit time of carriers crossing a junction is comparable to the signal’s period (i.e., high frequencies), some of the carriers may diffuse back to the source or emitter. This effect is termed transit-time noise. These high- and low-frequency effects are relatively unimportant in the design of receivers since the critical stages (the front end) will usually be working well above 1 kHz and hopefully below the device’s high-frequency cutoff area. The low-frequency effects are important, however, to the design of lowlevel, low-frequency amplifiers encountered in certain instrument and biomedical applications. The overall noise intensity versus frequency curves for semiconductor devices (and tubes) have a bathtub shape, as represented in Figure 4. At low frequencies the excess noise is dominant, while in the midrange shot noise and thermal noise predominate, and above that the high-frequency effects take over. Of course, tubes are now seldom used and fortunately their semiconductor replacements offer better noise characteristics. Since semiconductors possess inherent resistances, they generate thermal noise in addition to shot noise, as indicated in Figure 4. The noise characteristics provided in manufacturers’ data sheets take into account both the shot and thermal effects. At the device’s high-frequency cutoff, fhc, the highfrequency effects take over, and the noise increases rapidly.

Excess Noise noise occurring at frequencies below 1 kHz, varying in amplitude inversely proportional to frequency

Transit-Time Noise noise produced in semiconductors when the transit time of the carriers crossing a junction is close to the signal’s period and some of the carriers diffuse back to the source or emitter of the semiconductor

Device noise Excess noise

Transit time effects Shot and thermal noise

1000 Hz

FIGURE 4

fhc

f

Device noise versus frequency.

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17

4

NOISE DESIGNATION

AND

CALCULATION

Signal-to-Noise Ratio

Signal-to-Noise Ratio relative measure of desired signal power to noise power

We have thus far dealt with different types of noise without showing how to deal with noise in a practical way. The most fundamental relationship used is known as the signal-to-noise ratio (S/N ratio), which is a relative measure of the desired signal power to the noise power. The S/N ratio is often designated simply as S/N and can be expressed mathematically as signal power PS S   N noise power PN

(12)

at any particular point in an amplifier. It is often expressed in decibel form as PS S  10 log10 N PN

(13)

For example, the output of the amplifier in Example 5 was 1 mV rms and the noise was 0.514 mV rms, and thus (remembering that P  E2R) S 12 R   3.79 or 10 log10 3.79  5.78 dB N 0.5142 R

Noise Figure

Noise Figure a figure describing how noisy a device is in decibels

Noise Ratio a figure describing how noisy a device is as a ratio having no units

S/N successfully identifies the noise content at a specific point but is not useful in relating how much additional noise a particular transistor has injected into a signal going from input to output. The term noise figure (NF) is usually used to specify exactly how noisy a device is. It is defined as follows: NF  10 log10

Si Ni  10 log10 NR So No

(14)

where SiNi is the signal-to-noise power ratio at the device’s input and SoNo is the signal-to-noise power ratio at its output. The term (SiNi)(SoNo) is called the noise ratio (NR). If the device under consideration were ideal (injected no additional noise), then SiNi and SoNo would be equal, the NR would equal 1, and NF  10 log 1  10  0  0 dB. Of course, this result cannot be obtained in practice.

Example 6 A transistor amplifier has a measured SN power of 10 at its input and 5 at its output. (a) Calculate the NR. (b) Calculate the NF. (c) Using the results of part (a), verify that Equation (14) can be rewritten mathematically as NF  10 log 10

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18

Si So  10 log 10 Ni No

Solution Si Ni 10  2 So No 5

(a)

NR 

(b)

NF  10 log10  10 log10

Si Ni  10 log10 NR So No

(14)

10  10 log10 2 5

 3 dB Si 10 log  10 log10 10  10  1  10 dB Ni

(c)

10 log

So  10 log10 5  10  0.7  7 dB No

Their difference (10 dB  7 dB) is equal to the result of 3 dB determined in part (b). The result of Example 6 is a typical transistor NF. However, for low-noise requirements, devices with NFs down to less than 1 dB are available at a price premium. The graph in Figure 5 shows the manufacturer’s NF versus frequency characteristics for the 2N4957 transistor. As you can see, the curve is flat in the midfrequency range (NF  2.2 dB) and has a slope of 3 dB/octave at low frequencies (excess noise) and 6 dB/octave in the high-frequency area (transit-time noise). An octave is a range of frequency in which the upper frequency is double the lower frequency. Manufacturers of low-noise devices usually supply a whole host of curves to exhibit their noise characteristics under as many varied conditions as possible. One of the more interesting curves provided for the 2N4957 transistor is shown in Figure 6. It provides a visualization of the contours of NF versus source resistance and dc collector current for a 2N4957 transistor at 105 MHz. It indicates that noise operation at 105 MHz will be optimum when a dc (bias) collector current of about 0.7 mA 12

Noise figure, NF (dB)

range of frequency in which the upper frequency is double the lower frequency

2N4957 VCE = 10 V I C = 1 mA RS = 150 Ω

10 8

Octave

3 dB/octave 6 dB/octave

6.0 4.0 2.0

0.001

0.01

0.1

1.0 10 Frequency, f (MHz)

100

1,000

10,000

FIGURE 5 NF versus frequency for a 2N4957 transistor. (Courtesy of Motorola Semiconductor Products, Inc.)

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The Agilent N8975A is a high-performance noise figure analyzer designed to make fast, accurate, and repeatable noise figure measurements. (© Agilent Technologies, Inc. 2007 Reproduced with Permission, Courtesy of Agilent Technologies, Inc.)

and source resistance of 350  is utilized because the lowest NF of 1.8 dB occurs under these conditions. The current state of the art for low-noise transistors offers some surprisingly low numbers. The leading edge for room temperature designs at 4 GHz is an NF of about 0.5 dB using gallium arsenide (GaAs) FETs. At 144 MHz, amplifiers with NFs down to 0.3 dB are being employed. The ultimate in low-noise-amplifier (LNA) design utilizes cryogenically cooled circuits (using liquid helium). Noise figures down to about 0.2 dB at microwave frequencies up to about 10 GHz are thereby made possible.

Source resistance, RS (Ω)

1000 700 500 1.8 dB

300

2.0 dB

200

2.5 dB 100 70 50 30 20 10 0.1

3.0 dB 2N4957 VCE = 10 V f = 105 MHz 0.2 0.3

NF = 3.5 dB

0.5 0.7 1.0

2.0 3.0

5.0 7.0 10

Collector current, IC (mA)

FIGURE 6 Noise contours for a 2N4957 transistor. (Courtesy of Motorola Semiconductor Products, Inc.)

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20

Reactance Noise Effects In theory a reactance does not introduce noise to a system. This is true for ideal capacitors and inductors that contain no resistive component. The ideal cannot be attained, but fortunately resistive elements in capacitors and inductors usually have a negligible effect on system noise considerations compared to semiconductors and other resistances. The significant effect of reactive circuits on noise is its limitation on frequency response. Our previous discussions on noise have assumed an ideal bandwidth that is rectangular in response. Thus, the 10-kHz bandwidth of Example 7 implied a total passage within the 10-kHz range