ELECTRONIC AND
`
`RADIO ENGINEERING
`FourtH EDITION
`
`FREDERICK EMMONS TERMAN
`
`Professor of Electrical Engineering
`Dean of the School of Engineering
`Stanford University
`
`Assisted by
`
`ROBERT ARTHUR HELLIWELL
`Associate Professor of Electrical Engineering
`Stanford University
`
`JOSEPH MAYO PETTIT
`Professor of Electrical Engineering
`Stanford University
`
`DEAN ALLEN WATKINS
`Associate Professor of Electrical Engineering
`Stanford University
`
`WILLIAM RALPH RAMBO
`Associate Director, Applied Electranics Laboratory
`Stanford University
`
`ASIAN STUDENT S’EDITION
`
`McGRAW-HILL BOOK COMPANY, INC.
`New York
`Toronto
`London
`
`KOGAKUSHA COMPANY LTD.
`TOKYO
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 001
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 001
`
`

`

`1922, 1932, 1937,1947
`
`ELECTRONIC AND RADIO ENGINEERING
`
`ASIAN STUDENTS’ EDITION
`
`TOSHO PRINTING CO., LTD., TOKYO, JAPAN
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 002
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 002
`
`

`

`PREFACE
`
`This fourth edition has the same objective as the three prior editions,
`namely, to provide a text and reference book that summarizes in easily
`understandable terms those principles and techniques which are the
`basic tools of the electronic and radio engineer.
`In keeping with current
`trends, increased emphasis is placed on the general techniques of elec-
`tronics, without regard to the extent of their use in radio systems. This
`change is reflected in the new title, ‘Electronic and Radio Engineering,”
`which is more descriptive of the subject matter actually covered in the
`present volume than is the previoustitle, “Radio Engineering.”
`The keynote continues to be thorough coverage combined with a pres-
`entation that allows the reader to study a particular topic without having
`to read the entire book. The level of presentation, particularly the
`mathematical level, remains unchanged. Thus the present volume is
`designed to serve as a text and reference for the sameclientele that found
`the previous editions so useful.
`To keep pace with a rapidly advancing technology, new material has
`been added in practically every chapter. More than half theillustrations
`are new,andall have been redrawn to conform to new graphic standards.
`A new chapter dealing with microwave tubes makes available for the first
`time an explanation in simple language of the basic mechanism of oper-
`ation of traveling-wave tubes and backward-wave oscillators (carcino-
`trons).
`In the treatment of wideband video and tuned amplifiers,
`primary emphasis is placed on the rise time, overshoot, and sag, since
`these characteristics are more indicative of the performance underactual
`conditions than is the older approach in terms of amplitude and phase
`behavior as a function of frequency. The material on nonlinear wave-
`forms and pulse techniques has been greatly expanded to provide more
`complete coverage of this important aspect of electronics. The chapter
`on television has been thoroughly revised, and a compact and simple
`explanation is given of the system of color television now standard in the
`United States.
`Increased attention is also Placed on propagation
`phenomenainvolving the troposphere,
`Of particular importance is the chapter on Transistors and Related
`Semiconductor Devices, one of the longest in the book. Here is pre-
`sented a simple, straightforward explanation of the basic phenomena
`oceurring inside the transistor, and of how these phenomena lead to the
`terminal characteristics. This treatment is such that it can be under-
`stood by undergraduate students; at the sametime,it is sufficiently com-
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 003
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 003
`
`

`

`vi
`
`PREFACE
`
`plete and fundamental to provide a firm foundation for further study of
`this new and very important subject.
`Special attention has been given to the needs of the teacher. Because
`of the growth of electronics, it is no longer possible to cover every impor-
`tant topic adequately in a one-year course.
`‘Electronic and Radio
`Engineering’’ provides the instructor with an opportunity to select those
`topics which he himself wishes to emphasize, and at the same time pro-
`vides the student with a reference book of comprehensive coverage and
`continuing value.
`It will be observed that the book breaks down into
`three distinct parts, namely, a group of chapters dealing with circuits.
`(components,
`resonant circuits,
`transmission lines, waveguides, and '
`cavity resonators); a group of chapters concerned with the fundamentals
`of electronic engineering (vacuum tubes, transistors, amplifiers, oscil-
`lators, modulators, detectors, nonlinear waveforms, etc.), which are the
`heart of the book; and a concluding group of chapters concerned with
`radio systems and radio engineering (antennas, propagation, transmitters,
`receivers,
`television, radar, and radio aids to navigation). Thus an
`instructor can, if he desires, concentrate on the material concerned with
`fundamental electronics and regard the remaining subject matter as
`available to the student, should he need to extend his knowledge at a
`future date. "Alternatively, the instructor can choose to cover a series
`of selected topics, for example, waveguides, wideband systems, pulse
`circuits,
`television, ete. Another possibility is to concentrate on the
`material concerned primarily with radio systems. Many other combi-
`nations, are, of course, possible.
`An important feature for the teacher is the more than 1250 Problems
`and Exercises. Many of these involve numerical calculations, but more
`than half of them are thought questions that will require the student to
`give further consideration to topics covered in the text. Such Exercises
`can be used to extend andsolidify the student’s knowledge; they are also
`suggestive of questions suitable for use on examinations, The numberof
`Problems and Exercises is so large that the same problem need not be
`assigned to a class more often than once every two or three years.
`The collaborators listed, on the title page have made important con-
`tributions to the preparation of this volume. Dr. Helliwell worked on the
`sections dealing with ionospheric propagation, and Dr. Pettit is in large
`measure responsible for the general character of the chapter dealing with
`transistors and semiconductors. The treatment of traveling-wave tubes
`and backward-wave oscillators is due to Dr. Watkins. William Rambo
`prepared the background material used in revising the presentation on
`radar.
`In addition, acknowledgment
`is made to Dr. B. H. Wadia,
`Bruno Ludovici, and Arthur Vassilaides, graduate students at Stanford,
`for assistance in preparing illustrations.
`
`Freprerick Emmons TERMAN
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 004
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 004
`
`

`

`CONTENTS
`
`Preface.
`
`2
`
`2 we ewa
`
`Carter 1. The Elements of a System of Radio Communication
`
`.
`
`.
`
`1
`
`CIRCUIT ELEMENTS AND CIRCUIT THEORY
`
`. we 1
`-
`_2. Circuit Elements.
`.
`.
`.
`.
`3.
`Properties of Circuits with Lumped Constants
`.
`,
`44
`4. Transmission Lines
`.
`.
`soe ee eee BD
`5. Waveguides and Cavity Resonators oe ee ew ee 17
`
`ELECTRONIC ENGINEERING FUNDAMENTALS
`
`169
`228
`252
`288
`
`Fundamental Properties of Electron Tubes
`6.
`.
`.
`.
`.
`.
`7. Electron Optics and Cathode-ray Tubes.
`.
`.
`.
`.
`.
`8. Voltage Amplifiers for Audio Frequencies.
`.
`.
`.
`.
`.
`9. Voltage Amplifiers for Video Frequencies.
`.
`10. Amplifier Distortion, Power Amplifiers, and Amplifier Sys-
`tems
`.
`.
`toe ee ee BID
`11. Negative Feedbuek iin1 Ainplifiers toe ee ew BNE
`12. Tuned Voltage Amplifiers
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`400
`13. Tuned Power Amplifiers
`©.
`2.
`. . .
`1
`.
`.
`.
`.
`448
`14. Vacuum-tube Oscillators
`.
`2.
`2.
`1
`1 ww. 489
`15. Amplitude Modulation.
`.
`2.
`2.
`2.
`2.
`1
`1 1.
`.
`588
`16. Detectorsand Mixers
`.
`.
`.
`woe ee ee (84F
`17. Frequency Modulation.
`.
`.
`.
`586
`18. Wave Shaping, Nonlinear Waves, and Pulse Techniques
`.
`618
`19. Microwave Tubes... rr 51)
`20. Power for Operating Vacuum Tubes
`.
`.
`.
`.
`702
`21. Transistors and Related Semiconductor Devices.
`.
`.
`.
`738
`
`RADIO ENGINEERING AND RADIO SYSTEMS
`
`22, Propagation of Radio Waves
`.
`. . . . 6808
`23. Antennas. ..
`¢
`864
`24, Radio Transmitters, Receivers, and Communication Systems 935
`25, Television.
`.
`.
`2 ee ww OFF
`26. Radar and Radio Aids to Navigation .
`»
`oa
`ew
`ew
`hw 1015
`
`Name Index
`
`.
`
`Subject Index 2
`
`2
`
`2
`
`0. ee ee ee eww ew ww 1057
`
`6 eee et ee we ww ww 1081
`vii
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 005
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 005
`
`

`

`CHAPTER 1
`
`THE ELEMENTS OF A SYSTEM
`OF RADIO COMMUNICATION
`
`1-1. Radio Waves. Electrical energy that has escaped into free space
`exists in the form of electromagnetic waves. These waves, which are
`commonlycalled radio waves, travel with the velocity of light and consist
`of magnetic and electric fields that are at right angles to each other and
`also at right angles to the direction of travel.
`If these electric and
`magnetic fluxes could actually be seen, the wave would have the appear-
`ance indicated in Fig. 1-1. One-halfof the electrical energy contained
`
`@ |
`
` eee
`
`
`
`(bd) SIDE VIEW
`
`oe
`
`{0} FRONT VIEW
`THROUGH PLANE o@
`
`Thesolid lines repre-
`Fic, 1-1. Front and side views of a vertically polarized wave.
`sent electric flux; the dotted lines and the circles indicate magnetic flux.
`
`in the waveexists in the form of electrostatic energy, while the remaining
`half is in the form of magnetic energy.
`The essential properties of a radio wave are the frequency, intensity,
`direction of travel, and plane of polarization. The radio waves produced
`by an alternating current will vary in intensity with the frequency of the
`current and will therefore be alternately positive and negative as shown
`in Fig. 1-1b. The distance occupied by one complete cycle of such an
`alternating waveis equal to the velocity of the wave divided py the num-
`ber of cycles that are sent out each second andis called the wavelength.
`The relation between wavelength d in meters and frequency f in cycles
`per second is therefore
`
`d
`
`_, 300,000,000
`f
`
`(1-1)
`
`The quantity 300,000,000 is the velocity of light in meters per second.
`The frequency is ordinarily expressed in kilocycles, abbreviated ke, or in
`megacycles, abbreviated Mc. A low-frequency wave is seen from Eq.
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 006
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 006
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`

`

`(Cuap. 1
`SYSTEM OF RADIO COMMUNICATION
`2
`(1-1) to have s long wavelength, while a high frequency corresponds to a
`short wavelength.
`.
`The strength of a radio waveis measured in terms of the voltage stress
`produced in space by the electric field of the wave, and it is usually
`expressed in microvolts stress per meter. Since the actual stress pro-
`duced at any point by an alternating wave varies sinusoidally from instant
`to instant, it is customary to consider the intensity of such a wave to be
`the effective value of the stress, which is 0.707 times the maximum stress
`in the atmosphere during the cycle. The strength of the wave measured
`in terms of microvolts per meterof stress in space is also exactly the same
`voltage that the magnetic flux of the wave induces in a conductor 1 m
`long when sweeping across this conductor with the velocity oflight.
`The minimum field strength required to give satisfactory reception of a
`wave depends upon a numberof factors, such as frequency, type of signal
`involved, and amount of interference present. Under some conditions
`radio waves having signal strengths as low as 0.1 pv per m are usable.
`Occasionally signal strengths exceeding 1000 wv per m are required to
`ensure entirely satisfactory reception at all times.
`In most cases the
`weakest useful signal strength lies somewhere between these extremes.
`A plane parallel to the mutually perpendicularlines of the electric and
`electromagnetic flux is called the wavefront. The wave always travels
`in a direction at right angles to the wavefront, but whetherit goes forward
`or backward depends upon the relative direction of the lines of magnetic
`and electric flux.
`If the direction of cither the magnetic or electric flux
`is reversed, the direction pf travel is reversed; but reversing both sets
`of flux has no effect.
`The direction of the electric lines of flux is called the direction of
`polarization of the wave.
`If the electric flux lines are vertical, as shown
`in Fig. !-1, the waveis vertically polarized; when the electric flux lines
`are horizontal and the electromagnetic flux lines are vertical, the wave
`is horizontally polarized.
`Propagation of Radio Waves of Different Frequencies. As radio waves
`travel away from their point of origin, they become attenuated or weak-
`ened. This is due in part to the fact that the waves spread out.
`In addition, however, energy may be absorbed from the waves by the,
`ground or by the ionized regions in the upper atmosphere termed the
`ionosphere, and the waves mayalso hereflected or refracted by the iono-
`sphere, or by conditions within the lower atmosphere, or by the ground.
`Theresulting situationis quite complex and differs greatly for radio waves
`of different frequencies, as shown in Table 1-1, which summarizes the
`behaviorof different classes of radio waves.
`1-2. Radiation of Electrical Energy. Every electrical circuit carry-
`ing alternating current radiates a certain amountof electrical energy in
`the form of electromagnetic waves, but the amount of energy thus radi-
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 007
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 007
`
`

`

`Sec. 1-2]
`
`RADIATION OF ELECTRICAL ENERGY
`
`3
`
`ated is extremely small unless all the dimensions of the circuit approach
`the order of magnitude of a wavelength. Thus, a powerline carrying
`60-cycle current with a 20-ft spacing between conductors will radiate
`practically no energy because a wavelength at 60 cycles is more than
`3000 miles, and 20 ft is negligible in comparison. On the other hand, a
`coil 20 ft in diameter and carrying a 2000-ke current will radiate a con-
`siderable amount of energy because 20 ft is comparable with the 150-m
`TABLE 1-1
`CLASSIFICATION OF RADIO WAVES
`
`
`Class
`
`Frequency Wavelength
`range
`range
`
`.
`:
`.
`Propagation charscteriatice
`Typical uses
`
`
`
`
`
`
`Very low fre- 30 ,000—10,000) Low attenuation at all times|Long-distance point-10-30 ke
`
`quency (VLF)
`m
`of day and of year; charac-|
`to-point communica-
`teristics very reliable
`tion
`Low frequency 10,000 1000|Propagation at night similar} Long-distance point-30-300 ke
`
`
`(LF) te VLF but slightly leas|to-point servive, ma-m .
`
`
`
`reliahle; daytime ahbsorp-|rine, navigational
`tion greater than VLF
`aids
`Medium fre- {1000-100 m|Attenuation low at night|Broadcasting, marine300-3000 ke
`
`quency (MF)
`and high in daytime
`coinmunication,
`navigation, harbor’
`telephone, ete.
`High frequency Transmission over consider-|Moderate and long-3-30 Me 100-!0 m
`
`(HF)
`able distance depends
`distance communics-
`solely on the ionosphere,|tion of all types
`and so varies greatly with
`time of day, season, and
`frequency
`Very high fre- Substantially straight-line{|Short-distance com-30-300 Mc Wim
`
`quency (VHF)
`propagation analoxdus to} munication, televi-
`that of hght waves; un-
`sion, frequency mod-
`affected by ionosphere
`ulation, radar, sir-
`plane navigation
`
`
`
`quency (UHF)*
`munication, radar,
`relay systems, televi-
`sion, ete.
`Buper-high fre- 3000-30,000|10 1 em Same Radar, radio relay,
`
`
`
`
`quency (SHF)*|Mc navigation
`
`* Frequencies higher than about 2000 Mcare frequently referred to as microwave frequencies.
`
`
`
`
`
`
`
`Ultra-high fre- 300-3000 Me|100-10 cm Same Short-distance com-
`
`wavelength of this radio wave. From these considerationsit is apparent
`that the size of radiatur required is inversely proportional to the fre-
`quency. High-frequency waves can therefore be produced by a small
`radiator, while low-frequency waves require a large antenna system for
`effective radiation.
`Every radiator has directional characteristics as a result of which it
`sends out stronger waves in certain directions than in-others, Directional
`characteristics of antennas are used to concentrate the radiation toward
`the point to whichit is desired to transmit, or to favor reception of energy
`arriving from a particular direction.
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 008
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 008
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`

`

`4
`
`[Curap. 1
`SYSTEM OF RADIO COMMUNICATION
`and Control of Radio-frequency Power. The radio-
`1-3. Generation
`and
`d by a radio transmitter is practically always
`frequency power require
`i
`i
`Vacuum tubes
`can
`acuum-tube oscillator or amplifier.
`ine
`otamower into a-c energy for all frequencies from the very lowest
`upto30 000 Me, or even higher. Under most conditions the efficiency
`with which this transformation takes place is in the neighborhood of 50
`percentor higher. At frequencies up to well over 1000 Mc,the amountof
`_fo1
`foi TELEGRAPH CODE SIGNAL
`(f} SOUND VIBRATION
`
` {@) RADIO WAVE AFTER MODULATION BY
`
`(@) RADIO WAVE AFTER MOQULATION BY
`SOUND VIBRATION
`
`TELERAPH CODE SIGNAL
`
`ENOUGH EE
`TET ET
`
`{e)}
`
`AVERAGE
`
`+” VALUES —~.
`
`Ww)
`MOOULATED WAVES AFTER RECTIFICATION,
`SHOWING AVERAGE VALUES
`
`Fra. 1-2. Diagram showing how a signal may be transmitted by modulating the
`amplitude of a radio wave, and how the original signal may be recovered from the
`modulated wave by rectification. For the sake of clarity the radio frequency is shown
`as being much lower than would usually be the case.
`
`powerthat can be generated continuously by vacuum tubesis of the order
`of kilowatts.
`‘
`Modulation.
`If a radio wave is to convey a message, some feature of
`the wave must be varied in accordance with the information to be trans-
`mitted. One way to do this, termed amplitude modulation, consists in
`varying the amplitude of the radiated wave.
`In radio telegraphy, this
`involves turning the radio transmitter on andoff in accordance with the
`dots and dashes of the telegraph code, as illustrated in Fig. 1-20.
`In
`radio-telephone transmission by amplitude modulation the radio-fre-
`quency waveis varied in accordance with the pressure of the sound wave
`being transmitted, as shown in Fig. 1-2e. Similarly in picture trans-
`mission, the amplitude of the wave radiated at any one time is made
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 009
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 009
`
`

`

`5
`.
`RECEPTION OF RADIO SIGNALS
`Sec. 1-4}
`proportional to the light intensity of the part of the picture that is being
`transmitted at that instant.
`Intelligence may be transmitted by other means than by varying the
`amplitude. For example, one may maintain the amplitude constantand
`vary the frequency that is radiated in accordance with the intelligence,
`thus obtaining frequency modulation. This results in a wave such as
`shown in Fig. 1-3b, which is to be
`compared with the corresponding
`amplitude-modulated wave of Fig.
`1-3a. Frequency modulation is
`widely used in very high-frequency
`communication systems.
`1-4. Reception of Radio Signals.
`In the reception of radio signals it
`is first necessary to abstract energy
`from the radio wave passing the
`receiving
`point. Any
`antenna
`capable
`of
`radiating
`electrical
`
`energy is also able to absorb en-
`
`(8) SAME INFORMATION TRANSMITTED BY
`FREQUENCY - MODULATED WAVE
`
`ergy from a passing radio wave.
`This occurs because the electro-
`Fic. 1-3. Character of waves produced by
`amplitude modulation and by frequency
`magnetic flux of the wave, in cutting
`modulation, where the modulation is
`across the antenna conductor, in-
`sinusoidal in both cases. For the sake
`duces in the antenna a voltage that
`of clarity the radio frequency is shown
`much lower than would usually be the
`varies with time in exactly the same
`case.
`way as does the current flowing in
`the antenna radiating the wave. This induced voltage, in association
`with the current that it produces, represents energy that is absorbed from
`the passing wave.
`Since every wave passing the receiving antenna induces its own voltage
`in the antenna conductor, it is necessary that the receiving equipment be
`capable of separating the desired signal from the unwanted signals that
`are also inducing voltages in the antenna. This separation is made on
`the basis of the difference in frequency between transmitting stations and
`is carried out by the use of resonant circuits which can be made to dis-
`criminate very strongly in favor of a particular frequency. The ability to
`discriminate between radio waves of different
`frequencies is called
`selectivity and the process of adjusting circuits to resonance with the fre-
`quency of a desired signal is spoken of as tuning.
`Althoughintelligible radio signals have been received from radio trans-
`mitters thousands of miles distant, using only the energy abstracted from
`the radio wave by the receiving antenna, much moresatisfactory recep-
`tion can be obtained if the received energy is amplified. This amplifica-
`tion may be applied to the radio-frequency cursnts before detection, in
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 010
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 010
`
`

`

`
`6 SYSTEM OF RADIO COMMUNICATION—{Cuar. 1
`which case it is called radio-frequency amplification; or it may be applied
`2
`rectified currents after detection, in which case it is called audio-
`to the res
`lification.
`The use of amplification makes possible the
`satatartoryreception of signals from waves that would otherwise be too
`sone to give an audible response. The only satisfactory method of
`amplifying radio signals that has been discovered is by the use ofvacuum
`tubes or transistors. Before vacuum tubes were discovered, radio recep-
`tion had available only the energy abstracted from the radio wave by the
`reivi
`ntenna.
`Detection. The process by which the message being transmitted ig
`reproduced from the modulated radio-frequency current present in the
`receiveris called detection, or sometimes demodulation. With amplitude-
`modulated waves, detection is accomplished by rectifying the radio-
`frequency currents to produce a current that varies in accordance with
`the modulation of the received wave. Thus, when the modulated wave
`shown ate of Fig. 1-2 is rectified, the resulting current, shown atf, is seen
`to have an average value that varies in accordance with the amplitude of
`the original signal.
`In the transmission of code signals by radio, the
`rectified current reproduces the dots and dashes of the telegraph code,as
`shown at Fig. 1-2c, and could be used to operate a telegraph sounder.
`Whenit is desired to receive the telegraph signals directly on a telephone
`receiver,it is necessary to break up the dots and dashesat an audible rate
`in order to give a note that can be heard, sinve otherwise the telephone
`receiver would give forth a succession of unintelligible clicks.
`The detection of a frequency-modulated wave involves two steps.
`First, the waveis transmitted through a circuit in which the relative
`response depends upon the frequency. The wave that then emerges from
`the circuit is amplitude-modulated,since as the frequency of the constant-
`amplitude input wave changes, the output amplitude will follow the
`variation of circuit transmission with frequency. The resulting amplitude-
`modulated wave is then rectified.
`1-5. Nature of a Modulated Wave. A sine wave conveys very little
`informationsinceit repeats over and over again. When a wave is modu-
`lated, either in amplitude or frequency,it is no longer a simple sine wave,
`but is instead a mixture of several wavesof slightly different frequencies
`Superposed upon each other. The actual nature of a modulated wave
`can be deduced by writing down the equation of the wave and making a
`mathematical ahalysis of the result. Thus, in the case of the simple
`sine-wave amplitude modulation shownin Fig. 1-3a, the amplitude of the
`radio-frequency oscillation is given by H = Ey + mE,sin 2eft, in which
`Hurpresents the average amplitude,f, the frequency at which the ampli-
`tudeis varied, and m the ratio of amplitude variation from the average to
`the average Amplitude, which is called the degree of modulation. The
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 011
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 011
`
`

`

`Src. 1-5)
`
`NATURE OF A MODULATED WAVE
`
`7
`
`equation of the amplitude-modulated wave can be hence written as
`
`e = Eo(1 + main 2xf,t) sin 2nft
`(1-2)
`in which f is the frequency of the radio oscillation. Multiplying out the
`right-hand side of Eq. (1-2) gives
`
`e = Eysin 2nft + mEy sin 2af,é sin 2xft
`
`By expanding the last term into functions of the sum and difference
`angles by the usual trigonometric formula, the equation of a wave with
`simple sine-wave amplitude modulation can be written in the form
`
`e= Ey sin 2nrft + 8 con aef — jot -— me—" cos Qn(f +f.)é
`
`(1-3)
`
`Equation (1-3) shows that the wave with sine-wave modulation consists
`of three separate waves. The first of these, represented by the term
`Eo sin 2xft,
`is called the carrier.
`Its amplitude is independent of the
`presence or absence of modulation and is equal to the average amplitude
`of the wave. The two other components are alike as far as magnitudeis
`concerned, but the frequency of one of them is less than that of the
`carrier frequency by an amount equal to the modulation frequency, while
`the frequency of the other is more than that of the carrier by the same
`amount. These two components, called sideband frequencies, carry the
`intelligence that is being transmitted by the modulated wave.
`Thefre-
`quency of the sideband components relative to the carrier frequency is
`determined by the modulation frequency. The relative amplitude of the
`sideband components is determined by the extent of the amplitude varia-
`tions that are impressed upon the wave, i.e., by the degree of modulation.
`When the modulation is more complex than the simple sine-wave
`amplitude variation of Fig. 1-3a, the effect is to introduce additional side-
`band components. Thus,if the wave of a radio-telephone transmitter is
`amplitude-modulated by a complex sound wave containing pitches of 1000
`and 1500 cycles, the modulated wave will contain one pair of 1000-cycle
`sideband components and one pair of 1500-cycle sideband components.
`The analysis of a frequency-modulated wave is somewhat more com-
`plex but leads to an analogousresult. The principal differenceis that the
`frequency-modulated wave not only contains the same sideband fre-
`quencies as does the corresponding amplitude-modulated wave, but in
`addition contains higher-order side bands. Thus, if a wave has its fre-
`quencyvaried at a rate of 1000 times per second, the resulting modulated
`wave will contain not only a pair of 1000-cycle sideband components,
`but in addition a pair of 2000-cycle sideband components,possibly a pair
`of 3000-cycle sideband components, etc. The amplitude of these various
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 012
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 012
`
`

`

`8
`
`SYSTEM OF RADIO COMMUNICATION
`
`[(Cuar. 1
`
`sideband pairs will depend upon the extent and uponthe rate of frequency
`variation.
`Thecarrier and sideband frequencies are
`Significance of the Sidebands.
`not a mathematical fiction, but have a real existence, ag is evidenced by
`the fact that the various frequency components of a modulated wave can
`be separated from each other by suitable filter circuits. The sideband
`frequencies can be considered as being generated as a result of varying
`the wave. They are present only when the wave is being varied, and
`their magnitude and frequency are determined by the character of the
`modulation.
`It is apparent that the transmission of intelligence requires the use of a
`bandof frequencies rather than a single frequency. Speech and music of
`the quality reproduced in standard broadcasting involve frequency com-
`ponents from about 100 cycles up to 5000 cycles; when modulated upon a
`carrier wave, the total bandwidth involved is therefore 10,000 cycles.
`If
`this entire band is not transmitted equally well through space, and by the
`circuits in both transmitter and receiver through which the modulated
`wave must pass, then the sideband frequency components that are dis-
`criminated against will not be reproduced in the receiving equipment with
`proper amplitude, and a loss in quality will result. With telegraph
`signals, the required sidebandis relatively narrow because the amplitude
`of the signals is varied only a few times a second, but a definite frequency
`band is still required.
`If some of the sideband components of the code
`signal are not transmitted,
`the received dots and dashes tend to be
`rounded off and run together,-and may become indistinguishable.
`1-6. The Decibel. The decibel (abbreviated db) is a logarithmic unit
`used in communication work to express power ratios.
`If the powers
`being compared are P, and Py, then
`Decibels = 10 logue 5
`(1-4)
`The sign associated with the number of decibels indicates which poweris
`greater; thus a negative sign means P> is less than P,.
`The decibel has no other significance than that given in Eq. (1-4).
`Thus,if decibels are used to express amplification, this simply means that
`the presence of the amplification increases the power output by the num-
`ber of decrbels attributed to the amplification. Again, under many
`conditions relative power is proportional to the square of the voltage Z
`(or current J, or field B, etc.). Under these conditions
`(1-5)
`Decibels = 20 logy Zz = 20 logie 7? = 20 logio a etc.
`1
`1
`These relations must be used with caution, however, as they hold only
`when theresistance associated with £; (or I; or B:) is the same ag asso-
`ciated with F, (or J; or B)).
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 013
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 013
`
`

`

`Suc. 1-6}
`
`9
`
`THE DECIBEL
`TABLE 1-2
`(2) POWER, VOLTAGE, AND CURRENT RATIOS FOR ASSIGNED
`DECIBEL VALUES
`
`Current and
`
` Db voltage ratio
`Loss
`
`Powerratio
`Gain
`Loss
`
`
`
`
`
`0.0|1.001. 0.316 10.00 0.100
`
`
`0.2|1.02)0. 0.251 15.8 0.063
`
`
`
`0.4|1.05 (0. 0.200 251 0.040
`
`
`
`0.6|1.070. 0.158 39.8 0.025
`
`
`
`0.8|1.100. 0.126 63.1 0.016
`
`
`1.0
`{1.12 /0.8!
`0.100
`100.0
`0.010
`
`
`1.5|1.19 0.841) 1. 0.056 3.16 X 109} 3.16 X 107%
`
`
`2.0|1.26 10.794) 1. 0.032 10# 10-8
`
`
`
`2.5|1.33 |0.750) 1. 0.018|3.16 X 10) 3.16 x 10-¢
`
`3.0|1.41 0.708] 2. 10.010 104 10~4
`
`
`
`3.5|1.50 |0. 668} 2. 10.006 3.16 X 104] 3.16 X 1078
`
`
`4.0|1.580.631} 2. 0.003 105 10-*
`
`
`
`
`
`4.5|1.68 /0.596) 2.82 1,000/0.001 10¢ 10-*
`
`5
`1.78 0.562) 3.16
`3, 160}0.0003
`107
`10-7
`6
`2.00 (0.501) 3.98
`16 ,000/0.0001
`108
`10-*
`2.24 10.447) 5.01
`7
`31 ,600/0.00003
`10°
`10°
`
`
`8|2.51 (0.398) 6.31 )0. 100 ,000/0.00001 10° 10-10
`
`
`
`2.82 |0.355] 7.94
`|0. 126] 120 |1,000,000/0.000001
`9
`10%
`10-"
`
`
`(®) DECIBEL EQUIVALENT OF POWER, VOLTAGE, AND
`CURRENT RATIOS
`
`
`
`Dbequivalent
`Db equivalent
`Dbequivalent
`
`
`Ratio Voltage or|Ratio Voltage or|Ratio Voltage or
`Po
`current,
`Po
`current
`Pow
`current
`
`
`
`10-* ~={—60.00) —120.00|]1.2|0.79 10|10.001.58 20.00
`
`
`
`
`
`10-§ |—50.00] —100.00|1.4|1.46 12|10.792.92 21.58
`
`
`
`
`
`
`10—« 1.6|2.04 14|11.46—40.00] ~—80.00] 4.08 22.92
`
`
`
`
`0.001 |—30.00) -~-60.00]1.8|2.55 16|12.045.10 24.08
`
`
`
`0.003 |~25.23) —50.46|2.0;3.01 18|12.556.02 25.10
`
`
`
`
`0.005 |—23.01; —46.02] 2.5|3.98 20|13.017.96 26.02
`
`0.01 3.0|4.77 25|13.98|—20.00) -—40.00] 0.54 27.96
`
`
`
`
`
`
`
`
`
`
`
`
`0.08 3.5|5.44 30|14.77|-15.23| ~—30.46} 10.88 29.54
`
`
`
`
`0.05 |—-13.01] —26.02|4.0|6.02 40|16.0212.04 $2.04
`
`
`
`
`
`0.10 4.5|6.53 50|16|-10.00) —20.00} 13.06 33.98
`
`
`
`
`0.15|—8.24] —16.48] 5.0|6.99 60|17.7813.98 35.56
`
`
`
`
`0.20|—6.99} —13.98} 5.5|7.40 80|19.0314.81 38.06
`
`0.30|—5.23; 6.0|7.78 100|20.00-—10.46/ 15.56 40.00
`
`
`
`
`
`
`
`
`
`0.40|—3.98 -—7.96|6.5|8.13 10?|30.0016.26 60.00
`
`
`
`
`
`0.60|—3.01) 7.0|8.45 10¢|40.00—6.02] 16.90 80.00
`
`
`
`
`
`0.60|—2.22) 7.5|8.75 10*|50.00~4.44] 17.50 100.00
`
`
`
`
`0.80|—0.97 -1.94|8.0|9.03 10*|60.0018.06 120.00
`
`1.00 9.0|9.54 107|70.00|140.000.00) 0.001 19.08 |
`
`
`
`
`
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 014
`
`Momentum Dynamics Corporation
`Exhibit 1010
`Page 014
`
`

`

`10
`
`SYSTEM OF RADIO COMMUNICATION
`
`(Cap. ]
`
`The practical value of the decibel arises from its logarithmic nature.
`This permits the enormous ranges of power involved in communication
`work to be expressed in terms of decibels without running into incon-
`veniently large numbers, while at the same time permitting small ratios
`to be conveniently expressed. Thus,
`1 db represents a power ratio