rca electronic training series · 2019. 7. 17. · rca electronic training series published by -...

RCA electronic training series

Published by -

POINT -TO -POINT

RADIO RELAY SYSTEMS

44 MC TO 13,000 MC

overiment Service Department RCA Service Company, Inc., Camden, N. J.A Radio Corporation of America Subsidiary

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POINT-TO-POINT

RADIO RELAY SYSTEMS

44 MC to 13,000 MC

PREPARED BY

RCA SERVICE COMPANY, INC.A Radio Corporation of America Subsidiary

CAMDEN, N. J.

for

AIR FORCE CAMBRIDGE RESEARCH CENTERAIR RESEARCH AND DEVELOPMENT COMMAND

Reprinted by permissionAir Force Cambridge Research Center

30 September 1954

TABLE OF CONTENTS

POINT-TO-POINT 1111110 REM SYSTEMS

TABLE OF CONTENTS

CHAPTER AND CONTENTS Page

FOREWORD ix

CHAPTER 1-BASIC WAVE PROPAGATION 1

Mechanics of Wave Propagation 1

Waves in General-Electromagnetic Waves-Wave Fronts-Reflection and Refraction-Dif-fraction-Fresnel Wave Interference-Earth Reflected Zones.

Propagation Characteristics 10Free Space Transmission-Conductive and Dissipative Wave Media-Characteristic Impedance-

Q Value-Propagation Constant-The Poynting Theorem-Atmospheric Transmission-The Troposphere.

CHAPTER 2-ATTENUATION 15

Path Attenuation 15

Free Space-Atmospheric-Field Strength-Obstacle Gain.Frequency Characteristics 20

30 mc to 300 mc-300 mc to 3,000 mc-3,000 mc to 13,000 mc.

CHAPTER 3-FADING 25

Types of Fades 25Inverse Beam Bending-Multipath Fading-Height, Frequency Dependence.

Atmospheric Effects 26M Profile-Diurnal Signal Variations.

Types of Signals 28Fading vs. M Profile-Frequency Dependence-Effective Earth's Radius.

Diversity Reception 30Space Diversity-Frequency Diversity.

CHAPTER 4-WEATHER VERSUS PROPAGATION 33

Weather vs. Propagation 33Atmospheric Conditions-Homogeneous Air.

Air Masses 34Polar-Tropic-Subsidence-Diurnal Change.

Precipitation Attenuation 36Rain-Fog-Snow-Hail-Sleet and Glaze.

Atmospheric Characteristics 38Refractive Index-Refractive Modulus-M Profile.

TABLE OF CONTENTS

TABLE OF CONTENTS (cont'd)


CHAPTER 5-EQUIPMENT SITING 41

Survey Procedures 41Methods of Siting-Points of Consideration-Use of Contour Maps-Field Inspection-Siting by

Radio Altimeter-Siting by Helicopter-Siting Considerations-Summary.System Reliability 44

Governing Factors-Acceptable Reliability.

CHAPTER 6-TRANSMISSION LINES 47

Basic Theory 47Electric and Magnetic Fields-Capacitance and Inductance-Line Terminations-Characteristic

Impedance-Losses and Attenuation.Practical Transmission Lines 52

Two Wire Lines-Four Wire Lines-Shielded Pair-Coaxial Cable.Waveguides 54

General-Modes of Operation-Rectangular Guides-Circular Waveguides.Transmission Line Uses 58

Frequency Control Elements-Filters-Phase Shifters and Delay Lines-Impedance MatchingSections-Attenuators.

Installation Notes 63Bends and Twists-Waveguide Junctions-Pressurizing.

CHAPTER 7-ANTENNAS 65

Basic Antenna Principles 65Antennas Resonant Circuits-Antenna Bandwidth-Radiating Efficiency-Antenna Dimensions-

Antenna Gain-Antenna Directivity-Directivity Patterns-Front-to-Back Ratio-EffectiveRadiated Power-Parasitic Elements-Yagi Arrays.

Radio Relay Antenna Types 72Linear Arrays-Reflector Antennas-Reflector Construction-Horn Antennas-Lens Antennas

CHAPTER 8-THE TERMINAL TRANSMITTER 81

Oscillators 81VHF Oscillators-Microwave Oscillators.

Frequency Stabilizing Systems 85Frequency Stabilizers-Automatic Frequency Control Systems.

Modulators 87VHF Modulating Systems-Microwave Modulating Systems.

Power Amplifiers 90VHF Amplifiers-Microwave Amplifiers.

Installation and Maintenance 91Maintenance-FITCAL.

CHAPTER 9-THE TERMINAL RECEIVER 93

Superheterodyne Receiver Principles 93

Receiver Characteristics 93Sensitivity-Signal-to-Noise Ratio-Bandwidth-Selectivity-Image Ratio.

TABLE OF CONTENTS



CHAPTER 9 -THE TERMINAL RECEIVER (Cont'd)R -F Amplifiers 94

Lumped Constant Circuits-Grounded Grid Triode-Cascode Amplifiers.Tuning 94

UHF and VHF Tuners-Butterfly Tuners-Microwave Tuners.Local Oscillators 96

Mixers 96

I -F Amplifiers 97

Detectors 97

AFC Systems 98

AGC Systems 98

Video Amplifiers 98Pulse Restoration.

Direct Detection Receivers 99

CHAPTER 10-REPEATERS 101

Types of Repeaters 101Through Repeaters-Drop Repeaters-Terminal Repeaters.

Service Units 103

Passive Repeaters 103

CHAPTER 11-MULTIPLEXING 105

Frequency Division 105

Pulse Time Modulation 106Introduction-Pulse Amplitude Modulation-Pulse Duration Modulation-Pulse Position Modu-

lation-Pulse Code Modulation-Clipping.Signal -to -Noise Ratio 109

Specialized Channels 110Drops and Order Wire-Audio Channel Width.

CHAPTER 12-INTERFERENCE 111

Natural Noises 111Atmospheric-Cosmic and Solar.

Man -Made Noise 112Electrical Noises-Selective Interference.

Receiver Noise 114Thermal Agitation-Noise Figure-Signal-to-Noise Ratio.

CHAPTER 13-INTERFERENCE ELIMINATION 119

Natural Noise Reduction 119Atmospheric-Cosmic and Solar.

Man -Made Noise Reduction 120Electrical Noises-Selective Interference-Shielding.

Receiver Noise 122Noise Figure-Crystal Mixers.

iii

TABLE OF CONTENTS



CHAPTER 14-COMPUTATIONS OF WAVE PROPAGATION FOR RADIO RELAYAPPLICATION 125

The Bullington Nomograms 125Paths within the Optical Range-Obstructed Line of Sight-Paths Beyond the Radio Horizon-

Conclusions.

Siting Example 132Construction and Use of Profiles-Path Y -X Computations-Path Z -X Computations-System

Calculations.

General Summary 139Line of Sight Paths-Obstructed Line of Sight Paths-Non-optical Paths.

CHAPTER 15-IONOSPHERIC TRANSMISSION (30 to 100 mc) 151

Ionospheric Propagation 151

The Earth's Atmosphere-The Ionosphere-Radio Transmission.

CHAPTER 16-EQUIPMENTS TEST AND CALIBRATION 157

High Frequency Measurements 157Wavemeters-Standing Wave Measurements-R-F Power Measurements.

Current Standard Test Equipment 166

APPENDIX I 175Working Nomograms-The High Frequency Spectrum -4/3 Earth Profile Chart-Glossary-

MKS Symbols.

INDEX 223

iv

LIST OF ILLUSTRATIONS

LIST OF TABLES AND ILLUSTRATIONS

Figure

1- 1 Types of Waves1- 2 Interference of Waves1- 3 Induction Field1- 4 Electromagnetic Wave1- 5 Huygen's Wavelets1- 6 Electric & Magnetic Vectors1- 7 Reflected Wave1- 8 Refracted Wave1- 9 Diffraction1-10 Fresnel Zones1-11 Fresnel Zone Clearances1-12 Earth -Reflected Fresnel Zones1-13 Radiation Pattern1-14 Poynting Power Flow1-15 Refraction through Standard Atmosphere2- 1 Relative Attenuation2- 2 Relative Antenna Gain2- 3 Polar Diagram of Field Strength2- 4 Four -Ray Path2- 5 Attenuation with Obstacle3- 1 Single & Multipath Fading3- 2 Typical M Profiles3- 3 Types of Signals3- 4 Fading Comparison3- 5 Fading Causes by Frequency4- 1 Relation between Dewpoint, Temperature and M -Profile6- 1 Field Created by Current Flow6- 2 Lumped Constants6- 3 Open and Shorted Transmission Lines6 -4 Coaxial Modes of Operation6- 5 Rectangular Waveguide Modes6- 6 Circular Waveguide Modes6- 7 Common Tuning Methods6- 8 Types of Cavities6- 9 Bazooka Line Balance Converter6-10 Phase Inverter as Line Balance Converter6-11 Cutoff Attenuators6-12 Waveguide Joints7- 1 Antenna Feed Systems7- 2 Dipole Current and Voltage Distribution7- 3 Dipole Reactance Variation7- 4 Dipole Impedance Excursions7- 5 Dipole Impedance Variation7- 6 End Effect Factor7- 7 Dipole Field Pattern7- 8 Horizontal and Vertical Directivity Patterns7- 9 Antenna Radiation Pattern

Page

v


LIST OF TABLES AND ILLUSTRATIONS (cont'd)

Figure Page

7-10 Antenna Array with One Parasitic Element 717-11 Folded Dipole Impedances 727-12 Vertical Directivity of Broadside Array 727-13 Four Element Broadside Array 737-14 Endfire "Flat Top" Array 747-15 Reflector Types 747-16 Parabolic Reflector Beaming Action 757-17 Gratings for Passive Reflectors 767-18 Reflector Power Loss 767-19 Low Frequency Reflector Antenna 777-20 Horn Types 787-21 Horn Fed Parabola 787-22 Lens Antenna Characteristics 787-23 Lens -in -Horn Antenna 798- 1 Lighthouse Tube (Cross -Section) 828- 2 Lighthouse Tube Oscillator Circuit 828- 3 Two -Cavity Klystron Oscillator 838- 4 Bunching in Two -Cavity Klystron 838- 5 Reflex Klystron Oscillator 848- 6 Efficiency -Frequency Diagram 848- 7 Electric Field in Linear Magnetron 858- 8 Electron Trajectories in Linear Magnetron 858- 9 Cross -Section of Multicavity Magnetron 868-10 Electron Flow in Traveling Wave Tube 868-11 Amplitude Modulation Waveforms 878-12 Waveforms Developed in Nonlinear Coil Modulator 899- 1 Block Diagram of Superheterodyne Receiver 949- 2 Cascode Amplifier 959- 3 Butterfly Tuner 969- 4 Pulse Restoration 99

10- 1 Types of Repeaters 10210- 2 Heterodyne Repeater 10311- 1 Types of PTM 10611- 2 Pulse Restoration 10911- 3 Single Channel S/N Ratios 11012- 1 Sources of Radio Noise 11312- 2 Thermal Agitation Noise 11513- 1 Harmonic Rejection Stubs 12214- 1 Empire State Building to Hauppauge Circuit 12614- 2 Alliford Bay to Marble Island Circuit 12814- 3 Curves by Gerks 13014- 4 Limitations of Bullington Nomograms Beyond the Radio Horizon 13114- 5 Fading Margin 13214- 6 Contour Map and Profiles 13314- 7 Types of Paths 13414- 8 Clear Radio Paths 13514- 9 Obstructed Radio Paths 137

vi



Figure Page14-10 Non -Optical Paths 13814-11 Free Space Field Intensity and Received Power between Half Wave Dipoles, 1 Watt Radiated 14114-12 Received Power in Free Space between Two Antennas of Equal Effective Areas, 1 Watt Radiated 14214-13 Minimum Effective Antenna Height 14314-14 Received Power over Plane Earth between Half Wave Dipoles, 1 Watt Radiated 14414-15 Diffraction Loss Caused by Curvature of the Earth Assuming Neither Antenna Height is

Higher than Shown on Scale A 14514-16 DB Loss Relative to Free Space Transmission at Points Beyond Line of Sight over a Smooth

Earth 14614-17 Distance to Horizon 14714-18 Shadow Loss Relative to Free Space 14814-19 Shadow Loss Relative to Smooth Earth 14914-20 Median Signal Levels Relative to Free Space 15015- 1 Major Characteristics of Ionospheric Layers 15215- 2 RF Sounding of Ionosphere 15315- 3 Ionospheric Dispersion 15416- 1 Coaxial Line Wavemeter 15816- 2 Coaxial and Transition Wavemeters 15916- 3 Cylindrical Wavemeters 16016- 4 Standing Wave Indicator 16116- 5 Crystal Probe 16216- 6 Bolometer Littelfuse 16316- 7 Bolometer Bias Circuit 16416- 8 Coaxial Water Load 16416- 9 Johnson Wattmeter 165

Nomogram

A Path Attenuation 179B Attenuation Due to Rainfall 181C Reliability 183D Characteristic Impedance of Open Wire Lines 185E Characteristic Impedance of Air -Filled Coaxial Lines 187F Input Reactance for Open Wire and Coaxial Lines 189G Characteristic Impedance of a Quarter Wave Section Used as an Impedance Transformer 191H First Fresnel Zone Clearance 193J Radio & Optical Line -of -Sight Distances 195K Gain of Parabolic Antennas 197L Attenuation between Parabolic Reflectors of Equal Size 199M Plane to Normal Curved Earth Profile Conversion 201N Pressure vs. Wind Velocity 203O Dbm Conversion to Microvolts 205

Chart

P 4/3 Earth's Profile Chart 207Q High Frequency Spectrum 209

vii



Table Page

4-1 Number of Raindrops (per m3) in Different Rains 37

4-2 Attenuation in Rains of Known Drop Size Distribution (db/km) 37

8-1 Comparison of Microwave Transmitting Tubes 90

13-1 Stub Shorting Lengths 122

14-1 Comparison of Theoretical Computations and Long Term Field Intensity Measurements forLine of Sight Circuits 127

14-2 Comparison of Theoretical Computations and Long Term Field Intensity Measurements forCircuits Extending Beyond the Radio Optical Horizon 129

14-3 Comparison of Distance Beyond Radio Optical Path Length and Limiting Values fromFigure 14-4 131

viii

FOREWORD

FOREIIORD

This publication is intended to present, in a simplified fashion, the many problems encountered whenoperating radio -relay systems. The material is limited to the frequency range extending from 44 to 13,000megacycles, since the majority of radio -relay systems are designed to operate within this range.

The first four chapters deal exclusively with anomalous factors such as wave propagation, fading, andweather effects. Although the effect of these factors on the successful operation of radio -relay systems may becalculated for any given set of conditions, there is no easy way to predict, in advance, the amount by whichsuch factors will vary. Therefore, it is necessary to engineer radio -relay systems to operate over a wide range ofvarying conditions.

A great portion of the basic material in this publication, then, is devoted to the problems of equipmentsiting, system reliability, and interference elimination. However, since the characteristics of each individualsystem component (transmitters, receivers, antennas, etc.) determine the overall operation of the system,these components are covered under separate chapter headings.

Additional information also presented includes (1) computations of wave propagation based on a series ofnomograms (2) general ionospheric transmission problems, and (3) a section on testing and calibration, com-plete with a list of present standard test equipment.

This text is intended to cover only the basic problems of radio -relay system operation, to give a readymethod for computing such systems, and to provide additional information where necessary.

ix

CHAPTER 1

BASIC WAVE PROPAGATION

C II la I' T It

INTRODUCTION

The movement of a wave washing up on a beachor the disturbance caused by a stone when droppedinto still water is easy to understand. In turn, aleaf floating on the pond where the stone wasdropped will not be disturbed except for a slightbobbing motion. This shows that the wave travelsthrough the water without moving very much of thewater itself. Such movement of visible waves througha substance like water, or invisible waves through theatmosphere, is called wave propagation. The manykinds of invisible waves include sound, heat, andelectromagnetic waves.

In this chapter we shall deal with electromagneticwave propagation of frequencies ranging from 44through 13,000 megacycles per second. It is primarilya chapter of definitions intended for use throughoutthe remainder of the book. A good knowledge ofwave propagation is an important aid towardsunderstanding the construction and use of radio -relay communications equipment.

MECHANICS OF WAVE PROPAGATION

WAVES IN GENERAL. Probably everyone hasthrown a stone into quiet water and watched ever -widening circular waves spreading over the surfacefrom the point where the stone entered the surface.The water does not move as a whole, but rather, onlythe surface pattern. In order to set up such a motion,the individual particles of water must move intransmitting the wave, but they move over rathershort paths.

Waves can also be produced by vibrations otherthan those of material particles. For example, the

1

BASIC WAVE

PROPAGATION

current in an antenna circuit of a radio stationproduces an alternating field in the region around it.As the current oscillates, this field continually buildsup and collapses, and in so doing creates electro-magnetic waves which are propagated outward fromthe antenna. However, these waves are not trans-mitted by the motion of air particles, but by changesin the electric and magnetic conditions of space.

Wave motion in general can be classified as eitherlongitudinal or transverse. A longitudinal wave is onein which the oscillating motion vibrates forward andbackward, parallel to the direction in which thewave is propagated. Sound waves produced by aradio loud speaker as it vibrates in and out arelongitudinal. The oscillating motion of a transversewave, however, is always at right angles to thedirection of propagation. Water waves are a goodexample of transverse waves, since the wave crestsand troughs move up and down while the wavepattern as a whole moves outward from the source.Electromagnetic waves are also propagated as trans-verse waves, because the, stress produced by suchwaves in space is perpendicular to the line ofpropagation. The two types of waves are illustrateddiagrammatically in figure 1-1.

CHARACTERISTICS OF WAVE MOTION. Inorder to interpret the characteristics of wave motion,four basic wave measurements must be known andare listed as follows:

1. The period of oscillation which is the time neces-sary to complete one cycle,

2. The frequency, or the number of cycles com-pleted in one second,

1

CHAPTER 1


111LONGITUDINAL WAVE

11.=

ONE WAVELENGTH ( LI

AMPLItUDE

Figure 1-1. Types of Waves

3. The amplitude of oscillation which is the maxi-mum displacement of the wave from its un-disturbed or null position, and

4. The wave length which is the distance, measuredalong the direction of propagation, from anypoint on a wave to a corresponding point on thepreceding or following wave (one cycle). TheGreek letter lambda (X) is used to signifywavelength.

Two waves moving simultaneously along the sameline of propagation produce characteristics which arethe direct result of their combination, although theyadvance independently. For the case where the twowaves are oscillating at the same frequency, thecharacteristics are as follows:

1. An in phase relationship occurs when they con-tinually pass through corresponding points oftheir paths at the same time. Otherwise, theyare out of phase.

2. Wave reinforcement is produced when suchwaves are in phase. The combined action ofboth waves can be pictured by adding thecoordinates of the component waves, point bypoint, as illustrated in figure 1-2A.

3. Phase opposition occurs when the two wavesreach their maximum amplitudes in oppositedirections at the same time.

4. Destructive interference is produced when suchwaves are in phase opposition, and further,if they have equal amplitudes, the result is acomplete annulment, as illustrated in figure1-2B. Destructive interference also occurs,although to a lesser degree, when the waves areonly partially in phase opposition, or if they donot have equal amplitudes.

When two waves of a slightly different frequencyare propagated in the same direction, they combineto produce a type of pulsating interference. Theresultant amplitude is alternately large and small,producing pulses or throbs which are known as beats.

R

WAVE REINFORCEMENT

(A)

DESTRUCTIVEINTERFERENCE

(B)

PULSATING INTERFERENCE

Figure 1-2. Interference of Waves

ELECTROMAGNETIC WAVES. It is customaryto speak of radio waves traveling through theatmosphere or along a transmission line. Such wavesare not simple in form like sound or heat waves butcomplex in nature. To start with the foundationunderlying electromagnetic phenomena, we have thefield theory as developed by James Clerk Maxwell.This theory states that an electromagnetic wavecontains two fields: a moving electric field whichcreates a magnetic field, and a moving magnetic fieldwhich creates an electric field. The created field, atany instant, is in phase in time with its parent field,but is perpendicular to it in space. These laws holdtrue whether a conductor is present or not.

When an electric current flows in a single wireconductor, such as a simple antenna, a magneticfield, H, is set up around the antenna. Separatedpositive and negative charges also appear on theantenna, causing an electric field, E, to be set up.The magnetic lines of force form circles about theconductor, while the electric lines of force are normalto the conductor as illustrated in figure 1-3A. In thiscase, the sinusoidal variation in charge magnitudelags the sinusoidal variation in current by one -quarter cycle (90 degrees) and, therefore, the twoMelds must also be out of phase by 90 degrees. Thus,in spite of the fact that the two fields are perpen-dicular, they do not constitute the radiated electro-magnetic field referred to above. This energy sur-rounding the conductor is called the induction fieldwhich, since it is a static field, cannot be detachedfrom the antenna. Such energy travels along thesurface, or skin, of the antenna, and its amplitudevaries inversely as the square of the distance fromthe antenna. Consequently, its effect is local.

Now consider only the electric field set up about

2

CHAPTER 1

the antenna. As the polarity of the incoming voltagechanges, the charges producing the electric field areconstantly moving from one end of the antenna to theother. One end of the antenna may be at one instant,positive; an instant later, uncharged; and still later,negative. The antenna is then uncharged again andthe whole cycle repeats itself.

In figure 1-3B, flux lines are drawn betweenpositive and negative charges. An instant later, infigure 1-3C, the antenna is nearly discharged and thecharges approach each other, bringing with them thetwo ends of the flux lines. When the charges merge,they seem to disappear, and most of the inductionfield flux does disappear. However, some flux isrepelled by other lines nearer the antenna and, asshown in figure 1-3D, they become closed fields.Therefore, a closed electric field has been createdwithout an associated electric charge.

At some instant after the independent field hasbeen formed, the antenna charges again in the oppo-site direction, producing lines of force that repel therecently formed field. The repelling field is of theproper polarity to do this, as illustrated in figure1-3E, and the radiated field is forced away from theantenna with a velocity equaling that of light.

As previously stated, a moving electric fieldgenerates a perpendicular magnetic field in phasewith it. Since the independent electric field describedabove is moving, it therefore generates a magneticfield in accordance with this principle. The result is aradiated electromagnetic field, or wave, which may bepropagated to great distances.

By similar reasoning, the magnetic lines of forcemay also become detached from the antenna and, asthey move away, generate a perpendicular in -phaseelectric field. The result is also a radiated electro-magnetic field, or wave. Therefore, the electro-

(H) MAGNETIC LINESOF FORCE, NORMALTO THE CONDUCTOR

(E) ELECTRIC LINES OF FORCE,ABOUT THE CONDUCTOR

A


magnetic wave radiated from an antenna is made upof two components: the electric -generated field andthe magnetic -generated field. The two fields, identicalin composition but 90 degrees out of phase in time,will add vectorially and produce a single sinusoidallyvarying radiated field.

In figure 1-4, a segment of an electromagneticwave is shown in three dimensions. Here, the electricfield is represented by the vector E, and the magneticfield is represented by the vector H. The direction ofpropagation is along the vector Z. The direction ofthe electric field is called the direction of polarizationof the wave. In the case of the electromagnetic wavein the figure, the electric field lines are in the verticalplane, and, therefore, the wave is vertically polarized.If the electric field lines were horizontal, then thewave would be horizontally polarized. As an electro-magnetic wave moves forward, the electric field mayrotate, thereby producing a circularly polarized field.Should little or no rotation exist, the field is linearlypolarized.

The transfer of electromagnetic energy in a mediumdepends on certain electromagnetic properties of themedium as well as on the similar properties of thebounding media. Thus wave transfer in the atmos-phere will depend in varying degree on the propertiesof the earth over which the transmission takes place.These pr9perties are defined by the three parameterslisted below.

1. The dielectric constant (K) or the capacity ofelectrostatic energy a medium will store. A dielectricis a nonconducting material and, therefore, an in-sulator. Air, rubber, glass and mica are all gooddielectrics. The dielectric constant for a vacuum isexpressed by the symbol Ko, and is equal to 8.854 X10-12 farads per meter.

Figure 1-3. Induction Field

B

D

CD

C

E

3

CHAPTER 1


E ELECTRIC FIELDH MAGNETIC FIELDZ DIRECTION OF PROPAGATION

Figure 1-4. Electromagnetic Wave

2. The permeability (A) or the measure of thesuperiority of a material over a vacuum as a path formagnetic lines of force. Ferromagnetic materials suchas iron, steel, nickel, cobalt, and magnetic alloys allhave high permeabilities. On the other hand, diamag-netic substances such as copper, brass, and bismuthhave permeabilities comparable to that of free space.The value of µ for a vacuum is equal to 1.257 x 10-6Henrys per meter.

3. The conductivity (0-) or the measure of theability of a material to pass electricity. All puremetals are conductors with some having more con-ductivity than others. Conductivity is the reciprocalof resistivity and is measured in mhos.

While a is zero in a vacuum, K and µ never are;in fact, the velocity (v) of an electromagnetic wave inany medium is given by

V = 1_ meters per second (1-1)

where

K = The dielectric constant of the material throughwhich the wave is being propagated (MKSUnits).

1.4 = The permeability of the material (MKSUnits).

Since the values ofµ and K are essentially the samefor air as for a vacuum, it will be found that thevelocity of electromagnetic waves through bothmaterials is approximately 3 X 108 meters per second,or 186,000 miles per second. This value may be usedfor all electromagnetic waves through either air orvacuum without appreciable error.

WAVE FRONTS. The simplest antenna, or radiator,is a theoretical point source commonly called anisotropic radiator. In unobstructed space, such asource radiates equally well in all directions, and

electromagnetic energy is propagated fundamentallywith velocity of 186,000 miles per second. At the endof 1/1000 of a second, the field energy will be presenta distance of 186 miles from the source. Similarly,at the end of one second, the wave would be thesurface of a sphere with a radius of 186,000 miles.In each case, the spherical wave forms a frontsurface, or wave front, with the isotropic antennalocated at the center of the sphere. According toChristian Huygens, a wave front may be consideredto consist of an infinite number of isotropic radiators,each one sending out wavelets always away from thesource. The collective effect of such action constitutesa new wave front as illustrated in figure 1-5.

The illustration shows an isotropic antenna fromwhich is radiated the primary wave front, arc AG.Along this wave front, points A through G may beconsidered as an infinite number of isotropic radia-tors, each oscillating in phase. These radiators sendout little wavelets of their own, such as shown comingfrom point E on the wave front, which combine withthe wavelets sent out by all the other points on theprimary wave front to form a new wave front atsome distance further along the direction of propaga-tion.

As such a wave front advances, a small section ofits face would appear to be a plane, and both theelectric field intensity (E), and the magnetic fieldintensity (H) would be vectors perpendicular to eachother and located in the plane wave front as illus-trated in figure 1-6. The direction of wave propaga-tion would be perpendicular to the wave front.

REFLECTION AND REFRACTION. By study-ing the changes in a wave front which occur as awave advances through a medium of one density,it is possible to predict the effects that will be pro-duced when a wave encounters a medium of adifferent density which either reflects, refracts, orabsorbs energy.

The behavior of a wave upon striking a reflectingsurface may be determined by an adaptation ofHuygens' construction. In figure 1-7, an electro-magnetic wave is shown being reflected from theground somewhere between a transmitting and re-ceiving antenna. A close-up drawing of the wavefront at the point of reflection shows wave front ABimpinging upon the surface of the ground, throughwhich it cannot penetrate. If the earth's surface hadbeen absent, the wave would have advanced withoutchange in direction and, in a certain time interval,would have reached the position A'B. However, thepresence of the earth's surface causes a change in thedirection of the wave front as illustrated by the heavy

4

WAVELET FRONTS

NTRANSMITTING BONE -"'IWAVE-

LENGTHANTENNA

PRIMARYWAVE -

G FRONT

Figure 1-5. Huygen's Wavelets

line AOB. The line OB represents the incident wavefront, and the line AO represents the reflected wavefront. The angle i, which is the angle of incidence,and the angle r, which is the angle of reflection, areequal and lie in the same plane.

Inasmuch as we deal with the transfer of electro-magnetic energy in the case of wave propagation, it isconvenient to express the energy relations of theincident and reflected waves by a ratio called thecoefficient of reflection. The coefficient of reflection (p)is defined as the square root of a power ratio, and isfound by dividing the reflected energy per secondleaving a reflecting surface by the energy per secondincident to the same surface. If the two energies areof equal magnitude (p = 1), we have perfect reflec-tion. If the reflected energy is smaller than theincident energy, the difference is either dissipated atthe reflecting surface, or partially dissipated at thesurface and partially passed through the surface as arefracted ray. For example, when an electromagneticwave impinges upon a cloud, most of the energywill be transmitted through the cloud. However, dueto various particles in the cloud, a portion of thewave will be returned by reflection at the surfaceof the cloud and another portion will be absorbedwithin the cloud itself. When the wave energy is

CHAPTER 1


THESE WAVELETS ORIGINATEFROM POINT E. SIMILAR WAVE-LETS WILL ORIGINATE FROMPOINTS A, B,C,- -

absorbed, it is converted into heat. The part of thewave that is passed through the cloud will be re-fracted, or changed in direction, if the electro-magnetic properties of the cloud differ from thoseof the surrounding air. In fact, when a radio waveencounters any medium whose electromagnetic prop-erties differ from those of the previous medium,

1

E VOLTS PER METER

PLANE WAVE FRONT

DIRECTION OF WAVEPROPAGATION

H AMPERES PER METER

ONE CUBIC METER OF THEGENERAL WAVE FRONT

Figure 1-6. Electric & Magnetic Vectors

5

CHAPTER 1


SEE DETAIL Z

TRANSMITTER RECEIVER

Figure 1-7. Reflected Wave

reflection and refraction take place simultaneously. obliquely from one medium to another, will undergoIn figure 1-8 an electromagnetic wave is illustrated a change in direction if the velocity of the wave in

being refracted through a mass of air which is denserthan the air surrounding it. For the sake of sim-plicity, all the action is shown taking place at theinterface between the air mass and the surroundingatmosphere. Actually, however, the refraction occursin gradual steps, since air masses have no sharplydefined interface. Since the mass of air is denser thanthe surrounding air, the wave will be slowed downas it enters and therefore bent. If the air mass hadnot been present, point B on the wave front AOB-would have advanced to B' at a uniform rate ofvelocity. However, since the wave velocity is less inthe air mass than in the surrounding air, the line OBrepresents the new direction on the wave front, andthe angle r' which it makes with the normal is calledthe angle of refraction.

If the density of the air mass was less than thesurrounding air, the wave velocity would have in-creased and the wave refracted upward. Therefore, awave is refracted toward the normal when its velocityis reduced, and away from the normal when itsvelocity is increased. Consequently, the law of re-fraction states than an incident wave, traveling

one medium is different from that in the other. Itwas discovered by Willebrod Snell, Dutch astronomerand mathematician, that the ratio of the sine of theangle of incidence to the sine of the angle of refractionis the same as the ratio of the respective wavevelocities in these media, and is a constant for twoparticular media. Expressed as a formula, Snell'slaw becomes

Sin i vi- Sin r' v2

(1-2)

where n is called the refractive index of the secondmedium relative to the first. The absolute refractiveindex of a substance is its index with respect to avacuum, and is practically the same value as theindex with respect to air. Thus, if the velocity of awave is v in a particular substance, v° in a vacuum,and va in air, the refractive index of the substance isgiven by the formula

= p° = approximately v. (1-3)

where the symbol t represents the index of refraction.

6

It is the change in the index of refraction that deter-mines the path of electromagnetic waves through theatmosphere, as will be discussed later in this chapter.

DIFFRACTION. The amount of r -f energy in theform of electromagnetic waves that will travel from atransmitting antenna to a receiving antenna is deter-mined by the path over which the waves must go.It was often thought that high frequency wavestraveled according to geometric optics (geometricline of sight) or slightly below this line if atmosphericrefraction existed. However, experiments have shownthat, at frequencies below approximately 100 mc,waves may reach much farther beyond the horizonthan refraction can account for.

Wave reflections do not originate at one point only,but, according to Huygens' wavelet principle, fromthe entire surface of an obstacle which is in the pathof electromagnetic waves. Wavelets, therefore, willre -radiate in all directions from a multitude ofelementary radiation centers at the earth's horizonas they receive incident wave energy. Electromag-

TRANSMITTER

CHAPTER 1


netic diffraction is, therefore, the bending of wavesas they graze the earth's surface or any other in-tervening obstacle, and is caused by Huygens' wave-lets. Diffraction of electromagnetic waves into thegeometrical shadow region behind a mountain ridgeis illustrated in figure 1-9.

FRESNEL WAVE INTERFERENCE. As men-tioned previously, each wavefront progressing from atransmitting source to a receiving point consists of aninfinite number of secondary sources. Therefore, evenin the simple case of transmitting energy from pointT to point R in free space (figure 1-10) there are aninfinite number of paths to consider, each pathoriginating from a secondary source on the pro-gressing wavefront. In figure 1-10, the wavefrontdescribed by the arc AG is a particular part of thebeam of energy that is being sent from a transmittingantenna. The points A through G on the wavefrontare designated as secondary sources, otherwise knownas Huygens' radiation centers. The radii of the circleswhose diameters are described by the point AG, BF,

SEE DETAIL X

Figure 1-8. Refracted Wave

7

CHAPTER 1


WAVE TROLt.GHS

WAVE CRESTS

DIRECTEDCONE OF ENERGY

FROM ATRANSMITTING

ANTENNA

POSITIVE ANO NEGATIVEREINFORCEMENT

DIFFRACTIONWAVE FRONT

( UNOBSTRUCTEDREGION )

DIFFRACTIONWAVE FRONT

( APPARENTSHADOW REGION )

Figure 1-9. Diffraction

and CE are so chosen that the total path length fromT to R via each circle is n X/2 greater than theshortest path TDR, where n is an integer. Therefore,the distance ER is longer by a half wavelength thanthe distance DR, and the distance FR is longer thanthe distance ER by a half wavelength. The circularregions formed by these radii are called Fresnel zones,and are not equal, but decrease in energy in propor-tion to the distance from the central or first Fresnelzone. The field contributed by each zone at point Ris alternately positive and negative, as determined bythe difference in path lengths of the secondary waves.the total field received at point R is, therefore, thevector sum of all the incident fields. For example,consider the wave arriving at point R from thesecondary source C on the wavefront. Since the pathlength CR is one-half wavelength longer than thedirect path DR, the wave arriving from point C willbe out of phase with the direct wave and its contribu-tion to the total received field will be negative.Conversely, a wave arriving at point R from point Bon the wavefront will be in phase with the directwave and its contribution to the total received fieldwill be positive, since the path BR is longer by a fullwavelength than the path DR. Therefore, Fresnelzones of odd numbers are zones whose contributionto the total received field is positive, while Fresnelzones of even numbers are zones whose contributionto the total received field is negative. Actually, thereare an unlimited number of Fresnel zones on a wave -front, but, for simplicity, the number is limited tothree in the diagram.

The region described as the first Fresnel zoneaccounts for approximately one -quarter of the totalreceived field energy, and, if possible, should be clearof all path obstructions if the received signal is tohave a maximum signal strength. It must also be

FIELD STRENGTH,F NO

FIELD 1.0ENERGY

OBSTRUCTIONPRESENT

APPARENTSHADOW REGION

z0

w

remembered that the area of the first Fresnel zonedepends upon both the transmitting and receivingantennas and upon the operating frequency. Theradius of the first Fresnel zone at any point (P) alongthe transmission path may be found by the expression

R = 13.14 Xx D2D3

(1-4)

where

R = The first Fresnel zone radius in feet at anypoint P.

= The distance in miles from the transmittingantenna to any point P.

D2 = The distance in miles from the receivingantenna to any point P.

D3 = D1 + D2.X = Wavelength in centimeters.

Optimum Fresnel zone clearance actually occurswhen the edge of an obstruction is located a slightamount within the first Fresnel zone. This slightpenetration into the first Fresnel zone causes wavereinforcement to occur since the reflected wave isone-half wavelength longer than the direct wave andalso reversed in phase by 180° at the reflection point.The reflected wave is therefore in phase with thedirect wave, thus increasing the effective signalstrength at the receiving antenna. Optimum clear-ance is illustrated in figure 1-11A. When there ismore than optimum clearance, such as illustrated infigure 1-11B, multipath fading may occur, caused byimpinging waves from the 2nd or 4th Fresnel zonesreflecting from the surface of the obstacle. Less thanoptimum clearance, as illustrated in figure 1-11C,may cause a possible shadow loss of power, dependingupon the degree of obstruction, due to multiple re -

8

3',d FRESNEL ZONE

Figure 1-10.

flections from the obstructed side of the first Fresnelzone.

EARTH REFLECTION ZONES. When a radiowave is incident upon the earth's surface it is notactually reflected from a point on the surface, butfrom a sizeable area. This reflection area may belarge enough to include several Fresnel zones, or Itmay be in the form of a ridge or peak including only apart of the first Fresnel zone. For the case where thewave is incident upon a plane surface, the resultingFresnel zones formed on the reflecting surface takethe form illustrated in figure 1-12A. The ellipticalzones formed on the reflecting surface are similar tothose which would be formed on an oblique planeplaced between a transmitting source and a receiverin free space as shown in figure 1-12B. Therefore,the earth -reflected Fresnel zones are simply a pro-jected image of the free -space Fresnel zones at theplane of reflection and may be determined by thesame geometry as that used for the free -spaceFresnel zones.

The significance of the ground reflected Fresnelzones is similar td that mentioned for the free -spacezones. However, as radio waves are reflected fromthe earth's surface, they are generally changed inphase depending upon the wave polarization and the

CHAPTER 1


1

St FRESNEL ZONE

1st FRESNEL ZONE

2nd FRESNEL ZONE

Fresnel Zone

angle of incidence. For horizontally polarized wavesat the range of frequencies encountered in this book,such waves reflected from the earth's surface areshifted in phase by about 180°, effectively changingthe electrical path length by a half wavelength. Onthe other hand, for vertically polarized waves, aconsiderable variation in the phase angle will befound to exist for different angles of incidence andreflection coefficients, and will vary between 0° and180° lag depending upon ground conditions. Forhorizontally polarized waves, therefore, (and in somecases for vertically polarized waves) if the area of thereflecting surface is large enough to include the totalarea of any odd -numbered Fresnel zones, the result-ing wave reflections will arrive out of phase at thereceiving antenna with the direct wave and causedestructive interference.

The radiation pattern of an antenna near a re-flecting surface such as the ground differs from thefree -space pattern primarily because of the existenceof ground reflections. Since the direct path and thereflected path will not be of the same physicallength, and since there will be a phase change uponreflection, the two waves may arrive at the receivingantenna with any phase relationship. This phaserelationship of the two waves will cause either anincrease or decrease in the signal strength at the

9

CHAPTER 1


(A)

T

I st FRESNEL ZONE2nd FRESNEL ZONE

3rd FRESNEL ZONE

. ..

( B ) st FRESNEL ZONE2nd FRESNEL ZONE

3rd FRESNEL ZONET

"*--------'POSSIBLE REFLECTION POINT

1 st FRESNEL ZONE2nd FRESNEL ZONE

3rd FRESNEL ZONE SHADOW LOSS OF SIGNAL

POSSIBLE REFLECTION POINT

Figure 1-11. Fresnel Zone Clearances

receiver and will produce the effect of distinct lobesand nulls in the radiation pattern since the two raysadd vectorially at the receiver.

PROPAGATION CHARACTERISTICS

FREE -SPACE TRANSMISSION. According to theIRE, free -space transmission is electromagnetic radi-ation over a straight line path in a vacuum or in anideal atmosphere, sufficiently removed from allobjects that might affect the wave in any way. Inthis case, only the direct wave propagated from atransmitting antenna is effective at the receivingantenna, and the electric field intensity present atany point in space is commonly called the free -spacefield strength, E0. The field strength obtained in freespace is a convenient standard for reference. Signalfluctuations of high -frequency waves as propagatedthrough the lower atmosphere may, on occasion, riseabove the free -space value, but the average fieldstrength of such fluctuations will always be some-where below the free -space value.

Free -space field strength depends only upon the

amount of power transmitted a the distance overwhich the wave is propagated, and may be found bythe formula

where

Pr =

Pt =

P G1 G2 X2 PtPr =(47)2 d2

(1-5)

Power in watts at the terminals of the re-ceiving antennaPower in watts at the terminals of thetransmitting antenna

GI, G2 = Power gains of the transmitting and re-ceiving antennas, respectively

d = Distance between antennas in metersX = Wavelength in meters

In the above formula, the transmitting and receivingantennas are assumed to be properly oriented formaximum transfer, and the receiving antenna isassumed to be properly matched to its receiver.

In order to determine the direction of maximumradiation or maximum response, a radiation pattern

10

CHAPTER 1


may be used. A radiation pattern of a transmittingantenna is a diagram indicating the intensity, in alldirections, of the radiated field as it would occurunder actual operating conditions. In the case of areceiving antenna, it indicates the response of theantenna to a signal of uniform intensity arriving fromall directions. Such patterns may be plotted in termsof field strength in volts per meter or in terms ofpower in watts per square meter. Figure 1-13illustrates a typical power radiation pattern for alinear antenna whose physical length equals approxi-mately one-half wavelength of the frequency used.This type of pattern gives the relative directivitiesbased on a percentage of power, but not the absolutemagnitude of the field.

The radiation patterns of a transmitting antennaand a receiving antenna with the same physicalcharacteristics are the same. Therefore, for example,at a given distance, with a transmitting antennaheight of 100 feet, and a receiving antenna height of50 feet, the received field would be the same eventhough the transmitting and receiving units wereinterchanged. This fact is called the law of reciprocity.

CONDUCTIVE AND DISSIPATIVE WAVEMEDIA. In a conducting wave medium such ascopper wire, we have found that electromagneticfield energy is absorbed because of the internal re-sistance of the wire itself. The energy that is absorbedis converted into heat. When the medium surround -

Is FRESNEL ZONE2nd FRESNEL ZONE

(A) FRESNEL ZONES 3rd FRESNEL ZONE

ON A REFLECTING SURFACE

1st FRESNEL ZONE2nd FRESNEL ZONE

3rd FRESNEL ZONE

(B) FRESNEL ZONESPROJECTED ON AN OBLIQUE PLANE

Figure1 -12. Earth -Reflected Fresnel Zone

A- RADIATION PATTERN 13 -PICTORIAL VIEW, RADIATION PATTERN

Figure 1 -1 3. Radiation Pattern

ing an electromagnetic current -carrying conductor isnot a perfect dielectric but exhibits a certain con-ductivity, heat losses will also occur in the medium.Therefore, we have, in addition to the induction fieldand the propagated field about a conductor, radiatedheat generated in the electromagnetic field.

A medium that is not a perfect dielectric is termeda dissipative medium. As an electromagnetic wave ispropagated through a dissipative medium, heat losseswill occur, and account for the attenuation of thewave's energy. In the earth's atmosphere, at fre-quencies above approximately 10,000 mc, precipita-tion and water vapor are two factors that can causesignificant attenuation of energy by absorption.

CHARACTERISTIC IMPEDANCE. The value ofthe total opposition that transmission media offer tothe flow of electromagnetic field energy is called thecharacteristic impedance (Z0) and is measured inohms. The characteristic impedance of free space isrepresented by the formula

Z. = = 377 ohms (1-6)where

= the permeability of a vacuumKo = the dielectric constant of a vacuum

The characteristic impedance of free space alsoexpresses the ratio E/H of the associated electric andmagnetic fields. Since

Z° = -H = 377 ohms (1-7)

whereE = electric fieldH = magnetic field

for electromagnetic waves in unobstructed normalatmosphere, the electric field in volts per meter atany space point is numerically 377 times larger thanthe numerical value of the associated magnetic fieldin amperes per meter at the same space point.

11

CHAPTER 1


Q -VALUE. The figure of merit (Q value), which mustbe a large numerical value for an efficient wavemedium, is given by the ratio

Q = WK

a

where

(1-8)

= 2irf with f in cycles or 6.28 X 106f with f inmegacycles

K = the dielectric constant of the medium

o = the conductivity of the medium

Since the conductivity of dry air is zero, it will beseen from the formula that the Q -value of theatmosphere is infinite, and therefore waves of anyfrequency may be propagated. The numerator (WK)is a measure of the displacement current or the currentat right angles to the direction of propagation ex-pressing the rate of expansion and contraction atwhich the field energy changes. The denominator (a)is a measure of the conduction current or the currentin watts, moving in the direction of propagation, thatmay or may not be absorbed because of the heatlosses. The conduction current may be measured inamperes per square meter by using the formula

Conduction current (J) = E amp/m2. (1-9)

In general wave media, conduction and displace-ment currents exist by virtue of an electromagneticfield. For a pure dielectric medium only displacementcurrents are present, but when a wave strikes theearth's surface or other obstacle, such obstacles ex-hibit the characteristics of a dissipative medium. Towhat extent the obstacle is a dielectric or a reflectordepends upon the operating frequency.

PROPAGATION CONSTANT. In free -space as wellas in all other media, there is a propagation character-istic which defines both the wavelength and thedissipation of electromagnetic field energy. Thischaracteristic is called the propagation constant,r = a + jfi, and expresses what happens because ofenergy transfer. The part of the propagation constantwhich defines the wavelength is known as the phaseconstant (0) and is by no means fixed, even thoughthe frequency may be perfectly stabilized. The wave-length of any given frequency will vary, dependingupon the media through which the wave is propa-gated. The part of the propagation constant thatdefines the dissipation is generally known as theattenuation constant (a) and will explain the lossesthat account for the amplitude decay of both theelectric and magnetic field vectors. The propagation

constant is complex in nature and is included in thischapter only for the purpose of definition.

THE POYNTING THEOREM. We have estab-lished some of the components that offer oppositionto the flow of electromagnetic field energy in variousmedia. Now we must establish the rate of flow of theenergy through these media. The Poynting Theoremstates that the rate of flow of electromagnetic fieldenergy is at any instant proportional to the magni-tude of the resultant vector product of the electricand magnetic field intensities.

A vector is a quantity having both magnitude anddirection. A current, for instance, is a vector, sinceit has a magnitude expressed in so many amperesand a definite direction of flow. The electric fieldintensity (E) is a vector, since it has a magnitudeof so many volts per meter in a certain space direc-tion, just as the magnetic field intensity (H) is avector, since it has a magnitude of so many amperesper meter in a certain space direction. Volts, degreescentigrade, or energy in watts are known as scalarmagnitudes, since they are completely characterizedby magnitude alone.

The vector product of the Poynting Theorem istermed the Poynting vector, whose magnitude inwatts per square meter gives the amount of totalfield power transmitted. Since it is a vector, it mustalso give the direction in which the power flow occurs.In figure 1-14 is illustrated the effective electric field(E) in volts per meter propagated along the vertical(x) direction (vertical polarization) and the associatedeffective magnetic field (H) in amperes per meterpropagated along the horizontal (y) direction. ThePoynting power flow, p = EH watts per squaremeter, is then along the direction of propagation (z).The quantity p, therefore, represents the absoluteamount of the Poynting vector and is the amount ofenergy which crosses an area of one square metereach second, perpendicular to the direction of powerflow. The formula

P = E2/Z. = E2/377 (1-10)

represents the energy density per square meter atany point in space between transmitting and receiv-ing antennas. Similarly, the formula

P = 1/2 (0-12 XE2) (1-11)

represents the energy density per cubic meter offield energy.

ATMOSPHERIC TRANSMISSION. The electro-magnetic wave intercepted by a receiving antennamay have been propagated in the form of threedifferent waves, or any combination thereof. They

12

CHAPTER 1

H

VOLTS/METER

M M

11111111 11111111

1111111

AMPERS/METER

VOLTS/METER

Z(p WATTS/SQUAREMETER)

Figure 1-14. Poynting Power Flow

are: the ground wave, which is propagated over theearth; the ionospheric wave or sky wave, which ispropagated by way of the ionosphere; and thetropospheric wave which is propagated by reflectionfrom a place of abrupt change in the dielectricconstant or its gradient in the troposphere.

The ground wave includes all components of aradio wave over the earth except ionospheric andtropospheric wages. Better transmission is nearlyalways obtained over water than over land, and oversoil of high conductivity rather than soil of poorconductivity. The ground wave may also be refractedbecause of variations in the dielectric constant(which determines the index of refraction) of thetroposphere including the condition known as asurface duct. At frequencies below about 3 mc,ground wave propagation up to 200 miles may beobtained because of the diffraction of the wave belowthe radio horizon. At higher frequencies, diffractioneffects become less prevalent than refraction effectsin regard to the propagation of the ground wavebeyond the earth's horizon.

The ionospheric wave may be employed for com-munication over greater distances since it can bereflected from the ionosphere, thus returning to theearth at points remote from the transmitting source.Generally the higher the frequency, the less thewave is reflected, until at frequencies above 100 mconly an extremely small portion of the signal is everreflected from the ionosphere. Ionospheric return forsuch frequencies does not occur often and when itdoes it is erratic in nature (see chapter 15). Thefrequencies above 100 mc are, however, affected bywhat is known as the troposphere.

THE TROPOSPHERE. The troposphere extendsupward from the earth's surface to about 6 miles, andcontains almost all the atmospheric conditions andchanges known as "weather". Ionized layers of airoccur rarely in the upper part of the troposphere,and not at all in the lower half. For this reason, wavesreturned from the troposphere are almost always theresult of changes in the atmospheric characteristics,


rather than reflections from ionized layers. Wherereflections do occur from these ionized layers, there islittle effect on propagation since the reflecting abilityof the layers is very low. Another source of reflectedwave from the troposphere is an air mass differingconsiderably in its dielectric constant from the sur-rounding air. Electromagnetic waves reflected fromsuch a mass are called tropospheric waves, and mayseriously interfere with radio propagation. Wavestraveling through the lower part of the troposphere(ground waves) on the other hand are not reflected,but curved. The curvature is caused by the gradualchange in the refractive index of air that accompaniesan increase in elevation.

The refractive index of air depends on the tem-perature, atmospheric pressure, and water vaporpressure of the air, and ordinarily decreases uni-formly with elevation. As stated above, this resultsin a curving of the radio beam, usually downward.This curving follows the law of refraction whichstates that a beam passing from a lighter to a densermedium is refracted toward the normal, or perpen-dicular to the surface between the two media. Infigure 1-15A, this is illustrated between the trans-mitting antenna and the midpoint. At the midpoint,however, the beam commences to travel from thedenser to the lighter medium. The beam continues tobend downward, since, according to the law of re-fraction a beam traveling from a denser to a lightermedium is refracted away from the normal. Thiscondition is shown in the figure between the midpointand the receiving antenna, and the whole path, there-fore, is curved downward.

In figure 1-15A, both the earth's surface and thebeam are curved. Any calculations based on suchcurves may be simplified by multiplying the earth'sradius by some constant that will cause the radiobeam to appear as a straight line (figure 1-15B).

9019"1

(A)

(B)

E.TRUE EARTH'S RADIUS

\\\-011!F°7\7,777-\\

fklIA

4/3 EARTH'S RADIUS

Figure 1 -15. Refraction through Standard Atmosphere

13

CHAPTER 1


This constant, "k", is dependent upon the rate ofchange of the refractive index of air with altitude,which in turn is dependent upon weather conditions.The symbol k may vary between 0.8 and 3.0, with avalue of 4/3 generally in agreement with conditionsnormally found to exist in the atmosphere. Theactual path over which the radio waves are propa-gated is called the radio path, and the radio horizon

is the point at which such a path is tangent to theearth. Radio horizons and path attenuation valuesbased on 4/3 times the true earth's radius are foundto be in agreement with values determined by fieldstrength measurement, and most of the formulas andnomograms used in this book are based on the 4/3earth radius, rather than true earth radius.

14

I II A I' T E It

INTRODUCTION

ATTENUATION may be defined as a decrease inthe intensity of energy, such as the energy of electrc-magnetic waves. There are a great many factorswhich cause attenuation. In the case of radio wavespropagated through the atmosphere, the funda-mental loss is the spreading of energy.

When installing radio -relay stations, the distancebetween stations is of great importance. The attenua-tion of the transmitted signal will largely determinethe maximum range obtainable for reliable receptionof the signal. Attenuation will occur in the trans-mission lines from the transmitter to the transmittingantenna and from the receiving antenna to thereceiver, but most of the signal attenuation will befound in the radio path between antennas. Figure 2-1illustrates the attenuation of electromagnetic fieldenergy from the transmitter output circuit to thereceiver input circuit.

PATH ATTENUATION

FREE SPACE. The light radiated from an ordinarylight bulb is a good example of path attenuation. A60 -watt bulb may supply sufficient light for a smallroom but not for a large room. In both cases, anequal amount of light is supplied (60 watts), but inthe larger room the light is distributed over so muchmore space that the amount of light per unit volumebecomes relatively small.

A point source (isotropic antenna) in free spacetheoretically radiates electromagnetic field energyequally well in all directions in much the same way asa light bulb radiates light. The wave so radiated

ATTENUATION

CHAPTER 2

ATTENUATION

spreads out in a spherical form and is called aspherical wavefront. As the spherical wavefront ex-pands in free space, no energy is actually lost, butonly spread over a larger spherical surface. Althoughthere is no decrease in the total amount of radiatedenergy, there is a decrease in the amount of energyper square meter of the wavefront. This decrease inenergy between transmitting and receiving antennaterminals is called path attenuation and is generallyexpressed in decibels. The decibel expresses the magni-tude of a change in signal level, and is equal to thecommon logarithm of the ratio of power level trans-mitted over power level received. The general at-tenuation formula

P=PAttenuation in db = 10 logioP-r

where

(2-1)

Pt = Power in watts at the terminals of the trans-mitting antenna

Pr = Power in watts at the receiving antennaterminals

may be used for any situation, regardless of fre-quency, to determine path attenuation betweentransmitting and receiving antennas when the effec-tive power at both antennas is known.

ATMOSPHERIC. When an electromagnetic waveis propagated through the atmosphere with a certainPoynting power flow (p) watts per square meter, theavailable power at the output terminals of a receivingantenna (Pr) is dependent upon the antenna's effec-tive area. The formula

15

CHAPTER 2

ATTENUATION

o -10 -

20 -

-a 30 -0

a 40cc

50 -*-

.o1:3 60 -z

70 -0

80 "-

90 -100

110

120

130

TRANSMITTEROUTPUT POWER

ANTENNA ANTENNALINE LOSS GAIN

Pr = p x (Ar)

EFFECTIVE RADIATED POWER ( )

(0 db ATTENUATION )

A

O

ANTENNAGAIN

Figure 2-1. Relative Attenuation

)-2where

Ar = The effective area of the receiving antennain square meters may be used to determine theavailable power, or antenna gain, if the Poyntingpower flow is known. The value Ar is expressed interms of the wavelength of the received wave.

In order to determine the Poynting power flow (p)at any given distance from the transmitting antenna,the following formula may be used:

(2-3)

't A tPoynting power flow (p) - P watts/meter'd X'

where

At = The effective area of the transmitting an-tenna expressed in square meters

d = Any given distance from the transmittingantenna expressed in meters; i.e., betweentransmitting and receiving antennas

X = Wavelength in meters

By combining formulas (2-2) and (2-3) and solvingfor Pt/P we find the general attenuation formulabetween transmitting and receiving antennas to be

Pt__ d' X'Pr At Ar

(2-4)

or

ANTENNALINE 1:)SS_.)

RECEIVERSIGNALINPUT

(2-5)

Pr d2 x2Attenuation in db = 10 logo= 10 logo

At

where all units are consistent.

Since an isotropic radiator is the basic, theoreticalform of antenna, it is used as a relative standard forall other antennas. The effectiveness of an antenna'sdirectivity, such as that used with radio -relay sta-tions, as compared with an isotropic antenna, is calledantenna gain, or power gain. A half -wave dipole isquite often used as a standard for practical workinstead of the isotropic antenna, but for theoreticalwork the isotropic radiator is more convenient. Theactual power directivity of a half -wave dipole andthe equivalent power directivity for an isotropicradiator with the same energy content are shown infigure 2-2. The effective area of an isotropic radiatoris given by

2A=e 4r (2-6)

and the gain of such an antenna is taken as unity.Therefore, the effective area of any antenna may beexpressed by

AGX2

0.08GX274 - (2-7)

16

CHAPTER 2

where

G = Power -gain ratio of the antenna over anisotropic antenna.

By assuming that, in radio -relay stations, the sametype and size of antennas are used for both trans-mitting and receiving, we can simplify formula (2-5)by substituting formula (2-7) in the place of A, andA,. The formula

Attenuation in db = (2-8)

Pt 4.1 G2 1012d210 logic, = 10 logic

is the simplified version of formula (2-5) where

d = The distance between antennas in milesG = The power -gain ratio of the antenna over an

isotropic antennaX = Wavelength in centimeters

Formula (2-8) is intended for use when expressingthe attenuation between antennas under free spaceconditions, and may be found in nomogram form inthe appendix. (See nomogram A.)

The power intercepted by a receiving antenna is indirect relation to the path attenuation between trans-mitting and receiving antennas. Assuming again thatin radio -relay stations identical antennas are used forboth transmitting and receiving, we can use formula(2-1) to determine the power in watts occurring atthe output terminals of the receiving antenna.

or

PtAttenuation (a) in db = 10 login (2-9A)

logic Pr = logic P, = a/10 (2-9B)where

a = Attenuation in db as derived from formula(2-8).

Formula (2-9B) may be used to express receivedpower under any conditions if the path attenuationis known. If the value of (a) is taken from formula(2-8) then formula (2-9B) is used to express powerunder free space conditions only. Free space condi-tions are nearly realized when the antennas used areplaced high enough to give first Fresnel zone clear-ance, except with frequencies above approximately8000 mc when the transmission is through rain.

Rain scatters radiation from a passing electro-magnetic wave. In addition, if the particles ofprecipitation are comprised of a dissipative medium,they will absorb energy from the wave and convertit into heat. Both phenomena have little effect on

ATTENUATION

waves below the frequency of 8000 mc; but as thefrequency increases, attenuation, due to scatteringand absorption, becomes more and more noticeable.For frequencies above 10,000 mc both scattering andabsorption are quite pronounced and impose aserious limitation on wave propagation through rain.However, at times, radiation may be scattered farbeyond the radio horizon making it possible to re-ceive signals which would otherwise be unintelligible.

When water, such as in fog or clouds, forms indroplets, each drop acts as a small particle of absorb-ing and scattering material. If the drop size is smallin relation to the wavelength of the impinging wave,the absorption is independent of drop size and de-pendent only upon the total water content per unitvolume. Since the concentration of water in fog orclouds is extremely small, except possibly in the caseof very heavy sea fogs, attenuation by these mediais negligible.

If the drop size increases as compared to the wave-length, absorption will increase at a fairly rapid rate.When the concentration of the rain is large enough,scattering will also result in an appreciable rate ofattenuation.

Since it is extremely difficult to measure drop sizein a typical rainstorm, attenuation by rainfall isgenerally expressed in terms of rate of precipitationper unit of time. The following empirical formula is aclose approximation of attenuation by rain

Attenuation in db = 10 d R (2-10)A2

where

R = Rate of rainfall in inches per hourd = Path length in milesX = Wavelength in centimeters

The above formula may be found in nomogram formin the appendix. (See nomogram B.) Attenuation by

270

1.0RADIUS

I. 64RADIUS

0°EQUIVALENT

POWER DIRECTIVITYFOR AN

ISOTROPIC RADIATOR ( 1 1

Pi

Pd

GI 0.612

d

Pd= I. 64

Pi GI

ACTUALPOWER DIRECTIVITY

OF AHALF -WAVE DIPOLE ( Pd

Figure 2-2. Relative Antenna Gain

17

CHAPTER 2

ATTENUATION

rain is additional to the free -space path attenuationas given in formula (2-8). It must be rememberedthat there are many irregularities in a typical rain-storm and any attenuation calculations for pathlengths much over three miles will be of an approxi-mate value only.

For frozen precipitation, the absorption loss isconsiderably smaller than for a liquid. However, ifthe particles, such as hailstones or snow, are suf-ficiently large, the scattering loss will again result inan appreciable rate of attenuation.

FIELD STRENGTH. Field strength refers to thequantity of the electric field (E) at any given pointand is measured in terms of volts per meter. Onevolt per meter is equivalent to a potential of onevolt induced in an antenna wire one meter long. Sincethe unit, one volt per meter, is too large for mostpractical considerations, millivolts per meter andmicrovolts per meter are used more frequently. Forexample, if 50 microvolts are induced in a conductorone meter long when a radiated wave cuts across it,the field strength is 50 microvolts per meter or50 Av/ m.

The variation of field strength around an antennasystem can be shown graphically by polar diagrams,which are simply circular charts which resemble theface of a compass. The antenna is taken as the centerof the chart and the circumference of the chart islaid off in angular degrees. Computed or measuredvalues of field strength then may be plotted radiallyin a manner that shows both magnitude and directionfor a given distance from the antenna. (See figure 2-3).Field -strength values of this sort may be measureddirectly in the field by the use of a standard field -strength meter. Field strengths in the vertical planeare plotted on a semi -circular polar chart and arereferred to as vertical polar diagrams.

The expected free -space field strength (E0) in voltsper meter, at a distance (d) in meters from a trans-mitting antenna, is given by

E. = N/30 GtPt /d (2-11)

where

G, = Power -gain ratio of the transmitting an-tenna over an isotropic antennaTransmitter power in wattsDistance in meters

Pt =d =

Formula (2-11) is simply a straight line relationshipbetween the effective radiated power (GtPt) of atransmitting system, and the distance traveled bythe wave. It is often convenient to determine theexpected field strength of a definite antenna by

using the value of one watt for (Pt). The answersobtained by this procedure may then be plottedgraphically resulting in field -strength below one watt.A quick reference is then available for determiningthe expected strength below one watt by multiplyingthe field strength below one watt by the square rootof the desired transmitter power (-VP,).

At frequencies above 300 mc, where the operatingwavelength is considerably less than one meter, thereceived field is generally measured in terms of powerrather than in field strength. The conversion fromvolts per meter to watts per square meter under freespace conditions is given by the formula

E2P =377

(2-12)

where

P = Field strength in watts per square meterE = Field strength in volts per meter

By substituting in the above formula the free -spacevalue of E as given in formula (2-11), the followingfield strength equation is obtained:

P = 0.08GtPt/d2 watts/meter' (2-13)

where all units are the same as given for formula(2-11).

OBSTACLE GAIN. In VHF and UHF transmission,the first requirement has always been a clear pathbetween the transmitting and receiving antennas,with approximately first Fresnel zone clearance aboveobstructions as a second, and less important, con-sideration. While there has been a definite minimumclearance acceptable for relay work, very few pathshave been rejected for reason of excessive clearance,and any land mass intercepting the radio beam morethan about 20 percent has been considered reason fordiscarding a site in favor of another with a clearradio path. Occasionally in the past, field strengthmeasurements made with a land mass interveningbetween transmitting and receiving antennas haveshown less attenuation than indicated by calcula-tions, but these values were generally credited toexceptional atmospheric conditions, and ignored.There was no attempt made to calculate the effectsof a large mass obstructing the signal, since it wasgenerally believed that the attenuation would be fartoo great to give an intelligible signal at the receivingantenna.

Now it has been found that a large mass of landintercepting the signal path may actually improvethe field strength over the value found for a similarpath above smooth earth. This possibility was noted

18

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CHAPTER 2

ATTENUATION

in articles by Schelling, Burrows, and Ferrell, in 1933,and by Bullington (Proc. I.R.E. Oct. 1947), althoughno installations based on this principle have beenmade until quite recently. According to an article inthe Proc. I.R.E. for Sept. 1953 entitled `Large Re-ductions of VHF Transmission Loss and Fading bythe Presence of a Mountain Obstacle in Beyond -Line -of -Sight Paths", by Dickson, Egli, Herbstreit, andWickizer, higher field strength may be obtained, aswell as better fade conditions. This article describesresults found on a 38 mc, 160 mile path betweenYakutat and Gustavous, Alaska. The transmittingand receiving antennas are approximately 200 feethigh, with Mt. Fairweather intercepting the path as asingle knife-edge, 8,775 feet high. Such a path, by allprevious beliefs, would guarantee a signal completelylost in the noise. Instead of finding an extremely lowfield strength, the attenuation was found to be 134db, as compared with 207 db attenuation for thesame path over smooth earth. This amounts to anincrease of 73 db, which is referred to as the "obstaclegain" of the intervening mountain. Recorded obser-vations made over a considerable period of timeshowed a remarkable absence of fading.

This increase in signal strength, and almost com-plete absence of fades, is most easily explained byreferring to the diffraction of light over a knife-edge.The radio signal is also diffracted by a knife-edgeinterception, and may also be reflected from theearth's surface. Figure 2-4 shows a source of anelectromagnetic wave at T, and the point where thewave is received R. H represents the effective heightof the intercepting obstacle, which is not necessarilythe true height. The effective height is higher, and isdetermined by the ray paths from points T and R asthey follow a grazing path over the mountain. PointsP' and P" are reflection points on the earth's surface.As shown in the figure, there are four paths the radiobeam takes in traveling between the two antennas:(1) direct -direct (T -P -R), (2) reflected -direct (T -13,-P -R), (3) reflected -reflected (T -P1 -P -P2 -R), and (4)direct -reflected (T -P -P2 -R). It might appear that thereflected paths in mountainous country would beunimportant, due to irregularities of the ground.Actually, reflection will be surprisingly high, sincethe angle of incidence is almost at the grazing point.With such a high angle of incidence, the irregularitiesof the surface have far less effect than if the anglewere more nearly at right angles to the surface. It isobvious from the figure that these paths will vary inlength, and therefore the different rays arriving bythe four paths will vary in their phase relationshipat the receiving antenna. The four -path diffraction

Figure 2-4. Four -Ray Path

problem- of optics applies in this case, and may beused to determine the phase relationship. Any changein path lengths or operating frequency will alter thephase relationship of the four waves arriving at thereceiving antenna. For any set condition of antennalocation and obstacle height, a frequency may bedetermined that will allow all four rays to arriveat the receiving antenna in phase, or nearly in phase.Naturally, some may arrive many wavelengths be-hind, but still in phase, and no appreciable effecton the audio signal will be noted. A graph of attenua-tion against varying depth of penetration of the beamby the knife-edge will show the possible range ofattenuation. (Figure 2-5.) The attenuation will befound to vary from near infinity to almost free spacevalue, as the phase relationship of the arriving wavesvaries from opposing to aiding phase relationship.

This discussion of the effect of large obstacles onradio propagation is included primarily for its in-terest. At preSent, methods of using large obstaclesto improve reception have not been definitely ap-plied, and it is therefore best to use methods thathave been tried and proved. There can be littledoubt but that the useful effects of obstacles will be ofvalue in the radio relay field, but considerable workremains before it can be satisfactorily applied.

FREQUENCY CHARACTERISTICS

For all practical purposes it is convenient toclassify radio waves into bands of frequencies withinwhich propagation effects are similar. However, anysuch classification must be of a general nature only,since changes in propagation characteristics withfrequency are not sharply defined. Thus, when anupper or lower limit of frequency is designated for acertain propagation effect, it does not mean that suchan effect stops at those limits, but rather that itbecomes negligible beyond such limits.

30 MC TO 300 MC. This range of frequencies ispart of the oldest known frequency band of the entireradio spectrum, since both Hertz and Marconi con-ducted their famous experiments in the region from30- to 3,000-mc.

As a rule, ionospheric propagation is negligible at

20

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210

220

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250100

CHAPTER 2

ATTENUATION

THEORETICAL OBSTACLE GAINS AT 100 McASSUMING FOUR-RAY KNIFE-EDGE DIFFRACTION THEORY

Transmitting and Receiving Antenna Heights Each 100 Feet Above the Surface

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10,000 20,000 30,000 50,000

21

CHAPTER 2

ATTENUATION

these frequencies and cannot be relied upon forpropagation to great distances. However, irregularionospheric reflections are possible (due to sporadicE variations) and can cause a signal in the lowerpart of this band to be propagated several hundredmiles. Such propagation, by way of sporadic Ereflections, decreases rapidly with frequency andbecomes of little importance above 100 mc.

The most common method of propagation at thesefrequencies is, therefore, through the atmospherealong the surface of the earth. Over a smooth terrain,power radiated from an elevated antenna varies in-versely as the square of the distance, and undernormal operating conditions ground reflections areparticularly important and depend upon the co-efficient of reflection of the reflecting surface. Forcertain antenna heights the reflected wave will cancelthe direct wave, while for other antenna heights wavereinforcement occurs. Within the horizon, inter-ference between the direct and reflected waves willproduce a series of maximum and minimum fieldstrengths which are a function of the earth's dielec-tric constant and conductivity.

Since the density of the earth's atmosphere andalso its index of refraction normally decrease withaltitude, radio waves are propagated along a curvedpath by refraction. This is often represented as astraight-line propagation path occurring over anearth whose radius is 4/3 the true earth's radius. Ineffect, refraction tends to increase the range of atransmitted wave slightly beyond the geometrichorizon, such a distance being called the radiohorizon. In this frequency range, the radio horizonis governed not only by refraction, but by diffractionas well.

Diffraction plays a major role in this frequencyband, depending upon the path over which the wavesare propagated. The effect of obstacle gain causedby the diffraction of radio waves over a mountainridge was first discovered in this frequency range.Diffraction effects are primarily important in regardto irregular terrain where it makes possible thereception of signals in the geometric shadow regionof a hill or other intervening object. Generally, thehigher the frequency, the less the diffraction effects.

Atmospheric noise at these frequencies is fairly lowand decreases with increasing frequency. Such noiseis usually caused by local electrical storms only.However, one of the more important sources of noisein this range is man-made noise such as that fromignition systems, diathermy machines, and X-rayequipment. Receiver noise also begins to becomeprevalent here, although considerable improvementin circuit design has made possible its reduction.

300 MC TO 3,000 MC. Almost all the energy trans-mitted at these frequencies is propagated throughthe earth's atmosphere along a curved path. The re-fracted path may again be assumed as a straight-linepath over an earth's radius of 4/3 the true radius.

Ground reflections are still present at these fre-quencies and can cause multipath fading due todestructive interference, although such reflections be-come of less importance at the higher end of theband. However, a second type of multipath fadingcan occur when parts of the wave are refractedthrough other higher layers of the atmosphere andbecome bent sufficiently to return and combine withthe wave received over a lower and more direct path.

At frequencies above 1,000 mc, attenuation of thetransmitted signal by trees or other vegetation canrange anywhere from 12 to 46 db per mile, although ifthe antennas are located to give first Fresnel zoneclearance above the trees such attenuation becomesnegligible.

Atmospheric noise in this frequency band is ex-tremely low, as well as man-made noise, with theexception of ignition pulses which can become seriousat times. Receiver noise is somewhat greater at thesefrequencies and increases with increasing frequency,thus calling for special receiving tubes and circuitdesign.

3,000 MC TO 13,000 MC. At these frequencies,transmission is strictly limited to line of sightdistances based on 4/3 true earth's radius. Very littlewave reflection will radiate from the earth at thesefrequencies. Instead, the earth will act as if it weremade up of an infinite number of small mirrors, eachreflecting the incident wave in a different direction.This is sometimes called diffuse reflection. In addi-tion, incident radiation will also be absorbed by theearth's vegetation. Consequently, the amount ofreflected energy from the earth's surface is small, andvery little wave interference will occur from thissource. However, multipath fading caused by tropo-spheric reflections or the multiple refraction ofseveral propagation paths through the atmosphere isimportant throughout the entire band. There is alsoa tendency for buildings and other man-made objectsto cast sharp shadows at these frequencies and, if thesurface of such objects is smooth, even to reflect thewaves in a new direction.

Rain scattering and absorption can cause a seriousloss of radiated power at the higher end of thisfrequency range. If the drop size is comparable to thewavelength of the propagated wave, a very sub-stantial portion of the transmitted energy will be re-radiated from the raindrop in a wide range of direc-

22

CHAPTER 2

ATTENUATION

tions. This phenomenon, known as scattering, has anattenuating effect on radio waves somewhat like thatof diffuse earth reflections. However, not all theenergy incident upon a raindrop is re -radiated, butinstead, it is virtually trapped or absorbed and con-verted into heat. If the drop size is comparativelysmall in relation to the wavelength, such losses aredependent only upon the volume of water in suspen-sion and therefore are generally negligible.

The use of sharply beamed waves to overcome thelosses due to atmospheric attenuation in this band

23

conserves enough power to enable a few watts ofdirected power to be as effective at a distant receiveras many kilowatts of undirected power.

Receiver noise at these frequencies has a greateffect on the practical range of a receiving system.Special techniques, such as the use of crystal mixers,have been developed to minimize this noise by con-verting the received signal to a lower frequencybefore amplification. Such noise depends both uponthe operating temperature and the receiver band-width and increases directly with both.

CHAPTER 3

FADING

II A T E

INTRODUCTION

The term "fading" as used in this chapter is definedas the variation of radio field strength caused bychanges in the transmission medium with time. Thereare two general sources of fades, inverse beam -bend-ing and multipath interference, with multipath in-terference by far the more common of the two.

TYPES OF FADES

FADING DUE TO INVERSE BEAM -BENDING.In this type of fade, only the direct beam betweenthe transmitting and receiving antennas need beconsidered, since the fading is caused by changes inthe refractive index of the air through which thisbeam passes. Ordinarily, the beam follows a slightlycurved path between the transmitting and receivingantennas, with the center of the beam striking thereceiving antenna under standard atmospheric con-ditions. Any change in the refractive index of airthrough which the beam passes will result in achange in the beam path. Such changes will cause thebeam to pass above or below the antenna, and aweaker received signal will result. The name, inversebeam -bending, is given because the bending is mostlikely to occur in an upward, or inverse, direction(figure 3-1A). It is possible, in extreme conditions,for the beam to be bent upward to such a degree thatthe signal becomes lost in the noise. Extreme fadesof this type rarely take place, however, since a con-siderable change in the index of refraction mustoccur, and when they do occur, they are usuallyslow in nature.

MULTIPATH FADING. The beam directed at the

3

FADING

receiving antenna is not a narrow pencil of energy,but spreads out in the form of a cone, with its apexat the transmitting antenna. Under normal condi-tions the central part of the cone strikes the receivingantenna, with part of the beam passing above andpart below the receiving antenna. Should the upperpart of this cone enter a region of the atmospherewith an unusually small index of refraction, it wouldbe refracted downward toward some part of theearth's surface. Such a refracted beam might easilystrike the receiving antenna and cause fading, thedegree of the fade depending upon the signal strengthof the refracted beam, and the phase relationship ofthe refracted and direct beam (figure 3-1B).

The comparative strength of the two signals willbe determined more by the part of the cone refracteddownward than by the difference in path length. Forpaths of fifty miles or less, the difference in pathlengths will be comparatively small. The phase re-lationship between the two beams, however, mayeasily vary from 0 degrees to 180 degrees, dependingupon the path length and the transmitted frequency.Should the path of the refracted beam, for example,be one wavelength longer than the direct beam, thesignals would arrive in phase, and the resultant fieldstrength would be approximately twice the expectedfield strength. A difference in path length of one-halfwavelength would result in the arriving signals op-posing each other, and deep fading would result. Itshould be noted that the refracted beam might arrivemany wavelengths behind the direct beam, and stillbe in phase, or any odd multiple of half -wavelengths,and still be 180 degrees out of phase with the directbeam. In either case, the modulating signal would beunaffected, except by fades, because of the tre-

25

CHAPTER 3

FADING

mendous length of the modulating signal at audiofrequencies. Since the 'difference in paths is measuredin wavelengths, rather than miles, such fades wouldbe expected more often at shorter wavelengths thanlonger ones; and so it is found to be in practice.

Fading caused by radio signals reflected fromsome part of the earth's surface are similar to fadesdue to refracted signals, although the operation is alittle different. The received signal strength will de-pend not only on the initial strength of the trans-mitted beam, but on the amount of energy reflectedfrom the earth and the phase lag introduced at thereflection point. As the angle of reflection in radiorelay work is small, seldom exceeding 2 degrees, thesurface will be smooth for practically all wavelengthsover approximately ten centimeters. (Under 3,000mc.) At frequencies above 3,000 mc, earth reflectionsgenerally become diffuse in nature, and their effectupon the received field gradually becomes negligible.

HEIGHT-FREQUENCY DEPENDENCE. At fre-quencies below 30 mc, antenna height above theearth is important, since the radiated signal is af-fected by the presence of the earth. Antenna heightsunder one-half wavelength cause the radio signal tobe deflected downward to such an extent that thesignal is rapidly attenuated. By increasing antennaheight to one-half wavelength, or higher, the trans-mitted wave will then travel outward, instead ofdeflecting downward. Obviously, since the wave-length height of the antenna, rather than its physicalheight, is the measure of elevation, antenna heightmay be increased by increasing the operating fre-quency, or by actually raising the antenna. Theearth's surface will affect the signal to a lesser extentas the height (or frequency) is increased, until fullfirst Fresnel zone clearance is obtained. At such time,the signal will radiate with no shaping of the waveby the earth's surface. Beamed signals such as areused for microwave relay work may therefore beconsidered as originating in free space so long as first

DIRECT WAVE

RECEIVEDSIGNAL LEVEL

TRANSMITTER

(A) INVERSE BEAM BENDING

SUPER -REFRACTED WAVE

1,1111151101/1.,

DIRECT WAVE

RECEIVEDSIGNAL LEVEL

RECEIVE

( B ) MULTIPATH FADING

Figure 3-1. Single & Multipath Fading

Fresnel zone clearance is obtained over the full pathlength. Fading may still take place, however, sincesome part of the beam may be reflected from theearth with sufficient intensity to affect the receivedsignal. Such conditions are particularly true wherethe path is over a good reflector, such as sea water.For example, a beamed s gnal from Los Angeles toCatalina Island was first tried by using extremelyhigh antennas, in order to obtain line of sight trans-mission. Reflections from the surface of the watercaused almost completely unintelligible signals, how-ever. Had it been feasible to raise the antennashigher, a point would eventually be reached wherefree space conditions would prevail, and such reflec-tions cease to cause trouble.

ATMOSPHERIC EFFECTS

M -PROFILE. An M -profile is a graphical cross-section of the atmosphere showing the change of theindex of refraction with altitude, and is drawn byplotting (M) as abscissa, and (H) as ordinate. Understandard atmospheric conditions, the value of Mincreases by 3.8 per hundred feet, and the standardM -profile will therefore be a straight line, having aslope of 3.8 per hundred feet. Field strength at thereceiving antenna, calculated on the basis of astandard M -profile will be the normal field strengthto be expected, that is, with neither fades, norabnormally strong signal. The field strength valuebased on the standard M -profile agrees with valuescalculated by use of effective earth's radius equal to4/3 the actual radius.

The standard M -profile is dependent upon homo-geneous atmosphere, the most commonly found con-dition, but weather changes can produce variationsin the M -profile, and in the transmission of radiosignals. (See Chapter IV.) In figure 3-2A is shown astandard profile; figure 3-2B shows the effect ofan abnormally high surface temperature or watervapor content. Such a condition will result in chang-ing the curvature of the radio signal so that it willapproach a straight line (based on true earth radius)or in curving the beam away from the earth. Such acurve is called inverse beam -bending, and may occurif the area is sufficiently deep, or sub -standard.

Figure 3-2C illustrates a condition that is just theopposite of that shown in 3-2B, both in the curve ofthe M -profile, and in the effect on the radio signal. Asharp rise in temperature with increasing height, or asharp decrease in water vapor content, or both willproduce such a condition. This phenomenon producesa marked bending of the wave path and is known assuper -refraction. Since the radio signal will tend tostay within the elevation limits shown as A and B,

26

CHAPTER 3

FADING

the condition is frequently referred to as ducting,or trapping. Where the M value is decreasing withelevation, at elevations close to the earth's surface, asurface duct will result, and the effect on the radiosignal will depend on the degree of change in the Mvalue with elevation, and the height of the duct. Asimilar condition, known as an elevated duct, isshown in 3-2D. As in 3-2C, the boundaries of theduct are indicated by A and B. Such elevated ductshave been found near San Diego, Cal., while surfaceducts are often found over a large body of water,such as the Caribbean Sea, where a surface wind isprevalent.

Trapping of a radio signal may not be relied onfor transmission other than for short periods of time,since the conditions producing the duct are subject tochange. The trapping found in the Caribbean Sea,for example, is predominantly a daytime phenomena.

Observations have shown that a duct tends to con-fine electromagnetic waves with an action much likethat of a waveguide. Field strength measurementstaken inside a duct are considerably higher thanthose taken outside the duct. Therefore, in order for aduct to be used to maximum advantage, both thetransmitting and receiving antennas should be locatedwithin the duct. Another factor to consider intrapping is the transmitted frequency. A duct, like awaveguide, is frequency sensitive and will confinecertain frequencies much better than others. As ageneral rule, the higher the duct, the lower thefrequency that may be used. The strength of thetrapped signal will also vary according to the natureof the duct boundaries. If the rate of change of theM -profile is considerably less than standard, therefraction at the boundary of the duct will begreater than in the event of a slight change, and agreater part of the signal will remain within the duct.

DIURNAL SIGNAL VARIATIONS. Assumingthere is no degree of obstruction or object penetrationof the transmission path (first Fresnel zone clear-ance), steady transmission occurs when the air alongthe path is well mixed, as on sunny afternoons, or instormy, windy weather. The M -profile is then nearlystandard except where irregular temperature andwater vapor pressure conditions near the groundcause a slight increase in the M value at that eleva-tion. Signal fading occurs in the presence of irregu-larities in the M -profile. A marked change in signallevel invariably accompanies these irregularities overnon -optical paths because of multipath fading, butfor optical paths the change in signal level is morediurnal in nature, indicating the fading to be of thesingle -path variety. In general, a diurnal signal

MODIFIED INDEX H --a.(a)

STANDARD M PROFILE

MODIFIED INDEX M --OP

(c)SURFACE DUCT

MODIFIED INDEX M

SUBSTANDARDSURFACE LAYER

MODIFIED INDEX II

(d)ELEVATED DUCT

Figure 3-2. Typical M Profiles

changes from a steady condition at midday to a typecharacterized by pronounced fading at night. It isusually observed that on non -optical paths theaverage signal level rises when fading occurs, as inover -water paths, but on optical paths it may eitherrise or fall for considerable periods. Diurnal signalvariations are considerably more pronounced insummer than in winter because of the high water -vapor content of the air in summer, which increasesthe effectiveness of temperature gradients in produc-ing strong M gradients.

Since changes in the M -gradient occur during orafter the passage of temperature fronts or high windconditions, it is possible to compare the passage ofsuch fronts with the change in signal level and arriveat an approximate relationship between the two.Here again, any hard and fast statement is dangerous,since exceptions occur due to seasonal effects, orcombinations of weather changes, but the generaleffects will be as given below.

Warm fronts are usually associated with lowersignal strength, whether or not the signal prior to thearrival of the front was normal or high. This may beaccepted as a fairly safe rule for most seasons,although in winter time, the warm front may producea higher signal strength, rather than a low one.A warm front with a high moisture content willoccasionally result in much stronger signals duringwinter. For example, television broadcasts originatingfrom Philadelphia, Pa., channel 3, have been received

27

CHAPTER 3

FADING

at Riverhead, L. I., far beyond the normal range ofthe frequency used.

Cold fronts are usually accompanied or followedby an increase in signal strength. This increase maycontinue for several hours after the passage of thefront.

High winds produce a thorough mixing of theatmosphere, and hence a normal signal will result.An exception would occur if the high winds should beaccompanied by an air mass that was either ex-ceptionally dry, or exceptionally moist.

Stormy conditions are often accompanied by avariable signal. The diurnal trend also is more notice-able during stormy conditions.

TYPES OF SIGNALS

FADING VS M -PROFILE. Four different com-binations of fades have been determined, as shownon records of field strength taken over a number ofyears. These types of fades are the result of a directcombination of inverse beam -bending and multipathfading, and are illustrated in figure 3-3.

Figure 3-3A shows the relationship between thetype of fade encountered with a substandard M -pro-file. Such fades occur quite rapidly, with signalstrength below normal. Occasionally slower varia-tions of signal strength are superimposed on thefading shown in the figure. This type of fading isknown as scintillation and is fairly common insummer, although almost non-existent in winter.

With M -profiles that are standard, or nearly so,the average signal level is steady within about ± 5db. Scintillation is usually present with an amplitudevarying between 5 and 10 db, although the upperlimit may approach 25 db. This is the kind of fadingmost frequently encountered throughout the year,and is often referred to as a standard signal (figure3-3B).

When shallow surface M -inversions, with theiraccompanying ducts, occur, the signal level is abovestandard and increases with duct height. The signalnever rises above the free -space value, and onlyminor, short -time fades occur. This is defined aspartial trapping, and is shown in figure 3-3C. Apartial -trapping condition is quite stable, with verylittle fading. This condition is quite common inwinter, when it may last for several days at a time.

With deep M -inversions at the surface, the signallevel is near the free -space value. The signal isunsteady, with roller fading of amplitudes as largeas 40 db and for periods ranging from a few minutesto an hour. As the M -inversion deepens, the ampli-tude of fading increases, and the period of fading

decreases. Roller fading is characterized by broadflat maxima and sharp deep minima, and representsthe most violent fluctuations possible. This type ofsignal, called the strong -trapping signal, (figure3-3D), occurs in the summer and fall and then onlyon rare occasions. These periods of extreme fadesmay exist from one to five hours, and usually occurbetween midnight and sunrise.

While these types of fading are distinct, one fromanother, changes from one type to another may takeplace quite rapidly. Such changes may affect eitherthe average level of the signal, or the type of signal,and may occur at the same time. The magnitudes ofthese changes generally increase with frequency.

FREQUENCY DEPENDENCY. Signal types havebeen found to vary, not only according to changes inthe M -profile, but according to frequency as well. Incases where a grazing path exists, substandard M -profiles will be accompanied by a scintillating signalat all frequencies considered in this book. The varia-tions due to scintillations are irregular and rapid,with periods of about 30 seconds duration, andamplitudes of at least 15 db. The decreases from astandard signal are approximately equal at fre-quencies between about 3,000 mc to 13,000 mc. Asthe clearance for the radio path is lessened by anobstacle, the signal strength becomes lower, providedthere is no counteracting effect, as noted in obstaclegain (Chapter II).

During periods of standard or nearly standardatmospheric conditions, the signal strength at all fre-quencies will be approximately standard as well. Nounusual signal strength due to ducts, or multipathconditions will occur, since these conditions them-selves are dependent upon unusual weather condi-tions. For any given path, for example, the signalwill be approximately as calculated, since such cal-culations would take into account standard refrac-tion, reflection from the earth's surface, or any otherunusual physical condition. Where a superstandardcondition occurs, as indicated by an M -inversion atsome layer of the atmosphere, different frequencieswill be affected differently. A shallow surface duct,as might occur over water, will have little effect on asignal at 3,000 mc, even though both antennas arewithin the duct. A signal of 13,000 mc transmittedthrough a shallow duct may increase in strength,due to the duct. If the duct increases in height, thesignal strength of the 13,000 mc signal will increase,although at first there will be no change in the lowerfrequency signal. As the duct size is increased to 50feet, the field strength of both the 3,000 and 13,000mc signals will rise above the value to be expected

28

-30

-0-40-

w

-Jik

CL(I) -60

W-20cc

oco4

w-J -40CD

C.)

0

I 0

LLI

-10

Cf)

z -20

(n

+20

STANDARD AT-36db

( a )

CHAPTER 3

FADING

1000

-500

0

1000

-500

- 0

1000w

STANDARD AT- 36db

(c)

+10-STANDARD AT-36db

2TIME IN HOURS

(d)

3 320 330 340 350REFRACTIVEMODULUS

(MI

Figure 3-3. Types of Signals

I 1 I

500

0

1000

-500

-0

29

CHAPTER 3

FADING

without the duct, and the higher frequency willapproach free space value. As the duct height ap-proaches about 70 feet, roller fading will occur at thehigher frequency, while the 3,000 mc signal will con-tinue to increase in strength. With duct heights ofgreater value, the 13,000 mc signal will decrease instrength, with increased effects of multipath fading,and roller fading will begin to occur at the 3,000mc level.

The discussion on signal strength and fading ismentioned as occurring at the two levels; actually,the intermediate frequencies are also affected, withthe effect varying between the two extremes men-tioned. If the duct height is too low for any givenfrequency, it will have little effect; if too high, rollerfading will take place, succeeded by a reduction infield strength, as the duct height is further increased.Should the elevation at which the M -inversion occursbe sufficiently high for the wavelength under con-sideration, no ducting will occur, but a multipathfade, caused by refraction of the signal at the layermay take place. At any given distance within theradio horizon, the period and amplitude of the fadeson the upper and lower frequencies are nearly equal.As shown in figure 3-4, the fading, however, is farfrom synchronous. Usually the higher the frequency,the shorter the fading period, with the amplitude offade increasing with increasing frequency.

EFFECTIVE EARTH'S RADIUS. Experimentaldata on fading at frequencies above 30 mc can becorrelated reasonably well with the concept of aneffective earth's radius if it be assumed that such avalue is rarely less than 0.8 times, or more than 3.0times, the true earth's radius. At higher frequenciesthe received signal at distances beyond the radiohorizon is seldom less than would be expected for anearth's radius of 0.8 true radius, and may be equalto or above the free -space value. The theory oftrapping would indicate that the received signal maybe considerably higher than indicated by free -spacetransmission. Instantaneous peaks of 18 to 20 dbabove the free -space value have been reported, butthe average signal is greater than 3 or 4 db above thefree -space value for only a small percentage of thetotal time. This means that the fading range at 3,000mc over a path ten miles beyond the radio horizonmay be as much as 60 or 70 db.

The percentage of time that the signal is eitherextremely high or extremely low depends on meteor-ological conditions as mentioned, which, in turn, arefunctions of geography and season of the year, aswell as daily weather conditions. Within the radiohorizon, the received power at frequencies above

+10

0-

-20 -t

-30--

50

+10

STANDARD AT-57db3000 mc

LOW ANTENNAS

0--10--

-20

- 30

-40STANDARD AT- 43db

13,000mcHIGH ANTENNAS

Figure 3-4. Fading Comparison

3,000 mc may vary from several db above, to 15 dbor more below the free -space value, even over a goodoptical path. A good optical path is defined as onewith full first Fresnel zone clearance as discussed inChapter 5. The fading appears to be more severeover sea water than over land, but whether thisdifference results primarily from a difference inatmospheric conditions or from a difference in thereflecting properties of sea water has not been clearlyestablished. An outline of fading causes plottedagainst frequency is illustrated in figure 3-5, althoughthe frequency divisions shown are general, and suchcauses may extend far beyond the ranges given.

DIVERSITY RECEPTION

SPACE DIVERSITY. Multipath fading may beminimized by the use of a practice called space -diversity reception. Two or more antennas are spacedseveral wavelengths apart, generally in a verticaldirection. It has been observed that multipath fadingwill not occur in synchronism at both antennas,although a diurnal change in signal intensity will.

30

CHAPTER 3

FADING

0

Sufficient output is almost always available from oneof the antennas to provide a useful signal, and onlythe strongest signal is applied to the receiver ampli-fier. The use of two antennas at different heightsprovides a means of compensating, to a certainextent, for changes in the electrical path differencesbetween direct and reflected rays by the selection ofthe stronger signal. However, fading due to inversebeam -bending is generally not affected by spacediversity.

The antennas should be separated far enough togive an approximate half wavelength between thegeometrical path differences of the two signals. Anapproximation of the spacing is given by

Spacing in feet = 43.4Xd/ht (3-5)

where

X = Wavelength in centimeters

d = Path length in milesht = Height in feet of the transmitting antenna

above a plane tangent to the earth at pointof reflection.

FREQUENCY DIVERSITY. Since the period offading decreases as the frequency of a signal in-creases, another method of diversity reception hasbeen utilized to some extent with varying degrees ofsuccess. This method is commonly known as fre-quency diversity, and must be used simultaneouslyat both the transmitter and receiver.

Frequency diversity is, as the name implies, simplythe use of two transmitters and two receivers, eachpair tuned to a different frequency. If the fadingperiod at a precise frequency extends a definitelength of time, the same signal on a higher frequencywill still be received. Likewise, if the amplitude offade tends to be too great, the signal at a lowerfrequency will be steadier. Since this method doublesthe amount of equipment necessary, it is used onlyon the most expensive systems, such as the trans -Atlantic network where high reliability is a necessity.

IONOSFHE RICAR EFIE CTIOT \;

L ND R Ef -ECTIONS/444 /z(z- //////r. /I% \-\_\ lM 1len#1431WITVZOI\

INVERSE EEAM SENDING:

PRECIPITATION

304 5 6 7 8 9100 2 3 4 5 6 7 8 91000

FREQUENCY IN MEGACYCLES PER SECOND

2 3 4 5 6 7 8 910000

Figure 3-5. Fading Causes by Frequency

2

31

CHAPTER 4

WEATHER VERSUS PROPAGATION

II A P T F It

INTRODUCTION

Weather is one of the many factors affecting elec-tromagnetic wave propagation. The ways in whichweather may affect wave propagation are many, andit is the purpose of this chapter to consider thevarious phenomena known as weather, and to showtheir relationship to radio propagation. Wind, airtemperature, and water content of the air can com-bine in many ways, with different combinationscausing radio signals to be heard many hundreds ofmiles beyond their ordinary range, or attenuated to apoint where the signals may not be picked up over anormally satisfactory path. Unfortunately, no hardand fast rules may be given concerning the effects ofweather on radio transmission, since the variables ofweather are extremely complex, and subject to fre-quent change. Any discussion on the effects ofweather on radio must be limited to general terms,therefore, and will be so treated here. As an illustra-tion, rain is considered to be a negligible factor inthe attenuation of radio signals at frequencies below6,000 mc. Rain may cause excessive attenuation ofsignals below 6,000 mc, in the event of a cloudburst,or a rain with exceptionally large drops. Normal rain-fall, even though it covers the whole radio path,will cause so little attenuation that it may be safelyignored. At frequencies above 6,000 mc, normal rainmay still be ignored, but the chances of attenuationby rainfall become greater, and increase as thefrequency increases.

WEATHER VS PROPAGATION

ATMOSPHERIC CONDITIONS. As stated in

4

WEATHER VERSUS

PROPAGATION

Chapter 3, wave propagation in free space issubject to path attenuation only. The total amountof power traveling outward from any antenna in freespace remains undiminished with distance, but theamount of power falling on a unit area will decreaseas the wave spreads outward from the antenna.Neither absorption nor refraction can take place infree -space propagation, only path attenuation due tothe distance between transmitting and receiving an-tennas. Free -space propagation, of course, representsan impossible ideal, since the earth's atmosphere willaffect wave propagation in a number of ways withthe result that the signal strength may fall far belowa satisfactory value, or possibly reach a value greaterthan free space. A consideration of the atmosphereand its make-up will be of help in understanding theeffects of weather on radio propagation.

The three basic elements of weather are atmos-pheric pressure, temperature, and vapor pressure.These elements are not uniform with respect toelevation above the earth, but tend to decreaseuniformly with increase in elevation. Their variationshave been determined from meteorological soundingstaken in the lower part of the troposphere, over aperiod of years, and standard gradients have beenestablished. These gradients are used to establishstandard atmospheric conditions. Pressure and tem-perature normally decrease with increase in eleva-tion; temperature, for example, decreasing approxi-mately 5.4° F. per 1,000 feet. Relative humidityincreases with elevation, and may be determinedfrom wet and dry bulb temperature readings appliedto relative humidity charts. In formulas concerningthe refractive modulus, vapor pressure is used, and

33

CHAPTER 4


may be determined from charts designed to show therelationship between wet and dry bulb readings,atmospheric pressure and vapor pressure.

Standard atmospheric conditions are based onhomogeneous air, which is defined as air that isuniform in composition, and having uniformly vary-ing temperature caused solely by uniform decreasein pressure with increase in elevation. Elevation hasno effect on the water vapor content, although boththe dew point and relative humidity will change withelevation due to change in pressure and temperature.It should be noted that temperature, pressure, andvapor pressure at the earth's surface are not specifiedfor standard atmospheric conditions, nor is theelevation of the surface considered. The importantfactors concerning standard atmosphere are uniformvertical change of pressure and temperature, withpressure, temperature, and vapor pressure constantat any given elevation.

HOMOGENEOUS AIR

Homogeneous air is the result of thoroughly mixingthe air, which may be done in a number of ways.One way in which the air becomes mixed is by meansof convection currents. Open areas of the earth'ssurface may be heated by the sun, producingwarmer, and lighter, air above the area. This mass ofair rises due to its comparative lightness until anelevation is reached where the pressure of the massof air is the same as the surrounding air. As the massof air moves upward, it is replaced by cooler air fromthe surrounding terrain. The result is a thoroughmixing of the air. Another source of homogeneousair is storms. Surprisingly enough, the winds pro-ducing storms also produce homogeneous air, whichis one reason why relay systems are superior to wiredlines. Storms that might damage a wired line containenough turbulence to produce homogeneous air, withconsequently good operating conditions for radiotransmission. A third source of homogeneous air iscool air moving over warm earth. The air massbecomes heated from the earth, with upward aircurrents resulting in a thorough mixing of the air.In discussing homogeneous air, it should be pointedout that the homogeneity is produced only in thelower troposphere. Similarly, only a small part ofthe earth's surface may be covered by homogeneousair, but this can still be great enough to be importantin radio propagation.

Where standard atmospheric conditions do notexist, the normal change in vapor pressure and tem-perature with elevation may be considerably varied.One cause of such a change is moving masses of air.

Throughout the earth's atmosphere, a continualexchange of air takes place between the equatorialregions and the poles. Large masses of polar airsweep downward in a south-easterly direction in thenorthern hemisphere, (north-easterly in the southernhemisphere), while masses of tropic air move towardsthe poles, resulting in a continuous, but irregular,exchange of air in intermediate areas. Polar airmasses are characterized by low temperature, moder-ately low vapor pressure, and high atmosphericpressure. Tropic air masses usually originate oversalt water near the equator, and hence have hightemperature, high vapor pressure, and low atmos-pheric pressure.

AIR MASSES

POLAR. While these air masses themselves may behomogeneous, they differ considerably from the airin the regions entered. The polar air mass will bedenser than the existing air mass, and colder. Thedenser air will tend to displace the lighter, warmerair, and will tend to underlay the lighter air. As aresult, the lighter air will rise, and a temperatureincrease with elevation (temperature inversion) will

temperature inversion, however, will notbe as great as might be supposed. As the warm airmass is pushed upward, the pressure will decrease,and the temperature will therefore also decrease. Thevapor pressure will increase, so that, while a tem-perature inversion will exist, the inversion will beless than if the displaced mass retained its originalpressure and temperature. The temperature from theearth's surface will decrease upward through thepolar air mass at approximately the standard rate of5.4° F. per thousand feet, to the boundary betweenthe two masses.

In the boundary between the two masses, thetemperature will increase with elevation, since thedisplaced air will be warmer than the polar mass.From the lower boundary of the displaced massupward, the temperature will again decrease withelevation, and at an approximately normal rate. Asmay be seen from this explanation, the boundarybetween the air masses is not sharply defined, butpossesses thickness. While the thickness may vary,there will still be a uniform change in temperaturethrough the boundary between the two air masses.

TROPIC. Tropic air masses moving into an area ofcolder air will overlay the colder air, so that similarconditions to those found when a cold air mass entersan area will prevail. Regardless of which air mass ismoving, the warm air will tend to overlay the coldair, and a temperature inversion will exist. It may

34

CHAPTER

occasionally happen that the warm air is denser thanthe existing air, and will therefore push the existingair mass upward. When this happens, the decrease intemperature at the boundary between the two masseswill be greater than standard, and thus the tempera-ture will decrease with elevation at a greater thannormal rate.

SUBSIDENCE. There are other air mass movementsthan those already mentioned. Air may move in acircular direction which is not necessarily accom-panied by a forward movement. A counterclockwisemovement, called cyclonic in the northern hemi-sphere, occurs as a low pressure area, and is character-ized by surrounding air at low levels flowing into thearea and upward through the center of the area.Such an air mass movement has little effect on radiopropagation, although the thunderstorms which mayaccompany such a movement will produce inter-ference.

Another stationary circular movement is clockwiseor anti -cyclonic, and is characterized by high pres-sure, downward flow through the center of the area,and outward flow at low levels. Where the area in-volved is large, and the sinking mass of air covers alarge area, the movement is called subsidence. As theair flows, or sinks, downward, the pressure of themass increases with a resultant increase in tempera-ture. As the sinking movement continues, the tem-perature and pressure continue to rise until the massreaches a level where the pressure is equal to thepressure of the surrounding air. At this point, thedownward movement ceases, for the air is balanced,as it were. The temperature is greater than that ofthe surrounding air, because of the temperature in-crease produced by the increased pressure. Thus, atemperature inversion exists due to subsidence. Thecondition produced by subsidence tends to be short-lived, because of the sinking layer spreading outwardas it reaches a level where pressure is balanced, anddownward movement ceases. As the spreading move-ment continues, the layer becomes increasinglythinner, eventually losing its identity altogether.While the sinking process is under way, however,and for some time after, a temperature inversionat the layer will exist due to warming by pressureincrease. Where subsidence exists, the vapor pressuremay or may not increase with atmospheric pressure.While it would be extremely difficult for the radiooperator to know whether to expect the vapor pres-sure to increase or decrease, vapor change canmaterially affect transmission characteristics of theair (see M -characteristics, this chapter). The trans-mission characteristics may be determined, where


necessary, by means of meteorological soundings ofthe atmosphere.

DIURNAL CHANGE. The air above the earth iscontinually subject to change by either heating orcooling from the earth's surface. This effect is, ofcourse, tempered by winds and the horizontal move-ment of air masses, and may be negligible in com-parison to effects caused by winds. In still air,however, cooling or heating of the atmosphere bythe surface of the earth can have appreciable effectson the refractive modulus, and hence on wavepropagation.

Heating of the atmosphere from the earth's surfaceoccurs almost exclusively in day time, when the sun'sheat is partially reflected from the surface. Thisheating results in upward convection currents ofwarm air. As the warm air rises, it displaces heavier,cooler air, which is in turn warmed by the earth'ssurface. This results in a thorough mixing of theatmosphere with a standard temperature gradient,and homogeneous air will result. Such heating iseffective above 1,000 feet elevation.

Just as heating from the surface is a daytimephenomenon, surface cooling is a nocturnal phenom-enon. The heat absorbed by the earth during the dayis dissipated during the early evening hours, the time ofdissipation depending on the temperature and typeof soil. Since no heat reaches the earth, further cool-ing will cause the earth's temperature to drop belowthat of the air, and produce a temperature inversionnear the surface of the earth. The cool air will beheavier than the overlaying warm air, and conse-quently, no convection currents can exist. Anyinterchange of heat between the layers of air willbe by conduction only. With no vertical air move-ment, no mixing can take place, and the air becomesstratified, with cool air underlying the warm air.This increase of temperature with elevation, ortemperature inversion, may or may not produce anM -inversion (see Chapter III), depending on thehumidity of the air, and the moisture content of theearth. If the air is not saturated, and the ground isdry, nocturnal cooling will produce a higher humidityof the cooling layer, and an M -inversion will result.If the ground is wet, or even moist, the problembecomes extremely complicated, and it is impossible topredict the M -profile, although it may be plottedfrom actual values of temperature and vapor pressureat different elevations. Since the ground is usuallymoist during winter, and dry during summer, noc-turnal cooling generally takes place during thewarmer months, and its effects are frequently ob-served on 24 -hour signal strength charts. Nocturnal

35

CHAPTER 4


cooling is sufficiently common during the summerand can be expected more than half of the summernights.

PRECIPITATION ATTENUATION

INTRODUCTION. Calculating the effect of weatheron radio propagation would be comparatively simpleif there were neither water nor water vapor in theatmosphere. The refractive modulus would dependonly on the temperature gradient, and a homogeneousatmosphere would probably exist most of the time.However, some form of water (vapor, liquid, orsolid), is always present in the atmosphere, even inarid regions, and must be considered in all micro-wave calculations.

The discussion up to this point has consideredonly the effect on the refractive modulus of theatmosphere due to temperature and vapor pressure.Water in the atmosphere, whether as vapor or liquid,will also affect radio transmission by attenuation.Water can attenuate an electromagnetic wave byabsorption and by scattering. These effects are soslight at frequencies below 6,000 mc, that attenua-tion by these causes at such frequencies may besafely ignored.

Attenuation by absorption is caused by the watermolecule acting as a dipole. This dipole absorbs theelectric component of the wave, dissipating theabsorbed energy in the form of heat. Absorption dueto the molecule acting as a dipole may occur withother gases, but such absorption affects radio signalsat frequencies beyond the range of this book.

RAIN. As previously stated, attenuation due toraindrops is greater than the attenuation due toother forms of water. Attenuation may be caused byabsorption, whereby the raindrop, acting as a lossydielectric, absorbs power from the electromagneticwave and dissipates the power as heat, or by scatter-ing. Scattering by raindrops will cause more attenua-tion than absorption at the frequencies consideredin this book, with the effects of scattering becomingquite pronounced at the higher frequencies. Thisscattering is similar to the scattering of light byminute particles in the atmosphere, as determined byLord Rayleigh in his experiments on light waves.The scattering of the electromagnetic wave is de-pendent upon the size of the raindrops, their densityin the atmosphere, and the wavelength of the electro-magnetic wave. Large drops produce greater at-tenuation than small ones, with the attenuationincreasing as the diameter of the drops approachesthe wavelengths of the radio wave.

One of the difficulties in attempting to determine

the attenuation by scattering is caused by the varia-tion in drop size. There is no uniformity of drop sizein any rainfall; the droplets vary in diameter fromless than one millimeter to five millimeters or more.As a general rule, the heaviest rate of rainfall isaccompanied by the greatest drop size, and, there-fore, the greatest attenuation. This tendency towardincreasing drop size with increasing rate of precipita-tion is shown in table 4-1, compiled from a study ofnine different rains by A. C. Best. * The table showsthe approximate number of raindrops per hour, ofdifferent sizes, as found in nine different rainfalls.As may be seen from the table, there is no exactrelationship between drop size and rate of precipita-tion, only a tendency toward larger drops withheavier rains. Column "E", in particular, shows thislack of relationship. While the rate of rainfall is 2times that of column "D", the smallest drops arestill predominant. Table 4-2 shows the relation be-tween attenuation and precipitation rates. This tablewas prepared from data in table 4-1, and representsthe approximate attenuation to be expected. Noticethat the column "B" is omitted in this table, sincethis rain is composed almost completely of droplets 1millimeter or less in diameter.

Another difficulty in calculating the expected at-tenuation by rain over a radio path is the variationof the rate of rainfall at different points along thepath. It is highly improbable that a path length of30 to 50 miles will ever have a uniform rate of rain-fall, and probable that somewhere along the paththere will be no rain at all.

In calculations involving attenuation due to rain,it probably will be simplest to obtain rates of rainfallto be expected in the area under consideration. Thisinformation is readily available from the weatherbureau for most parts of the world, and may beapplied to table 4-2, or some similar source, to obtainthe approximate expected attenuation. NomogramB, "Attenuation by Rainfall", (appendix I) may beused, and will give the maximum attenuation thatis to be expected. This nomogram is based on auniform rate of precipitation along the total pathlength. If the maximum rate of rainfall is used inconjunction with the nomogram, the computed at-tenuation will be at a maximum. A figure of 75%of the attenuation, as given by this nomogram willusually be a safe value for any path length over25 miles.

FOG. Fog may be considered another form of rain, asfar as attenuation is concerned. Fog remains suspended

*Water in the Atmosphere, Part I of the Interim Report of theUltra Short Wave Panel Working Committee, July 18, 1944.

36

CHAPTER 4


TABLE 4-1: NUMBER OF RAINDROPS (PER M') FOR VARIOUS RAINS

r)Distribution

E F

p,mm/hrD, cm 2.46 3.6 4.0 6.0 15.2 18.7 22.6 34.3 .43.1

0.05 28.5 476 752 61.4 3.33 323 245 47.60.10 71.8 512 30.8 25.6 59.7 12.8 134 108 3330.15 31 27 11.4 14 21.5 9.52 66 68.4 95.20.20 3.13 22 31.2 15.6 7.2 23.4 46.1 21.6 31.20.25 2.76 4.0 0.96 0 28.3 21.5 0

0.30 7.2 0 25.3 10.2 17.6 0

0.35 3.83 0 3.35 0 0

0.40 4.48 5.75 2.3 0 0

0.45 0 11.3 22.50.50 2.71

Liquid waterg/m3 0.130 0.439 0.217 n 212 0.521 0.673 0.930 1.25 1.55

After A.C. Best

TABLE 4-2: RELATION BETWEEN ATTENUATION (DB/KM') AND PRECIPITATION

mmfhr 1.25 8 10

X, cm15 20 30 50 75 100 q

2.46 1.93x10-' 4.92x10-' 4.24x10-3 1.23x10-3 7.34x10-4 2.80x10-4 1.52x10-4 6.49x10-5 2.33x10-5 1.03x10-5 5.85x10-' A

4.0 3.18x10-1 8.63x10-2 7.11x10-3 2.04x10-3 1.19x10-3 4.69x10-4 2.53x10-4 1.08x10-4 3.88x10-5 1.72x10-6 9.75x10-6 C

6.0 6.15x10-' 1.92x10-' 1.25x10-2 '3.02x10-3 1.67x10-3 5.84x10-.1 3.02x10-4 1.25x10-4 4.34x10-5 1.93x104 1.09x10-5 D

15.2 2.12 6.13x10-' 5.91x10-2 1.17x10-2 5.68x10-3 1.69x10-3 7.85x10-' 2.95x10-4 9.23x10-5 4.15x10-5 2.35x10-5 E

18.7 2.37 8.01x10-1 5.13x10-2 1.10x10-2 6.46x10-3 1.85x10-3 9.09x10-4 3.60x10-4 1.20x10-4 5.36x10-5 3.03x10-5 F

22.6 2.40 7.28x10-' 5.29x10-2 1.21x10-2 6.96x10-3 2.27x10-3 1.17x10-3 4.81x104 1.66x10-4 7.41x10-5 4.19x10-5 G

34.3 4.51 1.28 1.12x104 2.32x10-2 1.17x10-2 3.64x10-3 1.75x10-3 6.83x10-4 2.24x10-4 9.95x10-5 5.63x10-5 H

43.1 6.17 1.64 1.65x10-' 3.33x10-2 1.62x10-2 4.96x10-3 2.29x10-3 8.71x10-4 2.78x10-4 1.23x10-" 6.98x10-5 I

After A.C. Best

in the atmosphere, and the attenuation to be expectedis determined by the quantity of water per unitvolume, and the size of the droplets. Attenuationdue to fog is of minor importance at wavelengthslonger than 1.5 cm, since the droplets are exceedinglysmall, and the density rarely exceeds 1.0 gm/m3,usually being less than 0.5 gm/m3. Fog can causeserious attenuation by absorption, but only in themillimeter range.

SNOW. Scattering due to snow is difficult to com-pute, owing to the irregularities of the flakes. At-tenuation from smooth, spherical drops, such as rain-drops or hail, may be calculated quite easily fromRayleigh's formula for scattering:

Crxr,)6

where

a. = the attenuation due to scattering

X = the wavelength

rr = the radius of the drop.

Where the scattering object is snow, the parameter r,is harder to determine, and should be an averagedimension of the snowflake. While information on theattenuating effect of snow is limited, it is probablethat attenuation from snow is less than from rainfalling at an equal rate. This is borne out by thefact that the density of rain is eight times thedensity of snow. As a result, a rainfall of 1 inch perhour, for example, would have far more water percubic meter of atmosphere than an equal snowfall,even with the lower terminal velocity of snow.

(4-1) HAIL. Attenuation by hail is determined by the sizeof the stones, and their density. Attenuation ofelectromagnetic waves by scattering due to hail -

37

CHAPTER


stones is considerably less than by rain, since ice hasa lower index of refraction.

SLEET AND GLAZE. Sleet is defined meteoro-logically as very small pellets of ice, and as such haslittle effect on the electromagnetic wave in the fre-quency limits of this book. Glaze, defined meteoro-logically as rain that freezes on contact with anyobject, may be safely treated as rain having equaldrop size.

ATMOSPHERIC CHARACTERISTICS

REFRACTIVE INDEX. The refractive index of theair is determined by its pressure, temperature andwater vapor pressure, or relative humidity. Sincethese qualities vary with elevation, the refractiveindex also varies with elevation, so that any electro-magnetic wave is continually traveling through amedium of constantly varying refractive index. Infree space, or a uniform atmosphere, the electro-magnetic wave would travel in a straight line. Thuswe have an electromagnetic wave traveling in astraight line through the atmosphere which followsthe curvature of the earth. Since the refractive indexis gradually changing along the beam path, the beambecomes curved because of this changing index ofrefraction. This bending action takes place at allradio frequencies and at light frequencies as well,although to a lesser degree.

The change of the refractive index of air withincrease in elevation causes the radio signal to becurved downward, and as a result the radio horizonextends beyond the optical horizon. The radio hori-zon compares with the optical horizon in that it isthe point on the earth's surface where the transmittedbeam is tangential to the earth's surface. The 4/3earth's radius figure often used in microwave calcu-lations is the direct result of refraction of the radiobeam by the standard atmosphere.

REFRACTIVE MODULUS. In discussing the effectof the curvature in the atmosphere of a radio wave,only a standard atmosphere has been considered.When non-standard conditions exist, the radio beamwill be refracted to a greater or lesser degree, depend-ing upon the atmospheric changes that have takenplace. Since these changes affect the refractive indexat some elevation in the atmosphere, an allowancemust be made for the decreasing temperature andpressure to be found as the elevation is increased.This is done by use of the formula

77.6 (p 4810e) 3.8HM = (4-2)

where

M = refractive modulusT = temperature in degrees Kelvinp = pressure in millibarse = water vapor pressure in millibarsH = elevation above the earth in hundreds of feet

The value 3.8H is introduced to account for theearth's curvature.

Formula 4-2 gives the refractive modulus (M) ofthe atmosphere at any elevation where meteorologicalsoundings have been taken. The values used forplotting the M -profile are rarely taken at elevationsabove 3,000 feet, since the radio signal will usuallyremain below this elevation, if it is to be receivedwithin a few hundred miles. (Ionospheric reflection ofsignals is an exception, and represents a different typeof radio transmission.) While these values are takenat some specific point on the earth, they may besafely assumed to apply for the general area aroundthat point, since atmospheric conditions do notchange abruptly. The area will vary considerably insize, depending upon weather changes taking place atthe time the tropospheric soundings are taken.

M -PROFILE. The M -profile is a straight line, with aslope of 3.8 per hundred feet, under standard atmos-pheric conditions. Where the plotted values ofmeteorological soundings do not fall in a straightline, atmospheric variations will be noted, and theextent of these variations will be indicated by thedegree that the M -profile deviates from a straightline. The value of the refractive modulus at any onepoint is less important than the difference in therefractive modulus between two points that bound anabnormal condition. Where an abnormal conditionexists, the differences in values for M are noted, andreferred to as the M -gradient, usually expressed interms of the difference per hundred feet. Where theM -gradient is less than standard, refraction towardthe earth is greater than normal, while an abovestandard M -gradient is accompanied by less refrac-tion, so that the curvature of the signal will be lessthan normal.

A below standard M -gradient, or M -inversion,may vary in three ways; namely, in elevation, indepth, and in intensity. By intensity is meant theamount the M -gradient varies from the standard.

Figure 4-1 shows four different conditions of theM -profile, together with the associated dewpointtemperature (T,), and atmospheric temperature(T.). Standard conditions of T., T., and M are shownin figure 4-1A. Notice that the slope of T. and T. are

38

STANDARD CONDITIONS OF DEWPOINT,TEMPERATURE a REFRACTIVE MODULUS

INCREASE

To

(a

AI- INVERSION PRODUCED BYDECREASE IN STANDARD GRADIENT OF DEWPOINT

TEMPERATURE

TsT

INCREASE

T,T.M

( c)

= DEWPOINT, WET BULB TEMPERATURE= TEMPERATURE ABSOLUTE, DEGREES KELVIN= REFRACTIVE MODULUS

T

CHAPTER 4


Al- INVERSION PRODUCEDBY TEMPERATURE INVERSION

Ta

INCREASE

TEMPERATURE GRADIENT DECREASE OFF-SETTING DEWPOINT GRADIENT DECREASE LEAVINGREFRACTIVE MODULUS GRADIENT UNAFFECTED

Ts

INCREASE

Figure 4-1. Relation between Dewpoint, Temperature and M -Profile

such that at some elevation the dew point and atmos-pheric temperature will be the same, with completelysaturated air resulting.

Figure 4-1B shows a temperature inversion, such aswould be produced by a cold front or subsidence. TheM -inversion occurs at the same elevation, and thedegree of the M -inversion will be determined by thedegree of the temperature inversion. Figure 4-1Cshows an M -inversion produced by an increase indewpoint temperature, with the degree of the

Al

M -inversion determined by the extent of the changefrom the normal dewpoint temperature. In figure4-1D, a possible, although highly improbable, con-dition is shown whereby the increase in the M -gra-dient caused by an abnormal temperature decrease isoffset exactly by a decrease in the M -gradient pro-duced by a decrease in T,. This will show approxi-mately what to expect from the M -gradient, sinceabnormal changes in either T. or T. are almost al-ways accompanied by changes in T. or T,.

39

CHAPTER 5

EQUPMENT SITING

C II A I' T E It

INTRODUCTION

Siting might very well be called the practicalapplication of radio relay theory. All the variousfactors mentioned elsewhere in this book must betaken into account in order to lay out a radio relaysystem. It is entirely possible, of course, to set up arelay system by installing the repeaters on hills,without regard to any of the factors mentioned in thisbook. Such a system would probably work, too, butthe chances of satisfactory and efficient operation areremote. Consideration of the many factors involvedin radio relay work will produce a satisfactory relaysystem, using equipment that may be available. It isthe purpose of this chapter to point out the problemsencountered in siting, and explain the remedies com-monly used in overcoming them. Chapter 14 gives aproblem in siting, worked out according to the infor-mation contained in this chapter, so no attempt ismade to give a definite illustration here.

SURVEY PROCEDURES

In locating a radio relay system, especially wheremaximum reception time is necessary, considerableattention to the location of relay stations is required,particularly in rolling country, or in areas wherescattering or reflection may introduce problems.

While a straight line of relay stations, like a stringof telephone poles, may appear desirable, there aretwo good reasons why the stations will usually takea zigzag course. One reason is that the terrain seldomlends itself to a straight line of repeater stations with-out having some hops unnecessarily short and otherstoo long for satisfactory reception. Also, hills are

EQUIPMENT

SITING

rarely spaced so that the repeater stations may bealigned, and still have adequate clearance. A secondreason for zigzagging stations is to prevent signalskipping. Since atmospheric conditions can producevertical beam -bending, a signal beamed to an ad-jacent station may be picked up by another repeaterfarther away, assuming, that the transmitting stationand the other two repeaters are in a straight line,and use the same frequency. This produces interfer-ence and cross talk, since the skipping signal willmore than likely be out of phase with the signalintentionally beamed at the receiving repeater.

For every rule, there are exceptions, and zigzaggingis not invariably necessary. It is possible and practicalto align repeater stations and still have reliablereception. Alternate polarization of antennas, a highfront -to -back ratio for the antennas, and alternatefrequencies may be used, either separately or incombination, to give satisfactory reception.

METHODS OF SITING. Siting may be done by anumber of methods, or by a combination of methods.Contour maps, aerial photographs and aerial surveysmay be used satisfactorily. Generally speaking, thesites are tentatively chosen from contour maps, anda field trip or aerial survey made to verify the choice.While the aerial surveys are generally made in air-planes, helicopters fitted with microwave transmit-ting and receiving equipment have also been founduseful, especially where the terrain is too rough forvehicular travel.

POINTS OF CONSIDERATION. Some factors tobe considered in locating the relay stations are: powersupply, accessibility, type of ground on which the

41

CHAPTER 5

EQUIPMENT SITING

station is to be built, obstructions to be removedbefore building, and necessary antenna height inorder to clear obstructions. Many of these factorsmay be estimated from contour maps, profiles madefrom the contour maps, and aerial photographs,thereby saving a great deal of time in the field.

Terminal stations for military use are usuallylocated near the source of the messages to be trans-mitted, unless the terrain is such as to require remoteinstallation of the terminal transmitter. A good illus-tration of such a condition is a military encampmentlocated in a valley, or behind a hill. If the terminalstation is located away from the source of themessages, a wired link may be installed to the trans-mitter, or the messages may be transmitted by a lowpowered transmitter beamed to the terminal station.The latter method is recommended where the cost ofrunning the transmission line is greater than the costof a radio transmitting link. Such a system is fre-quently used in commercial installations where thestudio of an FM station, for example, is located in alarge city, and the transmitting antenna placed ona hill nearby.

USE OF CONTOUR MAPS. Contour maps are valu-able in laying out sites for the relay stations, sinceboth elevation and distance between the sites mayreadily determined. Sites may be tentatively chosenon the basis of information taken from the contourmaps, and profiles of the terrain beneath the radiobeams may then be drawn to determine the clearanceabove hills or other obstacles. In using these profilesto determine path clearance, both the curvature ofthe earth and the refraction of the radio beam in thetroposphere must be considered. If the profile isdrawn on rectangular coordinate paper, or graphpaper, corrections must be made for the earth's cur-vature, and refraction of the beam in the air. 4/3earth's radius paper, when available, is recommended,since corrections for curvature and refraction aretaken into account in the paper itself (See AppendixI). After plotting the profile, a straight line may bedrawn between the antennas at the repeater sites,and any obstacles to the radio beam will becomeapparent. The attenuation caused by the obstaclemay be determined from the nomograms in theappendix, and an alternate path chosen if excessiveattenuation is found. Some knowledge of the accessi-bility of the sites may be acquired from the contourmaps, but field inspections should be made in order todetermine the amount of work required to clear aroad to the site for inspection and maintenance.

FIELD INSPECTION. Since siting, as done oncontour maps, is easily changed before the relay

stations are built, it is advisable to locate severalpossible sites for alternate location of each relaystation. Some of these alternates will be discarded onthe basis of information obtained from the profiles,while the most desirable can best be determined frominformation acquired in the field.

The field trip should be for the purpose of locatingaccessible roads, determining whether the ground issuitable for the erection of the antenna and buildingfor the equipment, and the amount of clearing neededto prepare the site. Field parties equipped withbinoculars may operate in pairs, in order to checkthe actual line between the two points. This isespecially important where the path clearance maybe subject to question. Where portable beam -antennaequipment is available, a further check on signalattenuation may be made by the two parties betweenadjacent sites.

SITING BY RADIO ALTIMETER. A secondmethod of siting repeater stations is by means of anairplane equipped with an aneroid barometer (pres-sure altimeter) and/or a radio altimeter. The planemay be used to provide profile maps between tenta-tive relay sites. These maps can be made from arecording altimeter or from frequent readings taken

indicating altimeter. Thedifference in readings between the aneroid altimeterand radio altimeter can be used to determine theelevations of the terrain along the beam path, andthe values plotted on 4/3 earth's radius paper, aspreviously mentioned. In using these data, just aswith profiles developed from contour maps, the curva-ture of the earth and average refraction will be takeninto account. Earth's curvature, and atmosphericrefraction, will frequently elevate some obstructionseveral hundred feet higher than it appeared on aplane -earth, or rectangular coordinate profile, espe-cially where a long hop occurs. Photographs madefrom the plane would be of use in determining roads,power lines, or other details that might affect thefinal choice. An inspection of the site is still desirable,however, since some problem concerning the use ofthe site might arise that could not be definitely solvedeither in the office or by an aerial survey.

SITING BY HELICOPTER. The newest and quick-est method of siting is by use of helicopters. Tentativesites may be chosen from contour maps, or actuallyworked out in the field by observers in the helicopters.Even field trips may be eliminated, since the ob-servers can easily examine the sites from the heli-copter, or descend to the ground by means of a ropeladder for closer inspection. Antenna heights may beworked out to determine the minimum antenna

42

CHAPTER 5

EQUIPMENT SITING

height required; even the road to be built to the site,if one is needed, may be located from the helicopter.

The equipment required for siting by helicopter isas follows: a compass for triangulation, binoculars,two-way radio communication between the heli-copters, a beamed microwave transmitter situatedon one helicopter, and a receiver on the other, ananeroid altimeter or plumb line, preferably both.

The transmitter is equipped with a parabolicantenna on each side of the helicopter, each mountedto turn more than 180 degrees horizontally. This isnecessary, since the helicopter must head into thewind to hover, and unless a full 360 -degree coverageis available, the transmitted beam may not be aimedproperly at the receiving helicopter. The transmittedbeam should be fairly wide, since precise alignmenton the receiving helicopter is difficult, and the verticalbeam should be at least 90 degrees wide, to facilitatepicking up the signal in rolling or hilly terrain.

The antennas mounted on the receiving helicoptermust also be arranged for a full 360 -degree horizontalcoverage, but a much smaller beam angle may beused. Received signal strength may be estimatedaurally by an audio note modulating the carrier, orvisually, by means of an oscilloscope.

Observations are carried out as follows: Tentativesites are located by triangulation on known land-marks, and the helicopters hover above the sites tobe inspected. The transmitted signal is beamedtoward the receiving helicopter, and the signalstrength noted. The helicopters may then descend,until the signal is attenuated by some obstacle, andthe minimum antenna height noted, either by radioaltimeter or measured plumb line. This will com-plete all necessary observations regarding signalattenuation between the two sites, and the trans-mitting helicopter may then proceed to the sitebeyond the one occupied by the receiving helicopterfor another set of observations. By this method, thesites may be found adequate or inadequate, and asatisfactory alternate site quickly established ifnecessary.

SITING CONSIDERATIONS. In the ensuing dis-cussion on siting considerations, an attempt is madeto review the various phases of the siting problem.The relative weight of these considerations is notfixed, but will vary according to the conditions of thearea where the repeater is to be located. Certainly,if only one location is available for a repeater station,that location will be used, whether or not there is aconvenient power line and road nearby. By the sametoken, a repeater system operating on storage bat-teries charged from a power line could continue to

operate for several hours after a power failure, andsuch a type of system would have less need for stand-by equipment than a station powered directly fromthe power line. In other words, these recommenda-tions are intended for general guidance, and must notbe considered as hard and fast rules.

The most important requisite to be considered inchoosing the repeater site is accessibility. Occasion-ally a microwave repeater may be located near afire -tower, or some other form of observation post.Where this can be done, some sort of road to the sitewill already exist, and usually a source of power aswell. Many roads built to reach fire -towers are notdesigned for year round use, and will require addi-tional work if they must be used in all seasons.

Where no road exists to a proposed site, a field tripwill determine the amount of work necessary to builda road. For rolling terrain and a mild climate, roadconstruction will be rather easy, while in rocky, hillyterrain the problem of road construction may bedifficult enough to eliminate a site otherwise entirelysatisfactory. Another consideration is the damagingeffect of weather on roads. In hilly country, threatsof landslides and washouts could increase the initialcost, as well as the cost of maintenance. In flat,marshy country a site might be discarded because ofthe expense of the fill, and the additional work neces-sary in maintaining such a road.

The quality of the access road will depend consid-erably on the amount of use it will receive. If thereceiver must be powered by a local generator, fre-quent trips with fuel will be necessary, and the roadmust be built to withstand this extra use. The con-ditions governing the road construction, then, willdepend on climate, terrain, and the amount of usethe road will receive. In order that the repeater sta-tions may be kept operating satisfactorily, thesefactors must be taken into account in building theroad.

It frequently happens that the final choice betweenthe two sites is determined by the power supplyavailable. The reliability of the repeater, and there-fore of the whole system, is dependent upon thesource of power. If a power line is available at the site,which is highly unlikely, it should be examined care-fully to determine whether it is capable of carryingthe additional load of the repeater. The power shouldbe regulated, both in frequency and voltage, and thewires large enough to carry the extra load withoutvoltage variation due to line loss. Quite often a powerline may be run to a desirable site from a nearbypower line without excessive expense. In any case, asite requiring a local power supply, such as a motorgenerator, should be avoided if possible, because of

43

CHAPTER 5

EQUIPMENT SITING

the additional equipment maintenance required.The advantage of a radio relay system lies in its

freedom from breakdown by weather, but if the powersupply should fail due to an ice or windstorm, theadvantage is lost. A standby power plant installed inthe repeater station to take over in the event of powerfailure by the regular source will overcome thishandicap.

SUMMARY. The profiles will give most of the infor-mation required concerning the terrain beneath thebeam path, but field trips are important for a finalcheck on conditions, and to disclose any possibilitythat might give trouble, but is not otherwise shownon the profile or contour map. Contour maps rarelygive tree heights, and in many instances some man-made object, such as a power line, or building, mayhave been erected after the map was drawn. Seasonalproblems may also be present, yet not show up oncontour maps. A bare hill, for example, may be acornfield in certain seasons, and thus present a differ-ent problem in attenuation than it would if used asa pasture, or hay field. A flat area may appear on acontour map, and apparently be no problem, butinspection by a field trip might show that during arainy season it would fill with water, and perhapscause a reflected signal to appear at a receivingantenna. These field trips, then, serve two usefulpurposes, to verify calculations made from maps andaerial photographs, as well as to discover any sourceof trouble that might not appear on the maps. Need-less to say, a trained field crew could find such sourcesof trouble easier than an untrained crew, and findthem much sooner.

SYSTEM RELIABILITY

GOVERNING FACTORS. Like the automobilesalesman, expounding on the various gadgets of thenew car and forgetting the engine, it is easy to over-look the main purpose of the relay system. Just howwell is it going to work, once it's installed? Havingsatisfied all of the many requirements in selectingsites for the repeater stations, one question stillremains; how much of the time will the signal beintelligible? This may be figured out with reasonableaccuracy from available data, part of which is foundin the training manual (TM) on the equipment, andpart from Federal Communications Commission(FCC) charts.

There are many factors to be considered in esti-mating the reliability of a relay system, other thanfailures of the power supply or equipment. Trans-mitter output, distance between stations, and receiversensitivity are some of the characteristics that will

affect the reliability of the system. Other factors,such as reflected or refracted signals, fades due toionospheric storms, and even seasonal changes in theterrain can affect the received signal strength, andthereby affect the reliability. A formula for takingthese factors into consideration would be very com-plicated, and as a result, many of these variables areeliminated in careful choice of the repeater site, whileothers can be included in a "cushion", or allowancefor fades.

One way in which high reliability can be obtainedis to decrease the distance between repeaters. Morepowerful transmitters may be used, or larger para-bolic reflectors for the antennas, with a correspond-ingly larger gain. Such solutions, however, are expen-sive, and tend to become unsound economically.Repeater spacing of 30 to 50 miles is generally foundto be satisfactory for frequencies below 10,000 mc,provided good path clearance (first Fresnel zone orbetter) is available.

So far in this discussion, everything appears toindicate satisfactory performance. It still remains todetermine just how satisfactory it will be. It is notdifficult to estimate the signal strength arriving atthe receiver of the repeater station. Notice that thisis the signal at the receiver, not at the antenna. Sucha signal will be affected by the receiver antenna gain,and the transmission line loss between the antennaand the receiver. In order for the signal to be intel-ligible it must be stronger than the receiver noiselevel. The manufacturers of receiving equipmentdetermine a signal level for their equipment whichdepends upon the type of modulation used, and thereceiver design. This level is called the threshold level,and represents the lowest signal level that will beintelligible. Although the signal may be just barelyabove this level, satisfactory transmission will result,but with no allowance for fades. Since fades will lowerthe signal strength at the receiver, it is necessary tohave a much stronger signal arrive under normalconditions, in order that an intelligible signal may bereceived under expected fade conditions. The differ-ence between the field strength of the level normallyreceived, and the threshold level, is called the fademargin. The field strength to be expected for anyrepeater site may be calculated within ±5 db, usinginformation on the equipment to be installed, anddata taken on the individual links of the relay system.

ACCEPTABLE RELIABILITY. At this point, wecan discuss the reliability to be expected from thesystem. The reliability is determined by the percentof the time that the signal strength at the receiver isabove a predetermined level. This level may be found

44

CHAPTER 5

EQUIPMENT SITING

by applying the various factors concerning therepeater link to the nomograms given in the appen-dix, and is the signal strength to be expected 90percent of the time. It should be emphasized that thislevel is independent of the receiver characteristicsand fade conditions to be expected in the area wherethe link is to be installed. Should the signal strengthbe equal to the threshold level of the receiver, theoutage time would be 10 percent, obviously veryunsatisfactory operation. No relay system would beplanned to operate at the receiver threshold level,however, since a fade of any magnitude would imme-diately result in an outage. By designing the links sothat the received signal is higher than the thresholdlevel of the receiver, a cushion to absorb fades isavailable, and as a result, higher reliability may beobtained. Assume, for example, that the received fieldstrength at the receiver is -10 dbm, and the receiverthreshold level is - 50 dbm. The difference, 40 db,is the fade margin for the link. On the basis of pre-vious experience in radio, it has been found that a40 db fade may be expected not over 0.01 percent ofthe time, so that the 40 db fade margin gives areliability of 99.99 percent. It is possible to have still

higher reliability, but the cost of additional equip-ment necessary would hardly warrant the slightincrease to be obtained. Nomogram C in the appendixgives the relationship between reliability and fademargin, so that the relay system may be engineeredfor whatever reliability is desired. In most instances,the path attenuation will be the greatest source ofattenuation, so that where a lower reliability isacceptable, the repeater stations may be spacedfarther apart.

In calculating the reliability to be expected from arelay system, the simplest, and safest, method is toassume that outages do not occur simultaneously.For example, if a repeater system has 10 links, withan efficiency of 99% for each link, it is safe to esti-mate that each link will be out 1% of the time. Sincethe outages are assumed to occur at different times,the total outage time for the ten links would then be10%, so that the system as a whole would have areliability of 90%. As the number of links increase,the likelihood of the outages occurring simultaneouslyalso increases, so such a figure represents the blackestpossible condition.

45

III

so

s

C II . I' T E It

INTRODUCTION

A transmission line may be likened to a belt system,in that it is merely a means of transmitting powerfrom its source to the place where it may be used.The energy to be transmitted may be power to oper-ate a factory, or to supply a city. It may be a tele-phone conversation between homes in a city, or aradio program transmitted from the studio to thetransmitter. Each type of use has different problemsin transmission, and only the problems concernedwith radio relay systems will be considered here.

BASIC THEORY

ELECTRIC AND MAGNETIC FIELDS. Whilethere are many different types of transmission linesused in radio work, all may be considered modifica-tions of a two -wire line. Such lines, carrying directcurrent, present no difficulties other than the loss ofpower due to resistance in the wires. If the wires aresufficiently large, the power loss in the line will benegligible, and no particular problem will exist. Thereis a problem, however, when the rate of current flowthrough the line is changed. Consider a long pair ofwires connecting a battery to a lamp (figure 6-1).Before the switch is closed there will be no currentflow in the wires, nor will there be any magnetic fieldsurrounding the wires. At the instant the switch isclosed, current will start to flow outward, and anumber of changes will take place. As shown in thefigure, the current flow has started toward the lamp.The wires become charged just as a capacitor becomescharged, and an electric field will appear between thewires, exactly as in the dielectric between capacitor

CHAPTER 6

TRANSMISSION LINES

6

TRANSMISSION

LINES

plates. This will be a moving electric field, since thecurrent is flowing along the wire and establishing thefield as it flows along. Another type of field will alsoexist. Each wire will be surrounded by a magneticfield, with the field being strongest between the twowires since each wire contributes to the field in thespace between them.

Now, as the current flows outward along the wire,the two fields move outward with it, the magneticfield circling the wire, and the electric field normalto the wire. These fields will continue to move untilthe wire is completely charged, that is, until thecurrent has reached the lamp, which will then light.At this time the flow of current is uniform along theline, the magnetic and electric fields are establishedand are stable. The fields will continue to exist aslong as current flows through the wires, and willremain unchanged until some change takes place inthe rate of current flow.

After the stable condition is reached, let the switchbe considered as open. Current will cease to flowfrom the battery, but for an extremely brief intervalthe lamp will continue to light. The current in thewire will continue to flow due to the electric andmagnetic fields surrounding the wires. These fieldswhich were originally created by the current flow donot represent expended energy, but rather, storedenergy. Since the source which established and main-tained these fields has been removed, the fields willcollapse. In collapsing, the fields restore to the linethe energy originally used in creating the fields.Therefore, some part of the power to operate thelamp may be considered as being stored in the spacesurrounding the wires, and this power is referred to

47

CHAPTER 6

TRANSMISSION LINES

0 0 0 0 0 0ED ED (4) El)

EBSCOSED0 0 0 0 0

0 LAMP

Figure 6-1. Field Created by Current Flow

as an induction field, or the field produced by thecurrent flow (see Chapter I).

CAPACITANCE AND INDUCTANCE. Accordingto elementary theory, a magnetic field is producedby current flowing through an inductance, and anelectric field by current flowing into a capacitance.Since these fields exist in the region surrounding thetransmission line, obviously some capacitance andinductance must exist in the lines. The inductance ispresent, since the wires act as a coil of one turn, andthe capacitance is also present due to the two wiresacting as individual plates of a capacitor. For directcurrent work, or alternating current power (60 cy-cles), the capacitance and inductance of the line arenegligible except in the case of very long a -c lines.At radio frequencies, particularly at the higher fre-quencies, capacitance and inductance in transmissionlines can be a serious problem.

In many problems of circuitry, the evenly distrib-uted capacitances and inductances may be lumped,that is, considered as being concentrated in one ortwo places. In a transmission line, lumped constantswould mean that instead of having the inductanceand capacitance distributed evenly, they would belocated at different points along the line; with equiva-lent values substituted. While this would simplifycalculations, serious errors in the impedance of theline would result, and unsatisfactory calculationswould be obtained. In explanations, however, lumpedconstants are frequently used, in order to explain theresults of the line impedance, figure 6-2.

In the illustrations mentioned, where the directcurrent flows along the wire toward the lamp, certainconditions were described. These conditions wereproduced by the movement of the electrons along thewire, and took place only during the rise and decayof the current. In an alternating current flow, thevalue of the current is changing continuously, andthus an accompanying change is taking place in theinduction field.

Figure 6-2 shows lumped constants for a shortlength of transmission line, which could be consideredas continuing indefinitely. Alternating current flow-ing through the line will create both electric and

magnetic fields, just as were created in the examplegiven for the d -c line, but with the difference that thefields will be continually changing in value and direc-tion. In this figure, two values of resistance areadded, one in series with the line, and one across theline for each group. The series resistance representsthe resistance of the line itself, the resistance placedacross the line representing the conductance of thedielectric surrounding the wires. The series resistancemay be kept low by the use of suitable wires, andthe conductance is generally negligible if a satisfac-tory dielectric, such as air, can be used. The capaci-tance as shown represents the capacitance betweenthe two wires, although another also exists, notshown. Each wire has capacitance with itself.

In order to explain the capacitance of a wire withitself, the length of the wire must be taken intoaccount. This length may be measured either interms of physical length, such as feet, or miles, or itmay be measured in terms of its electrical length.One wavelength is the unit of electrical length, andit may be 3,100 miles for 60 -cycle current, or 118inches for 100 me current. In both cases, the wirelength is one wavelength for the current carried.Thus, in discussing the self -capacitance of a wire, thewire length and wavelength of the current must beconsidered. If the wire is long electrically, that is, interms of wavelength, there may be several pointsalong the wire where the voltage is momentarily at amaximum or minimum. Since this produces two ormore points of unlike potential, a capacitance willexist between these two points. It also follows thatsuch capacitance not only exists between the twopoints of maximum and minimum potential, but alsobetween any two points where a difference of poten-tial exists. Therefore, the wire may have self -capacitance.

The value of the self -capacitance is determined bythe frequency. In the case of 60 -cycle power, thepoints of maximum and minimum potential will beso far apart as to render the self -capacitance of thewire negligible. As the frequency increases, however,the physical length of the wire in terms of wavelengthdecreases, until at UHF self -capacitance becomes anappreciable part of the transmission line problem.

Figure 6-2. Lumped Constants

48

CHAPTER 6

The plates of the capacitor, in other words, are muchcloser together at UHF than at long wave frequencies,with the result that the capacitance will be corres-pondingly greater.

One other source of capacitance may exist, andthat is the capacitance between the wires and ground.This source is negligible in coaxial cables or wave -guides, and is less important than the capacitancebetween the wires themselves.

LINE TERMINATIONS. The length of a trans-mission line, and the termination or load fed by theline, has a considerable effect on the wave conductedby the line. If a line of infinite length could be built,the transmitted wave would be carried onward for-ever, (assuming that there was no loss of power dueto radiation, leakage between the conductors, orresistance in the wires). The amplitude of the voltagewould be determined by the potential applied to thetransmission line, and the loss in the line betweenthe point of interest and the source. The importantthing to consider in an infinite line is the fact thatthere is only one wave traveling along the line, andthat the wave travels outward from the source. Aninfinite line, having only one wave, is known as a

is terminated in such a way as to have no reflectedwave is also called a non -resonant line.

The conditions where the line is not infinite, but ofsome definite measurable value, will affect the wavemovement, and the manner in which the line is ter-minated will also affect the wave. For example, con-sider the transmission line as being any wholenumber of wavelengths long, and terminating in anopen circuit. When the transmitted, or incident, wavereaches the end of the transmission line, the opencircuit acts like a mirror, reflecting the incident waveback on itself. This reflected wave is actually a con-tinuation of the incident wave, so that two travelingwaves exist on the line. Since these waves bothappear upon the transmission line at the same time,a resultant wave will appear, which can be measuredboth for amplitude and wavelength. This resultantwave is called a standing wave, since its nodes andmaxima remain always at the same point along thetransmission line. Since the incident and reflectedwaves travel at the same speed, but in opposite direc-tions, the amplitude of the standing wave at anypoint is continually changing, but the nodes andmaxima do not travel along the transmission line asthey do in the case of the incident and reflected wave.

Continuing the discussion of the open -circuitedline, the next consideration is the value of the stand-ing wave voltage at some particular point along the

TRANSMISSION LINES

line. This value will be maximum at the open endof the transmission line, since at this point theimpedance will be very high. From this point backtowards the source, the voltage will decrease, reach-ing a minimum VI wavelength from the end, thenincreasing to a maximum M wavelength from theend, and so on back to the source. In the event thatthe transmission line terminates in a short-circuit,rather than an open circuit, the voltage at the ter-mination would be zero, since the extremely lowresistance of the short circuit would cause the voltageto drop, just as in any d -c circuit.

The amount of variation of the rms voltage devel-oped on a transmission line because of wave reflec-tions is called the voltage standing -wave ratio,VSWR. Such a quantity is defined as the ratio of themaximum rms voltage to the minimum rms voltageon the line. Transmission lines whose terminationshave the same magnitude of reflection coefficient (p)will also have equal values of VSWR. For a maximumtransfer of energy, it is essential that the VSWR of atransmission line be as low as possible, approachingunity for well -matched systems. A method formeasuring the rms standing -wave voltage is givenin chapter 16.

So far, other than to mention the fact that a trans-mission line possesses resistance, inductance, andcapacitance, the effect of line impedance has beenignored. It may be considered at this point, however,to illustrate the current flow along the transmissionline. The value of the current at any point is deter-mined by the impedance at that point, which in turnis determined by the type of termination of the line,just as in the case of the line voltage. An open -circuited line, as stated above, has a maximumvoltage at its end. The standing current wave will bezero at this point, since the open end acts as anextremely high resistance and the current flow at thispoint will therefore be negligible. At each half wave-length, then, measured back from the open end of thetransmission line, the voltage standing wave will bea maximum, and the current standing wave will beminimum. The intermediate values will vary sinus-oidally, according to the impedance of the line, andthe impedance may be determined at any point alongthe line by measuring the voltage and current atthat point.

Figure 6-3A shows a transmission line one wave-length long, open -circuited at the end. The source isshown at the left, with the impedance indicated abovethe line. At the outer end, the impedance, consistingof resistance, is very high as shown in the impedancecurve. One -quarter wavelength back from the openend, the resistance is low, as shown. As a result, the

49

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TRANSMISSION LINES

0

TYPE IMPEDANCE

360° 2'10° 180°

(A)

-TYPE I MPEDANCE

00

360° 270° 180° 90°

(B)

o

Figure 6-3. Open and Shorted Transmission Lines

current at this point is high, and the voltage is low.It should be noted that the impedance curve doesnot reach the base line at any point. This is causedby line losses due to dielectric leakage between theconductors, and resistance in the wires of the trans-mission line. The voltage and current, also, neverquite reach the zero point because of these samelosses. At each point along the line, the value of thecurrent, voltage and impedance is as indicated, withthe type of impedance also indicated. The diagramdoes not present a true picture of the resistance andreactance of the line, which is evenly distributedalong the line, but it does show the effective im-pedance.

The actual length of a UHF transmission line israrely as short as a single wavelength, usually beingmany wavelengths long, plus some fractional part ofa wavelength. It is this fraction, and only this frac-tion, that need be considered in discussing the lengthof the transmission line. Since the standing wave isreflected back from the end of the transmission line,the transmitter or source of power feeds a line thatis in effect only that fraction of a wavelength. Re-ferring to figure 6-3A, a source is shown one wave-length from the open end, but not connected. If thesource were connected at that point, it would bedirectly below the large resistance shown on theimpedance curve. In other words, the source would

be feeding a load consisting of pure, high resistance.As a result, the current would be low, since the highresistance would limit the flow of current, and thevoltage would be high. Now assume that the sourceis connected at the 270° point, and that the trans-mission line to the left of that point does not exist.The source will now be feeding on equivalent load oflow, pure resistance. As a result, the current will behigh, and the voltage low, just as shown on the volt-age and current curves. For any length of line, then,the load fed by the source will be of the type indi-cated on the impedance curve at that point, and thecurrent and voltage relations will also be as shown.If the transmission line is terminated in a shortcircuit, as shown in figure 6-3B, the impedance, volt-age and current relations will be as shown. It will benoted that the short-circuited line appears to thesource as an open -circuited line, V4 wavelength longerthan the open -circuited line.

A discussion based on infinite, open-ended, andshort-circuited lines may seem odd, since trans-mission lines are usually considered as being ofmeasurable length, and carrying a radio signal to aload. Actually, the lines may be used for much morethan the transmission of power. The infinite line, forexample, has no standing wave, since there is nopoint of reflection to return the incident wave. As aresult, all the power from the source continues out-ward. Such an arrangement is desirable in a trans-mission line feeding an antenna, since all the powerfrom the transmitter should be fed into the antenna.If the impedance of the antenna matches that of theline, then the line acts exactly as though it wereinfinite, with no reflections. Open-ended and short-circuited lines may be used as filters to removeunwanted harmonics. "Metallic insulators", trans-formers and test equipment (chapter 16) also arebased on transmission lines.

CHARACTERISTIC IMPEDANCE. Every trans-mission line, whether two -wire, coaxial, or waveguide,has a certain characteristic impedance. This imped-ance is constant for each type of line, and is deter-mined by the size of the conductors, their spacing,and the dielectric. In the case of coaxial lines usingbeads as spacers, the type of the material in the beadswill also affect the characteristic impedance. Whilethere are no conductors in a waveguide in the usualsense of the word, waveguides still possess charac-teristic impedance, just as in the case of any othertype of transmission line.

In the beginning of this chapter it was shown thatwhen a battery was connected to an uncharged pairof long wires, the voltage between the conductors

50

CHAPTER 6

does not jump instantly to a maximum at all pointsof the line. Instead, a steep voltage wavefront travelsat a definite speed towards the far end of the line.If the inductance in henrys per meter and the capaci-tance in farads per meter distributed along a line arerepresented by L and C, respectively, the wavefronttravels at a velocity of

1=

N/LCm /sec (6-1)

and reaches the lamp after a time interval dependingon the distance between the battery and the lamp.Generally, the time interval is extremely short as thespeed of propagation along transmission lines is ofthe same order of magnitude as the speed of light.

The voltage wavefront (V) is always accompaniedby a similar current wavefront (I) both traveling inphase, with the ratio of voltage to current being aconstant at any point on the line. This constant iscalled the characteristic impedance Zo, and in a losslessline is given by the relations

Zo = = (6-2)

Of fundamental importance is the fact that a waveof any shape is propagated without change in shapeor magnitude along a uniform infinite line at a con-stant velocity since the characteristic impedanceratio VL/C remains constant. The characteristicimpedance of the line must be matched at both thetransmitter and antenna (or receiver and antenna)for maximum efficiency. Theoretically, such matchingwould produce an equivalent infinite line, with nostanding wave; actually, there will always be a stand-ing wave, due to objects near the line or antenna thatmay affect the characteristic impedance.

LOSSES AND ATTENUATION. In the foregoingdiscussion, the characteristics of transmission linesare based upon the assumption that the lines arelossless. Actually, a small amount of power is alwaysdissipated along a transmission line, such lossesincluding the following:

a. Conductor loss, or power lost as heat because ofcurrent flow through the resistance of the conductors.

b. Dielectric loss, or power loss because of currentsflowing in imperfect insulating material betweenconductors, usually stated in terms of the conduct-ance of the dielectric.

c. Losses caused by radiation and by interactionof the fields with adjacent objects and circuits. Theselosses are eliminated in the case where the fields

TRANSMISSION LINES

surrounding the conductors are confined by a con-ducting shield, or in the case where coaxial lines areused.

Where such losses occur, the wave is propagatedin the same way as on a lossless line, in phase andat a velocity as given by formula (6-1) with anamplitude ratio equal to the characteristic impedanceof the line. However, as the wave progresses alongthe line, its power is continually decreased by theline losses. Likewise, the amplitudes of the voltageand current also decrease or attenuate as the distancefrom the source increases. Thus, the effect of a trans-mission line is to reduce the power of the travelingwave in a definite ratio.

If the input power is designated by PI, and theload power by P2, the attenuation of the line may bespecified by the ratio P2/Pi, or more convenientlyby the expression

11 P1

la" 2 n P2 (6-3)

where

a8 = Attenuation in nepers of a line of length s,or a = nepers per unit length.

In = Napierian logarithm (log2)

The neper, like the decibel, is a logarithmic measureof a power ratio and is equal to 0.1151 times thenumber expressing the same attenuation in decibels.Given in decibels, formula (6-3) for the attenuationof a line of length "s" becomes

P1adb = 10 login (6-4)

At the same time that the amplitudes of the voltageand current decrease with distance, the phase anglesalso change in proportion to the distance. The com-bined effects of attenuation and propagation velocitycan therefore be expressed as a constant, called thepropagation constant (r) given by the equation

= a + j13 (6-5)

The propagation constant is made up of a real(resistive) term called the attenuation constant (a),and an imaginary (reactive) term known as the phaseconstant (3). The attenuation constant (a) is gen-erally measured in nepers per meter while the phaseconstant (0) is equal to 27r times the reciprocal of thewavelength measured in meters.

Line losses also affect the characteristic impedanceof a transmission line, and for most cases encoun-tered in high -frequency practice Zo may be expressedby the formula

51

CHAPTER 6

TRANSMISSION LINES

Zo = joiL)/ (G jwC) ohms (6-6)

where

L = Line inductance in henrys per unit lengthC = Line capacitance in farads per unit lengthR = Line resistance in ohms per unit lengthG = Dielectric conductance in mhos per unit

length.

The value of the attenuation constant now becomes

a --2Z0

nepers/meter (6-7)

and the value of the phase constant will be given by

CZo radians/wavelength (6-8)

where the values given by the formulas are used todetermine various transmission line characteristics.

It was stated earlier that the propagation constantalso accounts for the velocity of propagation of awave along a transmission line. Electro-magneticwaves traveling along a transmission line have adefinitely slower velocity, and a correspondinglyshorter wavelength than that obtained in free space.The following expression may he used to determinewave velocity in any line, and consequently thewavelength.

= meters/sec

2. Four -Wire Line

3. Shielded Pair

4. Coaxial or Concentric Cable

5. Waveguide

TWO -WIRE LINES. The oldest and simplest typeof transmission line is the familiar two -wire line, suchas that mentioned in the early part of this chapter.A two -wire transmission line consists of two parallelwires or tubes uniformly spaced by means of insu-lators or spreaders, with a spacing between the wiressmaller than the operating wavelength.

Since the characteristic impedance of any trans-mission line is a function of its distributed inductanceand capacitance, an increase in the spacing of thewires increases L and decreases C, thus increasing Zo.Similarly, a reduction in the diameter of the wiresalso increases the characteristic impedance, for it isequivalent to decreasing the size of the plates in acapacitor in order to obtain lower capacitance.Changes in the dielectric material between the twowires also changes the characteristic impedance ofthe line due to a change in the distributed capacitanceand conductance.

For non -loaded open wire lines where the dielectricmaterial between the lines is air, the value for Zomay be found by the formula

(6-9) 2DZo = 276 logio ohms

The difference between the velocity of propagationin a transmission line and the velocity of light isusually expressed as a ratio for any particular in-stance, and is generally called the velocity constant(k), or

k = 1

3 X 108 - 3 x 10813 (6-10)

where k is always less than unity except in the casewhere waveguides are used. For example, the velocityconstant of the RG8/U cable is 0.659 or 65.9%. Thevelocity of a wave in the RG8/U cable thereforebecomes 0.659 X 3 X 108 or 1.97 X 108 meters persecond, and the wavelength in the cable becomes0.659 X 600 or 395.4 centimeters, 600 cm being thefree -space wavelength.

PRACTICAL TRANSMISSION LINES

Transmission lines may be generally classified intofive general groups, as follows:

1. Two -Wire Line

(6-11)

where

D = Distance between the centers of the wiresd = Diameter of the wires

This formula is sufficiently accurate at high fre-quencies where the value of Zo is practically pureresistance, and may be found in nomogram form inappendix I (nomogram D).

Another type of two -wire line is the twisted pair,consisting of two insulated wires twisted to form aflexible line without the use of spacers. Such a lineis not generally used at frequencies higher than about30 me due to extremely high radiation losses andleakage losses between conductors.

FOUR -WIRE LINES. One type of four -wire lineresembles a pair of two -wire lines with the four wiresuniformly spaced. Such lines have the advantage ofreduced radiation and less mutual effect on nearbylines when diagonally opposite wires are connectedin parallel. An improvement on the uniformly spacedsystem is the spiral -four line, where four wires insteadof two are twisted together to form the transmission

52

CHAPTER 6

TRANSMISSION LINES

line. Spiral -four lines are used mainly to carry audiofrequencies, and, like the parallel four -wire line,diagonally opposite wires are connected in parallel.

SHIELDED PAIR. The shielded pair consists oftwo parallel conductors separated from each other bya dielectric material. The conductors are containedin a copper -braid sheath which, in turn, is coveredwith a flexible coating of rubber to protect the linefrom moisture or friction. Thus, the shielded pairclosely resembles the sheathed cable used for electricpower wiring.

The shielded -pair transmission line possesses anoutstanding advantage in having its two conductorsbalanced to ground; that is, the capacitance betweeneach conductor and ground is uniform along theentire length of the line. Since the wires are com-pletely shielded, losses due to radiation are elimi-nated as well as interaction with adjacent objects andcircuits.

Radiation from an unshielded line may also beprevented provided the current flow in each con-ductor sets up a field equal and opposite to the fieldset up by its paired conductor. This condition maybe obtained if the line is sufficiently removed fromany conducting objects, and if the spacing betweenthe wires is small. If a conducting object is near thetransmission line, a certain amount of capacitanceexists between the object and the wires of the line.Unless this capacitance is identical for both wires,the current flow will be greater in the wire nearest theconducting object, resulting in unequal current flowin the two conductors. This unequal current flow willproduce incomplete cancellation of the electromag-netic fields resulting in radiation.

COAXIAL CABLE. The concentric or coaxial cablehas several important advantages which make itquite practical for reliable operation at high fre-quencies. The first advantage is the fact that radia-tion loss is eliminated by surrounding one wire bythe second which is at ground potential. Thus, theconductor to ground capacitance remains uniform atall points. Another advantage of a coaxial cable isthat the line is free from noise pickup as radiatedfrom external sources.

Two types of coaxial cables are in use, flexible andrigid. In the flexible cables, dielectric materials suchas synthetic rubber or polymeric resin compoundsare used to separate the inner and outer conductors.Such cables have the advantage of easy handling andinstalling, although they have a greater attenuationthan rigid coaxial cables because of a finite value ofdielectric conductance.

Rigid coaxial lines use a solid outer tube, ratherthan the braid used for flexible lines, and the innerconductor is held in place by uniformly spaced insu-lators. Since moisture increases the dielectric constantof air, the outer joints of a rigid coaxial line areusually sealed, and the dielectric within the cablecarefully dried. Occasionally, coaxial cables arepressurized with either dried air or nitrogen in orderto prevent moisture -laden air from entering thecable.

The spacers used in the rigid coaxial cable may beeither porcelain beads, regularly placed along theinner conductor; pins, or rods, through the conductor;or a plastic belt wound spirally around the innerconductor. While the ideal coaxial cable would havean air dielectric throughout, such a cable would nothave uniform spacing between the two conductors.Any spacing device, such as the beads surroundingthe inner conductors are necessary evils. Beads, forexample, tend to reflect the signal, thus altering thecharacteristic impedance of the line. This may becorrected by using undercut beads; that is, beadswhose inner diameter is less than the diameter ofthe inner conductor. This requires a stricture of theinner conductor at the point where the bead isattached. Cable using the spiral spacer mentionedhas a lower attenuation than the other types, and isalso sturdier, being capable of withstanding a blowthat might shatter a bead or rod.

As with all other transmission lines, the character-istic impedance of a coaxial line varies with itsdistributed inductance and capacitance, and there-fore with the size and diameters of the conductors.For air -filled coaxial lines, the characteristic imped-ance (Zo) may be found by the formula

Zo = 138 login -a (6-12)

where b is the inner diameter of the outer conductorand a is the outer diameter of the inner conductor.(See Nomogram E in Appendix I.) It will be found,in most cases, that the value for Zo ranges from 40to 80 ohms for coaxial lines.

The total attenuation imposed by a coaxial lineis made up of two components, namely the resistanceof the conductors themselves and by losses in thedielectric separating the conductors. The character-istic impedance of the conductors, for a given line,is 72 ohms when the ratio of b/a is equal to 3.59, sucha value being used in most cases. For the particularcase where the above ratio is satisfied, the attenua-tion contributed by solid copper conductors may befound by the formula

53

CHAPTER 6

TRANSMISSION LINES

0.187 -ViraR = db per meter (6-13)

and the attenuation contributed by the dielectric is

2730 -6, + tansac - db per meter (6-14)X

where

b = Radius of the outer conductorX = Free -space wavelength

= o -/WK, where 0- is the conductivity and K is thedielectric constant of the separating material.(5 = 0.003 for polyethylene)

Kr = The relative dielectric constant of the sepa-rating material (referred to a vacuum). (Kr =2.25 for polyethylene)

The total attenuation of a coaxial line is simply thesum of aR an, and is given in decibels per meter.For metals other than copper, the attenuation givenby formula 6-13 should be multiplied by the followingfactors: 2.0 for brass, 1.8 for dural, 1.3 for aluminum,and 0.58 for silver.

In a coaxial cable, the electric lines of force arenormal to the surface of the inner conductor. Theelectric field is made continuous by the presence ofthe two conductors so that the lines of force in thespace between the wires are everywhere perpendic-ular to the direction of propagation. Conversely, themagnetic lines of force form closed paths around theinner conductor and are also perpendicular to thedirection of propagation. Such a field configurationis called transverse electromagnetic (TEM), since bothfields are everywhere normal to the direction of prop-agation. The TEM wave is the basic form of fieldconfiguration in all transmission lines, with the excep-tion of waveguides, and is commonly called theprincipal mode of operation (figure 6-4A). In addition,however, there may exist higher modes of operationin a coaxial cable (figure 6-4B) if the mean diameterof the cable exceeds the free -space wavelength, al-though such waves are highly attenuated and notcommonly used.

In a waveguide, there is only one conductor and,therefore, no closed physical path through which thefield energy may be returned. Here, the lines of forcemust form continuous loops within the guide itself,and since the electric and magnetic fields are alwaysperpendicular to each other, one of the fields musttravel part of the time in the direction of propagation.Thus, both fields cannot be transverse to the directionof propagation at the same time and a TEM modeis impossible to achieve.

LINE OFZERO FIELD

I NTENSITY

0PRINCIPAL TEM MODE

( NO CUT-OFF WAVELENGTH )

0T E io MODE

(CUT-OFF WAVELENGTH v/2 (0 + b) )

- ELECTRIC LINES OF FORCEMAGNETIC LINES OF FORCE

Figure 6-4. Coaxial Modes of Operation

WAVEGUIDES

GENERAL. A waveguide may be defined as a struc-ture consisting of either a conductor or a dielectric,or both, in which the boundaries containing the guideare continuous. Waveguides are similar in action towire transmission lines in that they are used totransmit r -f energy from one place to another. How-ever, here the likeness to wire lines stops, as a wave -guide consists of only one hollow metal conductoror pipe, which is capable of guiding electromagneticwaves through its interior. Two types of metal wave -guides commonly used have either a rectangular orcircular cross-section. The dielectric waveguide, orrod, is not used extensively because its losses aregreat, and because the electromagnetic field cannotbe wholly contained within the rod. Other types ofwaveguides include elliptical, corrugated, and flex-ible, all of which are special forms and will not bediscussed here.

One reason for using a hollow waveguide is that ithas lower loss than either open -wire lines or coaxiallines in the frequency ranges for which it is practical.Generally, waveguides are used at frequencies rang-ing from 3000 mc and up, while wire lines are com-monly used below 3000 mc. A second reason for usinga waveguide is that it is capable of transmitting morepower than a coaxial line of the same size. The maxi-mum power transmitted on a coaxial line is given bythe formula

P = V2/Z0 (6-15)

where V is the voltage and Zu the characteristicimpedance of the line. Therefore, the power trans-mitted on a given line can be increased only by raisingthe voltage, which, if raised too high, will cause thedielectric to break down. The length of the voltagebreak -down path in a coaxial line is the distance fromthe inside surface of the outer conductor to the out-

54

CHAPTER 6

TRANSMISSION LINES

side surface of the inner conductor. This distance isless than half the voltage break -down distance in around waveguide of the same size, since when oper-ating in the principal mode, the maximum voltage ina round waveguide appears across its diameter.

Summarized, the advantages of a waveguide trans-mission line are as follows:

1. Complete shielding, eliminating radiation loss.

2. No dielectric loss, since there are no insulatingbeads within the guide.

3. Conductor loss due to the internal resistance ofthe guide is less than that of a coaxial line of the samesize, operated at the same frequency, since only oneconductor is used.

4. Greater power -handling capacity than for acoaxial line of the same size.

5. Simpler construction than that of a coaxial line.

There are, of course, important disadvantages to con-sider when using waveguides. First, the minimumsize of waveguide that can be used to transmit acertain frequency is proportional to the wavelengthat that frequency. The proportionality depends onthe shape of the guide and the manner in whichelectromagnetic fields are set up within it. In allcases, however, there is a minimum frequency, calledthe cut-off frequency, below which no other frequenciescan be transmitted. As a result of this characteristic,a rectangular waveguide would have to be wider thantwo inches to transmit a 3,000 mc signal, 20 incheswide for a 300 mc signal, and 17 feet wide for a 30mc signal.

Second, the installation and operation of a wave -guide transmission system are somewhat more diffi-cult than for other types of lines. The radius of bendsin the line must be greater than one wavelength toavoid excessive attenuation. In addition, if the guideis dented, or if solder beads are permitted to runinside when joints are made, the attenuation of theline will be greatly increased and the voltage break-down point will be reduced.

MODES OF OPERATION. Solutions of Maxwell'sequations, subject to boundary conditions imposedby perfectly conducting metal walls, show that anygiven guide can propagate an infinite number ofdifferent types of electromagnetic waves. Each typeor mode has its own individual electric and magneticfield configuration and is designated by that con-figuration. Each mode of operation has a criticalfrequency below which it will not be propagatedthrough the guide. The critical frequency or cut-off

55

frequency (ft) for that mode and the correspondingfree -space wavelength or cut-off wavelength (X0) arerelated by the formula

Xc fs

(6-16)

where c is the free -space velocity of light. In a givensize waveguide, the mode with the lowest cut-offfrequency is called the principal mode for that guide,and will be the only mode propagated if the frequencyis greater than the principal cut-off frequency but lessthan the cut-off frequency for the second lowest mode.It is a noticeable characteristic of waveguides thatthe cut-off wavelength of the principal mode is com-parable to the size of the guide. For example, in around air -filled waveguide, the cut-off wavelength ofthe principal mode is equal to 1.71 times the diam-eter, and in rectangular air -filled guides Xs is equalto twice the large cross-sectional dimension.

In general, two types of modes are possible. Theconfigurations of one type are called transverse electric(TE) since their electric fields are everywhere per-pendicular to the direction of propagation. Occasion-ally TE waves are referred to as H -plane waves sincepart of the magnetic field is parallel to the directionof propagation The second type of mode configura-tions are called transverse magnetic (TM) since theirmagnetic fields are everywhere perpendicular to thedirection of propagation. TM waves may also becalled E -plane waves because they have electric fieldcomponents parallel to the direction of propagation.

The operating wavelength (Xg) in a waveguide forany mode may be found by the expression

XXg =

K, V1 - 02(6-17)

whereX = The free -space wavelengthX s = Cut-off wavelength of a particular mode of

operationK, = The relative dielectric constant of the mate-

rial with which the guide is filled. Since mostguides are air -filled, K, may be taken as unity.

The guide wavelength (Xs) for all gas -filled wave -guides is always larger than the corresponding free -space wavelength. This longer wavelength is causedby the wave apparently traveling faster than light,although this seems to violate the fundamental lawof physics which states there can be no real velocitygreater than that of light. Actually, the rate of energyflow in a guide, called group velocity (vg), is alwayssomewhat less than that of light and approaches zeroas the free -space wavelength approaches the cut-off

CHAPTER 6

TRANSMISSION LINES

value. However, superimposed on the traveling elec-tromagnetic waves is a variation of field intensitywhich appears to move at a much higher velocity.This superimposed velocity of a change in field inten-sity is called the phase velocity (pc), and is related tothe group velocity by the expression

Pc X vp = C2 (6-18)

where c is the speed of light in free space. Therefore,since the point of maximum field intensity, but notthe actual energy, moves down the waveguide at thephase velocity, the apparent wavelength in a guideis always greater than'the wavelength in free space.Typical wavelengths found in practice usually runfrom 1 to 2 times the wavelength outside the guide.

Since the different modes have correspondinglydifferent wavelengths in a guide, it Is generally im-possible to make a guide which will be matched formore than one mode. Also at any discontinuity, suchas a junction or sharp corner, other modes will tendto be excited and, therefore, it is desirable to choosea guide which will propagate only the lowest mode.If this is done, then any mode beyond cut-off will dieout within a very short distance of its source. Ingeneral, higher modes are used only because of theirspecial polarization or attenuation features.

RECTANGULAR GUIDES. The lowest mode, orprincipal mode, in rectangular guides is the TE1,0mode. An instantaneous picture of its field is givenby figure 6-5A. The electric field can be representedby electric lines of force which extend from the bot-tom to the top of the guide. The intensity of the fieldvaries sinusoidally along the "A", or long dimension

L

I

1/2 PATTERN{ h- NO PATTERN -1

0',/,,,,,,,/.4,/,./IV/AV/Age/.60.11/2

1111

,,...

ce crOwz

A---1TE 1,0

X, 2A

-12 HALF PATTERNS

OWZ

a.

% 11

1!!

0 A

TE

ac A

Ornamiama*'ism-M-a-amm5MFIPM5P,Mt

A --"-1TE 01

ac 26

/2 PATTERN

2A8Xc

IT12 B2

- ELECTRIC LINES OF FORCE---- MAGNETIC LINES OF FORCE

I

I

of the guide, while along the "B", or short dimension,it is uniform. The magnetic field is pictured by meansof the magnetic lines of force, which are always per-pendicular to the electric lines of force. If the electricfield is known, the magnetic field configuration canbe determined and, for the TE1,0 mode, the magneticlines form plane loops which are perpendicular to theelectric lines.

The cut-off wavelength in an air -filled waveguidefor the principal TE1,0 mode is given by the expression

X, = 2A (6-19)

where A is the long dimension of the guide, and mustbe at least one-half the free -space wavelength in orderto propagate the TE1,0 mode. In a rectangular wave-guide which is filled with a dielectric other than air

X, = 2A -/ Kr (6-20)

where Kr is the relative dielectric constant of thematerial within the guide.

The various modes of any guide are designated bythe subscripts m and n, where m and n are wholenumbers. In a rectangular guide, the first subscriptm of a TE,,,,,, or a Tn.,° mode refers to the numberof half -cycle variations in the fields along the "A"dimension. The second subscript n refers to thenumber of half -cycle variations along the "B" dimen-sion. For example, the TE0,1 mode, as shown in figure6-5B, is just like a TE1,0 mode, which has beenrotated through 90°, but it has the subscript "0,1"because the fields are uniform along the "A" dimen-sion and have a half -cycle variation along the "B"dimension.

The cut-off wavelength for the TE0,1 mode may befound by the formula

X, = 2B (6-21)

where B is the short dimension of the guide. The nexthigher mode in a rectangular guide is the TE2,0 mode,shown in figure 6-5C. It is best described as twoTE1,0 Anodes side by side and 180° out of phase intime. The cut-off wavelength for the TE2,0 mode is

X, = A (6-22)

Thus, the above data on cut-off wavelengths may beused as a basis to determine the size of rectangularguide which will propagate only the TE1,0 mode. Thedimensions "A" and "B" of the guide must be suchthat

2A > X > A (6-23)X> 2B

where X is the free -space wavelength of the frequencyFigure 6-5. Rectangular Waveguide Modes to be propagated. The inequality (2A > X) allows

56

CHAPTER 6

TRANSMISSION LINES

the TE1,o mode to be propagated; the inequality(X > A) prevents the TE2,0 and higher modes; whilethe inequality (X > 2B) prevents the TE0,1 andsimilar modes. The cut-off wavelength for any TEm,,1or TMm,n mode in a rectangular guide is given by

" = (121 (-11-n2)A(6-24)

For any dielectric other than air, multiply the aboveexpression by Tc..

In ordinary transmission -line practice, charac-teristic impedance may be defined in terms of voltageand current, power and current, or in terms of powerand voltage. All three, under normal conditions, giveidentical results. For waveguides, however, they donot do so although their numerical differences arenot large. For an air -filled guide the characteristicimpedance, based on power and voltage, follows therelationship

7 54B X0Zo = ohmsA X

(6-25)

It may be seen from the formula that, dependingupon the guide dimensions, Zo may be given almostany desired value. However, representative values ofZo for most waveguides now in general use lie between500 and 1,000 ohms, although some have been usedwith values of Zo less than 100 ohms.

Another matter of prime importance in the prac-tical use of waveguides is the amount of attenuationpresent within the guide. Such attenuation may bedivided into two causes: (1) the attenuation due tolosses in the conducting walls of the guide, and (2)the attenuation due to the shunt conductivity of thedielectric filling the guide. For air dielectric, wherethe shunt conductivity may be neglected, the atten-uation developed in a rectangular copper guide isfound by

=0.104B-' + 0.52 X2A-3

N/1 - 0.25 X2A-3

CIRCULAR WAVEGUIDES. The principal modeof a circular waveguide is the TE1,1 mode, which isthe round waveguide equivalent of the rectangularTE1,0 mode. The TE1,1 mode is shown in cross sectionin figure 6-6A. The cut-off wavelength of such a modemay be found by the formula

x. = 1.71d (6-27)

where d is the inside diameter of the guide. However,cut-off wavelengths for the higher modes in circularguides cannot, as a rule, be expressed in easilyremembered terms since they involve roots of Besselfunctions.

(6-26)

PATTERN

ONEWHOLE

PATTERN

TE,0 MODEAc 1.71 d

TWO0 WHOLEPATTERNS

TE21 MODEXe 1.03 d

ZZ 1/1/1

ff://Z31:ZiAXIAL VIEW OF

ELECTRIC FIELD

TM01

MODE

T Moo MODE

ac .1.31d

- ELECTRIC LINES OF FORCE----- MAGNETIC LINES OF FORCE

Figure 6-6. Circular Waveguide Modes

In a circular guide, the first subscript m of a TEm,,.or TM mode indicates the number of whole (orfull -wave) patterns in the fields encountered aroundthe circumference of the guide. The second subscriptn indicates the number of half -wave patterns thatexist along a diameter of the guide. Thus, the TE.mode, for example, will have m angular modes(diameters) and (n-1) radial modes (circles).

The next highest mode of propagation which occursin circular waveguides is the TMo,i mode as illus-trated in figure 6-6B. The magnetic lines form con-centric circles and lie in planes perpendicular to thedirection of propagation. Since the magnetic linesare everywhere perpendicular to the guide axis, thesurface currents must everywhere flow parallel to theguide axis. Likewise, an axial view of the electric fieldwould show that each line of force emerges perpen-dicularly from the guide wall, turns and travelsparallel to the guide axis, and then bends back intothe guide. The cutoff wavelength for the TMo,i modein a round guide may be found by the expression

X, = 1.31d (6-28)

Similarly, the third mode of a circular waveguide is

the TE2,1 mode illustrated in figure 6-6C. The cut-offwavelength for this mode is

X. = 1.03d (6-29)

57

CHAPTER 6

TRANSMISSION LINES .

Therefore, to choose the correct size of circular guidewhich will propagate only the TEbi mode, for exam-ple, the guide diameter should be such that

1.71d > X > 1.31d (6-30)

where X is the free -space wavelength of the operatingfrequency. Since circular waveguides are very seldomused in present-day equipments, and the mathematicsinvolving a and Zo is beyond the scope of this book,no attempt will be made to go further into circularwaveguide theory.

TRANSMISSION LINE USES

The theoretical development of transmission linesand their use as a means of transmitting r -f powerfrom one point to another have been discussed pre-viously. However, transmission line sections arecommonly used for many other purposes. For ex-ample, r -f lines are used as:

1. Frequency control elements.

2. Filters.

3. Phase shifters.

4. Delay lines.

5. Impedance matching sections.

6. Attenuators.

FREQUENCY -CONTROL ELEMENTS. In thefrequency range from about 200 mc to about 1,000mc parallel line sections are commonly used to controlthe frequency of oscillators and amplifiers. The fre-quency stability of an oscillator is a function of theQ of its tuned circuits. The Q, or figure of merit, of atuned circuit is equal to the inductive reactance atresonance divided by the resistance and as such is afunction of frequency. Q may also be thought of asa constant times the ratio of the energy stored in acircuit to that dissipated in the resistance of thecircuit. For a given inside diameter of the outer con-ductor in a coaxial line, the Q is a maximum whenthe ratio of the diameters is equal to 3.59. This ratiocorresponds to a characteristic impedance of 76 ohmsso that the use of nominal 72 ohm coaxial line willapproximate the conditions of maximum Q. Thelarger the inside diameter of the outer conductor,while maintaining the same diameter ratio, the largerwill be the Q of the line. As discussed in the develop-ment of transmission lines, a finite length trans-mission line which is terminated in other than itscharacteristic impedance will have standing wavesand will reflect an impedance back to the source. The

value and type of impedance, resistive, capacitive orinductive, will depend on the type of termination andthe length of the line. A line one -quarter wavelengthlong terminated in a short circuit will reflect a veryhigh resistive impedance to the source and so act asa parallel resonant circuit. The same line terminatedin an open circuit will reflect a low resistive imped-ance and so appear as a series resonant circuit.

Tuning these lines may be accomplished by severalmethods as illustrated in figure 6-7A. An adjustableshorting strap can be used to change the effectivelength of the line if very low resistance connectionsare made so as not to lower the Q of the circuit. Asecond method of changing the effective line lengthis the use of a capacitor as a shorting bar to changethe resonant frequency of the line. Parallel platecapacitors with air dielectric are usually used for this

PARALLEL - DISKCAPACITOR

SHORTING

STRAP

A - TWO -WIRE LINE SECTIONS

SLIDING

SHORTINGDISK

TELESCOPICPLUNGER

PARALLEL -DISK METHOD 2

CAPACITOR

Ei - COAXIAL -LINE SECTIONS

Figure 6-7. Common Tuning Methods

58

purpose, but unless carefully designed and adjustedmay unbalance the line.

Coaxial lines are also used at frequencies rangingto about 3,000 mc as tuned circuits. Although theyare harder to tune (see figure 6-7B) they have verylittle, if any, radiation loss and the possibility of straycoupling is reduced, allowing a more compact designto be used. Increasing the diameter of the line willincrease the Q of the circuit, but the diameter shouldbe kept smaller than that required to propagate anymode other than the TEM mode, or oscillation atother than the desired frequency may result.

Harmonic response is controlled easily in a quarter -wave tank circuit, since it responds only to the oddharmonics. The third harmonic can be practicallyeliminated by loading with a small value of capacitivereactance or by tapping onto the tank at the third -harmonic voltage minimum. Although quarter -waveand half -wave line sections are most commonly used,the statements made here about the basic quarter -wave sections also are true for sections composed ofany odd multiple of a quarter wave. Statementsabout half -wave sections hold true for any multipleof a half wave.

By closing off both ends of a length of coaxial linewith conducting material, standing waves will be setup if any energy is introduced. When a transmissionline completely encloses the energy in the line, it iscalled a cavity resonator. If the cavity has a centerconductor so that the TEM mode can exist, thecavity will be resonant at any frequency for whichthe length is a multiple of a half -wave length. Addi-tional resonant frequencies will exist due to TE andTM modes of resonance. The number of modes otherthan TEM with a wavelength longer than the free -space wavelength in a given coaxial cavity can beapproximated by

N = 4.4 -VX'

(6-31)

where N is the number of modes, V is the volume inthe same units as X3, and X is any wavelength. Byhaving the diameter of the coaxial cable small enoughto prevent the occurrence of any mode other thanthe TEM mode near the operating frequency, astable frequency control element with a very high Qis obtained.

Coaxial cavities can be tuned in a number of ways.The most commonly used method is a plunger whichchanges the length of the cavity. Another methodused for fine tuning is the insertion of a tuning slugwhich may be either capacitive or inductive depend-ing on its position with respect to the electric andmagnetic lines of force.

CHAPTER 6

TRANSMISSION LINES

Cavity resonators can also be produced by closingoff both ends of a waveguide. Modes are identifiedby the addition of a third index to the mode desig-nation for waveguides, the third number being thenumber of half waves along the axis. The principalmode in a right circular cylindrical cavity is theTM0,1,0 mode in which the axial length has littlecontrol over frequency. Higher mode cavities can betuned by varying the axial length, which is usuallythe frequency critical dimension.

Cavity resonators may be made in almost anyshape in which a dielectric is completely enclosed bya conductor. Figure 6-8 illustrates some of the formswhich may be used, and gives their approximate Q.

Energy may be fed into or removed from a cavityby an inductive loop which couples the magneticlines, by a capacitive probe or antenna which couplesto the electric lines, or directly by a waveguideoriented so that the magnetic lines in the waveguideare parallel to the magnetic lines in the cavity.

FILTERS. Sections of coaxial line are often used asfilters to remove even harmonics. A quarter wave-length shorted section in parallel with the line willappear as a very high impedance at the fundamentalfrequency and all odd harmonics, but will appear asa very low impedance at the even harmonics. Elimi-nation of other frequencies requires the use of a half -wave shorted line at the interfering frequency plusan additional section to cancel out the reactance in-troduced to the desired frequency. For example, sup-pose the desired frequency is 400 mc and the interfer-ing frequency is 250 mc. A shorted half -wave sectionat 250 mc is placed across the line to short out the 250mc signal. This introduces a capacitive reactance at400 mc and requires the use of an inductive sectionto cancel the reactance out in order to prevent attenu-ation at the desired frequency. (See Nomogram F,Appendix I.)

Waveguide sections can be used similarly to filterout undesired frequencies either as a shunt filter orby placing a section of the proper size in the line toact as a high-pass filter. Low-pass filter action canbe obtained by shunting the transmission line witha section of waveguide with the proper cut-off wave-length and terminating it with a resistive load so thatno reflection of energy takes place. All frequenciesabove the cut-off frequency will be partially absorbedand all frequencies below the cut-off frequency willbe passed with little attenuation.

It is often desirable to be able to use the sameantenna for simultaneous reception and transmission.This can be accomplished by the use of antennaduplexers and different frequencies for reception and

59

CHAPTER 6

TRANSMISSION LINES

CUBE (Q28,000)

d

DOUGHNUT SHAPED

bCYLINDER (Q 31,000)

ras.m.zasimcia. psi

CYLINDRICAL RING (0.26,000)

Figure 6-8. Types of Cavities

transmission. Frequency sensitive sections of trans-mission line separate the signals. The transmissionline to the transmitter should have a high mismatchat the received frequency so as to avoid a loss ofpower in the transmitter, and the receiver trans-mission line should have a high mismatch at thetransmitter frequency to prevent power loss in thereceiver and possible damage to the receiver.

Since a shorted quarter -wave -long transmission linehas a very high impedance, it is often used as a"metallic insulator". Mechanically and electricallythe best coaxial lines for centimeter wavelengths arethe so-called stub -supported lines which are used toa great extent. The stub is in parallel with the lineand, if it is made exactly an electrical quarter -wave-length long, it will give no reflection at that frequency.Since a quarter -wave stub may be thought of as aloaded resonator, it will be perfectly reflectionless atonly one wavelength. At longer wavelengths, the stubis less than a quarter -wave and therefore shunts theline with an inductance, and at shorter wavelengthsthe stub is more than a quarter -wave and so shuntsthe line with a capacitance. To compensate for thiseffect, it is possible to place two stubs in the line anodd number of quarter -waves apart so that theirrespective reflections cancel.

PHASE SHIFTERS AND DELAY LINES. Sincethere is a progressive phase shift of 360° per wave-length along a matched transmission line, a shortlength of line can be used to obtain any desired

C

SPHERE (0 -26,000)

SECTION OF WAVEGUIDE

amount of phase shift between two points in a circuit.For example, a line one -eighth wavelength long willhave a phase shift of 45° between input and output.By lengthening the line a time delay may be obtainedwith the amount of delay depending on the lengthof the line. To obtain any large time delay wouldrequire a very long and bulky line. To avoid this,artificial transmission lines are built using lumpedcapacitance and inductance in which delays of sev-eral hundred microseconds may be obtained.

IMPEDANCE MATCHING SECTIONS. Quarter-wavelength transmission lines are often used forimpedance matching. By shorting one end of the linestanding waves are set up causing the line impedanceto vary from zero at the shorted end to a very highimpedance at the open end. Any impedance can beobtained by tapping on to the line at the point wherethe V/I ratio equals the desired impedance.

If the quarter -wave line is not shorted, but has aload impedance of Z. across the load end of thesection the input impedance will be

Z=Zr

(Zo)2(6-32)

where Z, is the input impedance and Zo is the char-acteristic impedance of the line. If Z, and Zr are bothknown, the required Zo to match the two can bedetermined from

Zo = Zr (6-33)

60

CHAPTER 6

TRANSMISSION LINES

For example, it is desired to match a 600 -ohm inputimpedance to a 72 -ohm output impedance. The re-quired line would have a characteristic impedance of208 ohms. (See Nomogram G in Appendix I.)

Usually in matching applications, the characteristicimpedance of a transmission line is of great impor-tance. However, by the use of half -wave or integralmultiples of a half -wave section, the impedance of theline becomes unimportant. The impedance of a deviceconnected to one end of a half -wave line will bereflected unchanged to the other end regardless of thecharacteristic impedance of the line although therewill be a 180° phase shift per half -wave section of line.

When connecting a device that is balanced toground to one which is not, some means of balanceconverter must be used. A typical example is theconnection of a dipole antenna which is usuallybalanced to ground to a coaxial line which is unbal-anced. One device that may be used is known as abazooka line balance converter (figure 6-9). This isused when the impedance of the devices alreadymatch and no impedance transformation is desired.It consists of a quarter -wavelength shield placedaround the end of the coaxial line. The balancetransformation can take place in either direction.

Another type of line balance converter is shown infigure 6-10. This functions as a balance converter aswell as an impedance transformer with a ratio of 1:4.Since the U-shaped line is a half -wave long, there isa 180° phase shift around it with both ends of theline at a high impedance to ground. If, for instance,50 volts is applied to the converter, 50 volts willappear at each end with respect to ground, but theends will be of opposite polarity to each other.Doubling the voltage while maintaining the samepower corresponds to an impedance transformationratio of 1:4. Like the bazooka converter, this con-verter can be used for transformation in eitherdirection.

Although waveguides have a definite characteristicimpedance, as yet no exact method exists for findingit. Approximations may be made from current, volt-age, and power ratios, but these all give differentvalues. Fortunately, it is not necessary to know thecharacteristic impedance to match two sections ofwaveguide. All that is required is to insert a taperedsection several wavelengths long between the two.Transformations of shape as well as size can be madein this way without reflection provided the taper isgradual.

Coaxial line to waveguide transformation usuallyconsists of a right angle junction with the centerconductor of the coaxial line extending into the wave -

guide approximately a quarter -wavelength and func-

DETUNING SLEEVE

UNBALANCED

tioning as an antenna. The end plate of the waveguideis about a quarter guide wavelength from the antenna,so that it reflects radiation in phase with that radiateddirectly down the guide.

In actual practice neither of these lengths is aquarter wavelength, but must be determined byexperiment. We may consider the end -plate distanceas varying the amount of coupling between thecoaxial line and the waveguide through the varyingphase of directly radiated and end -plate -reflectedfields. This produces a match of the characteristicimpedance of the guide to that of the coaxial lineexcept for the reactive component of the transition.This reactance may be matched out by adjustmentof the antenna length.

ATTENUATORS. Attenuators are of two generaltypes. The first class operates on the principle of awaveguide below cut-off. The second class operatesby introducing dissipative elements to absorb energy.These will be referred to simply as the cut-off typeand the dissipative type.

The cut-off type is commonly used as a variableattenuator. The calibration of such an attenuatormay be computed theoretically, and may be madesubstantially independent of frequency. The theoryunderlying this type of attenuator is as follows:

Propagation through a waveguide takes place with

MUNBALANCED BALANCED

IM U4

/1 2A

/BALANCED

1

4A

I TO I

EQUIVALENT CIRCUIT

Figure 6-9. Bazooka Line Balance Converter

B

C

61

CHAPTER 6

TRANSMISSION LINES

UNBALANCEDZ=I

BALANCEDZ.4

EQUIVALENT CIRCUIT

A

B

Figure 6-10. Phase Inverter as Line Balance Converter

very little loss provided the diameter or width of theguide is greater than the cut-off value. If thesedimensions are below cut-off, then there is no longerany true wave propagation, but instead the fields areexponentially attenuated down the length of theguide. The attenuation per unit length, for any givenmode, may be computed directly from theory. Fur-thermore, if the guide diameter is made small com-pared to the free -space wavelength, the attenuationis then substantially independent of frequency overa wide range. The mode which is most commonlyused in attenuators is the TEI,I. This mode is excitedby a loop or waveguide and energy is taken out againby another loop or by direct connection to anotherwaveguide (figure 6-11). The attenuation for thismode is as follows

32.0TE1,1 db/cm = 3.41d21Li (6-34)

2 X

where d is the diameter in cm of the cut-off attenua-tor. Since the attenuation is a linear function of thelength, the distance between source and load can becalibrated directly in db. Attenuators of this typeusually have a loss of 10 to 20 db at the position ofmaximum coupling or minimum length . In the imme-

diate vicinity of the loops, modes other than thedesired one exist, and as a result the attenuation isnot a linear function of the length for short distances.The usable portion of the attenuation range beginsat the point where the characteristic becomes linear.This will in general occur when the attenuator is longenough to obtain a loss of 25 to 35 db for the TE1,1mode.

Since a line terminated by a loop is substantiallyequivalent to a short-circuited line, an attenuator ofthis type presents a gross impedance mismatch look-ing in toward either the input or output ends. Thisis undesirable in many applications and may becircumvented in a number of ways. The most com-mon scheme is to pad the input and output endswith about 10 db of lossy cable so that reflectionsfrom the loops are substantially damped out at thefar ends of the cables.

Dissipative attenuators function by introducingresistive elements in the waveguide or coaxial line soas to dissipate energy in the form of heat. In coaxiallines the loss may be introduced either in the formof a series resistance or shunt conductance. Examplesof the former are platinized glass -rod and carbonizedrod attenuators. Shunt conductance types are ordi-nary lossy cable and sand loads.

The insertion of an attenuator may cause a con-siderable mismatch, which may be avoided in twoways. First, the dissipative element may be taperedso that the loss is introduced gradually. This schemeis more often used in waveguides than in coaxial lines.Second, a matching section of some sort may be used.

Lossy cable is a coaxial line made with a dielectricwhich has a high power factor. The attenuation ofthis cable is around 1.2 db/ft in the 10 cm band.The attenuation varies nearly linearly with bothfrequency and temperature, so that its use as a cali-brated attenuator is to be discouraged.

Sand load attenuators are used as terminatingsections to dissipate power. The space between innerand outer conductors is filled with a sand and carbonmixture which acts as the dissipative element.

A platinized glass attenuator is essentially a sectionof coaxial line in which the inner conductor is a lengthof glass tubing which has been coated with an ex-tremely thin platinum film. The film is resistive andthereby produces attenuation. By controlling thethickness of the platinum film during manufacturevarious degrees of attenuation may be achieved.

The carbonized rod attenuator is a series resistancetype. The center conductor is a quartz rod which hasa thin deposit of carbon.

Another type of coaxial attenuator makes use ofthe r -f absorbing properties of "polyiron". This

62

CHAPTER 6

TRANSMISSION LINES

material is insulated powdered iron of the kind usedextensively for magnetic cores at the lower radiofrequencies. If the space between the inner and outerconductors of a coaxial line is filled with a moldedslug of polyiron, attenuations of the order of 20 to30 db/cm may be obtained at 10 cm wavelengths.Molded slugs of polyiron are extensively used in r -fline filters where it is desired to keep r -f from leakingout through power leads.

Waveguide dissipative attenuators are either of theresistor -strip type, or of the sort in which the entireguide is filled with a lossy material.

In the resistor strip type, a strip of bakelite coatedwith resistance material is placed longitudinally inthe guide, with the plane of the strip parallel to theshort side. When the guide is excited in the TE1,0mode the electric field is parallel to the plane of thestrip so that current flows in the resistive material,and energy is dissipated in the form of heat. Theattenuation is an inverse function of the surfaceresistivity of the strip, with the lower the resistivity,the greater the attenuation (within limits) and thegreater the mismatch of the attenuator.

Since the electric vector varies from a minimum toa maximum across the guide, the amount of attenua-tion with a given strip may be varied by moving thestrip laterally across the guide. Attenuations up to70 db have been obtained with attenuators of thistype, using strips 4 inches long.

Resistor strip attenuators are matched either bymechanically tapering the strip or by cutting notchesin the end of the strip. The notched sections act asmatching transformers. By making the taper longenough, it is possible to get very low standing waveratios.

In the second type of waveguide dissipativeattenuator, the guide is filled with a conductivematerial, generally a plaster-of-paris and graphitemixture, the proportions of which are adjusted togive the proper attenuation. Matching is accom-plished either by means of a slow mechanical taperor by matching the ends. A bakelite plug has beenused instead of the plaster-of-paris mixture withresulting attenuations of about 1 db/cm having beenreported.

INSTALLATION NOTES

BENDS AND TWISTS. Occasionally it is necessaryto employ considerable lengths of waveguide and, ifthe guide is unable to proceed in a straight line, someform of bended or twisted section must be used. In arectangular guide, bends may be made in the H -planeby making the radius of curvature lie in the same

plane as the magnetic lines of force, or in the E -planewhere the radius is in the same plane as the electriclines of force. They may be smooth, gradual bends,or right angles where the outer corner of the guide isbeveled at a 45° angle.

Smooth bends in rectangular waveguides are theo-retically perfect since the reflections caused by themare very small. Actually, however, it is difficult tomake a bend in such a way that the guide retains itsproper width to avoid discontinuities. It is possible,when great care is taken, to have a reflection lessthan that corresponding to a standing wave ratio of1.05 of power if the radius of the bend is equal to Xgor more. Likewise, a waveguide may safely be twistedin order to rotate the electric field through 90° pro-vided that the guide is not deformed in the process.The length of the twist should also be equal to Xgat a minimum.

Bends in circular waveguides are more likely tocause trouble since the polarization is not defined bythe shape of the guide and the wave is made ellipticalin going around a bend. This effect may be compen-sated in any given system by squeezing the roundguide in such a way as to remove the ellipticity, orby arranging an even number of bends that canceleach other. Flexible guide may also be used, althoughthe attenuation is somewhat higher than in a solidguide, and some reflection will occur.

2 a

EXCITINGLOOP

WAVEGUIDE BELOWCUTOFF

1

PICK UP LOOP

TE MODE

RECTANGULAR GUIDE

RECTANGULAR GUIDE

- MOVABLE PICK UP LOOP

I

WAVEGUIDE BELOW CUTOFF

PICKUP PROBE

EXCITING LOOP

WAVEGUIDE BELOW CUTOFF

MOVABLE PICKUP LOOP

Figure 6-1 1 . Cutoff Attenuators

63

CHAPTER 6

TRANSMISSION LINES

If it becomes necessary to bend a section of rigidcoaxial line, the same care should be taken in orderto prevent any discontinuities. Here the problembecomes more severe, since the inner conductor mustat all times be evenly spaced from the outer conductorand the radius of the bend should, therefore, be largeenough to allow the spacing to remain constant.

For most purposes, custom-made bends and twistsare available for either waveguides or rigid coaxiallines, and should be used in preference to constructingthem from straight sections.

WAVEGUIDE JUNCTIONS. The losses and reflec-tions from a junction between two sections of wave -guide are negligible if care is taken to align the sec-tions for good electrical contact. A simple joint maybe constructed with the use of flat flanges soldered onthe ends of the waveguide and bolted together asshown in figure 6-12A. Such a joint can be mademore accurate than the average soldered joint if theflange surfaces are clean and if they contact uni-formly. However, since clean, flat, parallel surfacesare hard to achieve and maintain, the more compli-cated choke -flange joint as illustrated in figure 6-12Bmay be used instead.

The L-shaped cavity may be considered a shortedhalf -wavelength transmission line which effectivelypasses the conduction current developed in the wallsof the guide. Gap "A" in figure 6-12B is spaced A Xfrom the shorted end of the L, and therefore thevoltage across the gap is zero while the current isequal to the conduction current in the guide walls.Point "B" occurs at a I/4X point where the currentis zero, and thus the contact at B need not be perfect.In fact, for some applications, there is no contact atall at point B.

PRESSURIZING. Transmission line losses causedby moisture or dirt entering a waveguide or coaxial

C

( A ) FLANGE -TO- FLANGE JOINT

(B) CHOKE -FLANGE JOINT

Figure 6-12. Waveguide Joints

line can be minimized by pressurizing the line.Pressurizing also helps prevent component break-down at high -altitudes caused by corona discharge.

Usually the complete r -f line from the transmitterto the antenna is pressurized with dried air or nitro-gen, the various joints being sealed with rubbergaskets. On some systems, even the driven antennais sealed, in the case of a dipole, by means of a plasticcup which surrounds the dipole. If the line is a wave -guide, the pressurized portion can be isolated bymeans of a thin sheet of mica mounted between apressurized choke and flange joint. If the line iscoaxial, a bead may be used as a pressure seal,although it is better to make the seal in a standardcoupler. Such couplers are quite numerous and infor-mation relating to them is best found in the manu-facturer's data.

In general, the installation of a transmission linesystem depends upon the r -f equipment being usedwith it, and the location of each unit. In such cases,the transmission line network is usually "tailor-made" to the rest of the equipment with completeinstructions for installation and maintenance.

64

CHAPTER 7

ANTENNAS

I II .% I' 1' E

INTRODUCTION

The basic principles of radio -relay antennas do notdiffer from those of any other antenna. As in anordinary resonant circuit, changes in frequency causechanges in the current and voltage, which, in thecase of an antenna, affect its gain, bandwidth, imped-ance, and radiation pattern. These four factors canbe considered of practical importance, rather than oftheoretical interest. A lack of knowledge of any ofthese factors may lead to unsatisfactory results whenit is desired to choose an antenna for a specificapplication. In the following chapter these factorsare considered with regard to radio -relay antennas,which must meet certain desirable characteristics ifthey are to be used successfully.

When developing the subject of antenna charac-teristics, another important thing to remember is thetheory of reciprocity. In free space, the radiationpatterns of a transmitting antenna and a receivingantenna with the same physical characteristics areidentical. Therefore transmitting and receivingantennas may always be interchanged, this fact beingcalled the law of reciprocity. For example, if twoantennas are situated at a distance of several wave-lengths apart, a current equal in both phase andamplitude will be received, no matter which antennais used for transmitting. In the balance of thischapter, when the characteristics of an antenna arediscussed, such characteristics will apply to bothtransmitting and receiving antennas, unless other-wise specified.

BASIC ANTENNA PRINCIPLES

ANTENNAS AS RESONANT CIRCUITS. A re-

ANTENNAS

ceiving antenna intercepts a portion of the directedwavefront radiated from a transmitting antenna.This wave front creates a field around the receivingantenna which induces a voltage in the conductorsforming the antenna. As the changing electromag-netic waves go through a cycle, the induced voltageattempts to follow these changes, and, in so doing,reradiates a small portion of the intercepted energy.

Because of the current and voltage distributionswhich exist on an antenna, it will be found that at acertain frequency, the inductive and capacitive com-ponents will cancel, leaving only an effective resist-ance. The lowest frequency at which this occurs isthe fundamental resonant frequency of the antenna, orwhen the antenna is a half -wavelength long. This willalso occur at frequencies which are harmonicallyrelated.

Depending upon the point where a transmissionline is connected to an antenna, an antenna may beconsidered as a series or parallel circuit. These twoconditions are illustrated in figure 7-1. For a dipoleantenna which has a transmission line connected toits center, the current is a maximum and the voltageis a minimum at fundamental resonance or the lowestresonant frequency. The ratio of voltage over currentis then low, which means the impedance is also low,since

Z = V- ohms

where

Z = Impedance in ohmsV = Induced E.M.F. in voltsI = Induced current in amperes.

(7-1)

65

CHAPTER 7

ANTENNAS

X/2_

HIGH IMPEDANCE

A/2

LOW IMPEDANCE

Figure 7-1. Antenna Feed Systems

This low impedance can be considered the result ofresonating a series tuned circuit. For an antennawhich has a transmission line connected at a half -wavelength point (as measured from one end), or isend fed, the voltage at this point is a maximum andthe current is a minimum. The ratio of voltage overcurrent is then high, resulting in a high impedancevalue. An end fed antenha may therefore be thoughtof as a parallel tuned circuit which has a highresistance at resonance.

When an antenna is required to receive or transmitsignals over a wide frequency range, the conditionsillustrated in figure 7-2 are present. The voltage andcurrent distributions along the antenna dependmainly upon the length of the antenna with respectto frequency. At the fundamental and odd harmonicfrequencies, the impedance is low, but at the evenharmonic frequencies, the center impedance is high.Thus, it will be seen that an antenna required toreceive a wide range of frequencies will presentimpedances which vary in a periodic fashion like adamped wave train, or alternately present low orhigh impedances at various frequencies.

At some resonant frequency, the antenna willpresent its lowest impedance. Under this condition,the inductive reactance and capacitive reactance ofthe circuit cancel, leaving the circuit series resonant.Conversely, when the antenna passes through a valueof maximum impedance, the reactive componentshave cancelled, providing parallel resonance. Thiscondition is sometimes called anti -resonance. Figure7-3 shows the variations in the inductive and capaci-tive reactances of a practical dipole antenna. As thefrequency increases progressively, there are cycles ofseries resonant and parallel resonant conditions con-stituting a series of impedance changes from low tohigh. The effect is a gradual variation of impedancemade up of low to high impedance changes andgradually approaching 300 ohms. This effect is illus-trated in figure 7-4.

Unless special means are employed to reduce these

impedance excursions, an antenna can be matchedto a 72 -ohm transmission line only at its fundamentaland approximately at the odd harmonics. The varia-tion in impedance with frequency for a half -wavedipole is shown in figure 7-5. It will be noted thatthe minimum value is about 75 ohms and the maxi-mum value about 750 ohms.

ANTENNA BANDWIDTH. One of the inherentdifficulties in designing a satisfactory radio -relayantenna arises from the bandwidths generally re-quired. Such bandwidths extend upward to 40 me ormore when it becomes necessary to transmit anextreme number of messages simultaneously. Ingeneral, an antenna can be broadbanded by changingits shape in some manner to obtain the desired char-acteristics. Probably the easiest method is to increasethe diameter of the antenna conductors, thus pre-venting the impedance of the antenna from changingrapidly with frequency. Another method which canbe used to broadband an antenna is to use a trans-mission line with a higher impedance than that ofthe antenna at fundamental resonance. By using sucha line, the voltage developed at resonance is de-creased, but the voltage developed at other fre-quencies is increased. Hence the response curve ofthe antenna is effectively flattened, with resultingbroadband antenna characteristics.

Generally, the bandwidth of an antenna systemcan be arbitrarily specified by the frequency limitsf1 and f2 at which the voltage standing wave ratio(VSWR) on the transmission line exceeds an accept-able value. (See Chapter VI.) At times the frequencybandwidth is also specified as the ratio of f2 - f1 to fo,or in terms of per cent as given by the formula

where

I

ILOW Z

DIPOLE

f2 -B% = fofx 100

FUNDAMENTALFREQUENCY

E I

I LOW Z

DIPOLE

3RD HARMONIC

(7-2)

E I

W.," \---' \--1 1 i I

HIGH Z --'

DIPOLE

2ND HARMONIC

E 1

HIGH

DIPOLE

4TH HARMONIC

Figure 7-2. Dipole Current and Voltage Distribution

66

CHAPTER 7

ANTENNAS

B% = Bandwidth as a percentage of fofo = The center design frequency

RADIATING EFFICIENCY. For some applica-tions, it is necessary to obtain a high gain -to -sizeratio from an antenna of a given physical size, or toobtain a given gain with an antenna that is as smallas possible. Such attempts invariably reduce thebandwidth of the antenna and also its radiatingefficiency. Assuming no losses, the power radiatedfrom an antenna would be equal to the power deliv-ered to the antenna. Therefore, such power must beequal to the square of the rms current flowing on theantenna times a resistance, called the radiationresistance,

P - A X R

where

P = Radiated power in wattsI

R = The radiation resistance

Rms current

(7-3)

In actual practice, all the power that is deliveredto a transmitting antenna is not radiated, but isdissipated in the form of heat because of a certainloss resistance. Thus, the ratio of the power radiatedto the total power delivered to an antenna at a givenfrequency is defined as the radiating efficiency. Thetotal terminal resistance (I/ t) of an antenna maythen be considered as

Rt = R RL (7-4)where

R = The radiation resistanceRL = The equivalent terminal loss resistance.

Therefore, the radiating efficiency of an antenna maybe expressed by the formula

0z

Uz

500

400300

200100

0

-100-200-300-400

01 ILE IN DUCTI VE

ice;% /07,DI PDLE

11;

CAPACIT VE

FREQUENCY IN MEGACYCLES

Figure 7-3. Dipole Reactance Variation

300

70

FREQUENCY INCREASING

Figure 7-4. Dipole Impedance Excursions

Radiating Efficiency % = R RLX 100 (7-5)

Any antenna whose radiation resistance is large, ascompared to any loss resistance, has a high radiatingefficiency. Loss resistance may occur in the antennaconductors, supporting insulators, masts, or guywires, with faulty antenna installation being a greatcontributor to such losses.

ANTENNA DIMENSIONS. As mentioned previ-ously, an antenna is resonant when its length is ahalf -wavelength of the frequency used. This length,however, is not exactly a physical half -wavelengthsuch as that which would be developed in free space;instead, it will be somewhat shorter.

In free space, electromagnetic waves travel at aconstant velocity of 186,000 miles per second (3 X 108meters/sec.). The r -f energy on an antenna, however,moves at a velocity considerably less than that ofthe radiated energy in free space because the metalcomprising the antenna has a permeability greaterthan that of free space. Since the velocity of electro-magnetic waves in any medium is determined by theformula

1v = meters per second (7-6)

where

K = The dielectric constant of the material throughwhich the wave is being propagated (Mksunits).

= The permeability of the material (Mks units)

67

CHAPTER 7

ANTENNAS

It will be seen that as the dielectric constant (K)increases, the velocity of the wave decreases.

Because of the difference in velocity between thewave in free space and the wave on an antenna, thephysical length of an antenna no longer correspondsto its electrical length. In other words, such anantenna is a half -wavelength electrically, but some-what shorter than this physically. This fact is shownin the formula for the velocity of electromagneticwaves as expressed in terms of wavelength and fre-quency, which is

= f X (7-7)

where, (v) is the velocity, (f) is the frequency, and (X)is the wavelength. Since the frequency of the waveon a n antenna remains constant, a decrease in thevelocity also results in a decrease in the wavelength.

TI re actual value of the permeability of an antenna,and thus its physical length, depends upon severalfactors. As the circumferences of an antenna's con-ductors increase, the permeability increases and thewave velocity is decreased. Such changes in wavevelocity on an antenna are commonly called endeffect because the ends of the antenna are made closertogether physically than they are electrically. Endeffect is counteracted by making the actual lengthof the antenna shorter than the free -space wave-length, as expressed by the formula

L = K (492/f) (7-8)

where (L) is the required length in feet for a half -wave dipole, and (f) is the frequency in megacycles.The factor (K) takes into consideration the end effectjust mentioned, and may be found in figure 7-6 forvarious antenna conductor circumferences. For thinantenna conductors whose circumference is equal to0.001X or less, an average value of 0.95 may be usedfor K.

ANTENNA GAIN. The gain of an antenna is anindication of the antenna's concentration of radiated

1000

900800700

600

500 FUNDAM400300

200

100

0

2ND HARMONIC

II Ea ENNI LLf f

-1-

4THI

4TH HA8MONIC -

9

NTAL

Anrtv,,,AAA,A

IIPA rAn7fAri;'KKFr rAZ '

MIS3RD

HARMONIC

FREQUENCY IN MEGACYCLES

Figure 7-5. Dipole Impedance Variation

.01

005

.002

0010 .2 .4 .6 .8 10

( K )WAVE VELOCITY

FREE -SPACE VELOCITY

Figure 7-6. End Effect Factor

power in a given direction. It is the ratio of the powerradiated in a given direction to the power radiatedin the same direction by a standard antenna. Asmentioned in Chapter II, an isotropic radiator is thebasic, theoretical form of antenna, and is commonlyused as a relative standard for all other antennas.However, a half -wave dipole is quite often used as astandard antenna instead of an isotropic radiator,and for this reason an antenna gain figure shouldalways be followed with a note as to its referenceantenna.

Since the effective power radiated from a trans-mitting antenna, or the available power at the outputterminals of a receiving antenna are both dependentupon the antenna's effective area, the power gain ofan antenna also depends upon the antenna's effectivearea. The effective area of an isotropic radiator isgiven by the formula

A =e 4 r

X2

(7-9)

where

A, = The antenna's effective area expressed in thesame units as X.

X = Operating wavelength.

In this case, the gain of an isotropic antenna is takenas unity, and the relation between the effective area

68

CHAPTER 7

ANTENNAS

O

and the power gain of any antenna becomes

A e = 47rG X'

(7-10)

where

G = The power -gain of the antenna over an iso-tropic antenna.

If two identical antennas, one a transmitting and theother a receiving antenna, are placed a distance (D)apart (where D > 2A2/X), and A is the maximumaperture dimension, with their axes coincident, thegain of each antenna may be determined by therelation

4 71- D 1frX Pt

(7-11)

whereG = The power gain of each antenna over an

isotropic antenna.

Pr = Received power in watts at the antennaterminals.

P, = Transmitter power in watts.X = Wavelength in meters.

To find the antenna gain in decibels, the followingformula may be used:

Gdb = 10 logio G pou er-ga in (7-12)

If the gains of the two antennas are slightly differ-ent, then the value of G obtained with formula (7-11)satisfies the relations

G = X G2 (7-13)

where G, and G2 are the gains of the two antennas.When G is known, it is possible to determine Gi byplacing each of the two antennas on a receivingmount, and measuring the power received from athird transmitting antenna. If the readings are P,and P2, then

G, = GN/131/P2, and G2 = G A/P2/PI (7-14)

ANTENNA DIRECTIVITY. An important factorto be considered when selecting an antenna is itsdirectivity or lobe pattern, which actually determinesantenna gain. Because an antenna may radiate inany direction, it would theoretically be necessary toshow a three dimensional radiation pattern to obtaina true picture of its directivity. However, it is gen-erally sufficient to show various sections of the lobepattern, which will give the necessary information.

Figure 7-7 illustrates the doughnut -shaped patternof an ordinary half -wave dipole, representing the

radiated energy in all directions. For the horizontaldipole, this radiation is minimum in a directionextending from the ends of the dipoles; while in adirection broadside from the antenna, the radiationis maximum. Usually, an antenna directivity patternis shown for vertical and horizontal planes, such asillustrated in figure 7-8. From the figure it can be seenthat a half -wave dipole antenna has a non -direc-tional pattern vertically, which means that it willrespond equally well to any signal or noise arrivingat any vertical angle. However, such a dipole doeshave some directivity in the horizontal plane or"looking down" upon the dipole. It is bidirectionalin a direction at right angles to the antenna and,therefore, does not discriminate against signals arriv-ing from the rear. For this reason, all antennas usedin radio -relay applications are "backed -up" by areflector which concentrates the antenna's directivitypattern to one direction only.

Since a half -wave dipole antenna is bidirectional inthe horizontal plane, while an isotropic antennaradiates energy equally well in all directions, thedipole has a directive gain over an isotropic antenna.Directive gain is simply another way of expressingantenna power gain, and both terms may be usedinterchangeably. For example, because a dipoleantenna is more directive than an isotropic radiator,the dipole will radiate more power in some directionsand thus a power gain will be obtained. Numerically,the power gain of a half -wave dipole is equal to 1.64,or approximately 2.2 db over an isotropic radiatorwith a gain of unity.

DIRECTIVITY PATTERNS. Directivity consid-eration is very important in radio -relay work, andfor most purposes horizontal directivity patterns aresufficient to give the desired information. In orderto plot directivity characteristics, the antenna isplaced on a rotatable stand and a low power sourceof r -f energy is placed some distance away. A receiver,which is designed especially for these measurements,is connected to the antenna and used to determinethe voltage developed at the antenna terminals. Incertain laboratory setups, the directivity or lobe

Figure 7-7. Dipole Field Pattern

69

CHAPTER 7

ANTENWAS

DI POLEHORIZONTALDIRECTIVITY

DI POLE.VERTICAL

DIRECTIVITY

Figure 7-8. Horizontal and Vertical Directivity Pattern

patterns may be drawn by automatic curve tracingapparatus.

A special type of graph paper is used to plotantenna characteristics. As shown in figure 7-9, thecenter of the graph represents the location of theantenna, and around this point are drawn a series ofconcentric circles. These circles represent the mag-nitude of the voltage developed at the antenna ter-minals. Straight lines are also drawn, passing throughthe center of the graph, representing the orientationangle of the antenna. The point where the antennalobe pattern intersects one of the lines and a con-centric circle indicates the voltage developed at thatparticular orientation angle.

The example in figure 7-9 indicates that at 27degrees the voltage developed by the antenna is 0.70of the maximum voltage. This 0.70 voltage representsone half of the total power radiated in the forwarddirection, since

E volts per meter = VP Zo watts per meter' (7-15)

The antenna beam width given by the example is,therefore, twice 27 degrees or 54 degrees. It is con-ventional to place the 0° point at the top of the graphpaper, in line with the eye of the observer. Graphpaper, as actually used, contains a greater numberof straight lines and concentric circles, so that agreater accuracy in plotting can be obtained, and theexample of figure 7-9 has been simplified to demon-strate the principle involved.

FRONT -TO -BACK RATIO. In any radio relayrepeater, it is important that the signal transmittedis not picked up by its own receiving antenna. Whilethis trouble can be minimized by several methods,its main cause is the energy radiated from the rearof the transmitting antenna. Figure 7-9 illustratesthat, besides the main forward lobe, there is a secondsmaller lobe extending from the back of the antenna.The ratio of the maximum voltage or power effectivetowards the front to the maximum voltage or powereffective towards the back is called the front -to -back

ratio, and is usually expressed in db. Likewise, for areceiving antenna, the front -to -back ratio is a factorused to indicate its sensitivity to signals received atthe rear with respect to signals received at the front.This is determined by measuring the voltage ratioat these two positions. For example, if an antennadevelops 1 volt at 0°, and 0.1 volt at 180°, the front-to -back ratio would be 1/0.1 or 10, indicating thatthe antenna is 10 times more sensitive to signalsarriving in the desired direction. Expressed as aformula, the front -to -back ratio becomes

Front -to -back Ratio (db) =

20 logic,E volts per meter, front lobeE volts per meter, back lobe

Front -to -back Ratio (db) =

10 log, P watts per meter', front lobe(7-17)P watts per meter', back lobe

The less intense the back lobe, the larger the front -to -

back ratio, and, consequently, the less interaction orfeed back will be developed between transmittingand receiving antennas of the same repeater. Front-

to -back ratios approaching 40 db are quite possiblewith parabolic reflectors, while for lens and hornantennas, the front -to -back ratios can be as high as50 to 60 db.

(7-16)

EFFECTIVE RADIATED POWER. An importantdirectivity characteristic for transmitting antennasis the effective radiated power (ERP), or the powerradiated in a given direction due to antenna gain.Thus, ERP is simply an indication of a transmittingantenna's gain in terms of watts, and may be foundby the formula

ERP = G, X P, Watts (7-18)

1.0 MAXIMUM VOLTAGE

0. 27* - 0.707 VOLTAGE ORHALF POWER POINT

3°.083/3°. OCCURS AT 27BEAM WIDTH

01-0704, 2 x 27 54*

itA6 A 0.33 4,0.50 C)

ita1tall90° 90*

RESPONSE

SECTORIN THIS

*WOW/,00MINIMUM

\ 120%1 htk& IJA 12.0I 7 ft. #

150*

180°- 150'

DIPOLE WITH REFLECTOR

Figure 7-9. Antenna Radiation Pattern

70

where

Gt = Power gain of the transmitting antenna overa reference source.

Pt = Power in watts at the terminals of the trans-mitting antenna.

If transmission line loss is neglected, the actualtransmitter output power may be substituted. Forexample, a transmitting antenna with an input of 10watts and a power gain of 5, will produce the samefield strength in its direction of maximum radiation,as an isotropic antenna with an input of 50 watts.

PARASITIC ELEMENTS. It was mentioned pre-viously that an antenna collects energy in its elementsand reradiates a portion of this energy. This willoccur independently of the type of transmission lineused, and whether or not it is connected to theantenna. If two antennas are placed in close physicalproximity, the reradiated energy will produce aninteraction between the antenna elements. Therefore,a parasitic element may be regarded as a radiatingelement, not coupled directly to the transmission lineof the antenna but which materially affects theantenna's directivity pattern. Likewise, antenna ele-ments which have transmission line connections areknown as driven elements.

The magnitude of the current in a parasitic elementand its phase relation to the current in the drivenelement depends upon the tuning of the parasiticelement. Such tuning is usually accomplished byadjusting the length (L) of the parasitic element.Depending upon the tuning of the parasitic element,it can either act as a reflector sending the maximumradiation in the = 180°- direction as shown in figure7-10, or as a director sending the maximum radiationin the ck = 0° direction. A reflector will generally bemade at least 5% longer than the driven element,and a director approximately 5% less.

The following results can usually be expected whena reflector type of parasitic element is added to ahalf -wave dipole. The impedance of the combinationis decreased below that of a simple dipole from 30 to70% depending upon the length and spacing of thereflector. The directivity pattern is made essentiallyunidirectional at the resonant frequency, while theoverall bandwidth is generally decreased. The gainof the array, however, is greater and as much as 4 dbmay be added by careful design.

Basically, the increased gain results as follows:the reflector element intercepts r -f energy the sameas the driven element of the antenna. This energyis reradiated from the reflector and is intercepted bythe driven element, thus adding to the received

12

L

- DRIVENELEMENT

PARASITICELEMENT

CHAPTER 7

ANTENNAS

4, 0

# 180Figure 7-10. Antenna Array with One Parasitic Element

signal. Likewise, some of the energy reradiated fromthe driven element, reflected by the parasitic element,is intercepted again by the driven element. Withfixed antenna dimensions, the action of the parasiticelement is effective only over a portion of the band-width encountered, and as the frequency increases,the reflector becomes decoupled from the drivenelement.

YAGI ARRAYS. More than one parasitic elementmay be used with a driven element, although the netgain realized will be practical only at bandwidths upto approximately 10 me in the UHF band, for ex-ample. The impedance of such a combination is alsoreduced considerably as more and more parasiticelements are added. An antenna which consists oftwo or more parasitic elements is commonly called aYagi antenna or array. In this case, one of the para-sitic elements is placed behind the driven elementand is used as a reflector, while the other parasiticelements are placed in front of the driven memberand act as directors.

With antenna arrays, such as the Yagi, it isimportant that the antenna present a reasonableimpedance to the transmission line. A reasonableimpedance may be regarded as an impedance valuewhich approximates that of the transmission lineintended for use with the antenna. For example, ahalf -wave dipole with one reflector and several direc-tors may have an impedance as low, or lower than,25 ohms, due to the influence of the parasitic elements.

In order to provide an increase in impedance,folded dipoles such as illustrated in figure 7-11 maybe used. A standard folded dipole, with its upperand lower elements equal in diameter, has an imped-ance of nearly 300 ohms. When the upper elementof the folded dipole is several times larger in diameterthan the lower member, the impedance value becomesgreater than 300 ohms, the exact value dependingupon the ratio of the element diameters. If a verylarge initial impedance is required before the para-sitic elements are added, a three element folded dipolemay then be used, increasing the impedance valueto about 675 ohms.

71

CHAPTER 7

ANTENNAS

Z EQUAL TO 300.x1 Z GREATER THAN 30011

Z LESS THAN 30011. Z EQUAL TO 6751'L

Figure 7-1 1. Folded Dipole Impedances

RADIO RELAY ANTENNA TYPES

LINEAR ARRAYS. An antenna array may consistof a single driven antenna with one or more parasiticelements, or it may consist of combinations of drivenantennas, with or without parasitic elements. Of thelatter, the simplest array consists of two driven half -

wave dipoles which may be driven either in phase orin phase opposition. When the two elements aredriven in phase, the direction of maximum radiationis normal to the common plane of the two elements,or broadside. Therefore an antenna array, consistingof two or more elements driven in phase, is termeda broadside array, arid is the type most commonlyused for radio -relay applications at frequencies belowabout 300 mc.

Illustrated in figure 7-12 is a typical vertical -planepattern of a broadside array consisting of two verticalin -phase half -wavelength elements spaced one-halfwavelength apart. For sake of comparison, the pat-tern of a single half -wave dipole with the same powerinput is shown by the dotted line. When the spacingbetween the elements of a two -element broadsidearray is X/2, the gain realized is 3.9 db over a half -wave dipole, or 6.1 db over an isotropic antenna. Inorder to use such an antenna for radio -relay applica-tions, a plane sheet reflector is commonly used todirect the radiated energy in a single direction. Atypical broadside antenna, consisting of four half -

wave dipoles operating in phase, is illustrated in

z

BROADSIDE ARRAY

HALF -WAVE REFERENCEANTENNA

NN ANTENNA ELEMENTS

Figure 7-12. Vertical Directivity of Broadside Array

figure 7-13. Such antennas may have gains from 12to 26 db over an isotropic antenna when operated inthe frequency range from 44 to 300 mc.

When an array consists of two or more half -wavedipoles driven in phase opposition, the direction ofmaximum radiation is perpendicular to, and in thesame plane as, the antenna elements. Such an arrayis commonly called an end fire array and, when thespacing between elements is equal to X/4 or less, thegain realized is at its highest value. For the casewhere only two driven elements are used, the maxi-mum gain approaches 6.1 db over an isotropic an-tenna. End -fire arrays are sometimes called flat -topbeam antennas since the array is commonly operatedwith both elements horizontal to the ground asillustrated in figure 7-14. Since end -fire arrays areessentially bidirectional, a reflector would have to beused to make them suitable for radio -relay applica-tions. However, the use of a reflector with such anarray would actually reduce the overall gain bychanging the phase characteristics of the drivenelements, since one would be nearer the reflector thanthe other. End -fire arrays, therefore, are seldom usedas radio -relay antennas because it is impossible toobtain a high gain in one direction only.

REFLECTOR ANTENNAS. In order to modify theradiation pattern of an antenna for radio -relay appli-cations, reflectors are generally used to increaseforward gain and eliminate any backward radiation.Various types of reflectors are illustrated in figure7-15, the most commonly used being the plate sheetreflector, the corner reflector, and the paraboloidreflector. Many other shapes are possible, dependingupon the directivity pattern desired and the space -weight considerations.

Essentially, a reflector intercepts radio energy andreradiates it in another direction in the same manneras a mirror reflects a light beam. However, just assome light is scattered by a mirror, some of the powerof the radio beam is scattered by the reflector. Theamount of scattered power depends upon the smooth-ness and type of material used in a reflector. Smooth-ness here may be defined as the ratio between thesize of the irregularities of the reflecting surface andthe wavelength of the incident energy. If the irregu-larities of the reflector are small in comparison to theoperating wavelength, then a good reflector isobtained. In actual practice, if the irregularities ofthe reflector are no greater than X/8, satisfactoryreflection will be obtained with only a small amountof scattering. Since most antenna reflectors areexposed to weather, a definite advantage is found inthe use of a screen, or grill, which will offer little

72

Figure 7-13. Four Element Broadside Array

resistance to wind but will still reflect energysatisfactorily.

Perhaps the simplest reflector, other than a thinparasitic element, consists of a flat sheet of metal, orwire mesh, such as illustrated in figure 7-15A. Thegain realized with such a reflector is generally limitedto about 9.2 db over an isotropic antenna when thespacing between the driven element and the reflectoris equal to 0.1X. A flat reflector does not appreciablychange the radiation pattern, but only converts thenormal bidirectional pattern into a larger unidirec-tional pattern by eliminating backward radiation.Therefore, a flat surface reflector only increases for-ward gain and does not "beam" radiation. The for-ward gain in field intensity as a function of thespacing (S) is presented in chart form under figure7-15A. Provided that losses are negligible, very small

CHAPTER 7

ANTENNAS

spacings can be effectively used, although at suchspacings the bandwidth is considerably narrowed.

By bending the sheet reflector into a cylindricalparabolic shape, higher directivity and gain willresult. A cylindrical parabolic reflector is illustratedin figure 7-15B, showing a half -wave dipole locatedat the focus of the parabolic curve. If the distanceacross the aperture is several wavelengths, most ofthe directivity will be in the horizontal plane.

Even though high gains may be obtained withcylindrical parabolic reflector systems, they offer noadvantages over a corner reflector, such as thatillustrated in figure 7-15C. In practical form, a cornerreflector consists of two flat reflecting sheets inter-secting at right angles, thus forming a square corner.Corner angles greater or less than 90° can be used,although at angles much less than 60° no net advan-

73

CHAPTER 7

ANTENNAS

TOTRANSMITTER

Figure 7-14. Endfire "Flat Top" Array

tage is realized. If a dipole radiator is located withinthe plane bisecting the corner angle and parallel tothe intersection of the two sheets, gain figures from10 to 15 db over an isotropic source can be obtained.Curves of gain versus dipole -to -corner spacing forcorner reflectors of 90° and 60° are presented infigure 7-15C, assuming no losses. As with the planesheet reflector, small spacings are objectionable be-cause of bandwidth limitations, but on the other

(A)PLANE

SHEET REFLECTOR

00 0.1 02SPACING S

FLAT SHEETEREFLECTOR

ST1L HALF- WAVEANTENNA

03 04 05 0.6IN WAVELENGTHS

-S--4

07

(D) PARABOLOID

hand, too large a spacing results in low gain.Since the corner reflector and the cylindrical para-

bolic reflector concentrates energy in one plane only,they are not often used as radio -relay antennas,although they are occasionally used, along with theplane sheet reflector, as passive reflectors. For reliableradio -relay operation, an antenna which has highdirectivity in both horizontal and vertical planesmust be used in order to transfer a maximum amountof energy from one relay to another. The mostcommon reflector type used to accomplish this is theparaboloidal, or parabolic reflector as illustrated infigure 7-15D.

The surface generated by the revolution of a parabola around its axis is called a paraboloid or parabolaof revolution. If a half -wave dipole is placed eithervertically or horizontally at the focus of such areflector, considerable "beaming" action will takeplace. If the aperture of the parabolic reflector is verylarge in terms of X, a spherical wave striking thereflector will be converted to a plane wave uponreflection. Unfortunately, a half -wave dipole does notprovide an isotropic, spherical source of illumination,and it is impossible to provide uniform illumination

(B)CYLINDRICAL

PARABOLIC REFLECTOR

REFLECTOR

Figure 7-15. Reflector Types

-wza3Zt

O

12

10

(C) CORNER REFLECTOR

16

6

0°

6001 0.2 03 0.4 0.5 06 07

ANTENNA -TO-CORNER SPACINGIN WAVELENGTHS

74

of the "dish". The resultant beam, therefore, iselliptical in shape and somewhat broader than mightbe expected.

For a given reflector diameter, the characteristicsof the reflected wave are best when a shallow dishis employed, that is, a parabola with a somewhat longfocal length. Compared to a shorter focal length,however, the amount of incident illumination is thenreduced. If the distance (S) between the vertex andthe focus of the parabolic reflector (focal length) isan even number of quarter wavelengths, the directand reflected radiation, in an axial direction from thesource, will tend to be in phase opposition and there-fore cancel the central region of the reflected wave.However, if the focal length is held within the limitsgiven by the formula

S = 11: (7-19)

where n = 1,3,5,---, the direct radiation in an axialdirection from the source will be in the same phaseand tend to reinforce the central region of thereflected wave.

When the focal length of a parabolic reflector can-not be prescribed, direct radiation from the drivenelement can be minimized and reflector illuminationincreased by using a parasitic or small flat sheetreflector close to the dipole. This secondary reflectoris located so as to concentrate most of the radiationfrom the dipole into the dish.

The major factor contributing to the gain, orbeaming action, of a parabolic reflector is the totalarea of the reflecting surface. For a uniformly illumi-nated dish, the reflected beam angle is proportionalto the wavelength and inversely proportional to thelinear dimension of the aperture. The beam widthbetween first null points for large circular aperturesis given by the formula

Beam width = 140 degreesDO (7-20)

where Dx = the diameter of the aperture in wave-lengths. The beam width between half -power pointsfor a large circular aperture may be found by theformula

Beam width (P/2) = 58A degrees (7-21)D

The beam width given by formula (7-21) is actuallyan "equivalent beam angle" and is the cross sectionof the cone where the radiated energy is assumed tobe concentrated. Actually, the beam of a directiveparabolic reflector starts out in a cylindrical form,as illustrated in figure 7-16, to a certain point and

0

CHAPTER 7

ANTENNAS

CYLINDRICAL REGIONOR FRESNEL REGION

EQUIVALENT BEAM WIDTH

CONICAL REGIONOR

FRAUNHOFER REGION

Figure 7-16. Parabolic Reflector Beaming Action

then diverges progressively into a conical beam. Sucha beam has a cross section equal to the equivalentbeam angle with its apex located at the center ofthe reflector.

The cylindrical portion of the beam is called thenear field or Fresnel region and the conical part iscalled the far field or the Fraunhofer region. Thecylindrical region has a substantially constant fieldand a parallel beam, so that any reflector with suffi-cient cross section that is placed in that region willreflect the radiated energy with very little loss. Thecylindrical region's maximum distance is proportionalto the square of the aperture diameterproportional to the wavelength as given by theequation

Dx2Fresnel Region Length =2

(7-22)X

For example, at 2,000 mc, using a ten foot parabolicreflector, the Fresnel region is approximately 100 feetlong, and at 8,000 mc with a five foot parabola, thelength would be the same. However, a ten footparabola at 5,000 mc would have a Fresnel region of250 feet in length.

This definite Fresnel region is occasionally used toadvantage by relay systems employing passive reflec-tors. In this type of equipment the transmitter andantenna can be located at ground level and theantenna signal beamed at a passive reflector mountedabove the equipment. If the distance between theantenna and the passive reflector does not exceed thecylindrical region length, the passive reflector willthen radiate the energy to a receiving source with aminimum of loss when reflected.

The gain of a large parabolic reflector, where theaperture is uniformly illuminated, may be found bythe formula

Gain (db) = 10 login 6Dx2 (7-23)

where Dx = the diameter of the aperture in wave-lengths. For example, a parabolic antenna whose

75

CHAPTER 7

ANTENNAS

0 0 0El CI

FSIFW

(A) ROUND (B) FLATBARS STRIPS

EDGEWISE

(C) FLAT STRIPSFL AT WISE

THE AXES OF THESE GRATINGS LIE IN THE PLANE OFTHE REFLECTOR

GRATINGS FOR PASSIVE REFLECTORS

Figure 7-17. Gratings for Passive Reflectors

diameter is 15 wavelengths and is perfectly illumi-nated has a gain of nearly 32 db with respect to anisotropic antenna. Since, in actual practice, it isimpossible to achieve uniform illumination, a moreaccurate answer will be obtained when calculating

beam widths and gains by using an equivalent re-flector diameter equal, to 80% of the actual diameter.

Parabolic antennas of the type just described aresuitable for use in the frequency range from 250 toabove 13,000 mc with excellent results in all cases.At frequencies above about 3,000 mc, however, itbecomes impractical to use half -wave dipole antennasas the driven elements, and some other means ofdriving the parabola must be used. At these higherfrequencies, the horn type of antenna will giveexcellent results as the driven element, especiallywhen the horn is fed by means of a waveguidetransmission line.

REFLECTOR CONSTRUCTION. There is no rulethat states that reflectors mast be made of any par-ticular pattern of openings. If wind resistance wereno problem, the reflector could be made of sheetmetal. Since winds will cause the reflector to move,unless rigidly mounted, reflectors are made of gratings

5 -(CENTER TO CENTER SPACING IN WAVELENGTHS)yX

.05 .10 .15 .20 .25 .30 .35 .40 45

AT A= 0Wa100

- TT

_I

-1:-w

S 1_ :::; v.-#:

-.0175A-A=

4-0100 (V-)

(/)2TZ'

ct

co

Cf-Ct

(ki

0

.1.

IN

to43

, _n

O

-........, IN .1.11.1,NMI

Figure 7-18. Reflector Power Loss

.500

UJ

00fr) Z-

_I I-<01-1-1

0 LI-Z

o I0(i)

M(.1) D2 0< Cr

1-

00

U)

0

0

76

CHAPTER 7

ANTENNAS

or screens that give little wind resistance, but stillreflect almost all of the incident wave. The reflectormay be a rigid or reinforced woven metal screen, orit may be a piece of reinforced perforated sheet metal.

The openings in either the punched sheet or screenare limited in size by the frequency of the incidentwave. If the holes are square, as found in a screen,the edge length of the holes should be less than X/8.Where a sheet is punched with round holes, thediameter of the holes should be less than X/8. Thepower transmitted through the reflector can be keptwithin reasonable limits if the openings are keptsmall. For example, a copper screen woven of #17B&S wire with openings A" square will reflect about95.5% of the incident power at a wavelength of 9 cm.

Where greater rigidity for the reflector is needed,grates constructed of round, square, or flat bars, maybe used instead of screen. The flat bars may bemounted edgewise, or flatwise (figure 7-17). Whenflat bars, or strips, are used, they are generallymounted edgewise, since better reflection with lesswind resistance is obtained. The width of the stripis not of prime importance, except that, in general,the wider the strip, the better the reflection. Betterreflection may also be obtained by using thickerstrips. The spacing of the bars is of the greatestimportance. Spacing of the gratings should be lessthan X(1 -I- sin 0) center to center, where 0 is theangle of incident wave with the normal to the reflec-tor. It is a good rule to limit the opening betweenthe gratings to X/8.

In constructing gratings of flat strips, the thicknessmay be any desired value. Figure 7-18 shows valuesfor transmitted power (power lost through the re-flector, instead of being reflected from it) for differentopenings between the strips. Lost power is alsodetermined for different values of thickness. Thisdiagram may be used in determining the thicknessof the strips in designing a reflector.

Any grating, regardless of shape, is critical to pol-arization. In order that a minimum of power be lostthrough the reflector, the electric field vector (Evector) of the incident wave must be in the planedetermined by the incident wave and one of the barsof the grating. In other words, if the wave is hori-zontally polarized, the bars must be installed horizon-tally. Figure 7-19 illustrates a reflector antennadesigned for 300 me and constructed with a wiregrating.

HORN ANTENNAS. Several types of horn antennasare illustrated in figure 7-20; those on the left arerectangular horns energized from rectangular waveguides, while those on the right are circular types

Figure 7-19. Low Frequency Reflector Antenna

energized from circular wave guides. The transitionregion between the wave guide and the aperture issometimes given an exponential taper as illustratedin order to minimize reflections of the guided wave.However, horns with straight flares are more com-monly used since they are easier to manufacture.

The radiation pattern of a horn antenna is largelydetermined by the horn aperture and the field dis-tributions within the aperture. For a given aperture,the directivity is maximum with a uniform field dis-tribution while variations in the field across theaperture decrease the directivity. To obtain an aper-ture distribution as uniform as possible, a long hornwith a small flare angle is required, but for conven-ience the horn should be as short as possible.

The beam width and gain characteristics for cir-cular horns are the same as for parabolic reflectorsand formulas 7-20 through 7-23 may be used for such

77

CHAPTER 7

ANTENNAS

HORNWAVEGUIDE

URE

7.444111,11FrTHROAT

( A) EXPONENTIALLYTAPERED PYRAMIDAL

( B) PYRAMIDAL

(C) EXPONENTIALLYTAPERED

( D) CONICAL

Figure 7-20. Horn Types

calculations. For rectangular horns of optimumlength, the beam width between the first nulls is givenby the following formula

or

Beam width = 115AtoX172 degrees (7-24)E

Beam width (P/2) 56AtoEx67degrees

(Between half -power points)

Likewise, the gain of a rectangular horn, uniformlyilluminated is given by the formula

Gain (db) = 10 logo 4.5 AE x AHX (7-25)

where

AEX = E aperture in free -space wavelengths

AHX = H aperture in free -space wavelengths

when a horn antenna is used to excite a parabolicreflector, it is usually in the form illustrated in figure7-21, where the waveguide feeding the horn also actsas a support for the horn. When greater gains andhigher front -to -back ratios are desired at frequencies

FOCALLENGTH

HORN ANTENNA

_ - PARABOLICREFLECTOR

Figure 7-21. Horn Fed Parabola

above 3,000 mc. horn antennas are often used in con-junction with lens antennas which are situated in theaperture of the horn.

LENS ANTENNAS. A lens antenna is a structuretransparent to radio waves and with a relative dielec-tric constant different from unity, constructed in sucha manner as to produce a desired radiation pattern.Such structures may employ dielectric lenses madeof lucite or polystyrene, artificial dielectric lensesconstructed of flat metallic strips, or metal platelenses.

Dielectric lenses and artificial dielectric lenses in-crease the electrical path length of a spherical wavefront, thus retarding the incident spherical wave asillustrated in figure 7-22A. Such lenses follow thelaws of geometrical optics in that they may bedesigned by ray analysis. Metal plate lenses decreasethe electrical path length of a spherical wave frontand, therefore, accelerate the incident wave as shownin figure 7-22B. In this type of lens, metal plates areconstructed parallel to the plane of the electric fieldand guide the waves in a fashion similar to that of awaveguide transmission line.

All lens antennas either convert a spherical wavefront to a plane wave front or a plane wave front to

Thus, when used as a receivingantenna, a lens collects a portion of the incident planewave front and focuses it upon a primary antenna.When used as a transmitting antenna, a lens receivesthe energy radiated from a primary antenna andconverts it to a concentrated beam.

ANTENNA /

PRIMARY 0\)\\/

SPHERICAL yWAVE FRONT

PRIMARYANTENNA

SPHERICALWAVE FRONT

( A )

(B)

DIELECTRIC LENS

- PLANEWAVE FRONT

WAVE RETARDED

METAL -PLATE LENS

PLANEWAVE FRONT

WAVE ACCELERATED

Figure 7-22. Lens Antenna Characteristics

78

WAVE GUIDE

Figure 7-23. Lens -in -Horn Antenna

LENS

CHAPTER 7

ANTENNAS

For maximum radiation efficiency, a horn antennais generally used as a primary antenna for feedinglens antennas. The lens may be conveniently mounted.in the aperture of the horn, as illustrated in figure7-23, thus shielding the back surface of the lens. Lensantennas are in common use above 3,000 me wheretheir apertures can be made large in terms of wave-lengths, and gains up to 40 db are possible in someinstances.

79

CHAPTER 8

CHAPTE

INTRODUCTION

The terminal station of a radio relay system con-sists of a transmitter, a receiver, and associatedequipment to send and receive information to andfrom the other terminal stations in the system.Previously, the desired signaland the effects of the atmosphere and earth on thesignal have been discussed. In this chapter the meansof generating this signal and combining it with thedesired information in the form of a modulated r -fcarrier will be considered.

The transmitter consists basically of an oscillator,modulator, and amplifier, the complexity of theseunits depending on frequency, power output required,and type of modulation used.

OSCILLATORS

Conventional oscillators using lumped capacitanceand inductance operate satisfactorily, although withdecreasing efficiency, up to a frequency of about 150mc. Above this frequency special UHF and micro-wave oscillators must be used since conventionalvacuum tube element spacing becomes an appreciablefraction of a wavelength in size, and even a straightpiece of wire has enough inductance and capacitanceto affect the circuit. At first the attempt was madeto solve this problem by decreasing the tube spacingand by using connecting leads as short as possible,but this soon led to the limiting factor of arcingbetween elements. As frequencies increased above500 mc, completely new types of circuits weredeveloped in order to generate the required fre-quencies. In these oscillators, the tuned circuits be-

THE TERMINAL TRANSMITTER

8

THE TERMINAL

TRANSMITTER

come part of the tube in the form of resonant cavities,similar in effect to the tuned cavities used to produceaudio tones in many musical instruments.

VHF OSCILLATORS. Components of VHF oscil-lators must be designed carefully; physical layout ofparts and the use of short leads in circuit wiring areimportant. The use of lumped property componentsoffers the advantage of small physical size with cir-cuitry which is easily adapted to wide range tuning.Where space is not limited, distributed property com-ponents may be used increasing the efficiency andstability of operation.

Above 400 mc, distributed property componentsare used almost exclusively, since the stability andefficiency of lumped property components becometoo low, and the physical size of distributed propertycomponents becomes practical for use. At this pointvacuum tube design is also considerably changed andspecial lighthouse, pencil, or disk -seal planar -typetriodes are used. Figure 8-1 shows the cross sectionof a lighthouse tube. The effects of transit -time arereduced by making electrode spacing very small. Oneof the disadvantages of decreasing tube size is thatless power may be handled because of the decreasein heat dissipating area. In one type of tube, theinverted lighthouse or "oil -can" tube, the powerhandling capacity has been greatly increased bymaking the plate of the tube the largest element.These tubes are designed to be inserted into a reso-nant cavity in such a way as to make the tube itselfa portion of the cavity, thus eliminating lead induct-ance. Loss from radiation from the tube elements andleads is eliminated since the tube is completelyshielded by the resonant cavity.

81

CHAPTER 8


CATHODE

Figure 8-1. Lighthouse Tube (Cross -Section)

Figure 8-2 shows a lighthouse tube and cavity, thecombination forming short-circuited coaxial lines inthe cathode -to -grid and grid -to -plate circuits. Thecavity forms the outside conductor, while the tubeelements themselves form the inner conductor of thecoaxial line. The lines are tuned by sliding pistonswhich change the length of the coaxial lines. Oscilla-tion may be produced by providing regenerativefeedback either by connecting input and outputcoupling loops together in proper phase relationship,or by building capacitance into the cavity so that theproper phase of feedback is established. Other typesof UHF vacuum tubes may be used in similar circuitsby properly designing the resonant cavity for thetube.

MICROWAVE OSCILLATORS. As microwave fre-quencies are approached the triode coaxial oscillatorsbegin to fall off in efficiency and again new systemsmust be resorted to in order to produce oscillationsat these new frequencies. Three general types ofoscillators have been developed for use in theseranges: the klystron, the magnetron, and the travel-ing wave tube. While in the coaxial triode oscillatorsthe problem of interelectrode transit time was en-countered, these new types of oscillators takeadvantage of the finite speed of the electron.

The first type of microwave oscillator is the kly-stron. Two main categories of klystron oscillators

PLANE OF GRID WIRES

LIGHTHOUSE TUBE2 C 43

exist: the reflex klystron and the 2 -cavity klystron.The reflex klystron has low efficiency (about 1 percent) and generates relatively low power. It isprimarily used in receivers, local oscillators, and testequipment. Two -cavity klystrons are much moreefficient (from 20 to 40 per cent) and can be designedto generate high power levels. Most of the limitationsof conventional negative grid tubes do not exist inklystrons. The cathode and anode are outside the r -ffield and therefore may be made as large as desired.The cathode to anode spacing is of the order of oneinch so that extremely high voltages may be usedwithout danger of internal arcing. The only limitingfactor in the amount of power which may be producedby a klystron is the loss in the dielectrics making upthe windows between the output cavity and the load.

Figure 8-3 illustrates the operation of a 2 -cavityklystron. A stream of electrons from an electron gunpasses through a resonant cavity called a buncher.This cavity is the input cavity and contains an r -ffield corresponding to the signal input. In the caseof an oscillator, the input is fed back with the properphase relationship from the output or catcher cavity.The buncher either accelerates or retards the elec-trons in the stream depending on the portion of ther -f cycle. Following the buncher there is the driftspace where the electron beam is unaffected exceptby the uniform accelerating force of the anode volt-age. In this space the electrons form into bunches,the retarded electrons falling back and the acceler-ated electrons moving forward to the next bunch.When the electrons, now bunched, reach the catcher,they set up a varying electric field from which energymay be taken. The electrons themselves continue onto the anode, or collector, where their remainingkinetic energy is dissipated as heat. Figure 8-4 illus-trates the bunching effect by means of a graphrepresenting the distance -time relationship of eachelectron. The slope of each line repiresents the velocityof an electron emitted at the given time relationship

APPROXIMATELY

SHORTING PLUNGERFOR CATHODE TUNING

A

4

PLATE CHOKE-GRID LINE

,..---CATHODE LINE

PLATE LINE-'

3APPROXIMATELY 4

Ryvin,

C9

=Er

Figure 8-2. Lighthouse Tube Oscillator Circuit

ii+Ebb

PLATETUNING ROD

INSULATION

82

CHAPTER 8


with the input wave shown.A modified version of the 2 -cavity klystron is the

reflex klystron oscillator. The operating principlesremain nearly the same. In this klystron the couplingbetween the input and the output is accomplishedby the electron beam itself. In fact, the two resonat-ing cavities are replaced by one cavity which func-tions both as buncher and catcher. Figure 8-5 is asimplified diagram illustrating the operation of areflex klystron oscillator.

The electrons are produced and accelerated by anelectron gun as before. Then they pass through thecavity for the first time, being velocity modulated asin the buncher of a 2 -cavity klystron. The electronstravel into the drift -space but instead of being furtheraccelerated, they are in a uniform retarding fieldproduced by the negative repeller plate. The electronbeam slows to a stop and then reverses directionbeing accelerated back toward the cavity. As thebunched electrons pass through the cavity for thesecond time, they give up part of their energy to thecavity and are then stopped by the cavity, which alsofunctions as the collector. The frequency of operationcan be changed to a limited extent by changing therepeller voltage, thus changing the transit time in thedrift space.

BUNCHERCAVITY

CATHODE

BUNCHER

ACCELERATINGANODE

CATHODE - I

DRIFTOUTPUT

CATCHER

COLLECTOR

1

Figure 8-3. Two -Cavity Klystron Oscillator

The reflex klystron is less efficient than the 2 -cavityklystron because a single resonator performs bothfunctions of bunching and catching. On the otherhand the single resonator tuning and the ease ofelectrical tuning by varying the repeller voltage makeit better for use when only small amounts of powerare required. Another advantage of the reflex klystronis its greater stability as compared to a 2 -cavityklystron when used as a master oscillator. Figure 8-6illustrates the efficiency of operation of klystrons atvarious frequencies. It can be seen that the efficiencyof a klystron falls off slowly as the frequency isincreased and that the maximum power is not deter-mined by the wavelength.

TIME

Figure 8-4. Bunching in Two -Cavity Klysfron

83

CHAPTER 8


CATHODE -

+I -

RESONANT CAVITY

j(ELECTRON FLOW

IREFLECTOR

'-OUTPUT

Figure 8-5. Reflex Klystron Oscillator

The second main type of microwave oscillator isthe magnetron. To aid understanding of the principleof operation in a traveling -wave magnetron, the mostcommonly used, consider the movement of an elec-tron in magnetic and electric fields. An electronmoving at right angles to a magnetic field will beacted upon by a force perpendicular to both itsdirection of motion and the magnetic field. This forcedoes not change the velocity of the electron butcauses it to move in a circular path, the radius ofthe path being determined by the magnetic fieldstrength and the velocity of the electron. An electronmoving parallel to an electric field will be eitheraccelerated, taking energy from the field, or retarded,giving energy to the electric field.

In the magnetron, figure 8-7, there are two electric-100 KW

60

>-50 -

w 40 -

LL 30

at. 20

10-

010

.

0

0000o

0

0

0500 1000 5000

FREQUENCY MC

- 10 KW

1 KW

0100 W

1

0,G00W

CURVE 0 EFFICIENCY VERSUS FREQUENCY FORTYPICAL UHF TETRODE - 4X1506. ( PLATEDISSIPATION 150 WATTS.)

CURVE 0 EFFICIENCY VERSUS FREQUENCY FORTYPICAL UHF TRIODE - 2C39. ( PLATEDISSIPATION 100 WATTS

CURVE Q TYPICAL EFFICIENCY OF KLYSTRONS VERSUSFREQUENCY ( INDEPENDENT OF OUTPUT POWER.)THIS IS THE EFFICIENCY AT THE OPTIMUM FREQUENCYFOR EACH TUBE.

CURVE ® (DOTTED):MAXIMUM POWER OUTPUT OF THELARGEST COMMERCIALLY AVAILABLE NEGATIVE -GRIDTUBE AT VARIOUS FREQUENCIES.

POINTS 0 CW POWER OUTPUT OF VARIOUS KLYSTRONS(NOT THE LARGEST POSSIBLE.)

Figure 8-6. Efficiency -Frequency Diagram

fields operating. The first is a high voltage d -c fieldwhich accelerates the electron from cathode to anode.In addition, modifying the d -c field, is an r -f field atthe operating frequency moving as shown in thediagram. The direction of the magnetic field, whichis produced by a permanent magnet, is into the page.Under the action of these fields, the electrons emittedfrom the cathode will follow the path shown in figure8-8 under certain conditions. The first of these con-ditions is that the magnetic .field strength be highenough so that the electron, without the action of ther -f field, will not reach the anode, but will instead becurved back to the cathode. Secondly, the averageelectron motion to the right must equal the wavevelocity to the right. The slowed wave velocity isproduced by the action of the resonant cavitiesdecreasing the wave velocity to a value which can beequaled by the electron flow.

Under these conditions, the electron emitted frompoint 1 will find itself in a retarding field and will nothave enough energy to reach the cathode again beforestopping. When it stops, short of the cathode, itagain will try to reach the anode. Since it is movingto the right at the same rate as the r -f wave, it willagain find itself in the retarding field. This processwill continue, the electron giving up part of its energyto the wave each time until the electron finallyreaches the anode. If an electron is emitted from thecathode at a point where it would take energy fromthe field, it is speeded up and driven back to thecathode, thus removing it from further interactionwith the r -f field (figure 8-8, point 2). To produceregenerative feedback for oscillations, all that isnecessary is to bend the magnetron around upon itselfas shown in figure 8-9. The magnetron is basically afixed frequency device, but certain of the newer typesmay be frequency modulated by changing the poten-tials on certain elements.

Anode power is normally applied to a magnetronin very short pulses of very high amplitude. Voltagesof 40 kilovolts and currents of 100 amperes are notunusual in pulsed magnetron service. It is possibleto produce a peak power of 2.5 megawatts at 3,000mc with an efficiency as high as 50%. At frequenciesof 25,000 mc, more than 50 kw may be obtained, butthe efficiency will then fall to about 25%.

The traveling wave tube connected as an oscillatoris the last main type of microwave oscillator. It isessentially an amplifier which uses an electron beamand an r -f wave traveling together in such a way thatthe wave accepts energy from the electron beam. Insome ways it is similar to the linear magnetron dis-cussed previously. The traveling wave tube consistsof a helical coil inside a conductor. It may be con -

84

sidered as a coaxial cable with a helical inner con-ductor. The operation is as follows: the r -f wave tobe amplified travels along the helical coil whichgreatly reduces the velocity of the wave. This slowervelocity causes the r -f wave to travel at the samespeed as an electron beam centered in the helical coil,which enables the r -f wave to accept energy from thebeam. Figure 8-10 illustrates the r -f wave form andthe electron beam path.

Assuming the electron velocity and the wavepropagation velocity are the same, the electrons inthe beam will be retarded or accelerated by theelectric field. This will cause bunching to occur, withthe electron bunches forming in alternate points ofzero longitudinal electric field, as shown at points 1in figure 8-10. In producing these bunches, as manyelectrons are retarded as are accelerated and no nettransfer of energy is made in either direction. Sincethis would produce no amplification, some meansmust be found of obtaining a transfer of energy fromthe electron beam to the electric field. The bunchesnow form in the positions shown in the diagram.This can be done by a slight increase in the velocityof the electron beam. The electron bunches are nowat a retarding point of the electric field and theelectrons are retarded for a larger period of time thanthey are accelerated. This will produce a transfer ofenergy to the wave, and therefore the wave is ampli-fied. A necessary addition to the traveling wave tubeis some means of preventing the electron beam fromspreading. This is done by using a longitudinal mag-netic field. As long as the electron beam movesparallel to the magnetic field it has no effect on theelectrons. When the electron strays from a parallelpath, however, the magnetic field forces the electronback into the beam. By coupling the output to theinput in the proper phase relationship, oscillationmay be produced. The traveling wave tube can beused over a great range of frequencies with high gain,at a cost of low proper output and efficiency.

FREQUENCY STABILIZING SYSTEMS

An ideal oscillator would be one in which the fre-quency could be easily adjusted and once set, remainat that frequency regardless of temperature, outputload, or voltage input. At low frequencies these con-ditions are relatively easy to approach, but asoperating frequencies are increased, stability ofoperating frequency becomes more difficult to obtain.Even by attaining the same percentage of stability,which in itself is hard to do, serious frequency shiftsmay occur at microwave frequencies. A frequencyshift of .01% at 1 mc is only 100 cycles which presents

CHAPTER 8


RESONANT CAVITIES

WAVETRAVEL

Figure 8-7. Electric Field in Linear Magnetron

no problems, but this same percentage shift at 10,000mc is equal to 1 mc which is enough to interfere withsatisfactory operation.

Three primary factors affect the operating fre-quency of an oscillator. There are, first, geometricfactors in which the effective inductance and capaci-tance are changed directly through mechanicalmotion; second, pulling factors in which reactance iscoupled into the oscillatory circuit from the load; andthird, pushing factors in which reactance is intro-duced by changes in input conditions, such as voltage,current, or magnetic field.

There are two means of insuring stable operatingfrequencies. One is by the use of frequency stabilizerswhich tend to maintain a constant frequency ofoscillations, and the other is by automatic frequencycontrol systems which mechanically or electronicallyretune the oscillator when it shifts from a referencefrequency.

FREQUENCY STABILIZERS. Magnetrons havehigh geometric stability except during warm-up orduring periods of changing duty cycle as in certaintypes of modulation. This factor can usually beeliminated by maintaining the temperature of opera-tion within ± 5° C during operation. Pushing factorsare usually negligible up to 3,000 mc. Above thisfrequency highly stabilized power supplies may beused to counteract any frequency shift due to inputvoltage variations. Pulling effects are not normallyfound in microwave communication systems sincenone of the r -f system is required to move, thuschanging the output load. However, to counteractany possible shift due to pulling, a stabilizer tuner

Figure 8-8. Electron Trajectories in Linear Magnetron

85

CHAPTER 8


RESONANTCAVITIES

ANODE BLOCK

CATHODE

Figure 8-9. Cross -Section of Multicavity Magnetron

may be used on the output. This tuner consists of anexternal cavity resonator and a resistor in series,placed in parallel with the output line of the mag-netron. The placement is critical and should bemounted at a standing wave node.

AUTOMATIC FREQUENCY CONTROL SYS-TEMS. Sufficient frequency stability for com-munication may not always be obtained with theprocedures given above. In such case, some means ofautomatic frequency control (AFC) must be used,either at the transmitter, the receiver, or both.Normally, in point-to-point operation, AFC is appliedto the receiver so that it locks the receiver frequencyto the transmitted signal.

AFC systems fall into two classifications: electronicand mechanical. These systems may also be classifiedaccording to whether they adjust the oscillatorfrequency to an absolute frequency or to a relativefrequency. Terminal transmitters all fall under theclassification of absolute frequency systems, whilerepeaters normally compare their operating frequencyto the received signal.

An AFC system is a feed -back loop which samplesthe oscillator output, compares it with a reference,obtains an error signal, and uses this error signal toretune the oscillator. Electronic tuning may be usedwith the klystron and certain of the newer magne-trons, while mechanical tuning must be used on thetraveling wave oscillator, most magnetrons, andcoaxial triode oscillators, and may be used onklystrons.

Electronic tuning may be accomplished in thereflex klystron by varying the d -c voltage applied toeither the accelerator grid or to the reflector. A tuningrange of as much as ±60 me may be obtained inthis way without seriously lowering output power.Special magnetrons, designed for frequency modula-

tion, also may be tuned about ±0.5%. In the spiralbeam FM magnetron, electron guns with controlgrids are placed in several of the resonant cavities sothat the electron beam is parallel to the magneticfield. By varying the intensity of these electronbeams, the operating frequency may be changedslightly.

Mechanical tuning of any cavity oscillator may beaccomplished by changing either the shape or sizeof the cavity, or by inserting a tuning probe in sucha position as to appear inductive or capacitive. Themechanical changes may be operated either by anelectric motor, or by a high temperature -coefficient-of -expansion rod heated electrically. An error voltagewith which to retune the oscillator may be obtainedin several ways. Most absolute methods depend oncomparing the frequency of the oscillator to one ormore resonant cavities. One method uses a pair ofcavities and a pair of detector crystals in a circuitcomparable to the discriminator used at lower fre-quencies. The output of this circuit will be a d -cvoltage, the polarity depending on whether thefrequency is high or low, and the magnitude depend-ing on the magnitude of the error.

Another method uses a single cavity with avibrating diaphragm moved by an electromagnetoperating at the a -c input power frequency modulat-ing the resonant frequency. The output of this cavitywill be the oscillator frequency amplitude modulatedby twice the power frequency if there is no error inthe oscillator frequency. If there is an error in theoscillator frequency, the cavity output will be theoscillator frequency, amplitude modulated by thepower frequency. The direction of the oscillator errorfrequency, high or low, will determine whether themodulation is in phase or 180° out of phase withthe power or reference frequency. By demodulatingthe signal from the cavity and comparing it withthe power source, the error voltage may be used toretune the oscillator.

The error voltage developed from the comparisoncircuits may be either a -c or d -c. If the error voltageis d -c, it may be used, directly or after amplification,to drive a d -c tuning motor or it may be applied tothe voltage sensitive elements of the oscillator. If theerror voltage is a -c it may be used, directly or afteramplification, to drive an a -c 2 -phase motor to tunethe oscillator.

Figure 8-10. Electron Flow in Traveling Wave Tube

86

CHAPTER 8


MODULATORS

Some means must be found of making the carrierfrequency as generated by the oscillator conveyinformation to the receiver. This is done by changingsome characteristic of the carrier, such as the ampli-tude, frequency, or phase; or by turning the carrieron or off. The carrier may be modulated by a voice,tone, visual, or other desired signal.

MODULATION IN THE VHF RANGE. In theVHF ranges, where conventional vacuum tubes maybe used, modulation is relatively simple.

1. Amplitude Modulation. Amplitude modulationis a change in the amplitude of the carrier which isdirectly proportional to the modulating signal. Onehundred percent amplitude modulation exists whenthe amplitude of the radiated wave is (1) zero if themodulating signal is at its maximum negative value,and (2) twice the amplitude of the unmodulatedcarrier if the modulating signal is maximum positive.Figure 8-11 illustrates the waveforms of a carrier atdifferent percentages of amplitude modulation.

In producing amplitude modulation, frequenciesother than the carrier frequency are produced. Thesefrequencies, called sidebands, are the sum and differ-ence frequencies of the carrier and modulating fre-quencies. The sidebands for a 40 mc carrier amplitudemodulated by a 5,000 -cycle sine wave would be at40.005 mc and at 39.995 mc thus requiring a 10-kc-wide pass band. In general the pass band requiredfor AM signals is twice the highest modulatingfrequency. When complex wave forms such as voicesignals are being transmitted, the harmonic fre-quencies making up the complex wave must also beconsidered if the received signal is to be undistorted.With 100% modulation by a sine wave, the sidebandseach contain one-fourth the power of the carrierfrequency.

There are two general methods of producingamplitude modulation. One is by changing the inputto the plate of the tube and having the efficiency ofoperation remain constant, and the other is to allowthe plate power input to remain constant, and changethe efficiency of operation. Combinations of the twomethods, in which plate power input and efficiencyare both varied, are also used. Constant efficiency,variable input modulation, also known as platemodulation, is the most common and allows maxi-mum output from a given transmitter tube. Suchmodulation requires that the modulator be able tofurnish one-half as much power as is generated by ther -f system. The use of large and heavy componentscapable of handling the modulator power are there -

87

UNMODULATED0%

OVER50% 100% MODULATION

TI ME

Figure 8-11. Amplitude Modulation Waveforms

fore necessary. Constant input, variable efficiencysystems may be accomplished by modulating thevoltage applied to any of the other elements of thetube such as the cathode, control grid, screen grid,or suppressor grid. It is difficult to attain 100%modulation with good linearity in this manner. Com-promise designs may be made in which both theplate input and one of the grids, usually the screengrid, are modulated. The overall efficiency, includingthe modulator, of the two AM systems is about thesame.

Since the information is contained in the sidebandsand not in the carrier and only one sideband isrequired, the wasted power in the other portions ofthe modulated carrier need not be transmitted. Thissystem is known as single sideband (SS). The carrieris produced as usual and amplitude modulated at alow level in a balanced modulator which eliminatesthe carrier by phase canceling. One of the sidebandsis removed by filtering and the remaining sidebandis amplified and transmitted. Much higher effectivepower levels and decreased bandwidth requirementsmay be obtained in this way, but at the expense ofmore complicated transmitting and receivingequipment.

2. Frequency Modulation. Frequency modulationis a change in the output frequency of the carrierwhich is directly proportional to the amplitude of themodulating signal. In contrast to AM, one hundredpercent modulation is not physically defined, but isfixed by regulation. Modulation percentage is theratio of the frequency deviation to a fixed deviationwhich is set by FCC regulation, the amount ofpermissible deviation varying at different points inthe frequency spectrum.

As in AM, frequency modulation of a carrierproduces sidebands. In the case of FM however, agreat many more are produced than with AM. Thesidebands produced for a 40 mc carrier modulatedby a 5,000 -cycle sine wave would be not only at40.005 and 39.995 mc, but theoretically, sidebandswould also appear at 5,000 -cycle intervals to infi-nitely high and low frequencies. Practically, thenumber of sidebands which will have enough power

CHAPTER 8


to be capable of causing interference will vary withthe modulation index. The modulation index is theratio of the frequency deviation of the carrier to thefrequency causing that deviation. For example, a 75kc deviation caused by a 15 kc signal will have amodulation index of 5. This will produce 8 effectivesidebands on each side of the carrier frequency. Thevectorial sum of the sideband and carrier power is thesame as the power of the unmodulated carrier powerregardless of the percentage of modulation. Thetransmitted power remains constant; only the dis-tribution of the power among the sidebands andcarrier varies with the modulation index.

Frequency modulation may be produced by twogeneral methods. One method is direct, using areactance tube to modulate the frequency of theoscillator. The reactance tube is a conventionalvacuum tube connected so as to appear as a capaci-tive or inductive reactance that varies proportionallyto the applied grid potential. With a reactance tubemodulator, the ratio between the oscillator frequencyand the amount of frequency deviation is small, andtherefore a low -frequency oscillator followed byfrequency multiplying stages must be used. Thesestages not only increase the carrier frequency butalso increase the frequency deviation by the sameamount.

One of the disadvantages of the direct method ofproducing FM is that crystal -controlled oscillatorsmay not be used since reactance -tube modulatorshave negligible effect on their frequency. The secondmethod of obtaining FM, indirect FM or phasemodulation, produces FM following the oscillatorwhich operates at a constant frequency. In contrastto direct FM, which changes the frequency of theoscillator itself, phase modulation shifts the phaseof the constant frequency output of the oscillator.Since the phase of a voltage cannot be changedwithout also producing a frequency shift during thephase change, a form of frequency modulation is thefinal result.

The original method of producing phase modula-tion is still in use. This is the Armstrong system whichuses a balanced modulator to produce two sidebandsindependent of the carrier as in single-sidebandoperation. By recombining these sidebands, phaseshifted 90° with the original carrier, phase modulationof the carrier results. A second method of producingphase modulation consists of combining the carrierand the modulating voltage in a saturable inductor.This is a coil which reaches magnetic saturation at avery low current. The modulating voltage biases thecoil so that the saturation point will vary in time(figure 8-12). The pulse output of the saturable

inductor is amplified and shaped into a sine wave infollowing frequency amplifier stages.

In any of the methods of phase modulation, thefrequency deviation produced will vary directly asthe modulating frequency.

AF = foe (8-1)where

OF = Frequency deviationf = Modulating frequencyAO = Maximum angular shift of the carrier

(radians)

A low frequency signal therefore will not produce aslarge a frequency deviation as a higher frequency ofthe same amplitude. This is compensated by the useof a predistorting filter which decreases the phaseshift caused by the high frequency signals and allowsequal amplitude high and low frequency signals toproduce the same frequency deviation of the carrier.

Most of the received noise will be, in effect, highfrequency signals, so pre -emphasis networks are usedwhich effectively increase the transmission power ofthe high signal frequency, and de -emphasis networksare used in the receivers to restore the proper fre-quency response. Both predistorter and pre -emphasisnetworks are used in phase modulators. As in directfrequency modulation, only small amounts of fre-quency deviation can be obtained, and so lowfrequency oscillators are used followed by frequencymultipliers to obtain a high modulation index. Rela-tively small amounts of modulating power arerequired for frequency modulation, and since aconstant amount of power is handled by the tubes,they can be operated at maximum power levelswithout danger of overloading on modulation peaks.

MODULATION AT MICROWAVE FREQUEN-CIES. With microwave oscillators (see Table VI I I-1),modulation becomes simpler in some ways and moredifficult in others. The main problem in AM is toamplitude modulate the oscillators without producingfrequency modulation at the same time. Frequencymodulation is much simpler to obtain in microwavethan in VHF transmitters.

1. Amplitude Modulation. Magnetrons and travel-ing wave oscillators may be successfully amplitudemodulated by varying the power input by platemodulation. This method of modulation requires afast acting electronic AFC system to counteract theFM also produced. Spiral beam frequency controlmagnetrons are well suited for AM. By applying themodulating voltage to both the anode and the spiralbeam control grids, pure AM may be obtained. Plate

88

CHAPTER 8


CARRIER CURRENT

CARRI ER

VOICE CURRENT

AND VOICE CURRENT

INDUCTIVE PULSES GENERATED IN THE MODULATOR COIL

A

RECTIFIER OUTPUT

A A A I Ai A A A AV V V V V V V VFUNDAMENTALPHASE - MODULATED 'WAVE

I

Figure 8-12. Waveforms Developed in Nonlinear Coil Modulator

A

B

C

D

.7 -SATURATION

RAPID FLUXCHANGE

SATURATION

E

F

89

CHAPTER 8


TABLE 8-1: COMPARISON OF MICROWAVE TRANSMITTING TUBES

Type

Freq.Range

(mc)PowerOutput Cavity

TypeModulation Efficiency

TypeOutput Tuning

Disk -sealtriode

Up to3300

500 W External Pulse, AMFM difficult

2%-20% Coax Mechanical

2 -cavity 900 to 5 W Part of FM 5%-30% Coax or Mechanicalklystron 21,000 (avg.) tube AM difficult Waveguide

Reflex 1,200 to .005 to Part of FM Less than Coax or Mechanicalklystron 60,000 1 W tube AM difficult 10% Waveguide and

Electronic

Magnetron 700 to60,000

60 KW(c.w.)

Part oftube

PulseAM -FM difficult

50% Waveguide Mechanical

Travelingwave

500 toover 10,000

Low External Pulse AMFM difficult

10%-25% Waveguide Mechanical

modulation of klystrons, however, must be intro-duced at an amplifier stage following the oscillator,since the frequency variations produced cannot becontrolled.

The method of varying the amount of r -f powerallowed to reach the load may be applied to any ofthe microwave oscillators. In such a method anabsorption cavity is used which can be controlled byan electron beam. The electron beam absorbs energyfrom the r -f wave passing through the cavity, thuscontrolling the amount of r -f power reaching the load.This method has a poor efficiency of operation, butmodulating power requirements are low.

Another system for producing AM indirectlyemploys a subcarrier of 6 mc (or any other appro-priate value) which is amplitude modulated in abalanced modulator circuit. The output consists ofthe upper and lower sidebands without the carrier.The lower sideband is filtered out and the remainingsideband is used to frequency modulate anothercarrier, known as the tree carrier, which is 6 mc belowthe operating frequency. A low modulation index isused so that the first order sidebands predominate.Since a subcarrier frequency of 6 mc is used, thefirst -order FM sidebands occur 6 mc above and belowthe tree carrier. The tree carrier and all sidebandsexcept the first -order upper sidebands are rejected byfiltering. A new carrier, at the operating frequency,is now injected in the proper phase to produce AM.The distortion produced by this system is very low.

2. Frequency Modulation. Frequency modulationof microwave oscillators is relatively easy to obtain.

Klystron oscillators may be frequency modulateddirectly by placing the modulating voltage on theaccelerator grid, or on the repeller plate in the caseof the reflex klystron. Negligible power is requiredto modulate the oscillator and a large frequencydeviation with very little AM can be obtained.Frequency modulation of magnetrons may be usedin the special magnetrons using spiral beam frequencycontrol. This method was discussed in the section onfrequency stabilizing systems. As in FM klystrons,very little modulating power is required.

POWER AMPLIFIERS

The modulated signal may be passed to an ampli-fier to increase the amplitude of the outgoing signal.The same limitations of conventional circuits atmicrowave frequencies that applied to oscillatorsapply as well to amplifiers. In the microwave regionno amplification is possible with conventional vacuumtubes and circuits; either the oscillator itself mustsupply enough power, or specially designed amplifiersmust be used.

VHF AMPLIFIERS. R -F power amplifiers used atfrequencies up to about 400 mc may be of the con-ventional type using lumped property componentsand standard vacuum tubes. As frequencies areincreased, use is made of grounded grid circuits, inwhich the control grid is placed at r -f ground pro-viding a shielding effect to reduce interelectrodecapacitance. Grounded grid circuits have the dis-advantage of requiring more grid driving power than

90

CHAPTER 8


grounded cathode circuits, although the additionalpower is not lost but appears in the output of thestage.

Since the efficiency of operation of oscillators andamplifiers decreases as the frequency increases, onemethod of obtaining greater overall system efficiencyis through the use of frequency multipliers. Theoscillator can now be operated at a much lower fre-quency than the output carrier frequency. Usually abuffer amplifier follows the oscillator so that noloading of the oscillator will take place. The amplifierstages, following the buffer amplifier, consist ofamplifiers operated with a very high negative gridbias. This produces a large harmonic content in theoutput of the stage. By tuning the plate circuit ofthe tube to one of these harmonics, a frequencymultiplying action takes place. Frequency multipli-cations of up to four times per amplifier stage arecommonly used.

Another method of frequency multiplication whichoperates with much higher efficiency is the push -pushamplifier. In this circuit two vacuum tubes are usedwith the grid circuits fed 180° out of phase and theplates of the tubes connected in parallel. Two pulsesof plate current will appear in the plate load for eachcycle of the input. By tuning the plate load for thesecond or fourth harmonic of the input frequency,high efficiency frequency multiplication takes place.The same action can be made to occur by connectingthe grid circuits in parallel and the plate circuits inpush-pull. When using FM, frequency multiplyingalso has the advantage of increasing the frequencydeviation as well as the carrier frequency. However,there is the disadvantage of also multiplying thefrequency instability of the oscillator.

In the transition range, from 250 mc to 1,500 mc,distributed property components come into wide use.Amplifiers using miniaturized vacuum tubes andtuned transmission lines are used in the lower portionof this frequency range, and disk seal triodes incoaxial circuits in the upper portion. The coaxialamplifiers are identical with the coaxial oscillatorspreviously described except that the regenerativefeedback has been eliminated.

MICROWAVE AMPLIFIERS. As frequencies areincreased beyond the point where triode amplifierswill operate efficiently, klystron amplifiers and travel-ing -wave -tube amplifiers are used.

The klystron amplifier may be a 2 -cavity klystronas used for an oscillator or a special amplifier klystronused for high power, which is known as a cascade or3 -cavity klystron. This tube is effectively two kly-strons connected in cascade within the same envelope,

with the catcher for the first section functioning asthe buncher for the second section. The signal to beamplified is fed to the first cavity and the poweroutput is taken from the third cavity. The secondcavity is energized by the bunched electron beamand is not supplied with external r -f driving power.These tubes are capable of power gains up to 30 db,efficiencies of 30 to 40%, with a power output of12.5 kw.

Traveling -wave -tube amplifiers are the second typeof amplifier tube which may be used at microwavefrequencies. The tubes have inherent regenerativefeedback due to wave reflections in the tube. Whendesigned for amplifier service, some means of attenu-ating the reflected wave must be provided. However,they are capable of large amplifications with a widepass band and high efficiency.

INSTALLATION AND MAINTENANCE

Installation and maintenance procedures will varywith the equipment to be considered. Specificmethods of installation are described in detail in theinstruction manuals for each piece of equipment. Thesize and weight of the equipment, the permanencyof the installation, the power input requirements,the type of operation, and the frequencies used areall factors which will affect the installation.

MAINTENANCE. Maintenance will, in general,follow the same lines regardless of the type of installa-tion. There are two forms of maintenance which willbe considered here-preventive maintenance andcorrective maintenance. Preventive maintenance isany procedure which tends to reduce or preventfailure of the equipment. It should be a regularlyscheduled check of operations. It can be broken downinto six operations, abbreviated FITCAL, as follows:

F-feel: May be used to discover loose connections,plugs, and sockets; and overheating of components.

I-inspect: Visual inspection to discover leakageof sealing compound or liquid dielectric from com-ponents and corrosion of metal parts. Discolorationor blistered paint on metal surfaces is also an indica-tion of overheating.

T -tighten : Tighten any loose connections, plugs,sockets, or fastenings to the proper tension.

C -clean: Cleanliness around high voltage or pointsat high r -f potential is very important. Dust andmoisture decreases the voltage breakdown point ofdielectrics and can easily cause failure of theequipment.

A-adjust: Adjustment of necessary mechanicalparts and controls to insure proper operation.

91

CHAPTER 8


L-lubricate: Lubrication of moving parts accord-ing to the proper lubrication order.

By performing preventive maintenance at regularintervals many failures of equipment can be pre-vented before they have a chance to make theequipment inoperative.

Corrective maintenance involves the test andrepair of equipment after a breakdown has occurred.Spare units are usually available to replace thedefective equipment if continuous operation is re-quired. Test procedure remains the same for anyequipment. The first step is to localize the defect toa unit, then to a stage, and finally to the defectivecomponent itself. Voltage and resistance charts andwaveform diagrams, which will be found in themaintenance section of the instruction book for theequipment, are very helpful in this localizing pro-

cedure. After replacement of the defective component,performance tests should be run to insure properoperation of the equipment.

A military radio -relay system calls for compromisesin design in order to achieve simplicity, minimumweight, and maximum performance. Operating fre-quencies vary from 45 to 13,000 mc. Powerconsumption is a few watts in the most compactequipment increasing to hundreds of watts in fixedequipment, while power output varies from a fractionof a watt to about 250 watts. A minimum of 30 wattsis considered necessary for radio -relay links of 50miles. Reception is possible up to 10 miles for port-able equipment, with 50 mile ranges accepted asstandard for transportable terminal equipment.Under ideal siting and propagation conditions, rangesof 100 miles have been reported.

92

CHAPTER 9

THE TERMINAL RECEIVER

C II T E

INTRODUCTION

At frequencies ranging from 44-13,000 mc a vari-ety of differences in receiving conditions are foundas compared to lower frequencies. The fluctuationnoise of tubes and circuits in the receiver becomesgreater than external noises, such as atmosphericdisturbances and man-made interference. Therefore,receiver noise is one of the chief limitations ofreceiver sensitivity at such frequencies. The necessityof handling greater receiver bandwidths is also ofgreat importance, both for determining the maximumrate at which information can be received and as acontrolling factor of the total noise encountered.These greater bandwidths will increase the effectivenoise power originating in the resistors and tubes ofthe receiver as well as the received external noise(see Chapter 13).

SUPERHETERODYNE RECEIVER PRINCIPLES

The main type of receiver used at these frequencies,as at lower frequencies, is the superheterodyne.Variations of the individual stages occur as the fre-quency is increased, but the general principles ofoperation remain the same.

A superheterddyne receiver (see figure 9-1) basi-cally operates by heterodyning, or mixing, thereceived r -f signal with a locally generated r -fvoltage obtained from the local oscillator. These twovoltages are combined in a non-linear device such asa vacuum tube or crystal rectifier known as the mixer,producing, in addition to the original frequencies,the sum and difference frequencies. This process is

9

THE TERMINAL

RECEIVER

identical with amplitude modulation as used intransmitters.

The difference frequency, or the lower sideband, isselected and amplified by a fixed tuned intermediatefrequency (i-f) amplifier system. The i-f amplifierfrequency remains the same in a given receiverregardless of the incoming signal frequency. This isaccomplished by changing the local oscillator fre-quency so that the difference frequency between thedesired signal and the local oscillator signal remainsconstant.

After amplification, the i-f signal is demodulated.The information and the carrier are separated andthe signal containing the information is passed on tothe video amplifier. Here the signal is amplifiedenough to be used as desired.

RECEIVER CHARACTERISTICS

SENSITIVITY. Receiver sensitivity may be definedas the minimum signal strength capable of producinga given value of signal output. So defined, the sen-sitivity is a measure of the overall gain of thereceiver. However, random fluctuations, or noise,originating in the first stages of the receiver establisha limit to the useful sensitivity in VHF and higherfrequency receivers. As a result, receiver sensitivitymust also be defined in terms of the minimum signalwhich will produce a useable signal-to-noise ratio.

SIGNAL-TO-NOISE RATIO. The relationship be-tween a received signal and the prevailing noise isexpressed as a ratio, referred to as the signal-to-noiseratio (S/N). Generally, in the frequency range from44 to 13,000 mc, internal noise originating in the

93

CHAPTER 9


initial stages of the receiver is the determining factor(see Chapter 13). However, at lower frequenciesatmospheric and man-made noise can becometroublesome.

BANDWIDTH. Closely associated with the sensi-tivity of a receiver is the bandwidth of its circuits.The bandwidth of a communication system is definedas the range of frequencies within which the signallevel does not decrease more than 3 db below themaximum value of the signal. In services such astelevision and multi -channel radio -relay systems,receivers must possess a much greater bandwidththan that required for simple radiotelegraph or radio-telephone operation. For example, bandwidths of6 mc are required in television receivers and up to15 mc or more in certain radio -relay receivers. Toachieve this wide -band response with high gain is avery difficult problem, since the product of the gainand the bandwidth of an amplifier is a constant. Itis essentially a problem of initial design, and circuitsas well as tubes and other components must becarefully selected.

SELECTIVITY. The selectivity of a receiver is itsability to differentiate between the desired signal andsignals at other frequencies. Selectivity is usuallydefined as the ratio of the sensitivity for desiredsignals to the sensitivity for undesired signals, ex-pressed in decibels. The sensitivity of the receiverfor a range of frequencies about the desired frequencyis often plotted as a selectivity curve whose shape isprimarily determined by the response of the i-famplifiers.

IMAGE RATIO. The image ratio at the receiver isa measure of the rejection of that frequency which,when mixed with the local oscillator signal, producesthe same i-f as the desired signal. If the local oscil-lator is operated below the signal frequency, theimage frequency will be the same amount below the

ANTENNA

R -F

AMPLIFIER( PRESELECTOR )

GANGEDTUNING

MIXER

local oscillator frequency that the signal frequencyis above. The image rejection must take place priorto the mixer in the r -f amplifier or preselector stages.

R -F AMPLIFIERS

Receivers used at frequencies below 400 mc con-ventionally use amplifiers as the first stage or stagesfollowing the antenna. Advantages that may begained from the use of an r -f amplifier include sup-pression of image response, improvement in signal-to-noise ratio, and isolation between the antenna andthe local oscillator to prevent local oscillator radiation.

LUMPED -CONSTANT CIRCUITS. When conven-tional coils and capacitors are used at frequenciesranging from 44 to 400 mc, a point is reached wherethe capacitance has been reduced to that inherentlypresent in the tube, socket, wiring and coil, and theinductance is as small as possible for the, requiredL/C ratio. Upon replacement of the tube, therefore,there will generally be a different input capacitance,the difference being a large enough fraction of thetotal circuit capacitance to render inaccurate a cali-brated tuning dial or other control arrangement.Reduction of the tuning capacitance to the point thatit consists of only inherent minimums also has theobjection that if automatic gain control is applied tothe stage, the resulting variation of tube inputcapacitance in triodes may also cause excessivedetuning.

Lumped -constant tuning, with a lumped induct-ance but only distributed capacitance, has beenwidely used in military equipment operating up to300 mc, and the limitations can be largely eliminatedby the use of pentode vacuum tubes. The tuning isdone inductively by inserting into the coil a sleeveof silver-plated metal to reduce the inductance, or byemploying a slug of compressed powdered iron toincrease the inductance. For covering a wide fre-

LOCALOSCILLATOR

4

AMPLIFIER

AGC

DETECTOR( DISCRIMINATOR)

AFCCIRCUITS

Figure 9-1. Block Diagram of Superheterodyne Receiver

VIDEOAMPLIFIER

VIDEOOUTPUT

94

CHAPTER 9


quency range, a composite core with iron at one endand silver plating at the other may be used toadvantage.

GROUNDED -GRID TRIODE. For signals in thefrequency range of 100 mc to approximately 1,000mc, advantages may be found in using a grounded -grid triode as an r -f amplifier, especially if the receiveris intended for wide -band operation. In a grounded -grid amplifier the high side of the input is connectedto the cathode and the low side to the grid, whichis grounded. The output is taken between plate andground in the normal manner.

The gain of a grounded -grid amplifier tube is givenby the formula

Voltage Gain = R1' + 1)Rp + RL (9-1)

where

RL = Load resistance, ohms= Amplification factor of the tube

R, = Internal plate resistance, ohms.

If the load resistance is much less than the internaltube resistance, and ifµ is much greater than unity,the gain simplifies to It Lg., where gm is the tubetransconductance. The value of the grounded -gridstage is essentially that the input and output circuitsare fairly well shielded from each other, as in ascreen -grid tube, while at the same time the low noiselevel of a triode is retained. Slightly less than criticalcoupling into a grounded -grid stage gives the bestsignal-to-noise ratio.

CASCODE AMPLIFIERS. The cascode (not to beconfused with cascade) amplifier has been developedas a method of obtaining adequate gain with a lownoise figure. The simplified circuit shown in figure9-2 uses two triodes effectively in series. V1 functionsas a grounded cathode amplifier which is directlycoupled to V2, a grounded -grid amplifier. Thisarrangement combines the desirable features of bothtriodes and pentodes, while eliminating some of theundesirable features of each. It has the high gain,high impedance input, and stability of a pentode,with the low noise figure of a triode. Neutralizationis not required but may be used to improve the noisefigure further.

TUNING

UHF -VHF TUNERS. For tuning in the generalregion of 300 to 1,300 mc, especially over limitedranges, transmission line sections can be used. AX/4 line shorted at the far end acts as a parallel tuned

95

6+

Figure 9-2. Cascade Amplifier

circuit at the near end, while other lengths of shortedlines act as high -Q inductors or capacitors. Balancedparallel -rod lines can be used up to 700 mc, andcoaxial lines above this.

When signals above 500 mc are to be received, itis a distinct advantage to change from the conven-tional type of tube to the lighthouse version (seefigure 8-1) and usually at the same time to employ acoaxial type of transmission line for tuning ratherthan the parallel -rod type. The lighthouse tube isconstructed with flanges or belts around the edge sothat large, low -inductance connections can be madeto the coaxial type of transmission line. The shortlengths of these coaxial transmission lines and thelarge circular contacts required for connection to thelighthouse tubes give equipment of this type anappearance which has led to the term "plumbing"as the usual informal name. In wide -band, r -famplifier service, the limit of usefulness for lighthousetubes is approximately 1,000 mc, although for localoscillators of the coaxial type the range can extendto over 3,000 mc. Two other types of UHF tubes arealso available, the acorn tube and the door -knob tube,which are so named because of their shapes and sizes.Both types are available in diodes, triodes, andpentodes.

BUTTERFLY TUNERS. Tuners of the butterflytype, such as illustrated in figure 9-3, are continu-ously adjustable over a wide frequency range. Butter-fly tuners of moderate size achieve tuning ratios as

CHAPTER 9


ROTOR

ROTOR

STATOR

ROTOR AND STATORASSEMBLED

ELECTRICALCONNECTION POINTS

STATOR

Figure 9-3. Butterfly Tuner

great as 5:1 in frequency, while larger sizes may bedesigned to achieve even greater ratios. These tunershave been used at frequencies as low as 40 mc andas high as 1,000 mc or more. The construction issomewhat similar in appearance to a variable capaci-tor, with the exceptions that (1) the circuit inductanceis built in and consists chiefly of the circular -strapportions of the stator plate, (2) both connections aremade to the stator, and, therefore, (3) there are nosliding contacts. When the rotor is turned towardsincreased meshing, the frequency is lowered by theincreased inductance and capacitance. The rotorturns through an angle of 90 degrees for its fullfrequency range.

Butterfly tuners are suitable for use where widefrequency ranges must be covered. In design for suchservice, the size and number of plates are made aslarge as possible while still obtaining the necessarytop frequency and freedom from spurious modes ofoperation. The necessary low frequency is thenobtained by reducing the air -gap clearance as far asrequired.

MICROWAVE TUNERS. At some point in thefrequency band about 1,500 mc, it is found that theuse of an r -f stage in a receiver results in a. lowersignal-to-noise ratio than without the stage. Kly-strons will produce amplification at these frequenciesand are useful as transmitting amplifiers, but theyare too noisy for use in receivers as r -f amplifiers.Tube noise is important only when small signal levelsare being handled. If the signal strength is of thesame order as the noise produced in a stage, a largeamount of distortion will result. However, if thesignal level is of much larger amplitude than the

noise, little if any effect will be produced. For thisreason, noise produced in amplifiers is of importanceonly in low power level stages such as the initialstages of a receiver. Traveling wave tubes areexpected to become useful as r -f amplifiers in re-ceivers as they are developed. Experimental tubeshave been made which have as low a noise figure asthe crystal mixers now used for the first stages inreceivers above 500 mc. The receivers now used forfrequencies above this point have as their first stages(1) the antenna, (2) a tuned circuit or preselector,and (3) a crystal mixer for converting the signal to alower intermediate frequency. The preselector iscomposed of one or more tuned circuits which rejectall frequencies except the desired frequency band.Butterfly tuners may be used for frequencies below1,000 mc and coaxial cavities from about 500 mc up.

In general, a preselector is fed from a low -imped-ance source, the antenna, and is coupled to the higherimpedance of a crystal mixer. The tuner must there-fore act also as an impedance transformer to obtainmaximum energy transfer. It must have a pass bandthat is at least as wide as the pass band of the i-famplifier and an off -frequency attenuation whichproduces the largest amount of image and harmonicrejection that can be obtained. If the desired attenua-tion characteristic cannot be obtained by a single -tuned circuit and still maintain the required passband, double- or triple -tuned circuits must be used.

LOCAL OSCILLATORS

The local oscillator used in the receiver must oper-ate at a frequency similar to the received frequency.The exact frequency of the oscillator is the desiredsignal frequency plus or minus the intermediatefrequency. The local oscillator may operate either ata higher or a lower frequency than the received signal,since the difference frequency will remain the same.The oscillators used up to 500 mc may be conven-tional vacuum tube oscillators, while coaxial oscil-lators are used up to about 3,300 mc. Klystronoscillators, usually of the reflex variety, are usedexclusively above this frequency.

MIXERS

The device used to produce the i-f from the receivedsignal and the local oscillator signal is known as themixer or first detector. Any nonlinear device may beused for this purpose, although at frequencies above100 mc triode and diode vacuum tubes and crystalrectifiers are usually used. At frequencies up to about500 mc, triodes such as the type -2C40 lighthouse tubemay sometimes be used in spite of the large amount

96

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of noise generated, since the relatively high conver-sion gain makes it possible to obtain a higher S/Nratio than if a diode or crystal rectifier were used.Conversion gain is defined as the ratio of the mixeri-f output to the r -f signal input and is usuallyexpressed in db. Above 500 mc crystal mixers areappreciably superior to any triode mixers now avail-able because of the small amount of noise generated.The conversion loss of type -1N26 crystals is low, evenat 23,000 mc, with a maximum conversion loss vary-ing from 5.5 to 7.5 db in the frequency range from3,000 to 16,000 mc. The maximum noise ratio, or theamount of noise generated by the mixer comparedto the noise produced in an equivalent impedanceresistor, varies from 1.5 to 2.5 in the same frequencyrange. Silicon crystal mixers have the disadvantagethat they damage easily if overloaded.

I -F AMPLIFIERS

The difference frequency produced in the mixermay actually be any desired value. Selection of thefrequency to be used in a given receiver will dependon several factors. A high i-f is desirable to eliminateimage response, but the selectivity and noise figureof an amplifier becomes worse with an increase infrequency, and ganged tuning of the local oscillatorand preselector becomes increasingly more difficult.The choice of the intermediate frequency is thereforea compromise between the desired image -rejectionratio, on one hand, and the desired sensitivity, selec-tivity, and circuit simplicity on the other.

A method of obtaining both good image -rejectionby using a high i-f, and good selectivity and simplicityof circuits through the use of a low i-f, is the double-

conversion superheterodyne receiver. A high i-f isfirst produced to obtain a good image -rejection char-acteristic. This frequency is then further reduced bya second frequency conversion, bringing the i-f downto a frequency that can be easily amplified and thatprovides good selectivity. The oscillator used to pro-duce the second i-f may be crystal controlled since itheterodynes with a fixed frequency. The disadvan-tage of this system is the additional local oscillatorand mixer stages required.

I -f amplifiers are required to have a wide bandwidth and high gain. These factors are mutuallyantagonistic as shown in the equation below for asingle -tuned amplifier stage.

where

G = The voltage gain per stage at the centerfrequency

(9-2)G X B = gm2 7 C

97

B = Band width of the amplifier stageg, = Transconductance of the tubeC = Total stage capacitance.

G X B is known as the gain -bandwidth product andis a constant for a given tube and associated com-ponents. Using a type-6AK5 pentode, the gain -band-width product is about 65.2 mc. With a bandwidthof 10 rr c, the available gain is only 6.52. When anumber of identical single -tuned amplifier stages areconnected in cascade, the overall bandwidth becomes

Overall B = (one -stage bandwidth) x -1 (9-3)This limits the overall bandwidth available. Forinstance, with one of the best tubes available for usein i-f amplifiers, the 6AK5, and obtaining a gain of100 db, a commonly needed gain, the maximumbandwidth theoretically available is 6.9 mc which inmany cases is inadequate. In addition, 23 stages arerequired to accomplish even that result.

It is easily seen that some means must be foundto obtain increased bandwidths with high gain. Thisis accomplished by stagger tuning. In this technique,the stages are tuned to several different frequencies,which makes wide -band operation with high gainpractical.

DETECTORS

Some means of separating the carrier from thedesired information must follow the i-f amplifier. Thesecond detector or demodulator is used for thispurpose.

If AM is being received, a simple rectifier and filtercircuit is used. Another way of looking at amplitudedemodulation is that the carrier and its sidebandsare heterodyned together and the difference frequencyrecovered as the information. When receiving single-sideband signals, the carrier must be injected at thispoint to heterodyne with the received sideband. Thisis usually done with a crystal controlled oscillatoroperating at the intermediate frequency.

The detectors used for FM are often called dis-criminatorsand utilize completely different principles.A discriminator is defined as a device which producesa d -c voltage proportional to the frequency of aninput signal. This may be accomplished in a numberof ways. One method uses two tuned circuits, onetuned above the center frequency and one tunedbelow, to obtain two i-f voltages whose amplitudesdepend directly on frequency. These voltages are thenrectified and combined so that zero voltage output isobtained at the center frequency. A difference voltageof the two i-f voltages which is proportional to the

CHAPTER 9


frequency is obtained when the frequency of the i-fsignal is above or below the center frequency. Adiscriminator of this type is sensitive to amplitudevariations in the input and so a clipper -limiter stagemust be used preceding the discriminator to removeany AM. Another method of obtaining frequencydiscrimination is the use of the phase detector. Thisoperates by comparing the phase relationships of twosignals, one the i-f signal and the other the i-f signalphase shifted in a resonant circuit tuned to the centerfrequency. The amount of phase shift will be pro-portional to the frequency of one signal. A limiterstage is also required for the phase detector.

To eliminate the need for a limiter stage, severaltypes of discriminators have been developed whichwill not respond to amplitude changes. The first ofthese is the ratio detector. Instead of the two rectifiedvoltages of the ordinary discriminator being combinedwith opposite polarity, they are combined so as toadd. The sum of the voltages is kept constant by alarge value capacitor. This eliminates any amplitudevariations of the i-f signal and makes the use of alimiter stage unnecessary. The ratio of the two volt-ages changes as the frequency input to the ratiodetector changes and the output is taken from oneof the rectifier loads.

Another type of discriminator, which combines ahighly efficient limiter and special type of discrimi-nator in one envelope is the gated -beam detectorusing a 6BN6 vacuum tube. This tube has an ex-tremely sharp cut-off and saturation characteristicand will operate with as little as 1 volt input to thelimiter grid. The discriminator action takes place dueto the gating characteristics of the tube. Two controlgrids are present and each must have a positive signalapplied for plate current to flow. The i-f signal isapplied to each of these grids, to the first, or limitergrid, directly, and to the second, or quadrature grid,through an L -C phase shifting network. The phaseof the quadrature grid voltage will depend on thefrequency of the i-f voltage. By comparing thesevoltages in the gating action of the tube the averageoutput current will be inversely proportional to thefrequency of the input. Several other discriminatorcircuits have been developed, but those describedabove are in widest use.

AFC SYSTEMS

Receiver stability is even more important thantransmitter stability. In contrast to the AFC systemsused in transmitters, which tend to keep the operatingfrequency at an absolute value, receiver AFC sys-tems usually compare the receiver's operating fre-

quency to the received signal. This is done by usinga discriminator in the i-f channel to develop the errorsignal used to retune the oscillator. An FM receivermay use the same discriminator for signal detectionand AFC provided the signal variation is averagedover a period of time so that the oscillator does notattempt to follow the modulation, but only slowfrequency drifts. With the exception of the develop-ment of the error signal, AFC is obtained by thesame methods as in transmitters.

AGC SYSTEMS

Since received signal strength will vary over a widerange some means of automatic gain control (AGC)is required in the receivers. This is accomplished byrectifying the received carrier and averaging thevoltage over several cycles of modulation. This volt-age is then used as grid bias for the i-f amplifiers sothat as the average signal strength increases, the gainof the i-f amplifier is decreased. The bias is usuallynot applied to the first amplifier stage since the stagetends to become noisier with AGC applied. Withsome types of modulation, such as for television, therectified i-f signal is not proportional to the carrierlevel, or the ratio of peak -to -average signal may betoo large to make practical the use of the averagevalue to control the receiver gain. Special techniquesmust be used to provide AGC in these cases.

VIDEO AMPLIFIERS

The detected modulation must be amplified forfurther use. If the modulating signal takes the formof pulses, an increase in S/N ratio can also be ob-tained at this point by pulse shaping circuits. Videofrequencies are those frequencies from near zero tofrequencies of several megacycles. The video amplifiermust amplify this complete frequency range, whichin some equipment is up to 20 mc, with uniformresponse. For pulse transmission, the bandwidth inmc must be at least twice the reciprocal of the pulseduration in microseconds if the pulse is to approxi-mate its original shape. Phase shift characteristicsare as important as band widths, since phase distor-tion will change the pulse shape by phase shifting theharmonics which make up the pulse difference angles.

R -C coupled pentode amplifiers are most satis-factory for these video amplifiers. The high frequencyresponse is limited by the output capacitance, theinput capacitance of the next stage, and the dis-tributed capacitance of the wiring. These threecapacitances appear in parallel and shunt the loadresistor, decreasing its impedance and therefore thestage gain, at high frequencies. The low frequency

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response is limited primarily by the time constant ofthe grid circuit which must be long compared withthe lowest frequency to be amplified.

High frequency response is increased by

1. decreasing the plate load resistors2. using tubes with low grid -to -plate capacitance

3. carefully laying out components and wiring4. decreasing the grid resistorsb. using multiple low gain stages6. using negative feedback7. using compensating networks.

Shunt compensation uses an inductor in series withthe plate load resistor of the stage. As the frequencyincreases, the impedance of the inductor increases,compensating for the decrease in impedance of thecapacitance in shunt with the load. Shunt compen-sation will increase the flat response of a stage by afactor of about 10. Series compensation uses aninductor in series with the coupling capacitor to thenext stage. The inductor is selected so that it is seriesresonant with the input capacitance of the next stageat a frequency higher than the desired high frequencycut-off of the amplifier. As the frequency is increasedthe voltage drop across the input capacitanceincreases, thus compensating for the high frequencyloss in the preceding stage. Series compensation canincrease the flat response of the amplifier by a factorof about 15. Combination compensation using bothshunt and series compensation may be used toincrease the flat response of the amplifier by a factorof about 18. Low frequency compensating networksare composed of a resistor and capacitor in parallel,connected in series with the load resistor. The highand low frequency compensating networks operateindependently and do not interfere with each other.Low frequency compensation is important primarilyto minimize phase distortion.

PULSE RESTORATION. The first stages of thevideo amplifier may be used when receiving pulsetransmissions to reshape the pulses and remove thenoise characteristics. Figure 9-4 illustrates the waveshapes of the pulse as received, and after clipping andlimiting. Most of the noise distortion is removed in

(a) ORIGINAL PULSE

(b) PULSE WITH NOISE

(c) CLIPPED PULSE, SHOWING PART OFPULSE TO BE AMPLIFIED IN RECEIVER

(d) RESTORED PULSE, WITH NOISEEFFECT EXAGGERATED

Figure 9-4. Pulse Restoration

this process. By increasing the band width of thesystem and using shorter pulses, greater reductionof noise can be made.

DIRECT DETECTION RECEIVERS

The simplest type of receiver is one in which acrystal detector is connected to the antenna and thevideo output is amplified to a suitable level for use.No local oscillator or mixer is used. Selectivity isprovided by a tunable or fixed -frequency r -f filterinserted between the antenna and the detector.

An application of this type of receiver is in smallportable receiver units where sensitivity and selec-tivity may be sacrificed to obtain simplicity of design.Receivers of this type are capable of detecting signalswith powers as low as 4x10-9 watts using a bandwidthof 10 me at a carrier frequency of 3,000 mc. At10,000 me and a bandwidth of 10 mc, a signal of8x10-9 watts may be detected. These sensitivitiesare lower than for comparable superheterodynereceivers which may have a sensitivity of the orderof 10-12 watts at the noise threshold.

99

I II I' T F. It

INTRODUCTION

Since radio transmission in the VHF and UHFbands are essentially short range, some form of relaymust be provided if operation over a great distanceis required. The relays used in radio -relay communi-cation are called repeaters. They are essentially justwhat the name implies-they receive a signal fromthe terminal transmitter or another repeater, amplifyit, and then transmit it onward to another repeateror terminal receiver.

TYPES OF REPEATERS

Two general groups of repeaters are used-activeand passive. Active repeaters actually amplify thesignal and re -radiate it, while passive repeaters arenothing more than reflectors whose only gain is thatdue to the change in direction of the radiation.Contained within the group of active repeaters are anumber of types that vary according to their use andmethod of operation.

Obviously two terminal radio equipments back-to-back, the receiver output from one feeding thetransmitter input to the other, could be used as arepeater station. This is done at what is called aterminal repeater, but then only for reasons ofrearranging the traffic channels within the baseband.The baseband is composed of the multiplexed signalsused to modulate the carrier. On a radio -relay systemof several hops, it is preferable for reasons of per-formance and cost to employ a heterodyne typerepeater. In this repeater the incoming carrier isheterodyned down to a frequency which may be easilyamplified, and after amplification heterodyned backup to the transmitting frequency.

10

REPEATERS

CHAPTER 10

REPEATERS

It is often necessary to drop or insert traffic at arepeater station to feed a branch, or a local user,without resorting to a terminal repeater. This is donein a drop repeater which has special provisions forextracting or "dropping" certain traffic from eitheror both directions and inserting complementarytraffic for duplex (two-way simultaneous) transmis-sion. Figure 10-1 is a simplified block diagram of thevarious types of active repeaters.

THROUGH REPEATERS. Straight -through re-peaters, in which the received carrier is amplifieddirectly making them the simplest type of repeaterthat could be designed, are not used for severalreasons. One reason is that noise -free amplifiers arenot available for frequencies above about 1,000 meat present. In addition, it is desirable to change thefrequency of transmission to prevent regenerativefeedback due to coupling between the antennas.

A heterodyne through repeater is the simplest typeof active repeater in use. Figure 10-2 is a blockdiagram of one type of heterodyne repeater. Thesignal is received and heterodyned to the intermediatefrequency, which can be amplified efficiently, and asecond mixer is then used to increase the frequencyto the desired output carrier frequency. This is thenamplified and transmitted with no demodulation andsubsequent remodulation required.

By the addition of another mixer stage the fre-quency of operation of the repeater is dependent onlyon the received frequency. The same oscillator is usedto heterodyne the frequency first down and then up,thus compensating for any frequency instability. Asecond crystal -controlled oscillator, equal in fre-quency to the frequency difference desired between

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REPEATERS

( NORTHBOUNDDROP)

( SOUTHBOUNDINSERT )

( NORTHBOUNDDROP)

( SOUTHBOUNDINSERT)

D

T

R

M

NORTH

TERMINALSTATION

HETERODYNEDROP -CHANNEL

REPEATER STATION

( NORTHBOUNDINSERT)

( SOUTHBOUNDDROP)

HETERODYNETHROUGH - REPEATER

STATION

TERMINALREPEATER STATION

( NORTHBOUNDINSERT)

(SOUTHBOUNDDROP)

TERMINALSTATION

SOUTH

ANTENNA DUPLEXER

TRANSMITTER

RECEIVER

MULTIPLEXING EQUIPMENT

* NOTE RECEIVERS AND TRANSMITTERS IN HETER-ODYNE REPEATERS DO NOT DEMODULATEAND REMODULATE CARRIER.

Figure 10-1. Types of Repeaters

the receiver and the transmitter, is used to changethe operating frequency, thus requring the additionalmixer stage.

A third type of through repeater may be used inwhich the same oscillator is used as the local oscillatorand the transmitting oscillator. The signal is received,demodulated, and the video signal then used tomodulate the oscillator. The transmitted and re-ceived signals therefore have a difference frequencyequal to the intermediate frequency. If this systemis used for frequency modulated signals, the i-f band-width must be twice the bandwidth of the receivedsignal. This is necessary because the oscillator mustbe arranged in such a way as to shift frequency whenmodulated in the direction opposite to the frequencyshift of the received signal. If this is not done theoscillator will try to follow the received signal andthe modulation index will be reduced by a factor oftwo through the repeater.

DROP REPEATERS. To drop channels, all that isrequired is to place a parallel branch on the receiveri-f amplifier and pass this signal to a demodulator andbaseband amplifier to recover the entire signal spec-trum originally passing through the main system.Those channels intended for local use are thenselected by appropriate multiplexing equipment. Allof the channels dropped at such a repeater also con-tinue through the system to the next terminalstation. No means is available for stopping thechannels at a drop repeater, but it has the advantagethat simpler multiplexing equipment may be usedthan is required for a terminal repeater. Insertion ofchannels is accomplished by modulating one of theheterodyning oscillators as shown in figure 10-2.

One-way channel insertion or dropping, that is,inserting or dropping a channel toward or from oneterminal only, is most common although in somecases the channel may be inserted in both directions.

TERMINAL REPEATERS. A terminal repeaterstation is one in which all signals are completelydemodulated and repeated by remodulation. In itssimplest form it consists of two complete terminalequipments, the receiver output from one feeding thetransmitter input of the other through multiplexingequipment.

It is dear that in a system having several dropchannel repeaters, where traffic is inserted anddropped, a substantial portion of the baseband wouldbecome loaded with traffic traversing only a part ofthe main truck. It may become necessary to reusesome of the baseband on portions of the system, so aterminal repeater is used to recover these channels

102

or to redistribute the channelling layout. At suchrepeaters the baseband is demodulated, those chan-nels intended for local use or onward transmission areselected, and the others eliminated. Beyond thispoint, the channel space used up to this point by theeliminated channels can be used again. The originalchannelling structure may be maintained or completerechannelling may take place.

SERVICE UNITS

Service units are used at both repeaters and ter-minals to provide a common party line for the use ofoperating and maintenance personnel. Usually thefirst channel of the system is kept open for thispurpose in frequency division multiplexing systems,since multiplexing equipment is not required foraccess to this channel (see Chapter 11). Ringingcircuits are also provided to permit calling anydesired point in the system.

In many cases repeaters are unattended, requiringthat some means of signaling equipment failures beprovided. The same equipment used to signal failureof the equipment can also be used to automaticallyswitch in standby equipment keeping service inter-ruption due to equipment failure to a minimum.Delay circuitsfrom more than one repeater at a time. A trans-mitter failure could show up as receiver failure at the

R.F. AMPLIFIEROR

PRESELECTOR

ANTENNADUPLEXER

CHAPTER 10

REPEATERS

next terminal if these delay circuits were not used.Fault indicators are placed at attended stations atdistances which depend on the repeater spacings andthe accessibility of the stations.

PASSIVE REPEATERS

The passive repeater is used in microwave radiorelay work to direct the beam round some obstaclethat cannot be removed. It occasionally happens thatno choice exists for the location of a repeater station,except one that contains an obstruction in the beampath. When this happens, one solution is a passivereflector. Since even the best of the passive reflectorsattenuate the signal considerably, they should not beused except as a last resort.

Two types of passive reflectors are used, depend-ing upon the terrain. These are plane reflectors andpassive repeaters. If the repeater stations are solocated that the signal can be bounced off a planereflector to the receiving station, then the plane typewill do. However, where a high ridge intercepts thebeam, or a situation exists where a plane reflectorcannot be made to reflect the signal toward thereceiver, the passive repeater is used. This typeconsists of two parabolic antennas, one facing eachrepeater station, and connected together by meansof a waveguide or a coaxial cable. The operation hereis somewhat different from that of the plane type of

WEST TO EAST PART OF REPEATER

MIXER

DISCRIMINATORBASE BAND

VIDEOAMPLIFIER

FIRSTHETERODYNEOSCILLATOR

I. FAMPLI FIER

PHASEMODULATOR

MIXER

TO DROP CHANNELWEST TO EAST

MULTIPLEX EQUIPMENT

TOSERVICE CHANNEL

CHANNELSHIFTER

OSCILLATOR

SAME ARRANGEMENT IN REVERSE FOR EAST TO WEST

* PARTS OMITTED IN A THROUGH REPEATER

Figure 10-2. Heterodyne Repeater

103

POWERAMPLI FIER

ANTENNADUPLEXER

_

CHAPTER 10

REPEATERS

reflector. The signal picked up by the receivingantenna is transmitted through the waveguide orcoaxial cable to the transmitting antenna of thepassive repeater, and thus sent on to the receivingrepeater. The passive repeater is merely a repeaterstation with no amplification power. It has the draw-back of causing considerable attenuation, since onlythe amount of energy falling on the passive receiverparabola is used, and there is additional attenuationdue to the interconnecting waveguide and passivetransmitting antenna. Another disadvantage of this

type is loss due to refraction. Since the passiverepeater transmits less than the power received,attenuation caused by the beam bending away fromthe receiving antenna can cause considerable fading.For these reasons, the passive repeater should be usedonly on extremely short hops, where attenuation inthe repeater and beam bending cannot have anyserious effect. It is most often installed in locationswhere terrain makes maintenance and inspection ofa repeater station difficult.

4

104

CHAPTER

INTRODUCTION

Each frequency range of the radio spectrum hascertain advantages that make it desirable for someparticular type of communication. Higher frequenciesare desirable for relaying information that mayrequire a wide bandwidth. At higher frequencies,highly directive antennas may be employed, allowinglow power transmitters to direct a signal to thereceiver, and thus obtain a good signal-to-noise ratio.In using these frequencies for relay work, the abilityto focus the radio beam gives an efficient method oftransmitting information over long distances. Therelay system is often more economical than a wiretransmission line, and more reliable, since the repeaterstations are less affected by storms than wire lines.

The wide bandwidth available at higher frequenciesmay be used where the message has a wide range offrequencies, such as television, or where it is desirableto send a number of low frequency messages simul-taneously, as in telephone communication. Whereseveral messages such as voice, facsimile, or teletypeare to be combined, two general methods are avail-able, and the combining of the messages is calledmultiplexing. The methods used for multiplexing arefrequency division, and time division, and maymodulate the carrier or subcarrier with either ampli-tude modulation or frequency modulation.

FREQUENCY DIVISION

Frequency division consists in separating the vari-ous messages to be combined so that each messageis limited to a certain frequency range, with no over-lapping between these ranges. This is accomplished

11

MULTIPLEXING

CHAPTER 11

MULTIPLEXING

by first limiting the audio bandwidth to definitevalues. This bandwidth may vary, according to thedesired quality of speech reproduction. By filteringout all frequencies below 200 cycles per second, andabove 3,000 cycles per second, the audio bandwidthbecomes 200 to 3,000 cycles per second. This frequencyrange is entirely adequate for intelligibility, althoughit is definitely substandard reproduction. An audiorange of 100 to 3,500 cycles per second sounds farmore natural to the listener, and is the standard setfor non-military telephone service.

Groups of telephone circuits must be combined insuch a way that they may be separated at the receiv-ing terminal and routed to their respective destina-tions with a minimum of crosstalk. This is done bymodulating a separate subcarrier for each voicechannel, with the subcarrier spacing a little morethan twice the highest audio frequency to be trans-mitted. Such a method gives entirely satisfactorycommunication, but requires a rather wide band.This band may be halved by using single-sidebandmodulation, which requires a carrier spacing of alittle more than the highest audio frequency, insteadof twice the audio frequency. The most commonmethod of frequency -division multiplexing is single-sideband, suppressed carrier, and it will be the typeconsidered here.

Frequency separation of voice for transmission isaccomplished by modulation with an audio frequencyin such a way that the various messages are separateduniformly over a range of frequencies. This range offrequencies, which includes the spacing betweenmessages, becomes the modulation bandwidth. Obvi-ously, the audio signals can not modulate the carrier

105

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MULTIPLEXING

directly, for the messages would be hopelesslyscrambled. They can be separated quite easily,however, by heterodyning each message with a differ-ent audio frequency, and filtering out the lowersideband. For example, four messages are to bemultiplexed by single-sideband multiplexing, eachmessage having an audio range of 100 to 3,500 cyclesper second. The first message would not need to beheterodyned with an audio signal, but could remainunchanged. The second message to be multiplexedhas a frequency of 4,000 cycles heterodyned with it,so that its range of frequency now becomes 4,100 to7,500 cycles per second. Combining these two mes-sages gives a bandwidth of 100 to 7,500 cycles persecond. The messages are easily separated at thereceiver by using a bandpass filter that will pass thefrequency range of one message, and block all others.In the same way, a third message would be hetero-dyned with 8,000 cycles per second, to produce arange of 8,100 to 11,500 cycles, and a fourth messagewould have a frequency range of 12,100 to 15,500cycles per second. The modulation bandwidth nowbecomes 100 to 15,500 cycles per second.

There is no reason for limiting the group ofmessages to four. Theoretically, as many messagesas the allotted bandwidth at the carrier frequencywill carry may be used, with the bandwidth in theUnited States being regulated by the FCC. Wheremany messages are to be transmitted by the samecarrier, the messages may be multiplexed as de-scribed for four messages, or they may be broken intogroups of any convenient number with each groupmodulating a separate subcarrier. The subcarriers,in turn, modulate the carrier for transmission. Need-less to say, the subcarriers must be spaced so thatno overlapping of frequency will occur at any pointin the ratio spectrum. The combined messages mayamplitude modulate or frequency modulate thecarrier (or subcarrier), as desired.

PULSE TIME MODULATION (PTM)

INTRODUCTION. As stated earlier in this chapter,messages may be combined for transmission by thesame carrier by separating the messages either infrequency, or time. In order to separate the messagesin time, each message is transmitted for a brief periodof time, in regular sequence. This process is calledsampling. The receiver separates the samples, andreconstructs the original messages from the samples.

PULSE AMPLITUDE MODULATION (PAM).One system of time -division multiplexing commonlyused, and the basis of nearly all time -division sys-

tems, is pulse -amplitude modulation, (PAM). In thissystem, the signal is periodically sampled, and a pulseobtained whose height, or amplitude, is proportionalto the amplitude of the signal at the instant ofsampling. As an illustration of PAM, consider a curveplotted on a sheet of graph paper (figure 11-b). Bydetermining the ordinates (amplitude) of the curveat uniformly spaced points along the abscissa (time),the curve may be readily plotted. The pulses areuniformly spaced in time, with their amplitudes de-termined by the amplitude of the signal. There is nonecessary limit to the maximum number of points inplotting a curve, but there is a minimum number ifthe curve is to be properly reconstructed. A similarlimitation exists in regard to the number of samplesto be taken in properly reconstructing the audiosignal. Experiments on pulse modulation have shownthat a sine wave must be sampled at least 2 timeseach cycle if it is to be reproduced by the receiver.The sampling rate is therefore determined by thehighest audio frequency tone to be transmitted,which is dependent upon the quality of reproductiondesired. If the highest frequency to be transmittedis 3,200 cycles per second, sampling must be takenat a rate of 8,000 per second.

In the above paragraph, only one of the multi-plexed messages has been considered. Where four

(a) SINE WAVE

(b) PA M

(c) PDM

(d) PPM

(e) P C M

Figure 11-b. Types of PTM

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MULTIPLEXING

messages are to be transmitted, each of the four mustbe sampled 8,000 times, with a total pulse repetitionrate of 32,000 per second. The sampling is done inrotation, so that every fourth pulse will be takenfrom the same message. One other considerationmust be taken into account, namely, identifying themessage to be sent to any particular circuit at thereceiver. Not only must the message be properlyreconstructed by the receiver, but it must also berouted correctly. In order to identify the messages,that is, identify which is channel one, two, three andfour, some form of coding must be included in orderto send each channel to its proper destination at alltimes. This may be accomplished by using a specialpulse for channel #1. If such a pulse were twice thewidth of the other three pulses in the group, thewidth could be used to establish the start of eachgroup of pulses. Another method used is to add anextra pulse to each group, with the extra pulse as amarking pulse, to identify the start of each pulsegroup.

PAM, like frequency -division modulation, dependsupon the amplitude of the signal as the major char-acteristic to be transmitted. While these systems arethe simplest forms of multiplexing, they are mostlikely to be affected by noise. Atmospheric noisepicked up by the repeaters, as well as internal noisein the repeaters themselves, will be transmitted alongwith the signal, with each repeater adding its ownincrement of noise. This may be partially overcomeby using a S/N ratio for each repeater that is con-siderably higher than the S/N ratio for the systemas a whole, a remedy that requires more powerfultransmitters or closer spacing of the repeaters, orboth. There are other forms of pulse time modulation,such as pulse duration modulation, that are lessaffected by noise than PAM (figure 11-1a).

PULSE DURATION MODULATION (PDM). Theideal pulse for use in time division multiplexing is asquare -wave pulse, with zero rise and decay time.This ideal wave shape is closely approximated in thetransmitter, but becomes distorted by the time itreaches the terminal receiver. This distortion iscaused partly by the time constants of the trans-mitters, and receivers in the system, and partly bythe noise added to the signal. In PAM -AM systems,this distortion can produce complete unintelligibility,unless a very high S/N ratio is maintained for eachrepeater. Other forms of time division modulation areavailable, which are less affected by distortion, par-ticularly the distortion produced by noise. One ofthese systems is pulse duration modulation, (some-times called pulse length modulation, or pulse width

107

modulation). PDM, as the name implies, transmitsthe amplitude information not by the height of thepulse, but by its duration. Any variation in the ampli-tude, such as produced by noise, will have less effecton the signal than when PAM is used (figure 11-1c).

The signal to be multiplexed may be sampled atthe same rate and in the same manner as for PAM.These pulses may then be used to determine theduration, or width, of the pulses to be multiplexed,so that the signal amplitude will be expressed by theduration of the pulse rather than its amplitude. InPDM the period of time allotted for each pulse isuniform, usually being measured from the leadingedge of the pulse or the center of the time interval.Where the leading edge of the pulse marks the startof each period the position of the trailing edge willbe determined by the amplitude of the signal at theinstant of sampling.

One disadvantage of PDM is the irregular powerdemand on the transmitter. Since the carrier istransmitting only during the pulse periods, the powerrequirements of PDM, with its varying duration,will result in the transmitter output being irregular.In systems using uniform pulses uniformly spaced,the power required of the transmitter will remainconstant. Another disadvantage of PDM, which isshared by PAM, is the use of the pulse shape todetermine the amplitude of the signal. Any distortionof the pulse shape will therefore affect the intelli-gibility of the message to some extent, although PDMis much less affected by distortion than PAM.

PULSE POSITION MODULATION (PPM). Themost desirable method of pulse modulation is onewhereby the message is transmitted by some meansother than by the shape of the pulse itself. This canbe accomplished in several ways. One method em-ploys pulses of uniform height and width, butdisplaced in time from some base position accordingto the amplitude of the signal at the instant ofsampling. Pulse position modulation (PPM), or pulsephase modulation, employs a uniform pulse whichtransmits the signal information by means of thepulse position within an allotted period of time(figure 11-1d). The pulse period is the same as forPDM, which is determined by the initial rate ofsampling. The trailing edge of the PDM pulse maybe used to determine the location of the pulse inPPM, as shown in figure 11-1d. Where PDM is usedto trigger the pulses for PPM, or where PDM is usedto modulate the carrier, the duration of the pulsemust never be greater than the period of time allottedfor each pulse. Actually it will be somewhat less, toallow deer y time for one pulse, and rise time for the

CHAPTER 11

MULTIPLEXING

following pulse, so that no crosstalk may occur.Another system of PPM shifts the pulse toward

either edge of the time period, with the pulse in thecenter of its allotted time interval in the event thatno message is being transmitted. A time intervalbetween pulses must also be employed, to reducecrosstalk to a minimum.

PULSE CODE MODULATION. Each type of timedivision multiplexing mentioned in this discussion isless affected by noise than the types preceding, andmore affected by noise than the types that follow.On such a scale, pulse code modulation (PCM),sometimes called pulse numbers modulation, belongslast, since it is least affected by noise. As with PPM,the information is not determined by the shape ofthe pulse, and therefore the S/N ratio will be muchgreater than for PAM.

PAM employs pulses determined by the amplitudeof the signal, and thus an infinite number of steps,or degrees of amplitude, may be expressed by thepulses. In PCM, an infinite number of pulses wouldbe required to express an infinite number of ampli-tudes. Fortunately, it is quite possible to expressvarious degrees of amplitude without using an infinitenumber of amplitudes. Because of the inability of thehuman ear to distinguish slight variations in ampli-tude, the original signal may be reproduced satis-factorily with surprisingly few degrees of amplitude.These degrees of amplitude, or steps, may be in-creased in several different ways. The increase fromone step to the next may be uniform, or may varywith a geometric or logarithmic ratio, as desired.Since the ear is insensitive to variations of amplitudemuch less than double the initial amplitude, the stepsare usually logarithmic, or arranged so that each stephas double the value of the preceding step.

The next consideration is the required number ofsteps to indicate the amplitude of the signal satis-factorily. A single step, for example, would indicatethe presence or absence of a tone, and nothing more.Obviously, one step would not be sufficient to conveyintelligence. If two steps were used, the tone wouldthen be either loud, or soft, or non-existent. In prac-tice, it has been found that if the amplitude of a sinewave, from its minimum (in a negative direction) toits maximum (in a positive direction) is divided into31 parts, satisfactory speech reproduction will beobtained. This means, then, that half of the 31 stepsindicate the negative part of the wave and halfindicate the positive half. In actual practice zeroamplitude would be represented by the 16th step,and each half -wave divided into 15 parts with eachstep outward from zero amplitude increasing logarith-

mically, or having twice the value of the precedingstep.

There is no magic in the number 31, only com-promise. If the amplitude is expressed in fewer steps,accurate reproduction of the original waveshape willbe impossible. Where it is desirable to recreate theoriginal signal very accurately more steps may beused, requiring more pulses, and therefore a widerbandwidth. By limiting the number of steps to 31satisfactory reproduction may be obtained and thenumber of pulses kept within a reasonable amount.

If sampling as indicated above is used, with 15steps above the 15 below the zero amplitude value,obviously 31 values of the amplitude must be trans-mitted. If bandwidth were no problem, this could bedone merely by using 31 pulses, each expressing adefinite degree of amplitude, with the first pulseindicating maximum positive amplitude and the 31stpulse indicating the maximum negative amplitude.Since 31 pulses would require an unduly wide band-width, the amplitude must be coded in such a waythat the 31 steps of amplitude may be representedby fewer than 31 pulses for each sample of the originalsignal. This may be done by use of only five pulsesoperating five binary counters, with the countersoperated in regular sequence by the groups of fivepulses. Let the values of the counters be 16, 8, 4, 2,and 1, respectively. An amplitude of 31 would berepresented by all five pulses (1 + 2 + 4 + 8 + 16= 31). An amplitude of 13 would be presented by8, 4, and 1. The code would therefore require all 5pulses for 31, and only 3 pulses for 13, hence thereason for each pulse triggering a particular binarycounter. Where a value is not needed, as in the casewhere the amplitude of 13 is to be transmitted, nopulse will appear. Thus, only the second, third andfifth pulses will be transmitted to indicate an ampli-tude value of 13.

There are two other methods of pulse time modu-lation: delta modulation, and random pulses. Neitheris in general use at present, but deserves mention inthis section. Delta modulation transmits informationconcerning the message by employing a pulse toindicate an increase in amplitude, and omitting thepulse to indicate a decrease in amplitude. It has theadvantage of giving exceptionally low distortionwhere the increments are small, which advantage ismore than offset by the wide bandwidth (100 kc)required. Random sampling is done by use of arandom pulse oscillator, similar to a noise generator,so that the sampling rate is approximately the sameas for other types of pulse time modulation. Decodingat the receiver is accomplished by employing a delayline in the transmitter, with paired pulses. The

108

CHAPTER 11

MULTIPLEXING

spacing between the paired pulses, one positive andthe other negative, is different for each message andidentifies each message. This is a comparatively newmethod and is not in general use.

CLIPPING. The effects of noise on the signal aregreatly reduced by using pulses whose shape is inde-pendent of the information being transmitted. Whilethe pulse will be distorted by noise, the message itselfwill be unaffected unless the pulse becomes badlydistorted. The effect of noise is shown in figure 11-2b,a condition that would produce almost completeunintelligibility in a PAM system. The pulses maybe improved by the process known as clipping,whereby the top and bottom of each pulse is removedleaving only the center section (figure 11-2c). Byamplifying the remaining segment of each pulse, theoriginal pulse may be approximately restored. Theamplitude of the pulse actually used amounts to nomore than 5 or 10% of the original pulse. Such aprocess not only removes the noise in the pulse itself,but also most of the noise that might affect the riseor decay time of the pulse. While the addition of theclipper circuits and amplifier circuit increases theequipment necessary, the S/N ratio may be corres-pondingly raised with satisfactory results. Further,the clipper circuits need not be installed at eachrepeater but only at the terminal receivers.

SIGNAL-TO-NOISE RATIO

The process of combining audio messages in orderthat more than one message may be transmitted overa single modulation bandwidth is divided into twoparts. First, the messages are combined with eachother in the process called multiplexing, and then themultiplexed messages are used to modulate the car-rier. Such a system is referred to as double modula-tion. Where the bandwidth of the carrier permits,several such carriers and their bandwidths maymodulate still another carrier of higher frequency.This is called triple modulation, and the intermediatecarriers are called subcarriers. The process could berepeated still further, if desirable, with the limitbeing determined by the permissible bandwidth ofthe final carrier. Triple modulation is most frequentlyused, with quadruple modulation rarely, if ever, usedat present.

Many combinations of multiplexing and modulat-ing the subcarriers and carriers are available, andabbreviations are used in order to designate the typeof double or triple modulation in concise form. Forexample, when PAM is used to amplitude modulatea subcarrier, which in turn frequency modulates the

(o) ORIGINAL PULSE

(b) PULSE WITH NOISE

(c) CLIPPED PULSE, SHOWING PART OFPULSE TO BE AMPLIFIED IN RECEIVER

(d) RESTORED PULSE, WITH NOISEEFFECT EXAGGERATED

Figure 11-2. Pulse Restoration

carrier, the triple modulation that results is expressedas PAM -AM -FM. In the same fashion, PCM-FM-FM indicates that pulse code multiplexing frequencymodulates the subcarriers, which in turn frequencymodulate the carrier. Double modulation is usedwhere there is no subcarrier, and, of course, one termwill be omitted. Thus, PDM-AM indicates that pulseduration modulation amplitude modulates the carrier.

The number of combinations of multiplexing andmodulating the subcarriers and carriers is almostinfinite, and listing all of the possibilities, or evenmost of them, would be impractical. Many of thecombinations would be comparatively worthless, andwhile others might be used, any advantage in S/Nratio, or increase in the number of messages, wouldnot offset the added complexity of the equipment.In discussing S/N ratios only the most commonlyused types of multiplexing and modulation will bepresented.

Frequency -division multiplexing may amplitudemodulate or frequency modulate the carrier, andsingle-sideband modulation may also be used. TheS/N ratio is different for each, and is also affectedby triple modulation, when used. In presenting theS/N ratios, three types of frequency multiplexing(AM, FM, and SS, or single-sideband), and four typesof time division (PAM, PDM, PPM, and PCM) areconsidered. These are presented in the table on S/Nratios, figure 11-3, together with the commonmethods of modulating the subcarriers and carriers.In order to reduce the various S/N ratios to a

109

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common denominator, they will be compared to theS/N ratio for single channel AM, with an S/N ratioof unity.

SPECIALIZED CHANNELS

DROPS AND ORDER WIRE. In any system ofcommunication where more than one message is tobe transmitted, it is seldom that all of the messageswill travel from one end of the system to the other.In many instances, some of the messages will be sentfrom an intermediate point to a terminal, or from oneintermediate point to another. Messages may bedropped at the repeater stations for transmission tosome nearby point, or they may be picked up fortransmission to some other point on the relay system.Where a message is dropped at a repeater station,an empty channel will exist from that station onwardunless it is used to transmit a message from thatstation to the terminal.

In most relay systems, one voice channel will bewithheld from voice transmission in order to use itas a service wire, or order wire. This channel willinform the nearest terminal station of a fault existingat a relay station, together with some indication ofthe type of fault existing. A complicated system ofblocking is employed, so that two repeaters cannot"report" trouble at the same time, which wouldhappen in the event of the failure of one stationdisrupting the operation of an adjoining station.

AUDIO CHANNEL WIDTH. While this discussionhas stressed the use of voice channels ranging infrequency from 100 to 3,500 cycles per second, thereis no reason why several adjacent voice channelscannot be combined, if desired, in order to transmita wider range of audio signals than are ordinarilyused in telephone communication. Many repeaterstations are designed to transmit both voice and

S/N RATIO FOR DOUBLE MODULATION,COMPARED TO A

S/N RATIO OF UNITYFOR SINGLE CHANNEL A M

SYSTEM S/N R M SRATIO SUMMATION SYSTEM S/N R M S

RATIO SUMMATION

AM -AMI

I4,/-n-PAM-AM len-

AM -FM a 8PAM(±) -FM

,r. 8

16 fs t/3" 12 f

FM -AM6 iF

PPM -AM28

16 frni;-13 9 f, VT.T3

FM -FM6

PPM - FM2 'FB-

16fri 1%/7 3n fr;

SS -AM1

VWPDM - AM

lT3n VE

SS -FM PDM- FM7

2 fc n /.-Fir

SS -FM -FMVT

PCM- XX co10 d /iWg

AFTER V.D. LANDON

WHERE'

B = EFFECTIVE NOISE BANDWIDTH OF THERECEIVER THROUGH THE R. F. AND I. F.CIRCUITS

di z THE ROOT- MEAN - SQUARE DEVIATIONOF THE MAIN CARRIER FOR ALLCHANNELS

n = TOTAL NUMBER OF CHANNELSfC

fm

SPACE BETWEEN SUBCARRIERS FORSS -AM; I/2 SPACE BETWEEN SUB -CARRIERS FOR AM - FM

HIGHEST MODULATION FREQUENCY FOREACH CHANNEL

Figure 11 -3. Single Channel S/N Ratios

television, with both modulating the same carrier.Similarly, a voice channel may be broken down intosubchannels for telemetering, or telegraphy. Thebasic method of multiplexing will in any case remainthe same.

110

IIAPTEIL

INTRODUCTION

The intelligibility of a received signal is limited bynoise, which, in the broadest sense, is any type ofinterference. Interference can be regarded, therefore,as noise resulting from the broad group of disturb-ances classed generally as static, either natural orman-made. The term noise may include continuousor discontinuous disturbances, the frequency withwhich such disturbances occur determining the char-acter of the noise.

Discontinuous disturbances may be classified intwo groups. Relatively infrequent, clearly separatedpulses, such as ignition noises, are called impulsivenoises. However, if the pulses occur so rapidly thatthey overlap and are not clearly distinguishable, thenthe noise is random. Tube and thermal agitationnoises are examples of random noises, as are atmos-pheric noises.

Continuous disturbances are primarily the resultof signal harmonics radiated from transmitters on thesame or adjacent channels and harmonics of othertransmitters or oscillators. This type of disturbanceis usually classified as selective interference or inter-ference whose energy is concentrated in a narrowband of frequencies. Radiation from unshielded dia-thermy apparatus is a good example of selectiveinterference.

Figure 12-1 illustrates the main sources of radionoise as plotted against operating frequency andaverage field strength. The curves were drawn withrespect to a carrier bandwidth of 10 kc, and areshown for comparative purposes only. The ranges andintensities of noises given are for the United Statesor regions of similar latitude.

CHAPTER 12

INTERFERENCE

12

INTERFERENCE

NATURAL NOISES

ATMOSPHERIC. At frequencies below about 100mc, atmospheric and precipitation noises are the mostimportant types to be considered. Nearly all atmos-pheric noise is considered to originate in the lightningflashes associated with electrical storms. As receivedfrom a distant point, this noise may be expected todisplay the same propagation characteristics as doordinary skywave transmissions propagated from adistant source by way of the ionosphere. In additionto these expected propagation characteristics, thereare the variations to be expected as a result of differ-ent concentrations of electrical storm activity invarious parts of the world, and the variation withfrequency in the noise intensity radiated from indi-vidual lightning flashes. The variations in noiseintensity are approximately inversely proportional tothe square of the operating frequency, and the abso-lute noise intensity is proportional to the square rootof the bandwidth. Thus, at a given location, theatmospheric noise level is composed of noise fromnearby centers of noise generation such as localelectrical storms, plus noise which has been propa-gated by way of ionospheric reflections from one ormore of the principal centers of noise generation, suchas the electrical storm centers in equatorial Africa,Central America, and the East Indies. The locationand activity of the various noise centers vary withthe time of day and season, and occasionally with the11 -year sunspot cycle. At frequencies above 100 mc,atmospheric noise originates from local sources only,since energy reflections from the ionosphere rarelyoccur at these frequencies. Generally, the higher thefrequency, the less the effect of atmospheric noises

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on a received signal.Precipitation noise arises from charged particles

striking a receiving antenna. Snow, ice, rain, and dustparticles are generally electrically charged, and, whensuch particles are wind-blown against a receivingantenna, the antenna will acquire a non -uniformlydistributed electrical charge. During turbulent airconditions, the magnitude and polarity of the chargevaries, causing the antenna to acquire a charge of onesign, then rapidly lose it, and so on. When theantenna loses electrical charges to the atmosphere,corona and electrical sparks often occur and causeelectromagnetic radiations known as precipitationstatic. Precipitation static depends upon the operatingfrequency, and, at times, may be a major source ofradio noise. Generally, the higher the operating fre-quency, the less noticeable will be the precipitationstatic.

COSMIC AND SOLAR. Cosmic radio noise of extra-terrestrial origin is known to be the principal sourceof interference to reception under many circum-stances at frequencies under 100 mc. This noise hasmuch the same characteristics as the random noisesof the atmosphere. The sources of cosmic noises arenot uniformly distributed over the sky but tend tobe concentrated in several regions on the celestialsphere, the primary source being in the regionScorpio -Sagittarius near the center of our galaxy.Consequently, when received on a directional an-tenna, the noise varies from hour to hour and fromday to day. The cause of this noise is not yet under-stood. Some investigators believe it is r -f radiationfrom eruptions similar to spot eruptions on our sun,occurring on all the stars in the galaxy, while othershave considered it to originate in free -field electrontransitions occurring throughout all of space betweenthe stars.

Cosmic noise intensity varies in proportion to theoperating frequency of the receiver in use. Therefore,the signal intercepted by a receiving antenna musthave a field intensity greater than that of the noisein order to be intelligible. The required field intensity,incident upon a half -wave dipole, for intelligiblereception in the presence of cosmic noise is expressedapproximately by the formula

2E = ____

fMicrovolts per meter (Ay /m) (12-1)

where

f = The operating frequency in megacycles (18mc < f < 160 mc).

For frequencies above 160 mc, the field intensity of

cosmic noise is extremely small and can be dis-regarded.

At the time cosmic noise was first discovered, anattempt was made to determine if similar phenomenawere observable in connection with our sun. Negativeresults were then obtained. Relatively recently,however, measurements of radio noise at 200 mc,made with a sensitive receiving system and a highgain directive antenna, disclosed the fact that the sunalso acts as a source of noise.

The theory of thermal radiation predicts that anyblack body will radiate a certain amount of energyat all wavelengths. If the theory is applied to the sun,assuming that the sun is a black body with a tem-perature of 6,000 degrees absolute, the intensity ofradiation at 200 mc would be below the thresholdlevel of present-day receiving systems. The inten-sities which have actually been measured at 200 mcare of magnitudes which correspond to a solar tem-perature of nearly a million degrees Kelvin. Further-more, at times of ionospheric storms, which areassociated with large sunspots, intensities of radiationhave been observed corresponding to temperatures ofa thousand million degrees Kelvin.

By the use of directional an tennas, it has beenobserved that the bursts of noise emanating from thesun are circularly polarized, either right-handed orleft-handed, depending on whether the sunspots arein the sun's northern or southern hemisphere. Thispolarization occurs only for noise bursts of highintensity; normal radio noise coming from a quiescentsun appears to have random polarization.

Measurements have also been made of solar radia-tion at frequencies of 3,000 to 24,000 mc, and thesealso give distinct evidence of radio noise coming fromthe sun. The intensity of this noise, however, corres-ponds rather closely to that which would be expectedfrom thermal radiation, with effective black -bodytemperatures of the order of 20,000 degrees absolute.Some plausible and complete theories have beenformed regarding the nature of solar noise and thefrequency distribution of its intensity, but only a fewexperimental measurements have been performedtoward confirming it. Except at the time of largesunspot eruptions, solar noise is important only onvery high frequencies when high gain antennas areactually pointed at the sun; consequently it usuallyneed not be considered in relation to practical prob-lems of propagation.

MAN-MADE NOISE

ELECTRICAL NOISES. Electrical interference iscaused by the operation of electrical apparatus other

112

CHAPTER 12

INTERFERENCE100

MINIIMM=11=1 111111111111611M

1

10,000FREQUENCY -MC

1000

Figure 7 2-1 . Sources of Radio Noise

1 1 3

100

10

0 I

10001

CHAPTER 12

INTERFERENCE

than transmitters and oscillators. Man-made elec-trical noise can be generated by a great variety ofelectrical devices such as power -line discharges,motor -brush sparking, and ignition systems. Thenoise so generated may be propagated to the receivingantenna direct from the noise source or be radiatedfrom power lines located near the receiver site.Electrical noise may also reach the receiver by directtransmission through the power lines.

NOTE

In general, electrical equipment of goodquality is constructed so that any radiatingnoise is of a minimum value. However,unless such equipment is installed and main-tained properly, satisfactory design is of noavail. Home appliances, in particular, areoften poorly maintained and may causenoise because of poor contacts or loose wires.Methods of shielding electrical equipmentare considered in the following chapter.

High -voltage transmission or power lines can causeexcessive radio interference unless they are con-structed and maintained properly. The main sourceof transmission line noise is corona, which is a dis-charge of electricity that originates from sharp pointsand corners of the line. Corona may also form oninsulator tie wires, pins, and hardware because offaulty insulator design. Since corona is a high -poten-tial electrical discharge, small sparks or arcs ofelectricity may occur anywhere along the line wherethere is a sharp point or corner and so introduceelectrical spark noise. Power -line systems cause noisein a variety of ways, including arcs at fuses andswitches, overloaded transformers, or simply as acarrier of appliance noises.

At frequencies above 30 mc, ignition noise is anextremely objectionable disturbance. The peak igni-tion noise produced by 90% of the vehicles passing100 feet from an antenna 35 feet high has been foundto be 9/A v/m for 450 mc and nearly 20/11 v/m for30 mc. As ignition interference is impulsive noise,each pulse shock -excites the usual r -f tuning circuitsof the receiver. The resulting oscillations have thefrequency of the receiver's tuned circuits and die outexponentially, with each disturbing pulse producinga damped train of oscillations. The damped pulseintensity dies away considerably before the occur-rence of the next pulse. The field intensity of elec-trical noises is greatest in densely populated andindustrial areas, and, according to the best availableinformation, the peak field strength of such noiseincreases substantially as the receiver bandwidth is

114

increased. The man-made noise curves as given infigure 12-1 show typical median values for the UnitedStates and are interpreted to mean that 50% of allreceiving sites will have lower noise levels than thevalues given. Conversely, 90% of all receiving siteslocated in the United States will have noise levels lessthan seven times these values.

SELECTIVE INTERFERENCE. In addition toelectrical noise, the efficiency of radio communicationsystems can be limited by the interference of unde-sired signals radiating from transmitters on the sameor adjacent channels to the one desired, unshieldedoscillators, harmonics of other transmitters, dia-thermy machines, or r -f heating generators. Interfer-ence from diathermy apparatus is perhaps the worstdisturbance of this kind, and signal strengths in excessof 100µv /m are commonly found in large cities.Diathermy and induction heating systems radiate arelatively narrow -band noise with the field strengthof such noise being the same, for instance, in a 100-kcbandwidth receiver as in a 10-kc bandwidth receiver.The FCC is attempting to reduce diathermy inter-ference by assigning several frequency bands for theuse of such equipment; however, many older ma-chines not conforming to the new regulations are stillin service.

If signals from two or more transmitters are pickedup by a receiver tuned to one frequency, the inter-ference so introduced is usually referred to as crossmodulation. Cross modulation may arise from poorlydesigned, improperly shielded receiver circuits, orfrom external sources. External cross modulationgenerally arises from poor contact between variousextended conductors in the vicinity of the receiver.Such contacts act as frequency converters or lineardetectors which produce new r -f signals that mayreach the receiver either by conduction or by re -radiation. Conductors which may form contactsacting as frequency converters include house electricwiring, BX-cable sheath, antenna and ground leads,water and gas pipes, metal lath, and rain spouts.

RECEIVER NOISE

THERMAL AGITATION. Random noises in theform of resistance and tube noise are always presentto some degree in even the most carefully constructedreceiver. These noises produce a characteristic hiss -like sound in loud speakers and "grass", or anextremely irregular sweep, on oscilloscopes.

The irregular motion of electrons in any resistorand in the space current of any tube produces a fluc-tuation type of noise. These irregular motions resultin small fluctuations of voltage and current, the

CHAPTER 12

INTERFERENCE

instantaneous value of such voltage or current obey-ing the probability law. There is a certain smallprobability that the value of instantaneous voltageor current will fall at any one point in particular,and the probability that a very large value will occuris extremely small. However, the probability of a largenoise amplitude increases as the bandwidth of theequipment is increased. Although the fluctuationshave no definite wave form, there is a definite rmsvalue and a definite average value for all positive andall negative noise amplitudes. The average positiveor negative values are equal and mount to 80% ofthe rms value, while the instantaneous amplitudesexceed the rms value approximately 32% of thetime. The noise so produced by fluctuations of voltageand current establishes a limit to the amount ofamplification that can be successfully employed inany receiving system.

If the random motion of electrons in a resistor isproduced by molecular agitation due to temperature,the resulting disturbance is called thermal -agitationnoise. The same effect occurs in a parallel resonantcircuit or other passive network, including thereceiving antenna, to the extent corresponding to theresistive component of the impedance. The magni-tude of the open circuit rms voltage for a giventemperature may be found by the formula

E = 0.0074 -VR B T microvolts (Av) (12-2)

where

R = Circuit resistance in ohmsB = Equipment bandwidth in megacyclesT = Temperature in degrees Kelvin

Values of H for various ranges of resistance andbandwidth based on normal room temperature areplotted in figure 12-2.

An important quantity associated with thermal -agitation noise is the available power output fromsuch a source. The available power or the maximumpower which can be delivered is obtained by matchinga resistive load to the internal circuit resistance inwhich the noise is generated. The available powerfrom thermal -agitation noise is given by the formula

P = 1.38 x 10-" B T microwatts (12-3)

A method for determining available noise power atroom temperature is given by the formula 4.0 x 10-21watts per cycle of bandwidth.

Random noise originates in tubes chiefly becauseof the irregular nature of electron emission at thecathode, and, if the tube has a screen grid, the incon-sistently changing distribution of current betweenplate and screen. Irregular electron emission was first

200

100

50_J

30NE 20

z > 10

cc3

100 1000 10 000R OHMS

Figure 12-2. Thermal Agitation Noise

discussed by Schottky along with resistance noise, allunder the name "shot effect" from the similarity ofthe noise to the sound of many small pellets fallingupon a hard surface. Shot effect is now defined as tubenoise resulting from random cathode emission so thatresistance noise is not included. The term partitionnoise is generally applied to tube noise resulting fromthe irregularities in current distribution betweenplate and screen. Maximum tube noise is obtainedwhen the temperature of the cathode approachessaturation, or the point at which no space chargeoccurs. When temperature saturation is present in atube, all electrons emitted from the cathode areimmediately drawn to the plate. In fact, a diodeoperated in this condition is a convenient standardnoise source for use in measuring the noise figure of areceiver. The presence of space charge in electrontubes is very fortunate, for it makes amplificationpossible and greatly reduces the tube noise.

Tube noise is commonly represented by using anequivalent resistance which, if connected at the con-trol grid of a noiseless tube, would produce the samethermal noise output. Values of equivalent gridresistance or grid noise resistance of various tubeshave magnitudes within the following ranges:

Triode amplifiers 200- 2,300 ohmsTriode mixers 900- 6,000 ohmsSharp -cutoff pentode

amplifiers 700- 7,000 ohmsGradual -cutoff pentode

amplifiers 2,400- 14,000 ohmsPentode mixers 2,800- 35,000 ohmsHexode and heptode mixers 190,000-300,000 ohms

Mixer noise increases beyond these values if theoscillator injection is insufficient. If the amplifier gainis reduced by the application of more negative gridbias, the effective input noise increases, but the out -

T = 300° K= 27° C

IIIIII

100000

115

CHAPTER 12

INTERFERENCE

put noise decreases. Equivalent noise resistances maybe substituted in formula 12-2 in order to determinethe rms noise voltage so generated.

Equivalent grid noise resistance does not apply ifthe tube is used in a feedback circuit or if it hasany input loading. To avoid these limitations, theinternal cathode resistance of the tube can be con-sidered as the noise source. In this case the tempera-ture of the internal cathode resistance is approxi-mately 0.6 times the absolute temperature of theheated cathode. After application of the 0.6 factorthe temperature is approximately twice the absoluteroom temperature for oxide -coated cathodes, threetimes for thoriated filaments, and five times for puretungsten filaments. The term generally applied tothe internal cathode resistance is called cathode noiseresistance and is measured in ohms.

For triodes, the cathode noise resistance may befound by the formula

R = 1 ohmsg + gwhere

(12-4)

gm = Tube transconductancegp = Plate conductance, or the reciprocal of the

a -c plate resistance R.

For multielement tubes, the cathode noise resistanceis the a -c resistance as measured from the cathode toall other electrodes joined together by capacitorswhile operating at their normal d -c potentials. Noisein multielement tubes is increased by partition noise,the sources of such noise being considered as due tothe internal cathode resistance being at a highertemperature than the initial 0.6 value.

NOISE FIGURE. The sensitivity of a receiver can-not be described in terms of thermal -agitation noisealone, because the set noise at the output is severaltimes the pure thermal noise. This increased set noisearises from amplifications and additions of thermalnoise as it passes through the receiver stages. There-fore, another quantity, called the noise figure, is usedto describe receiver noise. The noise figure (Nf) of areceiving system is defined by the formula

where

PN

Nf = PN_./PNPs_o/Ps

(12-5)

= The noise power as given by formula 12-3from the antenna that is delivered to thereceiver.

PN-o = The noise power at the receiver output.Ps = The signal power from the antenna as

delivered to the receiver.

= The overall noise figure= The noise figure of the kth stage

gk = The gain of the kth stage.

Equation 12-7 simply shows that most of the receivernoise originates in the early stages of reception. Italso shows, of course, that noise picked up at laterstages is much less amplified by the system than thenoise from the first stages.

In equipment specifications, the noise figure isusually expressed in the decibel scale as decibels abovethermal noise. Actual noise figures vary from a fewdecibels above thermal noise for receivers operatingat frequencies up to 300 mc, to larger values at thehigher frequencies.

SIGNAL-TO-NOISE RATIO. Since the intensitiesof both signal and noise can be measured in terms ofrms voltage or current, or in terms of power, such acomparison is used to express reception conditions.The ratio of signal intensity to noise intensity at theoutput of a receiver is called the signal-to-noise ratio(S/N), and is expressed in decibels. For signal andnoise intensities that are measured in rms voltagedirectly at the output terminals of a receiver, the S/Nratio in decibels may be found by the formula

S/N (db) = 20 log S/N (12-8)

(12-7)

Ps-. = The signal power at the receiver output.

The ratio Ps_o/Ps is called receiver gain (g) and isnot to be confused with antenna gain (G). By usingformula 12-3, formula 12-5 may be restated as

7.25 X 101° PN-oB T

If the receiver consists of several stages in cascade,including converters, amplifiers, and detectors, theoverall noise figure can be compounded from thenoise figures and gains of the individual stages orcomponents by the means of the formula

Nf = Nfl + NO2-1 Nr3-1gl gl g2 gl g2 gkwhere

NfNfk

where

(12-6)

Signal intensity in rms voltage (Peak voltagefor impulsive noises)Noise intensity in rms voltage (Peak voltagefor impulsive noises)

For signal and noise intensities that are measured atthe output terminals of a receiver in terms of power,the S/N ratio in decibels may be found by theformula

S =

N=

116

CHAPTER 12

INTERFERENCE

S/N (db) = 10 log Ps/PN (12-9)

where

Ps = Signal Power in wattsPN = Noise Power in watts

The signal-to-noise ratio of a receiving system canbest be analyzed by finding all the various noisesources and then referring them to a single point.When an equivalent noise resistance is used at thereceiver input to express the output noise of the firsttube of a series, noise sources beyond this point arealso referred back to this same input. Thus, a singleequivalent noise resistance can be used to express allthe noise sources at or beyond the first tube.

When there is external noise present at the inputof the first tube, the optimum signal-to-noise ratiodepends on the product of external noise and equiva-lent noise resistance. Even when the input resistanceis infinite or negative, the optimum signal-to-noiseratio is limited either by this external noise or by thebandwidth of the input circuit. The signal-to-noiseratio is also inherently limited by the receivingantenna and associated transmission lines whichdevelop noise of their own. The antenna noise maybe considered equal to the thermal -agitation noisedeveloped in an equivalent dummy -antenna re-sistance.

The signal-to-noise ratio of a radio receiver atultra -high frequencies, or higher, is primarily de-pendent on the above -mentioned noise relations fortubes and circuits. However, in addition to thesenoise relations, consideration must be given to themany types of signal modulation used. For example,there is a great difference between the signal-to-noiseratio in one of the telephone channels in a multiplexsystem and the carrier -to -noise ratio at the finaldetector. The received carrier -to -noise ratio dependsupon a number of factors. First, the propagation pathshould be clear of any obstructions such as hills andtrees. Other factors which determine the carrier -to -noise ratio include transmitter power, antenna gain,wavelength, distance between stations, receiver band-width, and receiver noise figure.

With either amplitude modulation or frequencymodulation, the signal-to-noise ratio at the output

of the receiver is not the same value as the carrier -to -noise ratio at the final detector. It is commonpractice to compare the signal-to-noise ratios of thevarious multiplexing systems to that obtained withamplitude modulation. The ratio of signal to noiseratio, comparing a single channel of a multiplexsystem to a single channel AM system having thesame average radiated power is called the wide -bandimprovement of a multiplex system.

In the case of amplitude modulation the equationfor the signal-to-noise ratio is given by the formula

NS(AM)

B,_f Ec213._f Nld

where

(12-10)

Bi-f = The intermediate frequency bandwidthBa_f = The audio frequency bandwidthM = The modulation indexEe = The carrier voltageNld = The noise ahead of the last detector

In frequency division multiplexing, where each signalmodulates a separate sub -carrier and the sub -carriersare so spaced in frequency as to prevent overlapping,the ratio of signal-to-noise voltage ratios as comparedto a single channel AM system is given by the formula

S/N (xx-xx)

whereS/N (AM) K1 M1 M2 K2 (12-11)

(xx-xx) = Type of modulationK1 = 1 for AM, Nr3 for FMM1 = Modulation index of the signal on each

channel for AM, or the deviation ratioif FM.

= Modulation index of the sub -carrier orindividual signal applied to the maincarrier

K2 = The second modulation constant.

The above formula may be simplified by using anAM signal-to-noise ratio of unity in the denominator.Figure 3 in Chapter 11 lists fourteen formulas ofS/N ratios for double modulation as compared to aS/N ratio of unity for single channel AM.

M2

117

CHAPTER 13

INTERFERENCE ELIMINATION

CIIAPTIElt

INTRODUCTION

Unwanted interference picked up by a receivingantenna along with the desired signal is, in effect,part of the modulated r -f wave. Such interference isthen amplified and demodulated together with thedesired signal. Therefore, noises which lie within theacceptance band of the receiver will be present at thereceiver output in spite of all possible precautionstaken in the initial system design.

Every type of receiving system in the frequencyrange from 44 to 100 mc has a definite signal -to -external -noise ratio below which the intelligibility ofthe signal is insufficient for reliable operation. If thesignal -to -external -noise ratio of the received wave isbelow this minimum value, one of the means availableto obtain an intelligible signal is to increase theeffective radiated power of the transmitter. Occa-sionally, advantage may be taken of the receivingantenna's directivity, making it blind to the sourcesof the noise and responsive only to the desired signal.This may be accomplished only when the noise andsignal directions are at wide angles to each other, andwhen suitable antenna directivity is possible.

In the frequency range above 100 mc, where theexternal noise intensity is very low, there are differenttransmission characteristics to be considered. In thisrange, very weak signals may be utilized by the useof high receiver gain, since the received field intensityis not limited by external noise. Receiver noise,however, can be a limiting factor in this case, withthe limitations increasing directly with the operatingfrequency. Under these conditions, the signal-to-noiseratio of the receiver is always improved by increasingthe signal power delivered to the receiver, although

13

INTERFERENCE

ELIMINATION

119

excessive power is too often employed in order tooverride engineering deficiencies, thus causing un-necessary interference with other services.

NATURAL NOISE REDUCTION

ATMOSPHERIC. Atmospheric noise varies through-out the day and season and with operating frequency,the effects of such noise decreasing with increasingfrequency. For the frequencies ranging from 44 to100 mc, local electrical storms are the main sourceof atmospheric noise, since noise from the principalnoise centers of the world is rarely ever propagatedby way of the ionosphere at these frequencies. It isgood practice, however, to make atmospheric noisemeasurements at locations where a receiving antennais to be installed. The measurements should be madein such a way as to reveal the diurnal and yearlyrange of noise intensities at the frequency rangesintended for use. Noise must always be taken intoaccount when choosing a site for a receiving station,and both atmospheric and man-made noise may beinvolved. In the frequency range above 100 mc, it isseldom necessary to make atmospheric noise meas-urements at receiver locations since even local elec-trical storms do not ordinarily cause any interference.

At times, precipitation noise may become seriousin some locations. Sandstorms, dry snow, and wind-blown fog are well-known causes of precipitationstatic interference. Such noise can be reduced sub-stantially by embedding all metallic antenna andfeeder system components in a low -loss dielectric inorder to prevent the charged particles which strikethe antenna from discharging directly to the metal.By preventing exposure of the metal antenna com-

CHAPTER 13


ponents to the charged particles, a reduction ofseveral decibels in noise level can be realized duringconditions of precipitation noise. The addition of ad -c ground to the antenna system, if one may beadded without upsetting the r -f response, may alsotend to eliminate precipitation noise.

COSMIC AND SOLAR. Radio noise of extraterres-trial origin has much the same characteristics asatmospheric noise, and its intensity varies in propor-tion to the operating frequency. Formula 12-1 inChapter 12 may be used to determine the necessaryfield intensity for intelligible reception in the presenceof cosmic noise. The formula is limited to an upperoperating frequency of approximately 160 mc, sincethe field intensity of cosmic noise is extremely smallat higher frequencies and can, therefore, be dis-regarded.

Radio noise emanating from the sun interferes withradio -relay operation only under certain conditions.For example, a receiving antenna that is directedhorizontally towards the east may intercept solarnoise at the particular time when the sun is justappearing over the horizon. Similarly, a receivingsolar noise emanating from the setting sun. However,antenna directed toward the west may interceptas this phenomenon occurs only a few minutes a dayand, at the most, several days a year, the noise sointercepted need not be considered. At the time oflarge sunspot eruptions, solar noise may then'be morenoticeable, although the use of highly directiveantennas offsets the noise considerably.

MAN-MADE NOISE REDUCTION

ELECTRICAL NOISES. A receiving site, for equip-ments operating in the frequency range from 44 to300 mc, must be as free as possible from electricalnoises. The site should be an adequate distance fromlarge cities or other places that might be sources ofelectrical noises. Automotive ignition systems arealso a major source of electrical noise and substantialdistance between receiving sites and well -traveledhighways should be allowed. The distance may bedetermined by direct measurement of such noise atvarious locations. The amount of man-made noisethat can be tolerated at a particular receiving sitedepends upon the prevailing natural noise levels, andany man-made noise present at the site should alwaysbe substantially less than the natural noise receivedduring low -noise periods. At a well -selected site,intelligible reception should be limited only bynatural causes.

The suitability of a receiving site will often dependupon the direction from which the noise is propa-

gated. If the dominant noise interference is alwaysfrom a direction substantially different from that ofthe desired signals, antenna directivity can beemployed to favor the signal and discriminate againstthe noise. The man-made noise may also arrive atthe site at a much lower angle than the incomingsignal, in which case the antenna may be tiltedslightly off horizontal in order to give the bestresponse to the incident signal and a relatively lowresponse to the noise.

There are times when a receiving site must belocated in a city or other region of severe man-madenoise. It may be necessary to attempt to suppressnoise from troublesome dominant sources in theneighborhood of the receiving station in order toobtain tolerable system performance. Especiallytroublesome are the clicking noises which arise fromelevator power controls where both the receiver andthe elevator relays are located in the same building.The preventive measures that can be successfullyapplied depend upon the nature of the device andthe kind of noise it emits, assuming that the sourcecan be located. Loose wires, poor contacts, worn motorbrushes, and transmission line corona are perhaps themost common electrical noise sources. Poor groundingand shielding of electrical devices may also be a majorreason for excessive electrical noise. Bypassingsparking contacts with suitable capacitors and theuse Of power line filters may be remedies for certaintypes of noise. Commercial filters are available forthis purpose. In many instances, 0.05 Af capacitors,connected across the power line at the point whereit enters the electrical equipment causing the problemwill prove effective. A brief summary of a numberof forms of electrical interference, together with adescription of the general noise they produce is givenbelow. The summary is not meant to be complete,but rather to serve as an indication of types of noisesources.

A. Whirring or Whining Noises (Often accompaniedby crackling)

Adding MachinesBarbers' ClippersBeauty Parlor Equip-

mentCash RegistersDental EquipmentDish WashersDough MixersElectric AddressographsElectric BlowersElectric FansElectric Refrigerators

Electric SewingMachines

ElevatorsFarm Lighting PlantsField Telephone

MagnetosFloor PolishersGeneratorsHair DryersHumidifiersMotor GeneratorsPortable Electric Drills

120

Printing PressesToy Electric TrainsVacuum Cleaners

Valve GrindersWashing Machines

B. Rattles, Buzzes, and Rapid Clicking NoisesAutomotive Ignition Dial Telephones

Systems Elevator ControlsBuzzers and Trembler Sewing Machines

Bells Vibrating RectifiersDental Equipment

C. Heavy Buzzing or Rushing SoundsAir Purifiers Neon SignsBattery Chargers Oil Burner IgnitionDiathermy Machines SystemsFlour Bleachers R -F Induction Heaters

X -Ray Equipment

D. Crackling or Spluttering NoisesBad Connections Poor Contacts in PowerDefective Light or Wiring

Power Sockets (Occasionally intermit -Elevator Controls tent breaks in con -High -Tension Lines necting cables)Partially -Grounded Trolley Cars

Power Lines

E. ClickingElectric TypewritersElevator ControlsFlashing SignsIncubators

Mercury Arc RectifiersOvensTelegraph RelaysTraffic Signals

A portable receiver with a loop antenna may beused as an interference locator. With the receiveroperating, gradually rotate the loop antenna. If apoint is found at which the interference diminishesor vanishes, the direction of radiation will then beat right angles to the loop. Once the direction ofinterference is found, it is not too difficult to movetoward the direction in which the interferenceincreases.

While this method of interference detection is themost satisfactory, it is only applicable in a fewinstances where the major interference comes fromone particular source which can be satisfactorilysuppressed. In urban areas, the source of the noise isusually not easy to determine, and when it is, thecost of filters is prohibitive. It is therefore best tofollow the procedure outlined below for improvingthe antenna system.

1. Use a more directional, high -gain antenna.

2. Attempt to find an antenna position whichgives a minimum noise pickup.

CHAPTER 13


3. Check antenna height for maximum signalpickup.

4. Make certain that the antenna, transmissionline, and receiver are correctly matched andalso well-balanced to ground.

5. Make use of antenna tilting, if possible, makingthe antenna blind to the noise sources andresponsive only to the desired signal.

SELECTIVE INTERFERENCE. The signal gener-ated by a transmitter, diathermy machine, or otherr -f oscillators operating on the same or adjacentchannels to the one desired, can have a componentwhich will interfere with the desired signal. Thecomponent can be a harmonic of the operating fre-quency, a parasitic oscillation, or it can be producedby cross -modulation. For example, an improperlyoperating c -w transmitter may give rise to spuriousemissions with sidebands that may extend manyhundreds of kilocycles either side of the steady carrierfrequency. These large sidebands are generally causedby a large, rapid frequency shift as the key is closedor opened.

In the various stages of a transmitter, the effec-tiveness of direct harmonic radiation may be mini-mized by short, direct leads and the isolation betweenstages afforded by link coupling. Good grounds andcomplete shielding of the lower -power stages shouldbe obtained if possible. Direct harmonic radiationfrom a high-powered final stage is minimized in thesame manner, although greater care must be takenbecause of the magnitude of the currents and larger -size components. Steps necessary to prevent harmoniccurrents from finding their way to the transmissionline and the antenna include low-paRs filters andtuned traps (transmission -line stubs) interposed be-tween the final tank and the transmission line. Itcannot be emphasized too strongly that if harmoniccurrents are permitted to flow to ground by way oflong paths, such as the a -c line, the transmission line,or the antenna, the resulting radiation will be a moredangerous source of interference than direct har-monic radiation from the transmitter stages. Like-wise, shielding should not be used as a convenientground for general use.

Flexible coaxial line is ideal for use as a tuned trapor rejection stub, since the field produced by out -of -phase currents flowing from the inner to outerconductor is contained within the cable. Coaxialstubs therefore strictly limit any direct radiation andmay be coiled up for convenience. A quarter -wave-length stub, figure 13-1 shorted at the far end presentsa very high resistive impedance across its unshorted

121

CHAPTER 13


terminals at the operating frequency. Such a stubbridged across the output terminals of the offendingtransmitter effectively shorts the even harmonicfrequencies. The most common stub lengths andhook-ups are given in table 13-1.

If additional harmonic attenuation is needed in aparticularly troublesome situation, a second rejectionstub may be placed along the main transmission line.The second stub is spaced one -quarter wavelength ofthe undesired harmonic from the first stub. Trans-mission line stubs may also be used at the receiverinput terminals and, in some cases, are a practicalmeans of selective interference elimination when suchinterference lies within a narrow frequency band. Thestub is cut to a length which is resonant at thefrequency of the unwanted carrier and bypasses itfrom the receiver input. Several commercial wave -traps are also available and are sometimes veryeffective.

Interference from diathermy apparatus may beparticularly troublesome at certain site locations.Although most modern diathermy machines areequipped with r -f filters so that radiation into thepower line is reduced, many machines will still inter-fere with wide -band receiving systems such as micro-wave relays and television receivers. When the fre-quency of the diathermy apparatus is nearly the sameas the i-f frequency of a nearby receiver, a buzzingsound may be heard over the entire receiver band -spread tuning range. Little can be done at the receiversite to remove this type of interference, althoughadditional shielding of the i-f amplifier and betterfront end selectivity may be tried. If the diathermymachine can be located, the owner should be askedto cooperate by shielding the machine, by keepingthe machine on its correct operating frequency, andby grounding it properly, all as prescribed by theFCC.

SHIELDING. Undesired electromagnetic energy inthe form of noise or r -f waves may be confined byblocking all undesired methods of propagation. Sucha process is called shielding. The placement of all the

TABLE 13-1: SHORTING STUB LENGTHS

Harmonicto be

Eliminated

Even Harmonics3rd Harmonic(two stubs needed)

5th Harmonic(two stubs needed)

Stub Length inTerms of Operating

Wavelength Conditions

X/4 Shorted at far end.X/6 Shorted at far end.X/12 Open at far end.

X/5 Shorted at far end.X/20 Open at far end.

EVEN 3RDHARMONIC STUB HARMONIC STUBS

Figure 13-1. Harmonic Rejection Stubs

components of an undesired radiation source withina grounded shielding box confines the electric fieldwithin the box. Even if the box contains holes, slots,or is constructed of wire screening, the shielding ofthe electric field is still almost complete, provided theresistance of the screen is very low. In most cases,copper and aluminum are entirely satisfactoryshielding materials for the electric field. Copperscreening is satisfactory if it is bonded to copperstrips at the edges, in order to insure a good lowresistance contact to each wire of the netting, despitea faulty contact between individual wires.

Generally, magnetic fields are produced by the flowof current along a conductor. Since high -frequencyr -f currents are propagated along the surface or skinof a conductor, no magnetic field can be producedexternal to a solid metal box, regardless of whetherthe box is grounded or not. Strong currents propa-gated along the inner surfaces of the box generate asecond magnetic field which neutralizes the firstinternal field, making the total field external to thebox zero. However, small holes in the box will permitpenetration of the magnetic field to the outside. Themagnitude of the flux penetrating a hole is a functionof the diameter of the hole, and for small holes (lessthan X/8) external flux exists only in the immediatevicinity of the hole. Slots, even if narrow, can beextremely dangerous if the magnetic lines of forceare parallel to the slot. On the other hand, if themagnetic lines of force are at right angles to the slot,the slot will be no more harmful than a row of holes.Slotted shielding is usually avoided because of thedifficulty of determining the direction of the magneticlines of force, and any small holes necessary forventilation should be carefully located with respectto the components. Individual secondary shieldsplaced around components that produce large mag-netic fields may also be used to advantage.

RECEIVER NOISE

NOISE FIGURE. While at frequencies below 300mc, man-made noises are the dominant types ofinterference in cities, receiver noise is prevalent in

122

CHAPTER 13

rural areas, and is dominant down to 44 mc, andpossibly still lower. Only recently has a good receiverbeen built which will amplify the received signal atradio frequencies above 500 mc. Hence, it is cus-tomary to convert the signal to a lower frequencybefore it is amplified. There are two methods of doingthis. The most direct approach is to rectify the signaland change it to an audio wave which may beamplified. However, in the majority of cases it ismore convenient to change the frequency of thesignal to some intermediate frequency, and firstamplify the intermediate frequency, demodulating itafter a large amplification. There are three mainreasons for this:

1. It is possible to detect weaker signals.

2. Greater selectivity is obtained.

3. It is more desirable to have the receiver gaindistributed between two frequencies, therebyavoiding feedback troubles.

It' is well known that if an amplifier has enoughgain, a random voltage appears at the output ter-minals. As discussed in Chapter 12; this randomvoltage produces noise in the output of the receiver.For any receiver, there will be a definite amount ofinput signal power which is needed to make theoutput signal power equal to the output noise power.The noise figure of a receiver is the difference, in db,between the actual noise present in a receiver and thethermal noise of a resistance equal to the input loadconnected to the receiver. Normally the noise figureof a receiver is expressed in decibels above thermalnoise.

CRYSTAL MIXERS. Ordinary heterodyne radioreceivers use tubes for first detectors. Many tubeshave been tried for the same purpose in microwavereception but all have proved quite noisy. In the3,000-mc band, tubes in service seem to develop about25 db more noise than the theoretical noise power,while the best of these tubes will develop 16 db. Thereceiver noise situation is even worse for receptionat 10,000 mc. As a result attention has been turnedto the crystal detector, once widely used at ordinaryradio frequencies but for many years completelysuperseded in this field by tubes.

A crystal used in this fashion is generally called a"mixer". Several housings have been designed forcrystals mounted in coaxial cables operating at 3,000mc. Such devices must have inputs for signal, localoscillators, and an i-f output. There also must be


provisions for bypassing the r -f, and a filter must beused to prevent the r -f from escaping through the i-fline.

The excellence of performance of a crystal used asa frequency converter will be determined primarilyby the conversion loss of the crystal and by the noisewhich it introduces into the receiver. It has beenfound experimentally that the power from the localoscillator causes the crystal to generate more noisethan an equivalent resistor at room temperature. Theoutput noise ratio (N.) of a crystal is defined as theratio of the available output noise power of thecrystal to the theoretical available noise power asdeveloped by an equivalent resistor.

A weak signal from the receiving antenna becomesstill weaker when it has become converted by thecrystal to the intermediate frequency. The conversionloss (L) of a crystal is defined as the ratio of theavailable r -f power as applied to the crystal over theavailable i-f power output from the crystal, and isalways greater than unity. The conversion loss andoutput noise ratio of the crystal are related to thereceiver noise figure by the expression:

where

NfNoNt(i-f)Lc

= Le(N. Nf(i-f) - 1) (13-1)

= The receiver noise figure= The crystal output noise ratio= The noise figure of the i-f amplifier= The crystal conversion loss

It has been found that L0 and No vary so widelyfrom crystal to crystal that it is necessary to measureeach unit and accept it for use only if it falls withinspecified limits.

The effect of the application of d -c bias on crystalperformance has been noted experimentally. It isfound that negative bias is undesirable in that thenoise output is increased and the signal reduced.However, an improvement is obtained with a smallpositive bias. This improvement also varies widelyfrom crystal to crystal and may be as much as 1 dbin the noise factor of a receiver having an i-f noisefigure of 5 db. The improvement occurs mainly in thereduction of output noise and is most evident inextremely noisy units, where there is usually animprovement in the signal output also. The mostfavorable bias appears to be in the neighborhood of+0.10 volt. Crystal detectors should be tested at oddintervals of time, since the slightest overload mayseriously impair the operation of such a detector.

123

et

al

ft

fe

CHAPTER 14

COMPUTATIONS OF WAVE PROPAGATION FOR RADIO RELAY APPLICATION

C II A I' T It 14

INTRODUCTION

When engineering radio relay systems, it is import-ant to have a relatively accurate means of predictingcircuit performance and reliability. Two frequencyranges will be considered in this chapter, the firstranging from 30 to 500 mc, and the second rangingfrom 500 to 13,000 mc. In the higher range of fre-quencies, generally speaking, present equipmentlimitations restrict the length of any individual hopin a system to line -of -sight distances. In the range30 to 500 mc, however, it is entirely possible to workover distances considerably in excess of optical.Therefore, the lower frequency range appears torepresent the optimum frequency range for radiorelay systems designed for a moderate number ofchannels. For a greater number of channels, or fortelevision applications, a higher frequency range,where greater bandwidths are readily available,should be used.

THE BULLINGTON NOMOGRAMS

One of the most useful tools available at the presenttime for the computation of path losses is the set ofnomograms prepared by Bullington.* These nomo-

*P.I.R.E. October 1947-Bullington: Radio Propagation atFrequencies Above 30 MC.

COMPUTATIONS OF

WAVE PROPAGATION

FOR RADIO RELAY

APPLICATION

grams (figures 14-11 through 14-19) are based on asmooth spherical earth .with a standard atmosphere,and have been designed to take into considerationreflection, refraction, and diffraction which are thefundamental properties of wave mechanics.

Provided these nomograms are used with a reason-able degree of care, relatively accurate predictions ofsystem performance can be made for all but thosecases where the system extends well beyond the lineof sight. For these latter cases, however, there is nowa considerable amount of experimental evidence indi-cating that field strengths may be expected which areconsistently higher than the predicted values givenby the nomograms.

When predicting system performance, it is essentialto know the received field to be expected over a longterm period for some percentage of the total time.Actually, it is not considered practical to predict fieldstrength values closer than 5 db, because of thevariations in the received field experienced in prac-tice. On the other hand, if the predicted values arenot within 5 db, the relay systems involved wouldhave to be engineered more conservatively, with aconsequent increase in capital cost.

In most applications, it is thought that the fieldstrength value experienced 90% of the total time isa good one to aim at. It might well be asked why thisvalue is taken, rather than 99.99%. The 90% value

125

CHAPTER 14


has been chosen arbitrarily as a good engineering com-promise between economy and efficiency, and is con-sidered to be satisfactory for all but very special applica-tions. To achieve a 99.99% value, it may be necessaryto provide a field intensity at the receiver which is asmuch as 15 to 20 db higher than the field intensityfor a 90% value, thus involving the installation ofquite a number of additional repeaters in a multi -hopsystem.

It must be remembered that the 90% value is anexpected field strength value and not the reliability of thesystem. For example, if calculations show a certainfield strength may be expected for 90% of the totaltime, and the fade margin of the receiver is 40 dbbelow this value, a fade of 20 to 30 db would be wellwithin the compensating abilities of the receiver. Inthis case, the total reliability of the system would bemuch higher than 90%, since a fade of over 40 dbis required for a complete outage. Only when the fieldstrength value expected for 90% of the time is equalto the threshold level of the receiver, will the relia-bility also be 90%. (See "reliability", Chapter 5.)

The problem now is to know whether the Bulling-ton nomograms are adequate to give an assessmentof expected field strength within 5 db for 90% of thetotal time for any given radio relay circuit. To checkthis it is necessary to apply the Bullington data toas many cases as possible where results of fieldintensity measurements over a relatively long termperiod are available. This has been done, and theresults of the analysis are indicated below.

PATHS WITHIN THE OPTICAL RANGE. For allsuch paths, the profiles will be taken to be drawnusing an earth's radius which is 4/3 times the trueradius. This, of course, provides an allowance forrefraction effects in a standard atmosphere. Pathswithin this category include those whose range wouldbe optical but for an intervening obstruction, otherthan that due to the earth's curvature.

Nine such paths, for which reasonably long termfield intensity measurements are available, have beenanalyzed and excellent correlation exists between thepredicted and measured field intensities received 90%of the time. A summary of these values is given intable 14-1, and shows that in no case is the predictedvalue 2 db greater than the measured 90% value. Aswould be expected also, the difference between the50% and 99% measured values for such paths isrelatively small. In only one case does it exceed 6 db.

It should be emphasized, however, that the methodof applying the Bullington nomograms can in samecases materially influence the value of the predictedfield. An example is the Empire State Building to

126

uji- I 000

LL

in 600

400

10 15 20 25 30 35 40DISTANCE IN MILES

Figure 14-1. Empire State Building to Hauppauge Circuit

Hauppauge circuit, the profile of which is shown infigure 14-1.

At first sight it would appear that the considerableelevation at each end will give a field at B due to atransmitter at A which should approach the free-space value. However, a closer check indicates thatpeak C falls within the first Fresnel zone (see nomo-gram H in Appendix I for determining first Fresnelzone clearance). Peak C is, therefore, a possible pointof serious reflection to be taken into account. Byconsidering an imaginary flat earth DCE runningthrough point C in such a manner as to make theangle of incidence equal to the angle of reflection, theantenna heights AD and BE will be found. By usingthese antenna heights in conjunction with the nomo-gram in figure 14-14, we find that such a proceduregives a predicted field which corresponds to the 99%value and is within 1.8 db of the measured 90% value.Any other method of applying the nomograms to thisparticular profile, such as taking an increased effect-ive height at each end on a plane earth basis, andincluding the shadow loss from figure 14-19, gives apredicted field considerably in excess of the measuredfield.

This method of drawing an imaginary plane earththrough any point on the profile which is within thefirst Fresnel zone has been applied to all the profilesexamined under this heading and, as can be seen fromtable 14-1, has yielded remarkably good correlationwith the measured fields.

OBSTRUCTED LINE OF SIGHT. The procedurefollowed for the obstructed line of sight paths will bemore readily understood by examining the two pro-files shown in figure 14-2.

In the Alliford Bay to Marble Island circuit, theantenna A is on the edge of a cliff and has completefirst Fresnel zone clearance in the immediate fore-ground. On the other hand, the antenna at B doesnot have first Fresnel zone clearance in the immediate

CHAPTER 14


foreground. The plane earth line has therefore beentaken as DC, giving antenna heights of AC and BD.The shadow loss from figure 14-19, using distance dand height h, has then been added to the plane earthloss given by figure 14-14.

In the Bridgeport to Riverhead circuit, the antennaat B does not have first Fresnel zone clearance,whereas the antenna at A does. The plane earth line,therefore, has been taken as running tangential to theearth's surface at F from the base D of the antennaat B. This gives antenna heights AC and BD to beused for assessing the plane earth loss from figure14-14. Distance d and height h are used in assessingthe shadow loss from figure 14-19.

Summarizing, therefore, it would seem that con-tours for clear line of sight and obstructed line ofsight paths can be analyzed to give a predicted value

of field intensity which can confidently be expectedto exist for 90% of the time, provided that thefollowing basic principles are observed.

1. Draw all profiles with an earth's radius of 4/3times the true radius.

2. For paths where complete first Fresnel zoneclearance exists over the entire path, take thefree -space path loss given by figure 14-10.

3. For clear line -of -sight paths where first Fresnelzone clearance does not exist over the entirepath, draw a plane earth through possiblepoints of reflection (whether they are in theimmediate vicinity of the antennas or wellaway), and use the effective antenna heights sogiven to find the plane earth loss from figure14-14.

TABLE 14-1

COMPARISON OF THEORETICAL COMPUTATIONS AND LONG TERM FIELD INTENSITY MEASUREMENTS

FOR LINE OF SIGHT CIRCUITS

Reference Hop

Freq.in

MC/S

CLEAR LINE OF SIGHT PATHS

PredictedValue of

FieldIntensity

Distance in Dbin above

Miles 1 Ay /m

Percentage of Time Measured FieldsIndicated (Db above 1 Av/m) Are

ExceededDuration

ofMeasure -

1% 50% 90% 99% 99.9% ments

RCA ReviewJune 1946

Prince Rupert-Alliford Bay

45 98 26 47.3 42.9 40.3 36.6 33.3 1 week

RCA Interna-tional FieldReport

Tel Aviv-Judian Hills

250 26.5 55 59.5 56 53 42 36 3 months

RCA Interna-tional FieldReport

Tel Aviv -Mt. Carmel

250 50 48 57 53.5 51 47.5 40 3 months

RCA ReportEM 61-17

Empire State -Hauppauge

288 42.5 51 63 55.7 52.8 50.9 49 3 months

RCA ReviewJune 1946

Alliford Bay -Marble Island

45 30 27.5 30 27.8 24.7 23.8 23.6 1 week

RCA ReviewJune 1946

Bella Coola-White Point

45 55 13 24.8 20.1 17.6 14.88 14.1 1 week

RCA ReportF 43-118

Alpine -Hauppauge

93.1 40.5 61.5 69 64 62 60.5 53 15 months

RCA ReportF 43-121

New York -Hauppauge

203.75 41.9 51.5 60 55 53.5 52.3 51 15 months

RCA ReportF 43-119

Bridgeport -Riverhead

534.75 33 52.8 62 55 53 49 42 21 months

127

CHAPTER 14


w 3000 -

z 2000 -w01- 1000

o -

400 -

200

-

A

C/ 11/1114111111

10 20DISTANCE IN MILES

ALL1FORD BAY - MARBLE ISLAND

10 20DISTANCE IN MILES

BRIDGEPORT - RIVERHEAD

Figure 14-2. Milford Bay to Marble Island Circuit

4. For obstructed line -of -sight paths, use the sameconcept of a plane earth as indicated in 3, andincrease the path loss due to the obstruction asgiven by figure 14-19.

5. The possible exception to 4 is the case of anobstructed line -of -sight path which would comeunder the free -space category but for theobstruction. Such a path would be analyzed byusing figures 14-10 and 14-18.

PATHS BEYOND THE RADIO HORIZON. Bull-ington has indicated that the received power at pointsfar beyond the horizon is relatively independent offrequency, antenna heights, and weather effects.From experimental data he has produced two empiri-cal curves, which are illustrated in figure 14-20, givinga value for the expected medium field in terms of dbbelow the free -space value for varying distances. Itis of interest to compare these curves with someexperimental curves published by Gerks.* Thesecurves are reproduced in figure 14-3, and on themhave been superimposed the free space and theBullington empirical curves for the particular con-ditions that apply.

This procedure shows that there is a good degreeof correlation between the work of Gerks and Bull-ington for paths extending well beyond the optical

*P.I.R.E.-November 1951-Gerks: Propagation at 412 mefrom a high power transmitter.

range. Bullington's statement that the field intensitywell beyond the horizon is independent of the antennaheight is also well substantiated by the bunchingbeyond the optical range of curves A, B, C, and D,which are curves for receiving antenna heights rang-ing from 10 feet to 15,000 feet.

Let us now turn to the paths beyond the opticalrange which have been considered. Nine such pathsfor which reasonably long term field intensity meas-urements are available (periods from one week to 41months) have been analyzed, and the results areindicated in table 14-2. In each case, two predictedvalues have been shown: one calculated on the basisof the Bullington nomograms, and the other calcu-lated from his empirical curves as shown in figure 10.These latter are median value curves, and wouldtherefore be expected to yield results reasonably closeto the measured median (50%) values.

Examination of table 14-2 indicates that for 6 ofthe 9 paths considered, the predicted values of fieldstrength (using figure 14-20) are within 3.8 db of themeasured median value. Of the next 3 paths, thepredicted value for one is within 6 db of the medianvalue experienced; and for the last two paths, thepredicted values correspond to the fields experienced99.9% of the time.

Consequently, with the exception of the latter twopaths, there is a very good degree of correlationbetween the median values predicted using figure14-10, and the measured median values. Insofar asthese latter two paths are concerned, it will beobserved that the duration of measurement was onlyone week. Also, as both paths are over water, it ispossible that a high degree of atmospheric stratifica-tion may have existed during the tests. Such atmos-pheric conditions would result in higher medianlevels of field intensity for a short term than wouldbe experienced over a long term.

A comparison of the measured values in table 14-2,and the values calculated using the Bullington nomo-grams, indicates that no consistent correlation ispossible for these paths. The problem is, therefore,to decide which method should be applied in com-puting path losses for any particular circuit extendingbeyond the optical horizon.

Bullington has indicated* that his nomogramsprovide a result which agrees reasonably well withexperimental results if the correction for earth's curv-ature is less than 20 or 30 db. If we assume that 20db is the maximum allowable curvature correctionwhen using the nomograms, it is possible from figure14-15 to plot a curve which will indicate the distances

*P.I.R.E. -January 1950 -Bullington: Radio Propagation Vari-ations at UHF and VHF.

128

CHAPTER 14


TABLE 14-2

COMPARISON OF THEORETICAL COMPUTATIONS AND LONG TERM FIELD INTENSITY MEASUREMENTS

FOR CIRCUITS EXTENDING BEYOND THE RADIO OPTICAL HORIZON

ReferenceFreq.

Hop Mc/s

Dis-tance

inMiles

RCA ReviewJune 1946

Prince Rupert- 45Ma-s.sett

76

RCA ReviewJune 1946

Prince Rupert- 45Langara Island

108

FrequenzJan. 1952

Berlin- 60Harz

133

RCA ReportF 43-118

Alpine -93.1Riverhead

67

RCA ReportF 43-118

Boston -92.9Riverhead

127

RCA ReportF 43-118

Boston -92.9Hauppauge

150

RCA ReportsF 43-106F 42-121

New York- 203.75Riverhead

69.5

RCA ReportEM 61-17

Empire State- 288Riverhead

70

PIRENov. 1951(Gerks)

100 Mile Smooth 400Earth Path -1KW Radiated

100

CalculatedValue of FieldIntensity-Dbabove 1 Av/m

Bulling -ton

Nomo- Fig.grams 10

36 24.5

36 18.2

46.5 28

46 44

-6.7 17.8

-10.5 13.3

29.5 36

28.2 25.4

-57.5 8.8

Percentage of Time MeasuredFields Indicated

(Db above 1 Av/m)Are Exceeded

1% 50% 90% 99% 99.9%

Durationof

Measure -of

ments

42.9 35.7 34.1 32.3 31.2 1 week

35.9 28.4 26.3 22.4 19.5 1 week

-- 30.8 21.6 7.3 12 months

59 43 38 29 17 16 months

38 18.5 7 -2 - 22 months

38 16 7 -2 - 15 months

55 30 22 17 12 41 months

48 24.5 22 18 3 months

44 5 -9 - 20 - 11 months

for varying frequencies beyond which the nomogramsshould not be used. Figure 14-4 illustrates a curvewhich has been produced from figure 14-15, assumingthat the antenna heights are restricted to the valuesgiven in Scale A of the figure. It is now of interest tosee which of the paths listed in table 14-2 could beanalyzed by using the Bullington nomograms whenthe limitations of figure 14-4 are taken into considera-tion. The actual distance beyond the radio opticalpath length for each case, and the limitations imposedby figure 14-4, are listed in table 14-3.

The radio optical distance in each case has beencalculated using the equation

Do = .V2h, (14-1)where

Do = Radio optical distance in miles (profile drawn

on an earth's radius 4/3 times true radius).ht. = Receiving antenna height in feet.ht = Transmitting antenna height in feet.

Formula 14-1 may be found as nomogram J inAppendix I.

An alternative method is to use figure 14-17 withthe antenna heights at each end taken above anaverage smooth earth. The addition of the two dis-tances to the horizon gives the radio optical horizon.

Examination of table 14-3 indicates that circuits1, 4, and 8 are the only ones for which figure 14-14clearly indicates permissible use of the Bullingtonnomograms. In these three cases it will be seen byreferring to table 14-2 that the nomograms give pre-dicted values within 3.7 db of the measured medianvalues. For circuits 2 and 3, the actual distancebeyond the radio optical horizon coincides with the

129

CHAPTER 14


+100

+ 80

4.+ 60

u.1

0a +40

0-

(7) + 20

zI-

0U

U-

- 20

40

.\..,

.\^. .,

..\.-

. ,.s,

FREE SPACE

A

,

\ %

'a ,ct %

N

\D%

\k kV

'i

,

\

PLOTTEDFIGURE 14

FROM-10 \

1,

oo

2 3 4 5 10 20 30 50 100 200 300 500DISTANCE IN MILES

CURVES A, B, C AND D , SHOW MEDIAN VALUES OF FIELD STRENGTHFOR VARIOUS RECEIVING ANTENNA HEIGHTS. FREQUENCY 410EFFECTIVE RADIATED POWER I KW. TRANSMITTING ANTENNAHEIGHT 40 FEET.

A - EXPERIMENTAL CURVE - RECEIVING ANTENNA 10 FEETB - 1,800 "

C - " 4,500 "D - " 15,000 "

Figure 14-3

limiting values given by figure 14-4, and the predictedvalues, using the nomograms, are seen from table 14-2to be 7.6 db in excess of the measured median values.The predicted values could, therefore, be classed asunreliable. Of the other 4 circuits, the nomogrampredictions for numbers 5, 6, and 9 are seen to bewell at variance with the measured median values,while for circuit 7, the nomogram prediction iswithin 1.2 db of the median value.

It is felt that the above analysis justifies the useof figure 14-4 as an indication of the limitations of theBullington nomograms. However, where the actualdistance beyond the radio optical horizon is withinabout 10 miles of the limits set by the figure, it isconsidered advisable to compute the path losses onthe basis of the nomograms and figure 14-20, andselect the lower value given as the expected medianvalue.

All the above information on paths extendingbeyond the horizon indicates that predicted valuesshould be considered as median values. The question

Curves by Gerks

now arises as to what fading margin should beallowed to bring such values up to the level to beexpected 90% of the time.

An examination of table 14-2 shows that the differ-ence between the measured fields received 50% ofthe time and 90% of the time vary in a rather randommanner. If these differences are plotted against fre-quency, as shown in figure 14-5, an arbitrary curvecould be drawn through the points as shown. It isrecognized, however, that there is insufficient data tojustify the shape of this curve, but it is felt that itprovides a reasonably adequate indication of the 90%fading range to be expected.

Summarizing the situation for paths extendingbeyond the radio optical range, the above evidenceindicates that field intensities for 90% of the timecan be predicted to within 5 db by adopting thefollowing procedure:

1. Check the smooth earth radio range for theparticular antenna heights involved (figure14-17).

130

CHAPTER 14


TABLE 14-3

COMPARISON OF DISTANCE BEYOND RADIO OPTICAL

PATH LENGTH AND LIMITING VALUES FROM FIGURE 14-4

CircuitNo.

1

2

3

4

5

6

7

8

9

HopFreq.MC/S

TotalPath

Length

RadioOpticalPath

Length

ActualDistanceBeyondRadio

Optical

LimitingValuefrom

Figure14

Prince Rupert-Massett 45 76 63 13 31miles miles miles miles

Prince Rupert-Langara 45 108 77 31 31Island

Berlin-Harz 60 133 105 28 28Alpine-Riverhead 93.1 67 52 15 24

Boston-Riverhead 92.9 127 39 88 24Boston-Hauppauge 92.9 150 49 101 24New York-Riverhead 203.75 69.4 47.7 21.7 18

Empire State-Riverhead 288 70 61.8 8.2 16

100 Mile Smooth Earth 400 100 13.4 86.6 14Path- (Gerks)

2. If the distance of the actual circuit beyond thesmooth earth radio range is greater than thelimits set by figure 14-14, use figures 14-10 and14-20 to obtain the median path loss. Increasethis path loss by the fading margin taken fromfigure 14-15 to obtain the value expected 90%of the time.

3. If the distance of the actual circuit beyond thesmooth earth radio range is within 10 miles ofthe limits set by figure 14-4, calculate theexpected median path loss from the Bullingtonnomograms and also from figures 14-10 and14-20. Select the most conservative value ofpath loss so given and increase by the fadingmargin taken from figure 14-5 in order toobtain the 90% value.

4. If the actual circuit exceeds the smooth earthradio range by a lesser amount than indicatedin step 3 above, use the Bullington nomogramsto assess the path loss. Consider the value givenas a median value and increase by the fadingmargin taken from figure 14-5 in order to obtainthe 90% value.

CONCLUSIONS. It is believed that the aboveanalysis of long-term propagation measurements hasshown that VHF and UHF path losses can be pre-

dicted with sufficient reliability to engineer radiorelay systems for satisfactory operation. A summaryof the recommended procedures and their applicationto a series of typical profiles is included in the follow-ing portion of this chapter.

For optical paths, and for paths that would beoptical but for an intervening obstruction, it is con -10000

5000

3000

2000

1000

500

300

200

100

50

30

20

ID10 20 30

DISTANCE BEYOND OPTICAL RANGE - IN MILES

Figure 1 4-4. Limitations of Bullington Nomogramsthe Radio Horizon

40

Beyond

131

CHAPTER 14


1000

500400

300

200

Z 100

0

LL

304030

20

1002 4 6 6 10

DECIBELS12 14 16

Figure 14-5. Fading Margin

sidered that procedures outlined will give a fieldintensity which is within 5 db of the value exceededfor 90% of the time over a long term period.

For paths beyond the optical range, at frequenciesup to 500 mc, it is considered that an equivalentdegree of reliability can be expected in the predictionof actual median field intensities. The assessment ofthe fading range to convert this predicted medianvalue to a value expected over a long term period for90% of the time cannot, however, be made with asmuch certainty. For thisreason, the arbitrary curveshown in figure 14-5 has been drawn in a conservativemanner through the practical points plotted. Furtherlong term studies will be necessary before a highdegree of reliability can be assured in the assessmentof this fading range. In the meantime, however, theallowances which figure 14-5 indicate are consideredto be adequate for use in systems engineering.

One point on which very little information has beenfound is the performance of circuits where bothterminals and the intervening terrain are at altitudesabove 10,000 to 20,000 feet. Under these circum-stances, it is questionable whether the concept of astandard atmosphere (which is the basis for an earth'sradius of 4/3 the true radius) is still applicable. Inaddition, there is the question of a possible "ObstacleGain" on non -optical paths. Until more informationis available on these points therefore, it is suggestedthat profiles for such circuits be drawn on a trueearth's radius and predicted accordingly.

Paths such as those mentioned in the last para-graph do not often occur, while paths containing aclear line -of -sight, or partially obstructed line -of -sight, are most commonly encountered. In order todetermine the suitability of a radio path under suchconditions, the following steps are arranged to deter-mine, first, whether the path is clear optical, ob-structed optical, or non -optical. Having determinedthis, the next step is to determine whether or not

the path attenuation under the condition found issufficiently low to permit use of the sites. It must beborne in mind that equipments will usually be in kitform, that is, the relay systems will not be suppliedwith a variety of antenna units, power supplies, andso on, in order to utilize particular sites. If, with theavailable equipment, a site will give satisfactory pathattenuation and reliability, then, other things beingequal, the site is practical. Otherwise, a site must bechosen that will conform with these requirements.In order to explain the use of these steps and nomo-grams, the contour map is used to show two possiblesites for relay stations, with a third site which isalready established by the location of other relaysites (not shown) along the system.

SITING EXAMPLE

In order to show the relationship between the areain which radio relay stations are to be installed, andthe actual reception conditions to be expected, theexample starts with the contour map illustrated infigure 14-6. This map shows rolling country in whichsite X has already been established, and either site Yor site Z yet to be chosen. In regard to a readilyobtainable source of power, site Y is considered as thebetter of the two. However, the path Y -X has thedisadvantage of an intervening rise of ground aboutseven miles southeast of site Y, which may causeexcessive shadow loss. On the other hand, site Z,which has an obviously clear line of site on the pathZ -X, requires an additional two miles of power lineconstruction.

CONSTRUCTION AND USE OF PROFILES.Clearance above hills, trees, or buildings should bedetermined by plotting the profile of the land belowthe transmission path, using standard 4/3 earthprofile paper.

NOTE

Unless the path has been purposely cleared,tree heights must be taken into considera-tion, either by plotting the profile along thetree tops, or by adding the average treeheight to the bare earth profile.

Since the profile is drawn on 4/3 earth profile paper,the radio beam must be a straight line between theantennas at the two sites. The distance between thisline and the path profile will be the path clearance,or extent of obstruction, and may be read in feet onthe elevation scale. General path classification maythen be determined by referring to figure 14-7, whichshows three types of paths, (1) clear line of sight,

132

A

2450240024502500255028002600-.255025002450 -24002350

23002250

2250

2300

230023002250

2200 -E

21502100

2100

2150

2200

2250 -2300

2250

2250

230023502350

2300-u

3400

3000

2600

2200

1800

1400

1000

IL 2500

2000

1500

81§11111g

1

I 1 §

0 2

CHAPTER 14


! N N b. § 11E 1 T O ;1 11

10 12 14 16 18 20 22 24 26MILES

LEG Z. X , CLEAR LINE OF SIGHTSHOWN ON 4/3 EARTH PROFILE PAPER

3400

3000

2600

2200

1800

1400

1000 0 2 4

VIEW OF AREA FROM THE SOUTHDEVELOPED FROM PROFILES A THROUGH H

8

I ma1900

18501800175017001650

1600

1550

1500

1450

140013501300

1250

1200

ET --I200

1250

1300

1350

1400

145015001550

16001600

6-1580

H

CONTOUR MAP SHOWING TENTATIVE TOWER SITES

6 e 10 IS 14 16 18 20 22MILES

LEG Y- X, OBSTRUCTED LINE OF SIGHTSHOWN ON 4/3 EARTH PROFILE PAPER

Figure 1 4-6. Contour Map and Profiles

24 26

MOO

1450

1400

3400

3000

2800

2200

MOO

1400

1000

2500

2 000 E

1500

133

CHAPTER 14


(2) obstructed line of sight, and (3) non -optical. Thefirst two classifications are self-explanatory, and thethird simply refers to a path which extends beyondthe radio horizon. These three general path classifi-cations are further classified into individual typescharacterized by varying amounts of first Fresnelzone clearance in the first two cases, and by distancein the third (non -optical) case. Each type is illus-trated in figures 14-8, 14-9, and 14-10, respectively.

Path Y -X, therefore, is classified as an obstructedline -of -sight condition, since the profile shows an

1 000

500

obstruction extending one hundred feet above theline of sight. No allowance for trees is necessary inthis case, as the contour map shows the obstructionto be a bare hill. Likewise, path Z -X is classified asa clear line of sight path.

PATH Y -X COMPUTATIONS. Since path Y -X hasbeen classified as an obstructed line of sight, we mayrefer to figure 14-9 to determine the proper method ofestimating path attenuation. In this case, the pathwould have first Fresnel zone clearance except for the

Am-/////4/tov

1000

500

Figure 14-7. Types of Paths

LINE OF SIGHT

OBSTRUCTEDLINE OF SIGHT

NON - OPTICAL

NON - OPTICAL

1 34

CHAPTER 14


PROFILE TREATMENT

A

C E

.. -.i D

SMOOTH EARTHWITHOUT FIRST FRESNEL ZONE CLEARANCE

A

DRAW TANGENT TO SMOOTH EARTH ,SUCH THAT AC: BD = CE s ED.

USE EFFECTIVE ANTENNA HEIGHTSAC AND BD WITH NOMOGRAM FIG. 14 -14 .

A

--'611111111111111111111- :..---; ... : . ,

FIRST FRESNEL ZONE CLEARANCEIN VICINITY ANTENNA A , BUT NOT B

B

DRAW PLANE EARTH LINE CD .

USE EFFECTIVE ANTENNA HEIGHTSAC AND BD WITH NOMOGRAM FIG.I 4 -14.

A C

DRAW PLANE EARTH LINE CD.

USE EFFECTIVE ANTENNA HEIGHTSAC AND BD WITH NOMOGRAM FIG.14 - 14.

..

NO FIRST FRESNEL ZONE CLEARANCEIN VICINITY ANTENNAS A a B

111W0 #.# 9/999,m999/fii/m/D. ..-

NO FIRST FRESNEL ZONE CLEARANCE AT -E ,NOR IN VICINITY ANTENNA B

D

DRAW PLANE EARTH LI NE C E D.

USE EFFECTIVE ANTENNA HEIGHTSAC AND BD WITH NOMOGRAM FIG. 14 -14 .

A E

DRAW PLANE EARTH LINE CE D ,SUCH THAT AC : BD = CE $ ED .

USE EFFECTIVE ANTENNA HEIGHTSAC AND BD WITH NOMOGRAM FIG.14 - 14 .

0/ 9 / i/luIIIIIIIIIIII..

FIRST FRESNEL ZONE CLEARANCEIN VICINITY A a B , BUT NOT AT E

A

C

F

DRAW PLANE EARTH LINE CD.

USE EFFECTIVE ANTENNA HEIGHTSAC AND BD WITH NOMOGRAM FIG 14 - 14.

- -

.,,d

FIRST FRESNEL ZONE CLEARANCEIN FRONT ANTENNA A, BUT NOT B

Figure 14-8. Clear Radio Paths

135

CHAPTER 14


obstruction, and therefore should be calculated asnoted under path A of figure 14-9. Here there aretwo sources of attenuation: free -space attenuation,which occurs in all clear line of sight paths with firstFresnel zone clearance, and the shadow loss causedby the obstruction. As noted in the figure, the totalpath loss is found by adding the free -space lossobtained from figure 14-11, to the shadow loss foundby use of figure 14-18. For path Y -X, figure 14-11shows a free -space loss of 126 db (at a frequency of1,800 mc, and path length of 28 miles). Figure 14-18shows a shadow loss of 16 db (100 foot obstruction,7 miles from an antenna, 28 -mile path length), givinga total path attenuation of 142 db.

PATH Z -X COMPUTATIONS. Path Z -X has beenclassified as a clear line of sight, according to figure14-7. The next step is to determine whether or notfirst Fresnel zone clearance exists over the entirepath, by use of nomogram H or figure 14-18. If firstFresnel zone clearance does not exist, further classi-fication is necessary, and figure 14-8 is used. In thiscase, however, adequate clearance is available, andthe total path attenuation may be found from figure14-11, a path loss of 124 db (at a frequency of 1,800mc, and path length of 27 miles).

SYSTEM CALCULATIONS. The two possibletransmission paths must now be compared in orderto determine whether or not they will be acceptable,and which is the better as regards attenuation. Anypeculiarities of the site that will effect signal attenua-tion should also be taken into account. Equipmentspecifications, taken from manufacturers' data, areas follows:

Equipment DataMake and type of systemCarrier frequencyTransmitter power outputTransmission line

Antenna typeReceiver input

Site X DataAntenna heightTransmission line length

Site Y DataAntenna heightTransmission line length

Site Z Data

Antenna heightTransmission line length

RCA CW-20A1,800 mc3 wattsRG-17/U (attenuation,

6.7 db per 100')6' parabolic reflector116 db below trans-

mitter output (min.)

100 feet150 feet

100 feet200 feet

100 feet125 feet

COMPUTATIONS, LEG Y -X

The attenuation and gain found in various com-ponents must be determined in db values in order toproperly compare the usefulness of the two sites inrespect to signal attenuation. The power output ofthe transmitter, 3 watts, may be expressed in termsof db above one watt. This is done by the formula

db = 10 Log PI /P2 (14-2)

where

P, = Transmitter output in watts= Reference level of one watt.

Thus the db output of the transmitter becomes 4.8dbw, or 4.8 db above one watt.

Transmission line loss at site Y is determined bythe attenuation of the transmission line in db per 100feet. For RG-17/U, this attenuation is 6.7 db per 100feet, giving a line loss of 13.4 db, which may also beexpressed as a negative gain, -13.4 db. Power sup-plied to the antenna will then be the dbw of thetransmitter, less the attenuation of the transmissionline, or 4.8 dbw -13.4 db, or -8.6 dbw. This mayalso be stated as 8.6 db below one watt.

Antenna gain must be figured, since with anydirectional antenna, the effective radiated power inthe beamed direction will be greater than the powerin the same direction from a non -directional antenna.Nomogram K in Appendix I will give the antennagain for a 6 foot parabolic antenna at 1,800 mc, as 26db over a half -wave dipole. The power output fromthe antenna will then become -8.6 dbw + 26 dbw,or +17.4 dbw. Path attenuation, already determined,is 142 db. Power received at the site X antenna willthen be the antenna output, 17.4 dbw, less the pathattenuation, 142 db, or -124.6 dbw. The antennagain, 26 db, added to this figure, gives the powersupplied to the transmission line, or -98.6 dbw.Transmission line loss between the site X antennaand receiver is 10 db (for 150 feet of RG-17/U line),and the power delivered to the receiver at site Xbecomes -108.6 dbw. Although this value is calcu-lated with site Y as the transmitting end, the sameattenuation will occur in signals transmitted from siteX to site Y.

COMPUTATIONS FOR Z -X LEGS

The calculations for this leg of the system arefigured exactly as for the Y -X leg, and will be shownin tabular form. Attenuation is indicated by a minussign, gain by a plus sign. For the sake of comparison,the Y -X computations are also shown.

136

CHAPTER 14


PROFILE TREATMENT

A aid, II /..d, I ,ZiI NIIIIIIIIII/ir../ - . -/

COMPLETE FIRST FRESNEL CLEARANCEEXCEPT FOR OBSTRUCTION

A

USE NOMOGRAM FIG. 14 - II TO COMPUTEFREE SPACE LOSS. INCREASE BY SHADOWLOSS FROM NOMOGRAM FIG.14- 1B ,

USING DISTANCE d1 AND HEIGHT h.

E

lihOP Ilpo B

USE EFFECTIVE ANTENNA HEIGHTS ACAND BD WITH NOMOGRAM FIG. 14 - 14 ,

TO COMPUTE PLANE EARTH LOSS.INCREASE BY SHADOW LOSS FROMNOMOGRAM FIG. I 4 - 19 , USING DISTANCEd1 AND HEIGHT h .

.// I / A10 ..--.- /// /

-,FIRST FRESNEL ZONE CLEARANCE

IN VICINITY ANTENNA A, BUT NOT B

filr/it I: NIIIIIIIIIIIILb ,...........pp.

C ' d ./ ii h.__ ._.111111.11)1111111,g'10,, , ...waif

NO FIRST FRESNEL ZONE CLEARANCEIN VICINITY ANTENNAS A AND B

C

USE EFFECTIVE ANTENNA HEIGHTS ACAND BD WITH NOMOGRAM FIG. 14 -14 ,TO COMPUTE PLANE EARTH LOSS.INCREASE BY SHADOW LOSS FROMNOMOGRAM FIG. 14 -19 , USING DISTANCEd, AND HEIGHT h .

1111'

//h1111.1 111.p.-

,,// f .1 2, ;%4,,,Z..:.-.,...,-1-'.* - ' --, ,-, /4

NO FIRST FRESNEL ZONE CLEARANCE AT F ,NOR IN VICINITY ANTENNA B

D

USE EFFECTIVE ANTENNA HEIGHTS ACAND BD WITH NOMOGRAM FIG. 14-14,TO COMPUTE PLANE EARTH LOSS.INCREASE BY SHADOW LOSS FROMNOMOGRAM FIG. 14 - 19, USING DISTANCEd1 AND HEIGHT h.

A E

E

USE EFFECTIVE ANTENNA HEIGHTS ACAND BD WITH NOMOGRAM FIG.14 - 14 ,TO COMPUTE PLANE EARTH LOSS.INCREASE BY SHADOW LOSS FROMNOMOGRAM FIG. 14 -19 , USING DISTANCEd, AND HEIGHT h.

C4

.../

dl;FIRST FRESNEL ZONE CLEARANCEIN VICINITY ANTENNA A, BUT NOT B

NOTE RAD/0 PATHS NOT SHOWN.Figure 14-9. Obstructed Radio Paths

1 37

CHAPTER 14


PROFILE TREATMENT

SMOOTH EARTH

A

USE BULLINGTON NOMOGRAMSFIGURES 14- II, 16 AND 17, TO OBTAINTHE SMOOTH EARTH PATH LOSS.

di/ /////im.-wq rm.77/"'" ./.

IRREGULAR TERRAIN

B

OBTAIN THE SMOOTH EARTH PATH LOSSFROM NOMOGRAMS FIGURES 14 - II , 16

AND 17, AND INCREASE BY THESHADOW LOSS GIVEN BY FIGURE 14 - 19,

TO OBTAIN THE DISTANCE d1 ANDHEIGHT h FOR USE WITH FIGURE 14 - 19,PLOT THE PROFILE ON RECTANGULARCO- ORDINATE GRAPH PAPER .

_000'4WOW lll...1.1111FT

C

DRAW PLANE EARTH LINE CED.USE EFFECTIVE ANTENNA HEIGHTSAC AND BD WITH NOMOGRAM FIGURE14 - 14 , TO COMPUTE PLANE EARTHPATH LOSS.

INCREASE BY SHADOW LOSS GIVENBY FIGURE 14- 19, USING DISTANCEd1 AND HEIGHT h.

Figure 1 4-1 0. Non -Optical Paths

138

CHAPTER 14

Item Z -X Leg Y -X Leg

COMPUTATIONS OF WAVE PROPAGATION FOR RADIO RELAY APPLICATICN

Transmitter output +4.8 dbw +4.8 dbwTransmitter line loss . . . -8.4 db -13.4 dbAntenna gain (xmtr) . +26.0 db +26.0 dbPath attenuation -124.0 db -142.0 dbAntenna gain (at X) . . . +26.0 db +26.0 dbTransmission line loss

(at X) -10.0 db -10.0 db

Power Level at the Re-ceiver - 85.6 dbw -108.6 dbw

These are the values to be expected at least 90%of the time; that is, the signal strength will have thesevalues, or better, 90% of the time. Since the receiveris capable of amplifying the signal, this figure isconservative, and a greater attenuation may bereceived and satisfactory reception will still result.

The CW-20A system requires a path attenuationof not more than 116 db between transmitter andreceiver, as given in the specifications for the system.Both paths, then, are entirely acceptable, since bothhave considerably less attenuation than the systemwill accept. The choice between these two sites wouldnot, therefore, be determined by the received signalstrength, but by accessibility. However, if the accessi-bility of both sites is approximately equal, the linkwith the least path attenuation should be used.

If the strength at the receiver were required inmicrowatts, instead of in dbw, the dbw figure maybe converted to power in microwatts as follows:

Power level (in dbw) = 10 Log P1/P2 (14-3)where

P2 = 1 watt.

Since the power for the Y -X leg is 108.6 dbw, thepower level referred to watts is

-108.6 = 10 Log P1and P1 = 7.3 X 10-10 watts.

Referenced to microwatts, this value becomes 7.3 X10-10 x 106, or 7.3 X 10-4 microwatts input to thereceiver.

GENERAL SUMMARY

1. Draw the profile for the path concerned on anearth's radius 4/3 times the true radius. If suit-able profile paper is not available a 4/3 earth'sradius curve can quickly be drawn on rectangularcoordinate graph paper using the followingformula:

h = 0.5 d1d2 (14-4)

where

h = height in feet under the curve at distance d1miles from the initial end, and d2 miles fromthe far end.

If for any reason it is desired to draw a profile ona true earth's radius the formula becomes h =0.667cl1c12.

2. Check whether the path can be classed as line ofsight, obstructed line of sight, or non -optical, asillustrated in figure 14-7. For the first three pro-files, the classification is obvious, for the fourthprofile, the line from A to B does not intersect thesea level earth's curvature. However, all theterrain is above the 500 -foot level, and this wouldtherefore be considered as the smooth earth line.Since AB intersects this 500 -foot line, the pathwould be classed as non -optical.

Line of Sight Paths

1. For line of sight paths check whether first Fresnelzone clearance exists. This may be found by usingnomogram H in Appendix I.

2. If first Fresnel zone clearance exists, obtain thepath loss from Bullington nomogram figure 14-11for free -space propagation when 1 watt is radiatedbetween half wave dipoles. Correct for actualtransmitter power and antenna gains proposed,and consider this the value to be expected 90%of the time.

3. If first Fresnel zone clearance does not exist drawa plane earth line CD, as indicated in the typicalcases shown in figure 14-7 and obtain the planeearth loss for one watt radiated between half wavedipoles from Bullington nomogram figure 14-14using antenna heights AC and BD. Correct foractual transmitter power and net antenna gainsproposed, and consider this path loss as the valueto be expected 90% of the time.

Obstructed Line of Sight Paths

1. For obstructed line of sight paths ignore theobstruction initially, and draw a plane earth lineCD in the same manner as in paragraph 2.3 above.Use the base CD to form a shadow triangle CDEas indicated in the typical cases shown in figure14-9.Use Bullington nomograms figures 14-14 and14-19, or 14-11 and 14-18, as indicated in thetypical cases in figure 14-8 to obtain a value ofpath loss for one watt radiated between half wavedipoles. Correct for actual transmitter power andnet antenna gains proposed, and consider this

139

CHAPTER 14


path loss as the value to be expected 90% ofthe time.

Non -Optical Paths

1. For non -optical paths check the value of the radiooptical range given when using the effectiveantenna heights above a smooth earth. As indi-cated previously, smooth earth is not necessarilytaken at sea level. The optical range for 4/3earth's radius is given by the formula (see nomo-gram J in Appendix I):

do = 1/2h1 -I- 1/2h2 (14-5)where

do = optical range in miles

h1 and h2 = effective antenna heights in feet.Alternatively, the radio optical range can beobtained by adding the distances from the top ofeach antenna to the smooth earth horizon as givenby figure 14-17.

2. If the length of the path beyond the optical rangeis greater than the limits set by figure 14-4, com-pute the path loss for one watt radiated betweenhalf wave dipoles using figures 14-11 and 14-20.Correct for actual transmitter power and netantenna gains proposed, and consider this pathloss as the median value to be expected.

If it is desired to assess the value to be expected90% of the time, increase the path loss by anamount indicated by figure 14-5.

3. If the distance of the actual circuit beyond theoptical range is within 10 miles of the limits setby figure 14-4, calculate the path loss for one wattradiated between half wave dipoles, both fromthe Bullington nomograms as indicated in figure14-10 and from figures 14-11 and 14-20. Correctthe most conservative value so given for actualtransmitter power and net antenna gains pro-posed, and consider this path loss as the medianvalue to be expected.If it is desired to assess the value to be expected90% of the time, increase the median value by anamount indicated by figure 14-5.

4. If the actual circuit exceeds the optical range bya lesser amount than indicated in step #3 above,calculate the path loss for one watt radiated be-tween half wave dipoles from the Bullingtonnomograms as indicated in figure 14-10. Correctfor actual transmitter power and net antennagains proposed, and consider this path loss as themedian value to be expected.If it is desired to assess the value to be expected90% of the time, increase the median path lossby an amount indicated by figure 14-5.

140

CHAPTER 14


SCALE 1

AFTER BULLINGTON

-100

-90H

2-_

3--

80.5-

.7-I--

-70

2-

3-

-60 -5- 0

- 0cc

-r-0

0

20- 0- co

30-

-4050-

00

-30

200-

300 -r

-20500 -_

- SCALE 2

-10

VI

-J

U4

U

-30,000-20,000

-10,000-7000-5000-3000-2000

-1000

-500-300- 200

-,100

-50-30-20

-10

SCALE 3

160-,

150-

130-

110-.

100 -

90 -

80

SCALE 4 --1

70-

Figure 14-11. Free Space Field Intensity and Received Power between Half Wave Dipoles, 1 Watt Radiated

141

CHAPTER 14


C

600

EFFECTIVE800 AREA OF

EACHANTENNA

1000 INSO. FT

1500

2000

2500

3000

4800 - -5000

6000

8000

10 000

15000

20 000

30 000

AFTER BULLINGTON

-100-80- 60-50- 40

-30

-20-15

-10-8

-6-5

-3

-2

-1.5

UILES

-100-80-60-50-40

30

20

-10

-8-6-5-4-3

75

70

-65

60

55

-50

-45

40

Figure 14-12. Received Power in Free Space between Two Antennas of Equal Effective Areas, 1 Watt Radiated

142

CHAPTER 14

1000

700

500

200

100

1- 50wwL.L

z

30CD

w

20

10

7

5

3

2


110

GOOD SOILK-30.02MHOS

PER METER

HORIZONTALPOLARIZATION

POOR SOILa-4o ..00I

GOOD SOIL.x- 30

- .02

VERTICALPOLARIZATION

SEA WATERK-80a-4MHOS

PER METER

AFTER BULLINGTON

20 50 100MEGACYCLES

200

Figure 14-73. Minimum Effective Antenna Height

500 1000

NOTE FOR FREQUENCIESABOVE 1000 MC,USE ACTUALANTENNA HEIGHTS

143

CHAPTER 14


S

I0

20

SO ...

-100

-200

-500

zh

cc

2000

-5000

-10,000

AFTER BULLINGTON

-5

-10

r-20

H 50

H100

-200

-500

-1000

-2000

-2

5

2

1

5

-50N,

100

-200

-SOO

-1000

-1h

Irha

al

030_J

CO

CO

0

Oa.

0

N L)ILCC

-60

-70

-so

-90

t-

-100

,110

-120

X130

h140

-ISO

-160

NOTES.-5000 I. THIS CHART IS NOT VALID WHEN THE

INDICATED RECEIVED POWER IS GREATERTHAN THE FREE SPACE POWER SHOWNON FIGURE 14 -

-10,0002. USE THE ACTUAL ANTENNA HEIGHT OR

THE MINIMUM EFFECTIVE HEIGHTSHOWN ON FIG14-13,WHICHIEVER tS THEL ARGER

Figure 14-14. Received Power over Plane Earth Between Half- Wave Dipoles, 1 Watt Radiated

144

CHAPTER 14


SCALE A

LIMITING ANTENNA HEIGHT IN FEET500 300 200 100 50 30 20 10

II

iI I I III1 T

20 50 100 200 500 1000 2000 5000 10,000MEGACYCLES

10.000110,000r-

5000 -4-5000-4-

3000 -4-3000 cr 5-tacr -0 2000 -2000 <

_o -r. -Z 61 _<_i 61 MOO MOO N

fn ft 10-cc a -I,-"I -I0 >- 00°Z 500 -4-* 500

_J

-,

-J < -4- 00J a. 20-s a/' la In -ccW 0 200 -4-200 W la

-) 30-> >i -i """R"--- ,..... 200 VI ........,IL Z

,.

-LAI la ...........,-I 100- -I.).1 xioo 0 .--&-er00 70-.- 0 Z -4 .......70 4 <

1.0I-

6 50 -.- 0*42 lal-.- 50 2 E -- toct-

20-4.-30

10-4.-20

AFTER KILLINGTON

200-

300-

2-

ya

Z

.57 -to _W

CC >D 0 0 II- 10 -4 in I- 413_> oft 4AZ -CC 0 33 _J 2 -u

.././ .11(top_ 1 5 - cz o -Op cn u -In r- 20-, I- cc 5-D a cc4 0

-. laIa ,,,

0 4 -sostb z 6i t- 1 0=0.30 > a

i: <U 'a

CO Ll040 i. 20 -

1a.1

W

SO 00t- SO -

70 cc

n -It100:

100

Icc< 30

0

Cr 20o//>z cr I5

0)0

40VI 70,

_J

OD

0

Figure 14-15. Diffraction Loss Caused by Curvature of the EarthAssuming Neither Antenna Height is Higher than Shown on Scale A

145

CHAPTER 14


9 641013

500

alit'C

LOSS RELATIVE TO FREE SPACEL.1+ L2+L3 IB 5 + 2.5+15 27 DB

20-3030

- 5050-

10000- 7

If4/3 D

200 -200...../ r3

is -2 g N.3...!.......0-4.e.b0W in

- I a3 o- .4Z 500 -500 4 cr cr4 4(...

-.-In -

5W V)

CC 4 or - -7 kw 1)1." IC) 00 -..- I 0 0 0 10 -> '-

.01> > .- rt0 tt 0 - lo <.0 ..),.,

_.,,., -J 1,1

U."a

C.. 2000 -*-2000 g@, Z U. D4 U.1 CE

cr: -1 3000 -3000 i.: -20 1-

a 8 0 100La I-

> >- 0

44 5000 -5000 14AY r..... W .- 50 a- I -....- ..I

U>- ,... _- x 200 -2004I.1 I 0, 0 00 --I 0,000 14

2O 0 100tol la-..- 2 300 ,-300

2 0, 000 - 20,000

o

30,000 -30,000

AFTER BULLINGTON

20

50

- 26I 30

26-i- 22

- 20-2 26- - (8

-3

6

qI

41

-5 22-I2in0- - ,-10 r-

- I - .--10 - 20--a 0

L.10 ,-id 19Y' 4o-

-- .4 V-

2000V

-6 0..n

La .4 .4,_ J 01

4 - 5 <0- 30 .1) .4z u8.3 - 0

-1 -J.- .1

O 03 .- 4 m-SO C C

N. si II

nJ

- ......-J -1

-..N.-3

-100 N19

2

20--

4

2

3

O

/-I-

1- 7

UJ

II

- 20 _I

- 30

- 40

- SO

- 60

70

- SO

Figure 14-16. Db Loss Relative to Free Space Transmission at Points BeyondLine of Light over a Smooth Earth

146

CHAPTER 14


-35 -

-.-- 4t 0

-5

-620 -

- 2

-3

-55-

-7 n 7-a

1"---9 O -J

50-10 .0- 10 / 4/3

Z g

500- 0

z6.1 -40z - 1000-.-4 -50

2000--60-70

-\-80-90

5000 -100

10,000 -4

AFTER BULLINGTON

-d"

2C12. e.-2 0

-- J Z--.._

21..1 --U....- ...--100 -0- Z- -20 .f( ..... --- -----15 w 3 -- P -u --- ------ r--', 30 6

Z 5--O -- o- - 50 N 7 -_,-

Z I- g -I-'- 0 1 I 0 --0- N

-30 Er-100 -

X200

-300

-500

20-

50 -

100 -

Figure 14-17. Distance to Horizon

147

CHAPTER 14


ANTLd

di(SEE NOTE)FEET MILES

50

30-20

10\5 \3 \2

5000

20 00

1000

500

200

100

50

20

10

AFTER BULLINOTON

5

.3

.2

di- dz LOSS IN DB

(H)FEET

\\

ANT-

- 10,000

-5000

-3000-2000

-1000

- 500

-300- 200

-100

50-30\-20

2

FREQ

NOTE H IS NEGATIVE

-

RAY

-

MC

WHENCLEARS

SECOND

/THIRD

NEGATIVEVALUES

OF H

5

THETHE 4

3

2

1

j-

FIRST -1 2,/0 -/

1 -4

/4' 0

-0.6

POSITIVEVALUES

OF H

- 7

8

9

10

12

14

16

la20

25

DIRECTOBSTRUCTION.

3060-

1 SO-300-600

I 500-3000-i6000-

1 5,000-

IFRESNEL\ZONES

- 30-10 /30,000-

1-5 / I-- 35-3-2 NOTE. WHEN ACCURACY

GREATER THAN t 1.5 DB-I IS REQUIRED, VALUES ON

THE di SCALE SHOULD BE: - 40

47di[1+

2J

45

- 50

Figure 14-18. Shadow Loss Relative to Free Space

148

CHAPTER 14


ai d2

- 4

-5

-64p-- al

-8d1

MILES FEET FREQ. - MC -10(SEE NOTE)

-50-10,000 -3 -12/-7000 -6. -14

"40 =5000 -15/ 1

-151=3000 30 - I 8

0 ,2000 - 60-20

^1500 / - 150

000 / -300 -22

-3 -700 -600 -24

2-500 - 1500

-1.5 -300 -28-1

-200-30

-.7

.5 r-100 NOTE: WHEN ACCURACY -32GREATER THAN ± 1.5 DB

70 IS REQUIRED, VALUES ON -34THE di SCALE SHOULD BE:

-50-36

-.15 -30di

1+d1

-38.1 2

^20 -40

AFTER OULLINOTON

coa

Figure 14-19. Shadow Loss Relative to Smooth Earth

149

CHAPTER 14


- _

(/) (/)-I ....la LI

2la-J °0-I 0< 1rZt., 0CT) 2Za3wm

O 0 0 o____In-.-- 0 oir

o 0 0 0 oNre}..---- vir 131---ce

93 930VdS 33LI3 ,10):1.4 GO

o-Jla>la-I

0-IM<0Z0 0M

V/

Z-°a 1*

0wm

.o o o O o o o 0 0 0Nsr if-- to r- 8 N1., 1:1 T T

30VdS 338.4 1408A GO

Figure 14-20. Median Signal Levels Relative to Free Space

150

CHAPTER 15

IONOSPHERIC TRANSMISSION (30 TO 100 MC

I' II I' T E

INTRODUCTION

As mentioned in Chapter 1, an electromagneticwave may be propagated in the form of three differentwaves, the ground wave, the ionospheric wave or skywave, and the tropospheric wave. Waves travelingthrough the troposphere (ground waves and tropo-spheric waves) are affected by atmospheric condi-tions, while the ionospheric waves are affected almostentirely by ionospheric conditions. It is the purposeof this chapter to discuss the problems connectedwith ionospheric waves, and the effects of ionosphericconditions on radio propagation in the frequencyrange from 30 to 100 mc.

IONOSPHERIC PROPAGATION

THE EARTH'S ATMOSPHERE. Although theearth's atmosphere outward to over 250 miles hasbeen described many times, a description will beincluded in this section for convenient reference. Thelower layer of the atmosphere, extending upwardapproximately 6 miles, is called the troposphere. Thislayer contains almost all of the gases comprising theatmosphere, and all of the phenomenon known asweather. Storms, warm or cold fronts, and air massesdo not rise above this level.

Above the troposphere, extending outward toabout 30 miles and containing a high ozone content,is the stratosphere. This region is characterized by acomplete lack of weather, and a nearly constanttemperature of - 57 degrees C. As far as is nowknown, the stratosphere does not affect radio trans -

15

IONOSPHERIC

TRANSMISSION

(30 TO 100 MC)

mission directly; however, since it acts as a reservoirof heat, it does affect the weather in the lower tropo-sphere, and thus indirectly affects radio propagation.The stratosphere also absorbs almost all of the ultra-

rays from the sun that have passed throughthe ionosphere, and thereby protects life on the earthfrom too intense radiation.

THE IONOSPHERE. In the regions above thestratosphere, the air particles become widely scat-tered, and consequently when electromagnetic radia-tions from the sun bombard the molecules composingthese air particles, they become ionized. Such radia-tions from the sun include ultraviolet light, X-rays,gamma rays, and cosmic rays, the most predominantionizing agent being ultraviolet light.

At high altitudes, the air particles are widelyscattered, and consequently less recombination occursbetween the free electrons and the positive ions.Therefore, these regions remain ionized for consider-able periods of time. The region of ionization whichaffects radio propagation lies between 30 and 250miles (50 to 400 km) above the earth's surface andis called the ionosphere.

The ionization in the ionosphere is not uniformlydistributed with altitude but is stratified, and thereare certain definite layers in which the ionizationdensity is sufficient to reflect radio waves. Such layershave no sharp boundaries and their altitude anddensity varies with the time of day, season, andsunspot activity.

The first layer, known as the D layer, exists onlyat times during the day at a height of about 30 to 50

151

CHAPTER 15

IONOSPHERIC TRANSMISSION (30 TO 100 MC)

miles, while the second or E layer exists at a heightof approximately 50 to 90 miles. The third and largestlayer, termed the F layer, exists as a single layer atnight while during the day it separates into twolayers, F, and F2. At night, the F layer is present atan altitude of approximately 100 to 250 miles. Duringthe day, the Fi layer is at a height of about 120 to150 miles, and the F2 layer is at a height of 150 to220 or more miles in the summer and from about 90to 190 miles in the winter.

According to Dr. W. A. Miller, * the stratificationof the ionosphere into definite layers is produced asfollows:

D layer (1) The first ionization potential of mo-lecular oxygen.

(2) The ionization of the metal atoms inthe upper atmosphere, sodium inparticular.

(3) Possibly the ionization of nitrousoxide.All of the above are sufficientlyabundant, and have a low enoughionization potential to permit ioniza-tion.

E layer (1) First ionization potential of molec-ular oxygen.

(2) Second ionization potential of molec-ular oxygen.

(3) Collision between two atoms of oxy-

*EM 62-47, The Solar Study Program of the RCA Laboratories,Rocky Point, Long Island.

F1

F2

gen resulting in a positively ionizedoxygen molecule, and a free electron.

(4) Pre -ionization of molecular oxygendue to the strong absorption bandsin the energy range 12.2 to 13.55 ev.Absorption of high energy photons.

The second ionization potential ofmolecular nitrogen.

(2) The first ionization potential ofatomic oxygen.

(1) The first ionization of molecularnitrogen.

(2) The first ionization potential ofatomic oxygen.

(3) The second and third ionization po-tentials of atomic oxygen.

(4) The first ionization potential ofatomic oxygen forming the F, layer,together with a height dependentrecombination coefficient and/or tidaleffect.

Possibly produced by the ionizingimpact of meteoric particles, or, inhigh latitudes, by bombardment bysuch fast solar corpuscles as produceauroras.

(5)

(1)

Es(Sporadic E)

Radio signals reflected from the ionosphere are notall reflected from the same part of the ionosphere.Each of the ionized layers reflects different radiofrequencies, allowing some frequencies to pass

MAJOR CHARACTERISTICS OF IONIZED LAYERS

HEIGHT OFMAX.

IONIZATION

MAX. AV.ELECTRON

DENSITY(Ne)

ELECTRONS / CM 3

TIMEOF

OCCURRENCE

Ne SUNSPOT MAX.

DENSITY OFNEUTRAL

PARTICLESPERC M 3

FREQUENCY ( f , )

AT1945 EQUINOXNe SUNSPOT MIN.

D LAYER 60 KM( 37 mi.)

I 5 x 104DAYTI

ONLYME2.0 8 x 1015 -

E LAYER 100 KM( 62 WI

I 5 x 106 24 HRS. 1.50 6 x 1012 3.7 MC

F, LAYER 200 KM(125 MI)

2.5 x 106DAYTI

ONLY1.56 I x 10" 4.9 MC

F2 LAYER 300 KM(106 MI )

I 5 x 106 24 HRS. 4.00 2 x le 10.5 MC

E, LAYER 100 KM - SPORADIC PATCHES OF IONIZATION DENSITY FAR HIGHER THAN NORMALLY( 62 M1.) FOUND AT THIS ELEVATION. PREDOMI NATES IN SUMMER, BUT NOT PREDICTABLE

FOR te OR TIME OF OCCURRENCE.

Figure 15-1. Major Characteristics of Ionospheric Layers

152

CHAPTER 15


through, and reflecting others. Figure 15-1 shows themain characteristics of each layer of the ionosphere.It must be understood that the values given in thetable are of necessity only approximate, since thesevalues are subject to diurnal, seasonal, and solarchanges. Since the degree of ionization is dependentupon energy from the sun, the ionization would beexpected to be greatest in the upper ionized layers,and so the table shows it to be. As the ultraviolet rayspenetrate the ionosphere, fewer and fewer reach thelowest ionized layers, and a correspondingly lowerdegree of ionization in these layers results. At night,when the solar rays are blocked from the ionosphere,changes take place in the layers. The D layer dis-appears entirely, and the F, layer merges with the F2layer. The E layer and the F layers show a lowerdegree of ionization and their height above earthincreases.

Changes in the ionosphere are geographical as well.At higher latitudes the degree of ionization is not asgreat as at the equator. Another change is the varia-tion of ion density in the layers due to change inseasons. Just as the amount of effective sunlightreceived during winter is far less than the amountreceived during summer, so is the amount of ultra-violet radiation, and consequently, we find that thelayers have a greater ion density during summer thanduring winter.

At times of excessive solar activity, the degree ofionization is again changed. There is a relationship,not clearly understood at present. between sunspotsand density of the ions. Since sunspots representgreater increased activity in the sun, the ionization ofthe various layers increases, just as might be expectedfrom such extra activity.

Another unusual source of radiation from the sunis solar flares. These flares, most easily seen duringan eclipse, are vast quantities of ionized gases, flungoutward perhaps hundreds of miles from the sun'ssurface. Many astronomers believe that some flaresreach out as far as the earth. These flares producesudden ionospheric disturbances, abbreviated S.I.D.,which cause rapid, short-lived fades in the ionosphericwave. If such a flare should occur near the center ofthe solar disk facing the earth, the resultant fade isusually followed some 8 to 36 hours later by anionospheric storm. The relationship between S.I.D.and the ionospheric storms which follow is not clearlyestablished, but it is believed that the fade is dueto an unusually great emission of ultraviolet rays(which travel with the speed of light). The followingstorm is believed due to a simultaneous emission of

153

TRANSMITTER - RECEIVER

STARTING PULSE -REPRESENTSTRANSMITTER

"A" SCOPE

REFLECTED PULSEREPRESENTSRECEIVER

Figure 15-2. RF Sounding of Ionosphere

solar corpuscles, probably calcium ions, which travelfar slower than the speed of light.

RADIO TRANSMISSION. The effect of the sun'sactivity on the ionosphere determines the criticalfrequency (fe), which is defined as the highest fre-quency that may be reflected from a particularionized layer. Any higher frequency will pass throughor be captured by the layer, rather than be reflected,as illustrated in figure 15-1. This critical frequencyis also affected by the ion density of a layer, and thegreater the ion density, the higher the critical fre-quency will be. It naturally follqyvs, then, that a radiosignal might have a frequency higher than the criticalfrequency of the E layer, and pa -es through, and yetbe reflected from the F2 layer. Figure 15-1 shows thatthis is exactly the way different frequencies arereflected. Any activity of the sun resulting in anincrease of ultraviolet rays will produce higher ioni-zation of the layers, and therefore a higher criticalfrequency for each layer.

The critical frequency is important in radio trans-mission since it determines the best frequency to beused in reflecting a radio signal from the ionosphere.

CHAPTER 15


IONOSPHERE

TRANSMITTA

ING CRITCAANTENNAANGLE L

SKIP DISTANCE

ESCAPE RAY

CRITICAL RAY

HIGH ANGLE RAY

LOW ANGLERAY

Figure 15-3. Ionospheric Dispersion

The best frequency is the highest frequency that maybe reflected from the ionosphere, and is called themaximum usable frequency (MUF). This frequency isgiven by a formula known as the "secant law.", or

MUF = fc sec 0 (15-1)where

= Critical frequency0 = Angle of incidence

Since the ionosphere is subject to a continuallychanging bombardment of ultraviolet rays, the criti-cal frequency, and consequently the MUF, is alsosubject to change. When a radio message of anylength is to be transmitted, it is entirely possible thatthe critical frequency may decrease during the timeof transmission due to a change in the ionized layer,causing the received signal to fade. In order to pre-vent this from happening, a lower frequency is used,called the optimum traffic frequency (FOT). This istaken as 90% of the MUF, and allows for a reason-able amount of fluctuation in the critical frequency.However, it does not allow for diurnal changes, whichare usually taken into consideration by periodicallychanging to a different working frequency accordingto the time of day.

There is another term used in connection withionospheric reflection that might well be mentionedhere, called the lowest useful frequency (LUF).

Attenuation of the reflected radio signal by theionospheric layers is determined by the frequency ofthe signal, with the greatest attenuation occurring atthe lowest frequency. Thus, the lowest useful fre-quency represents a compromise between a frequencythat may be transmitted without interruption due toionospheric changes, and frequency without excessiveloss caused by ionospheric attenuation.

The critical frequency is determined by reflectinga radio pulse at various frequencies from the iono-sphere. The returned pulse is picked up by a receiverlocated close to the transmitter. As the frequency ofthe transmitted signal is increased, a point will bereached where no pulse is returned, thus giving thecritical frequency of that layer. By timing the intervalbetween transmission and reception of the pulse, thedistance the pulse has traveled may be determined,and will be twice the height of the reflecting layer.Since the signal does not travel as fast through theionized layer as through the atmosphere, there willbe an error in the measured height. The height foundby timing the pulse will be the virtual height; that is,the height of the layer if it were a flat reflecting plane.This value is more useful than the true height,because it is the height that is used in determiningthe angle to beam the signal in order for the signalto reach the receiver.

The values of the critical frequency for any layerare different at different parts of the earth in accord -

154

CHAPTER 15

ance with changes in the ionosphere. For long-dis-tance transmission it is necessary to know the criticalfrequency at other points than the transmitter loca-tion. This is done by use of recording equipment thatcontinually beams pulses of varying frequency ver-tically into the ionosphere. The returned pulses arerecorded, and show both the critical frequency forthe layers of the ionosphere, and the virtual heightof these layers (figure 15-2).

There are a great many such recording instrumentsthroughout the world, and data from them may beused to construct iso-frequency charts, showing thecritical frequency for each layer above different partsof the world. These maps may be used for predictingthe MUF so that the most satisfactory transmittingfrequency may be chosen. It should be noted herethat, as might be expected, the receiver and trans-mitter may be on far distant parts of the earth, withdifferent critical frequencies for each location. In sucha case, a value for the critical frequency as found atone-third of the distance from the receiver to thetransmitter is used as being the best compromisevalue for the radio path.

Most of the ionospheric reflection takes place in


either the E layer, or the F, layer. However, there isanother layer that may be used for ionospheric trans-mission up to approximately 100 mc, namely, the Esor sporadic E layer. This layer, at the same level asthe E layer, consists of highly ionized areas and maybe used to obtain exceptionally good transmissionover medium distances. The sporadic E layer has oneserious drawback, however, in that it is extremelyunstable and therefore cannot be accurately pre-dicted, as compared with the E and F2 layers.

Transmission to an extremely distant point oftentakes place by means of multiple reflections, eitherbetween an ionized layer and the ground, or betweentwo ionized layers. Such an excursion of a radio wavefrom the earth to the ionosphere and back to theearth is called a hop, and the distance from thetransmitter to the point at which the wave returnsis called the skip distance (see figure 15-3). The skipdistance is defined as the minimum distance at whichradio waves of a specified frequency can be trans-mitted at a particular time by means of reflectionfrom the ionosphere. However, ionospheric waves arefrequently received at less distances than the skipdistance by way of sporadic and scattered reflections.

155

0

4

P

CHAPTER 16

EQUIPMENTS TEST & CALIBRATION

' II A I' T I. R 16

INTRODUCTION

The testing and calibration of high -frequencycommunication equipments are tasks requiring con-siderable skill, and should not be attempted withoutcareful preparation. However, a good knowledge ofequipment circuit design, together with the use ofsystematic methods of service and proper test equip-ment, will greatly reduce the possibility of error.Many types of test equipment have been developedin order to simplify the tasks of testing and calibra-tion. A description of some of the present standardinstruments is listed in a later section of thischapter.

Perhaps the most exacting high -frequency meas-urements are those concerning frequency, standingwaves, and r -f power levels. These measurements areimportant in all communication equipments and, inparticular, in radio -relay systems, where they con-tribute a great deal toward maximum reliability andoverall system performance.

HIGH FREQUENCY MEASUREMENTS

WAVEMETERS. To interpret most high -frequencymeasurements, it is essential to have an accurateknowledge of the wavelength or of the operatingfrequency of the equipments in use. Frequency is themost fundamental quantity in the sense that in anyfixed linear system the frequency of oscillation hasthe same value for all parts of the system. However,wavelength is generally easier to measure, and byadapting the resonant -line technique to high -fre-quency circuits, satisfactory measurements can bemade.

EQUIPMENTS TEST

Sz CALIBRATION

A coaxial -line wavemeter of the kind shown infigure 16 -la may be used at high frequencies, pro-vided that the mean value of the circumferences ofthe inner and outer conductors is less than one wave-length. The frequency range would be limited to anupper frequency of approximately 3,000 mc. Thismethod of wavelength measurement eliminates allwave modes other than the principal, or transverseelectromagnetic (TEM), wave for which the wave-length in a coaxial line is nearly equal to the corres-ponding free -space value. The theory of operation ofsuch a wavemeter is illustrated by an equivalentcircuit, as shown in figure 16-1b. Any couplingbetween the source and the detector is normallynegligible, but is increased to a large amount whenthe intermediate tuned circuit is brought intoresonance.

In the coaxial -line wavemeter, the tuned circuit isreplaced by a variable length of coaxial transmissionline, short-circuited at one end and open -circuited atthe other. A small amount of r -f energy is fed intothe line by means of an excitation loop (marked"source" in figure 16-1a. Resonance is then estab-lished by adjusting the length of the inner conductor,using a detector coupled to another loop opposite tothe excitation loop. A resonant condition will occurwhen the length of the inner conductor is approxi-mately one -quarter wavelength. Resonance can beobtained at even wavelength points (x/2, X) if the lineis short-circuited at both ends. If more than oneresonance point can be obtained on the wavemeter,it is self -calibrating, since the distance between suc-cessive resonances is one-half wavelength. If only oneresonance point can be obtained, the wavemeter must

157

CHAPTER 16


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Figure 1 6-1 . Coaxial Line Wavemeter

be calibrated, and it is important that the couplingloop be fixed in position if accurate results are to beobtained. Increased accuracy may be obtained bytaking equal readings on either side of the maximumresonant position, and the use of a vernier scale ishighly recommended. Figure 16-2 illustrates fourtypes of coaxial and transition wavemeters. Thetransition wavemeter is a cross between coaxial andcavity wavemeters.

Since a cavity resonator may be employed as atuned circuit in high -frequency circuits, it followsthat such a resonator may also be used as a wave-meter. Although a cavity -resonator wavemeter uti-lizes various wave modes of oscillation, its operatingtheory is much the same as that of a coaxial linewavemeter shorted at both ends. A cylindrical cavityis perhaps the most practical for use as a wavemeterbecause it is easier to machine accurately.

There are two main classes of wave modes thatcan be usefully employed in a cavity-wavemeter, theTM0,1,0 mode and the TE0,1,1 mode. A typical wide-

band wavemeter which operates in the TM0.1,0-0,1,0 modeis illustrated in figure 16-3A. A set of four wavemetersof this kind can be made to cover a frequency rangefrom 200 mc to 10,000 mc, with an accuracy betterthan one part in ten thousand. The design of thewavemeter illustrated in figure 16-3A is based on thevery large change in characteristic impedance whichoccurs between the two sections of coaxial line.

The use of the TE0,1,1 mode as applied to wave-

meters has several important advantages over theTM0,1,0 mode, and are summarized as follows:

1. The amount of energy dissipated on the cavity

walls is extremely low, and therefore a highQ -value results.

2. There is no radial current present on the endcavity walls.

3. The TE0 form of wave comprises only modeswhich have no angular variation of fieldstrength, and therefore does not introducespurious points of resonance.

A high Q -value is an essential feature of theresonance type of wavemeter, and a cavity excitedin the TE0.13 mode is superior in this respect to anyother. With the absence of radial current flow in theTE0 wave, there is no need to establish good electricalcontact between the end walls and the cylindricalsurface. In fact, the absence of such a contact willtend to suppress any other modes of oscillation in thecavity which might otherwise arise. If one of the endplates is made slightly smaller in diameter than thecylinder, and arranged to move axially over a limitedrange, the resonant frequency of the cavity may bevaried and the cavity may be used as a wavemeter.

Wavemeters excited in the TE0.1.1 mode are illus-trated in figures 16-3B and 16-3C. Coupling to thewavemeter in figure 16-3B is provided by means ofsmall loops similar to those in the coaxial type ofwavemeter. An alternative coupling method, whichhas the advantage of avoiding spurious wave -modeexcitations is illustrated in figure 16-3C. Cavityresonator wavemeters are usually silver-plated on theinside to improve their Q -value and for accurate workthe enclosure should be hermetically sealed orequipped with a dehydrator such as silica -gel.

The calibration of a cavity wavemeter is theoreti-cally calculable from the dimensions of the cavity.However, such dimensions are usually not known to asufficient degree of accuracy because effective cavitysize changes with temperature. A copper cavity maychange in resonant wavelength about three parts inten thousand between summer and winter, and sucha change is by no means negligible at frequenciesabove 3,000 mc. A cavity -resonator wavemetershould, therefore, have the calibration temperaturerecorded on the instrument, and if the working tem-perature differs greatly from that value duringoperation, appropriate allowance must be made.

Cavity -resonator wavemeters may be calibrated byeither of the two methods listed below:

1. By the use of a heterodyne frequency meter.2. With a coaxial -line wavemeter.

The first method is perhaps the most accuratesystem of calibration. Power from an r -f oscillator isfed into a matched waveguide, which is equipped

158

CHAPTER 16


TYPE MODE OF OSCILLATION

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159

CHAPTER 16


TYPE MODE OF OSCILLATION

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160

CHAPTER 16


a

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with short probes to couple the cavity and the hetero-dyne meter to the guide. The oscillator frequency isvaried and measured by the heterodyne frequencymeter while dial readings of the cavity wavemeterare taken. A calibration chart is then prepared andshould include the date, temperature, and humidityat the time of calibration. In the heterodyne methodof calibration, the component to be measured has itsfrequency decreased to a predetermined value byheterodyne action, and is then amplified and meas-ured at this frequency. The frequency of the unknowncomponent is determined from the heterodyne fre-quency that must be used in order to change theunknown frequency to the known fixed frequency.

Cavity calibration may be made as described aboveby substituting a coaxial -line wavemeter or anothercavity of known calibration in the place of the hetero-dyne frequency meter. Although the accuracy ob-tained with the use of these alternative standards isconsiderably lower than that obtained with theheterodyne meter, the calibration procedure can becarried out much faster.

The accuracy of a wavemeter depends upon theaccuracy with which its scale is divided, and alsoupon the loaded Q -value. For example, if an accuracyof ± 0.001 cm is desired, the scale must be fineenough to read at least three decimal places, and thesensitivity of the wavemeter must be great enoughto determine when the tuning is 0.001 cm or less fromresonance. In other words, the frequency responsecurve of the wavemeter must drop to its "half power"points within 0.001 cm of the resonant wavelength.The necessary loaded Q -value of a wavemeter maybe found by the formula

XQL =

where

(16-1)

QL = The necessary loaded Q -valueX = Operating wavelength in centimetersAX = Desired accuracy in centimeters

Therefore, at 10 cm, for an accuracy of ± 0.001 cm,the loaded Q -value must be

10/2 (0.001) = 5,000.

STANDING - WAVE MEASUREMENTS. Animportant part of high -frequency measurementtechnique is the precise determination of the stand-ing -wave pattern in transmission -line systems. If thedistribution of the electric or the magnetic field ofsuch a system is known, the reflection coefficient, andtherefore the impedance at any point along thesystem, may be found. The field distribution arising

from a standing wave on a length of transmission linemay be recorded by an instrument known as astanding -wave indicator. In a waveguide, a narrowlongitudinal slot cut into one face of the guide enablesa suitable detector to be loosely coupled to the fieldwithin the guide and moved axially. A similar methodis used to measure standing waves along a coaxialtransmission line system. The detector is coupled toa length of solid coaxial line by means of a longitudi-nal slot or evenly spaced holes cut along the line. Inany case, the slot length should be longer than onewavelength. Coupling is generally accomplished bymeans of a short electric probe which is inserted intothe longitudinal slot and moved along its length bymeans of a close -fitting spline. Such an arrangementis illustrated in figure 16-4. The position of the slidingcarriage along the guide must be accurately known,and a vernier scale is usually provided for thispurpose.

Several types of detectors are available for stand-ing -wave measurements, but those commonly usedmay be grouped into two classes:

1. Square law detectors which are comprised ofcrystal rectifiers, bolometer probes, or thermo-couples, and

2. Linear detectors, or crystal mixers with one ormore stages of i-f amplification.

Figure 16-5 illustrates a typical square law crystaldetector which is frequently used as a standing -waveindicator. The probe provides loose coupling with theelectric field in the transmission line, and the voltageintercepted is then rectified by the crystal andmeasured with a microammeter. This type of probeis frequency sensitive and needs adjustment when theoperating frequency is changed.

MICROAMMETER

BY PASSCONDENSE

SLIDING.(PLUNGER

SLOTTED WAVE GUIDE

Figure 16-4. Standing Wave Indicator

161

CHAPTER 16


PLUNGER

BARREL

PROBE-

WAVE GUIDE

180I;A,

_A A:

rA

TO METER

Figure 16-5. Crystal Probe

CRYSTAL

R F CHOKE

POLY -TAPECONDENSER

162

CHAPTER 16

By substituting a "bolometer" fuse for the crystalin the indicator described above, a tunable bolometerprobe is then obtained. "Bolometer" is a name givento a large class of components used in r -f measure-ments whose resistance changes with changes in tem-perature. A platinum bolometer fuse is illustrated infigure 16-6, with the protective glass cover and theupper cap removed. Temperature changes, and con-sequently, resistance changes in the platinum wireare brought about by the absorption of r -f power,such changes being measured with a suitable ampli-fier. A schematic of the circuit usually employed toaccomplish this is shown in figure 16-7. Bolometerprobes are normally used only for high-level, pulsed -power measurements, although they are adaptable tolow-level work if sufficient r -f energy or extremelysensitive amplifiers are available.

The thermocouple is important only because itprovided the first means of measuring standing waves.Such a device usually consisted of a sensitive vacuumthermocouple mounted in a small cavity and fed bya probe in much the same way as previously described.However, the thermocouple junctions were extremelyhard to match to the probe, very delicate, and some-times quite sluggish and insensitive because of theirhigh thermal capacity. Thermocouple probes havealmost entirely given way to the crystal and bolo -meter types as described above.

For nearly all standing -wave measurements, apoint of minimum field strength must be employedas an origin of reference. The location of such minimamay be found by sliding the standing -wave indicatoralong the longitudinal slot until a minimum readingis indicated on the meter. More accurate readingsmay be taken by recording the indicator positions forequal meter readings on each side of the minimumand then finding the average of these positions.

The voltage standing -wave ratio of any transmis-sion line is the ratio of the maximum to the minimumelectric field strength and is expressed by the formula

VSWR = E max/ -min (16-2)

With a square law detector, the formula for thevoltage standing -wave ratio becomes

VSWR = N/(Dn,../D, fl) (16-3)

where Din in and D. are the minimum and maximumdeflections of the meter used. With a linear detector,formula 16-2 may be used to determine the standing -wave ratio. If the law of the detector is unknown, acalibration curve must be plotted, giving the relativevalues of the electric field strength as a function ofmeter deflection.

Since the determination of the standing -wave ratio


GLASSINSULATOR

PLATINUMWIRE

Figure 16-6. Bolometer Littelfuse

by the instruments described above involves takingtwo readings and calculating their quotient, it hasbeen found necessary to devise various direct -readinginstruments for use in the field. Such apparatus isgenerally less accurate than the other, but is consid-erably easier to use for fast measurements.

For appli6ation to high -power systems, a neon -tubeindicator may be used. It consists of a long, thin, glasstube containing neon at a reduced pressure andarranged to penetrate a short distance into the trans-mission line in the same fashion as a probe. Excita-tion within the transmission line then has the effectof ionizing the neon gas in the tube so that a visibleglow extends outside the guide to a height propor-tional to the product of the electric field concerned.As the tube is moved along the transmission line, thepresence of a standing wave will then be shown bythe variation in height of the ionized column. Theeffect is as though the standing -wave pattern wereplotted as the tube is moved along the line. If theneon tube is calibrated initially, maxima and minimamay be read directly, but with little accuracy. Othertypes of direct -reading indicators include reflectom-eters, phase -shifters, and the "magic -tee" waveguidebridge.

R -F POWER MEASUREMENTS. High frequencyr -f power measurements are generally classified intotwo groups, high-level measurements and low-levelmeasurements. Several devices are now available formeasuring high level r -f power, some of which areoutlined below.

1. Continuous flow calorimeter.

163

CHAPTER 16


RF ENERGYe.

BOLOMETER

0 TO AMPLIFIER

TRANSFORMER

Figure 16-7. Bolometer Bias Circuit

2. Johnson power measurer.

3. Low-level power measurers equipped with anattenuator.

The continuous flow calorimeter is probably thesimplest to use and the easiest to build. Figure 16-8illustrates the construction of such a device as in-tended for use with a coaxial transmission line.

A section of coaxial transmission line is short-cir-cuited at the far end and closed at the other by meansof a thick dielectric bead which is usually made ofglass or micalex. The length of the device should besuch that the distance from the bead to the shortcircuit is se .reral wavelengths. This is in order toinsure complete absorption of the r -f energy. Thelength of the dielectric bead should be a quarterwavelength of the operating frequency, and thedielectric constant of the bead is chosen so that

Zd = N/Zair X ZH2o (16-4)where

Zd = The impedance of the dielectric -filled line.= The impedance of the air -filled line.

ZH20 = The impedance of the water -filled line.

Water flows continuously through the chamber andis heated by the r -f energy. Thermocouple probes areplaced in the water inlet and in the outlet to measurethe rise in temperature of the water flowing throughthe cavity. To find the r -f power, it is necessary tomeasure the rate of flow and the change in tempera-ture of the water. The r -f power may then be foundby the formula

W = 4.19 VT (16-5)where

W = R -F power in wattsV = The volume of water flowing through the

cavity per unit timeT = Temperature changes of the water.

In practice, T is not measured directly but rather,the current in microamperes flowing through thethermocouple. The difference in temperature of thetwo thermocouple junctions is a linear function of thecurrent. Therefore, it is necessary to know the cali-

bration of the thermocouples and meter. The constantmay be obtained by placing the thermocouple junc-tions in water baths which differ in temperature byTo and noting the deflection, d, of the meter used.Formula 16-5 may then be rewritten as follows:

ToW = 4.19 -d VD (16-6)

where

TO = The calibration constant for the componentsd usedD = The deflection of the meter during the power

measurement.ToSince the expression 4.19 -d in formula 16-6 is a con-

stant for a given set of components, the r -f powermay then be found by the formula

W = AVD (16-7)where

A = 4.19 To/d

Thus, once the constant A is known, the r -f powerabsorbed in the termination can be obtained by mul-tiplying the constant by the rate of water flow, V,and the meter deflection, D.

There are several advantages of measuring r -fpower by this method:

1. The measurement is absolute.

2. The rise in temperature can be made small,thereby limiting the energy lost by radiationand conduction from the transmission line.

However, in order to maintain a constant rate ofwater flow, it is necessary to use some device tosupply water at a constant pressure. The only seriousdisadvantage of the method is that such a devicemust completely terminate a line and, in so doing,absorb 100% of the r -f power. A continuous flowcalorimeter therefore cannot be used as a power

THERMOCOUPLELEAD

THERMOCOUPLELEAD

MICROAMMETER

Figure 16-8. Coaxial Water Load

164

3 X I /2

PROTECTIVECOVER BAKELITE _BRASS STRIP

CHAPTER 16


LAYER OF POLY TAPEUG

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BR

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monitor except by the use of a mechanical switchingarrangement.

A waveguide calorimeter is electrically the same asthat for a coaxial line, and is matched to the guideby a quarter -wavelength transformer. The trans-former consists of a section of guide whose electricallength is one quarter -wavelength of the operatingfrequency, and is filled with a material whose dielec-tric constant is the geometric mean of those of airand water.

A type of r -f power measure which may be used asa constant monitor is the Johnson Wattmeter. Thistype of meter requires only one percent of the r -fenergy in the transmission line as compared to the100 percent needed for the constant flow calorimeter.

OUTER(ON BRASS)

INNER(ON CONST)

INNER(ON CONST.)

17.10UTER(ON BRASS)

Figure 16-9 illustrates a type of Johnson wattmeterwhich is designed for use with a waveguide trans-mission line. A small longitudinal section of thewaveguide wall is removed and replaced with a pieceof high -resistance material. A sheet of constantan0.015 inch thick can be used. At high r -f power levels,enough heat is dissipated in the constantan to pro-duce an appreciable temperature change. Since theconductivity of the waveguide is greater than thatof the constantan, there will be a measurable differ-ence in the temperature of the two materials. Thisdifference in temperature is used to give an indicationof the r -f power level. The difference in temperatureis measured by a platinum resistance thermometerwhich consists of 200 ohms of 0.002 inch platinum

165

CHAPTER 16


wire wound on the constantan section and another200 ohms wound on the guide. The two windingsserve as two arms of a Wheatstone bridge as shownin figure 16-9.

If the bridge is initially balanced, any change intemperature of one of the coils with respect to theother will unbalance the bridge. The unbalanced con-dition is caused by the change in resistance of theplatinum wire around the section of constantan withtemperature. The unbalanced current in the bridgeis directly proportional to the power in the line, anda straight line calibration curve can be drawn bymeasuring only one point with an accuracy within 5percent. Since there is a time delay between theturn -on of the power and the thermal equilibrium ofthe measuring device, there is a time interval ofbetween one and three minutes after the turn -onbefore readings can be taken.

Low-level power measurements generally cannotbe carried out by the methods described above be-cause the temperature rise becomes too small foraccurate determination. However, three commondetectors may be used to advantage for such measure-ments; crystals, bolometers, and thermistors. Thecrystal detects by virtue of its rectifying property,while the bolometer and thermistor detect througha resistance change induced by the heating effect ofabsorbed r -f power. The thermistor consists of aresistance element made from certain metal oxideswhich have a high negative temperature coefficient,that is, the resistance of the thermistor decreases withincreasing temperature. Its sensitivity is approxi-mately ten times that of a bolometer, and it has bothmechanical ruggedness and good overload charac-teristics. Therefore, for accurate work, the thermistoris the most desirable of the three detectors mentioned.

Precise measurements of small r -f power levels aregenerally made with the use of balanced bridges. Thebridge is first balanced with a known amount of directcurrent, after which an unknown amount of r -f poweris applied to the detector, unbalancing the bridgeagain. Balance is restored by removing some of thedirect current from the detector, and the change indirect current power is used to calculate the magni-tude of the r -f power added. Most bridge circuits areso arranged that the difference in direct current powerbetween the two balanced conditions is exactly equalto the magnitude of the r -f power.

An unbalanced bridge may also be used to measurelow-level r -f power, and is easier and faster to usethan the balanced bridge. Such a bridge is initially

balanced on direct current, and the deflection of thebridge meter is noted when the r -f power is added.The meter scale is previously calibrated in r -f powerto give a direct reading r -f microwattmeter. Forinstance, with a thermistor detector and a lowresistance microammeter, it is possible to have a fullscale deflection represent 1 milliwatt with a calibra-tion that is appreciably linear.

CURRENT STANDARD TEST EQUIPMENT

The following list is, for the categories covered, theapproved list of recommended general purpose testequipment for use with prime equipment in the fieldof electronics. The models and types listed are thepresent standard equipment already developed andable to be procured as of 1 January 1953. Thecategories are taken from a comprehensive functionalclassification of test equipment as promulgated tothe Services by Research and Development BoardMemorandum RDB-EL 213/1 of 19 March 1952.The main headings of these categories are as follows:

Category Title

1 Voltage and current measuring equipment

2 Frequency measuring equipment

3 Waveform measuring equipment

4 Signal generating measuring equipment

5 Field intensity measuring equipment

6 Impedance and standing wave measuringequipment

7 Amplifying equipment for measuring pur-poses

8 Time based measuring and countingequipment

9 Nuclear energy test and measuring equip-ment

10 Combination and group test set

11 Associated devices for electronics testequipment

12 Miscellaneous test equipment

13 Calibrating equipment for electronics testequipment

14 Power measuring equipment

166

CHAPTER 16

1 VOLTAGE AND CURRENT MEASURING EQUIPMENT

Equipment

1.1 Voltage and/or Current Meter

1.1.1 Voltmeter

1.1.1.1 Electronic Voltmeter1. ME -6/U, (BuS) (Electronic Voltmeter)

4. TS -580/U, (SigC) (D -C Amplifier)


Range

0 5 to 5; 5 to 50; 50 to 500 my; 0.5 to 50; 50to 500 VAC, 10 cps to 250 kc.01 to 1.0 VDC

1.1.1.2 A -C Voltmeters5. Type IS -185, (SigC) (Voltmeter) 0 to 150V; 25 to 2400 cps; 0.75%6. ME -64/U, (SigC) (Voltmeter) 0 to 150/600V; 25 to 125 cps; 2%

1.1.1.3 D -C Voltmeters7. TS -443/U, (SigC) (Voltmeter) 0 to 3/150V; 0.25%8. AN/URM-45, (BuA) (Voltmeter) 0 to 50 my; 0 to 15/30V; 2% on 15V scale;

2M% on 30V scale1.1.1.5 A -C D -C Voltmeters

9. TS -340/U, (SigC) (Voltmeter) 0 to 150/300/750V; 25 to 125/1000 cps; 25 to2500 cps; 0.5%

1.1.2.3 D -C Ammeter10. TS -60/U, (SigC) (Test Meter) 0 to 1 ma, 75 ohm impedance; 3%

(Also known as SigC Type 1-139 Test Set)

1.1.24 Recording Ammeters12. TS -584/U, (SigC) (Milliammeter Recorder) 0 to 5 ma; 0 to 10 ma with ext shunt, accuracy

1%13. RD -49/U, (BuS) (Recorder-Milliammeter) 0 to 1 ma DC; 1%

1.1.2.5 A -C D -C Ammeter14. ME -65/U, (SigC) (Ammeter) 0 to 2/5/10/20/100/200 amp; Accuracy 1%

DC, 1 to 2% AC at 15-135 cps1.1.3 Multimeter

1.1.3.1 Electronic Type Multimeter

1.1.3.1.1 Electronic Volt -Ohm -Meter15. ME -25/U, (BuS) (Multimeter) 0-1/25/10/25/100/250 VDC-AC; 100/200/

500/1000 ma DC; 0 to 1K/10K/100K/1M/10M/1000M ohms; DCV ±4% up to 250V,±5% 250 to 1000V, ±6% 5000V; VAC ±5%;DC ±5%; Resist ±3° arc.

1.1.3.1.2 Electronic Volt -Ohmmeter16. AN/PRM-15. (SigC) (Multimeter)

(small, battery operated)(Input impedance 11 megohms DC)

17. AN/PRM-16, (SigC) (Multimeter)(small, line operated)(Input impedance 11 megohms DC)

0-2.5/10/25/100/250/1000 VDC at 3%; 0-1K/10K/100K/1M/10M/100M ohms at 3%

0-2.5/10/25/100/250/1000 VDC at 3%; 0-1K/10K/100K/1M/10M/100M ohms at 3%

167

CHAPTER 16


Equipment

18. TS -505/U, (SigC) (Electronic Multimeter)(Input impedance 20 megohms up to 400 VDC, 50megohms at 1000 VDC, 6 megohms shunted by 2MMF for ACV; 4% DC, 6% AC, 4% Resistance; 0to 500 MC on ACV)

1.1.3.2 Non -Electric Type Multimeter

1.1.3.3.1 Non -Electric Volt -Ohm -Ammeter19. TS -297/U, (SigC) (Multimeter)

20. TS -352/U, (WADC) (Multimeter)

1.1.3.2.3 Non -Electronic Volt -Ammeter21. ME -67/U, (WADC) (Multimeter)

22. ME -1/U, (SigC) (Multimeter) (Clamp Type)

23. 1-50, (SigC) (Volt -Ammeter)

1.2 Tester

1.2.1 Electron Tube Testers24. TV -7/U, (SigC) (Electron Tube Test Set)25. AN/USM-23, (BuS) (Electron Tube Test27. TV -2/U, (SigC) (Tube Tester) (Receiving28. AN/USM-31, (BuS) (Electron Tube Test29. AN/UAM-( ) (ERDL) (Image Converter

1.3 Combined Tester and Meter

Range

0-2/4/10/20/40/100/200 ACV; 0-2/5/10/20/40/100/200/400/1000 DCV; 0-1000/10,000/100K/1M/10M/100M/1000M

1000 ohms/volt 0-4/10/40/100/400/1000VAC& DC; 0-1K/10K/100K ohms; 0-4/40/100/400 ma DC; DC ± 3%; AC ± 5%20,000 ohms/volt DC and 1000 ohms/voltAC & DC up to 1000 VDC; 0-2.5/10/50/250/500/1000 VAC and DC; 0-5000VDC; 0-0.25/2.5/10/50/100/500/2/5K/10K ma DC; 0-1K/10K/1M/10M ohms

0-10/25/50/100/250/500 AC; 0-175/350/700V; 50-70 cps; 3%0-15/60/150/600 AC; 0-150/600 VAC; 50-70cps; 3%0-3/15/150 VDC; 0-3/15/30 DCa; 1%

(Receiving tubes)Set) (Geiger -Mueller and Voltage Reg. Tubes)and small transmitting tubes)Set) (Receiving and small transmitting tubes)Tube Test Set)

1.3 Tube Tester -Meter30. TV -6/U, (SigC) (Electron Tube Test Set) (Electrometer tubes, including high resistance ohmmeter)

2. FREQUENCY METERS

GROUP I. Accuracy + .00001% or + 1 cyclewhichever greater

32. AN/URM-18, (SigC) (Frequency Calibrator)33. FR -38/U, (BuA) (Frequency Meter)

34. FR -67/U, (SigC) (Frequency Meter)

35. AN/USM, (BuS) (Frequency Meter)36. FR -4/U, (SigC) (Frequency Meter)37. FR -5/U, (SigC) (Frequency Meter)38. FR -6/U, (SigC) (Frequency Meter)

10 kc to 100 me .0005%0-50 mc Accuracy: same as Group II, ± onecount20 cycles to 100,000 cycles Accuracy, same asGroup II ± one count15 kc to 30 mc 0.005%100 kc to 20 mc .001%10 me to 100 mc .001%100 me to 500 mc .001%

168

CHAPTER 16


Equipment Range

GROUP III. Accuracy + .01% to .001%

41. TS-186/UP, (BuS) (Frequency Meter) 100 mc to 10,000 mc

GROUP IV. Accuracy + .05% to + .01%

42. TS-174/UP, (SC) (Frequency Meter)43. TS -175/U, (SC) (Frequency Meter)44. BC -221, (SigC) (Frequency Meter)

GROUP V. Accuracy Less Than 0.05%

45. FR -63/U, (SigC) (Frequency Meter)46. TS -494/U, (WADC) (Frequency Meter)47. 1-209, (SigC) (Frequency Meter)48. TS -328, (SigC) (Frequency Meter)49. TS-117/GP, (SigC) (Wavemeter Test Set)50. AN/PRM-10, (RADC) (Test Oscillator Set) (Grid -

Dip Meter)51. FR -39/U, (SigC) (Wavemeter)52. FR-40/GSM-1, (SigC) (Frequency Meter)53. 1-129, (SigC) (Frequency Meter Set)54. TS -480/U, (SigC) (Frequency Meter)

3. WAVE FORM MEASURING EQUIPMENT

20 mc to 280 mc, .04%80 mc to 1,000 mc, .03%125 kc to 20 mc, .02% (SCR -211)

25 cycles to 60 kc, 2%49 cycles to 51 cycles, 0.5%58 cycles to 62 cycles, 3%380 to 420 cycles, 3%2,400 mc to 3,400 mc, 0.5%

2-400 mc, 1-12%55 to 400 mc ± 2%, Absorption Type50 to 70 cps ± 0.5%1 5 to 41 mc ± 3%, Absorption Type0 5 to 16 mc ± 2%, 16-150 mc ± 3%, Ab-sorption Type

3.1 Cathode Ray Oscilloscope74. OS -8/U, (BuS) (Oscilloscope)

(Technician type Communications)

3.2 Synchroscope75. TS-34/AP, (BuS) (Oscilloscope)76. AN/USM-24, (BuS) (Oscilloscope)

(Bench type; Supersedes TS-239/UP)

3.4 Analyzer

34.1 Spectrum Analyzer80. AN/UPM-33, (BuA) (Spectrum Analyzer) 8,970-9,630 mc, Formerly TS-148/UP81. TS-333/AP, (BuA) (Spectrum Analyzer) 23.5-24.5 kmc83. AN/UPM-17, (WADC) (Spectrum Analyzer Set) 10-16,500 mc, fixed

4. SIGNAL GENERATING EQUIPMENT

4.1 Signal Generators

4.1.1 Signal Generators-Unmodulated

GROUP A. Up to 30 KC (VLF)

84. TS-382A/U, (WADC) (Audio Oscillator) 20-200,000 cps, 2% accuracy86. TS -535/U, (BuS) (Signal Generator) 7-160 kc, 0.3% accuracy

GROUP B. 30-300 MC (VHF)

87. TS-47/APR, (SigC) (Test Oscillator) 40-500 mc, 1%

169

CHAPTER 16


Equipment

4.1.2 Signal Generators, Modulated

Range

4.1.2.1 Amplitude or Pulse Modulated

GROUP A. 30 KC -30 MC (LF, MF, HF)

88. AN/URM-25, (BuS) (RF Signal Generator Set) 10 kc - 50 mc89. TS -606/U, (WADC) (Signal Generator) 85 kc - 40 mc, 10 watts output

GROUP B. 30-300 MC (VHF)

90. AN/URM-26, (BuS) (RF Signal Generator Set)91. TS-497/URR, (SigC) (Signal Generator)92. TS-510/UR, (BuA) (Signal Generator)93. TS -608/U, (WADC) (Signal Generator)

3-405 mc2-400 mc25-440 mc40-400 mc, 5 watts output

GROUP C. 300-3,000 MC (VHF)

94. TS -406/U, (BuA) (Test Oscillator) 1,000-3,500 mc; Buzzer type shock excited,battery operated, 5 lb.400-1,000 mc, formerly TS -418/U900-2,000 mc, formerly TS -419/U1,800-4,000 mc, formerly TS -403/U

97. AN/URM-49, (BuA) (Signal Generator)98. AN/URM-64, (BuA) (Signal Generator)99. AN/URM-61, (BuA) (Signal Generator)

GROUP D. 3,000-30,000 MC (SHF)

100. TS -508/U, (BuA) (Test Oscillator) 3,000-11,000 mc103. AN/URM-52, (BuA) (Signal Generator) 3,800-7,500 mc, formerly TS -621/U104. AN/URM-44, (BuA) (Signal Generator) 7,000-10,500 mc, formerly TS -622/U

44.2.2 Frequency or Sweep Modulated

108. TS -452/U, (RADC) (Signal Generator) 5-100 mc, maximum sweep 5-55 mc in 6steps depending on center frequency

109. AN/URM-48, (SigC) (Signal Generator) 20-100 mc, dev. 0-15 kc internal; 0-50 kcexternal. Includes CW Crystal -controlled IFFrequency, formerly SG -12/U

4.1.2.3 Combined AM or PM and FM or Sweep Modulated

113. , (BuA)

115. , (BuA) (FM Signal Generator)

116. AN/USM-16, (WADC) (Signal Generator)

4.3 Pulse and Square Wave Generators

4.3.1 Pulse Generators

117. AN/USM-27, (BuS) (Signal Generator)

Boonton Type 207A 0.1-55 mc; 0.3-55 mcwith 200 kc carrier deviation, used with Boon-ton Type 202-BBoonton Type 202-B; 54-216 mc; FM devia-tion 0-80/240 kc; AM 30% and 50% cali-brated, variable 0-50% includes AF Oscillatorwith 8 fixed frequencies for either AM or FMmodulation10-440 mc, formerly TS-437(XA)/U, de-viation ± -.- 125 to ± 7.5 MC

0 5 to 11 usec; 1 to +40V at 70 ohms, 1 to+50V at 100 ohms and 1 to -70V at 100Kohms, 100 to 400 pps

170

CHAPTER 16


Equipment

118. SG-30/UP, (BuA) (Pulse Generator)

119. AN/UPM-15, (WADC) (Pulse Generator)

Range

0 2-20 usec, 5-50V into 5,000 ohms whenshunted by 2,000 mmf, 20-20,000 pps, includesscope0 15 to 110 .usec; 0 to ±200V; Impedance- 0.25 ohms below 20 my, 2.5 ohms from 20to 200 my, 50 ohms from 0.2 to 2V, 250 ohmsfrom 2 to 20V, 2,500 ohms from 20 to 200V;single and double pulses; 30 to 10,000 pps;formerly TS -592/U

4.3.2 Square Wave Generators

120. TS -583/U, (SigC) (Square Wave Generator) 20-10,000 cps impedance 500 ohms each sideof ground; Attenuator 0-75 db in 5 db steps;max output 75V

5. FIELD INTENSITY MEASURING EQUIPMENT

5.6 Noise Field Intensity Meter

121. AN/PRM*L°, (BuS) (Radio Test Set) 0 15-25 mc124. TS-587A/U, (BuS) (Noise -Field Intensity) 25-400 mc125. AN/URM-17, (BuS) (Radio Test Set) 375-1,000 mc126. AN/URM-6, (BuS) (Radio Test Set) 14-250 kc127. AN/URM-3, (SigC) (Interference Measuring Set) . . . 0.15-40 mc

6. IMPEDANCE AND STANDING WAVE RATIO

6.1 Impedance Measuring Equipment

6.1.1 Resistance Meters

6.1.1.1 Low Voltage Ohmmeters

130. ZM-17/U, (WADC) (Ohmmeter)131. ZM-4/U, (SigC) (Resistance Bride)

132. Navy Type 60089, (BuS) (Vacuum Tube Megohm-meter)

133. ZM-9/U, (SigC) (Resistance Bridge)

MEASURING EQUIPMENT

0 005-5 ohms, 2%, battery -operated0 001-100,000 ohms, up to 1 megohm withext. batt., 0/2%

0-10,000 megohms, battery -operated

0 1-10,000,000 megohms in five ranges; ACoperated

6.1.1.2 Working Voltage Ohmmeters

134. AN/PSM-1, (BuS) (Insulation Test Set) 0-100 megohms, 500V, hand crank135. 1-48, (SigC) (Test Set) 2-1,000 megohms, 500V, hand crank136. AN/PSM-2, (BuS) (Insulation Test Set) 0-1,000 megohms, 500V, hand crank

6.1.3 Capacitance Meter

137. ZM-3/U, (SigC) (Analyzer) 5uuf-10,000 of :1.1-100/10,000 megohms; leak-age current 0-50 ma; 0-600V

6.1.4 Combination Type Impedance Measuring Equipment

6.1.4.4 Q Meters

138. TS -617/U, (SigC) (Q Meter) 50 kc-75 mc, similar to Boonton 160A139. , (BuS) (Q Meter) 30-210 mc, similar to Boonton 170A

171

CHAPTER 16


Equipment Range

6.1.4.5 Combination R.C.L. Meter

140. TS -460/U, (SigC) (Impedance Bridge) 1,000 cycles -0.001-11 megohms, 1 uuf-1,100uf, 1 mh-1,100 h

141. ZM-11/U, (BuS) (Capacitance, Inductance, Resist-ance Bridge) 10 mmf-1,000 uf, 1 ohm -10 megohms, 200-

1000/10,000 megohms insulation resistance,100 mh-10 h

142. Navy Type 60094, (BuS) (RF Bridge) 400 kc-50 mc; 0-1,000 ohms Resistance,0-5,000 ohms Reactance at 1 mc

144. TS -269 ( )/UR, (SigC) (Test Set) ...20-1,000 kc, 0-111 ohms, 40-4,100 uuf, ± 5%

10. COMBINATION AND GROUP TEST SET

10.1 Combination Test Set (One Main Case)(Includes signal generator, frequency, and powermeter unless otherwise indicated)

145. TS-155/UP, (SigC) (Signal Generator) 2,700-3,400 mc, does not include frequencymeter

148. TS-147/UP, (BuS) (Test Set) 8,520-9,600 mc, frequency modulated150. TS-223/AP, (BuA) (Test Set) 23,500-24,500 mc151. AN/UPM-14, (BuA) (Radar Test Set) 34,000-35,600 mc

11. ASSOCIATED DEVICES

11.12 Voltage Dividers

194. TS-89/AP, (WADC) (Voltage Divider) ..20 KV, 100:1 & 10:1, 15% accuracy195. TS-265/UP, (SigC) (Voltage Divider) 50 KV, 100:1 & 10:1196. TS-453/UP, (RADC) (Voltage Divider) 100 KV; 500:1, 100:1, and 10:1, 5% accuracy

11.13 Electronic Switch

197. TS -433 ( ) /U, (SigC) (Electronic Switch) 10-2,000 cps switching range, 0-25 kc response,± 1 db, 10X Gain

12. MISCELLANEOUS TEST EQUIPMENT

12.6 Telephone, Telegraph, and Teletypewriter Test Equipment

12.6.1 Teletypewriter Test Equipment

198. TS-658/UG or TS-659/UG, (BuS)(Teletypewriter Test Set)

199. TS-383/GG, (SigC) (Distortion Test Set)200. TS-2/TG, (SigC) (Test Set)201. Sig C Type 1-193, (SigC) (Test Set)202. TS-660/UG, (SigC) (Teletypewriter Test Set)203. TS-657/FG, (BuS) (Teletypewriter Test Set)204. , (SigC) (Monitoring Printer)

(Teletype Corp. Model 14)205. TS-611/FG, (SigC) (Teletypewriter Test Set)206. TS-577/FG, (SigC) (Telegraph Monitor)207. Sig C Type 1-181, (SigC) (Test Set)

172

224. TS -430/U, (SigC) (Wattmeter)

14.2 Audio and Radio Frequency Power Measuring Equipment

GROUP A. 3-30 KC (VLF)

225. ME-22/PCM, (SigC) (Decibel Meter)

226. TS -585/U, (SigC) (Output Meter)

Equipment

208. , (BuS) (Relay Test Panel)(W.E. Type 111A)

12.12 Test Sets

12.12.8 Crystal Test Sets

CHAPTER 16


Range

211. TS-710/TSM, (SigC) (Crystal Impedance Meter) .. ..10 kc-500 kc212. TS-537/TSM, (SigC) (Crystal Impedance Meter) .. ..75-1,100 kc, p/o AN/TSM-3213. TS-330/TSM, (SigC) (Crystal Impedance Meter) .. ..1-15 mc, p/o AN/TSM-3214. TS-683/TSM, (SigC) (Crystal Impedance Meter) .. ..10-100 mc

12.12.10 Thermopile, Bolometer, and Photoconductive Cell Test Sets

215. AN-UAM( ), (BuS) (Thermopiles and BolometerTest Set)

12.19 Infrared Test Equipment

217. TS-724/SAC, (BuS) (Infrared Test Set) (InfraredCommunications)

218. AN/UAM-1, (BuA) (Infrared Test Set) (HomingEquipment)

219. TS-532/ASM, (BuA) (Test Set) (Homing Equipment)

13. CALIBRATING EQUIPMENT FOR ELECTRONICS TEST EQUIPMENT

13.1.3 Multimeter Calibrator

222. TS -656( )/U, (SigC) (Meter Tester) 0-2.5/5/10/25/50/100/250/500 VDC, VAC;0-100/250/500 DC ua; 0-1/2.5/5/10/25/50/100/250/500 DC ma; 0-12; ± 2% DC, ±5% AC

14. POWER MEASURING EQUIPMENT

14.1 DC and Line Power Frequency Power Measuring Equipment (0-3,000 cps)

223. TS -445/U, (SigC) (Wattmeter) DC and 25-125 cps; 5w to 15kw; 75 to 300V,5%0-30 kw; 25-125 cps

- 45 to + 26 dbm for 600 ohm circuit; 0/2-35 kc0 1-5,000 mw; 0.03-10 kc

227. TS -629/U, (BuS) (Audio Level Test Panel) - 40 to + 20 dbm 600 ohm circuit, - 20 to+ 20 dbm 12,500 ohm circuit, 0 db = 1 mw,600 ohm circuit, 0.03-15 kc

GROUP B. 30-3,000 MC

229. TS-118/AP, (SigC) (Radio Frequency Wattmeter) ..230. TS-107/TPM-1, (BuO) (Wave and Power Meter

Set)

.2-500 w, 20-1,400 mc; Pulse

0 5-120 mw; 900-1,350 mc; includes frequencymeter; Pulse

173

CHAPTER 16


Equipment Range

231. TS-125/AP, (SigC) (Power Meter) 0-200 mw; 2,400-3,335 mc; Pulse232. TS-206/AR, (WADC) (Radio Frequency Watt-

meter) 50-1,000 w; 20-60 mc233. AN-URM-43, (BuS) (RF Wattmeter) 0-15/60 w; 100-500 mc, formerly ME -11/U234. AN/URM-19, (RADC) (Bridge Summation) 0-100 mw avg, 2-20 w peak; 20-1,000 mc;

Pulse235. AN/URM-22, (RADC) (Bridge Summation) 0-5 w avg, 1-10 kw peak; 20-1,000 mc; Pulse236. TS-305/UP, (WADC) (Power Meter) 215-230 mc, 0-1 kw Peak Power Pulse Peak

Power Meter237. TS-226/AP, (WADC) (Power Meter) 400-425 mc, 0-1 kw; 500-530 mc, 0-10 kw;

Peak Power Peak Power Meter238. AN/URM-20, (RADC) (Bridge Summation) 0-100 mw, avg. 2-20 w peak; 1,000-4,000 mc;

Pulse239. AN-URM-23, (RADC) (Bridge Summation) .0-5 w avg; 0.1-10 kw peak; 1,000-4,000 mc;

Pulse242. ME-27/AP, (WADC) (RF Wattmeter) 0 1-1,000 mw; 8,500-9,600 mc; Pulse243. TS-230/AP, (BuS) (Frequency -Power Meter) 0 1-1,000 mw; 8,500-9,600 mc; includes fre-

quency meter; Pulse245. TS-254/AP, (WADC) (Power Meter) 1-632 mw; 23,520-24,480 mc; Pulse246. AN/URM-21, (RADC) (Bridge Summation) 0-100 mw avg; 2-20 w peak; 4,000-10,000 mc;

Pulse247. AN/URM-24, (RADC) (Bridge Summation) 0-5 w avg; 0.1-10 kw peak; 4,000-10,000 mc;

Pulse

174

APPENDIX I

WORKING AND SUPPLEMENTARY DATA

APPENDIX I


Page

Working Nomograms 177

4/3 Earth Profile Chart 207

The High Frequency Spectrum 209

Glossary 211

Mks Symbols 221

175

APPENDIX I

APPENDIX

,. The nomograms included in this section are in-tended to be used to simplify mathematics, as well asan aid in understanding the various factors that mayaffect radio propagation.

NOMOGRAM A. Path attenuation. To be used indetermining free space attenuation between iden-tical antennas. (Chapter 2.)

NOMOGRAM B. Attenuation due to rainfall. Thisnomogram is designed to be used in determiningattenuation due to rainfall where the maximumrate of rainfall is known. Results are based on theassumption that such a rate of rainfall is constantover the entire radio path. Since such a conditionis extremely unlikely, results obtained from thenomogram represent the worst possible conditionthat may be expected. (Chapter 4.)

NOMOGRAM C. Reliability vs. fade margin. Thisnomogram will give the percentage of outage timedue to fading, where the fade margin is known. Itis based on conditions found on the North Americancontinent, and may not be satisfactory for loca-tions with unusual fade conditions. (Chapter 5.)

NOMOGRAM D. Characteristic impedance, openwire lines. Self-explanatory. (Chapter 6.)

NOMOGRAM E. Characteristic impedance, coaxiallines. Self-explanatory. (Chapter 6.)

NOMOGRAM F. Input reactance. "Wavelength ofthe transmission line" in this nomogram refers only


WORKING AND

SUPPLEMENTARY

DATA

to the fractional part of a wavelength, and not tothe total number of wavelengths. Since the nomo-gram reads only to 1/4 wavelengths, treat shortedhalf -wavelength lines as open-ended quarter -wave-length lines, and open half -wavelength lines asshorted quarter -wavelength lines. (Chapter 6.)

NOMOGRAM G. Line matching impedance. Whilethis nomogram applies equally well to coaxial cableand open wire line, it is most useful for open wireline. Having determined the necessary impedanceof the matching section, Nomogram D may beused to determine the wire size and spacing of thematching section. (Chapter 6.)

NOMOGRAM H. Fresnel-zone clearance. This nomo-gram gives the required clearance above an ob-struction. The profile of the radio path will givethe actual clearance, which should be approxi-mately the same as the value given in the nomo-gram. (Chapter 14.)

NOMOGRAM J. Radio and optical line -of -sight.Self-explanatory. (Chapter 14.)

NOMOGRAM K. Parabolic antenna gain. Nomo-gram to be used in selecting parabolic reflectorswhere the use of a large reflector will give sufficientfield strength at the receiver. This nomogram com-pensates for effective antenna area. (Chapter 7.)

NOMOGRAM L. Path attenuation between para-bolic antennas. Free -space path attenuation under

177

APPENDIX I


varied conditions of path length, frequency, andparabolic reflector size. (Chapter 7.)

NOMOGRAM M. Increment to be added to planeearth profile for curved earth profile. Supplies cor-rection figures to enable plotting a normal curvedearth profile on rectangular coordinate paper.(Chapter 14.)

NOMOGRAM N. Wind pressure vs. velocity. Usethis nomogram to determine wind loading inpounds per square inch on antenna towers. Mostuseful in areas where wind of hurricane velocitymay occur. (Chapter 14.)

NOMOGRAM 0. Conversion of dbm to microvolts.Self-explanatory.

178

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Nomogram C. Reliability

z3cca2wca4u_

APPENDIX I


183

APPENDIX I


1000

900

800

700

600

500

400

300

200

100

2DZ0276 LOG10

d(-)OHMS

DAXIAL SPACING IN INCHES(WIRE SEPARATIONS ON CENTERS)d -WIRE DIAMETER IN INCHES

20

18

16

14

12

10

8

6

4

2

0

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.06

.07

.08

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.10

.20

.30

40

-.50

.60

.70

.80

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1.0

20Nomogram D. Characteristic Impedance of Open Wire Lines

185

S

alb

APPENDIX I


4 0 -

3 0

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FORMULAZo = 138 LOGio (d ) OHMS

D I NNER DIAMETER OF OUTER CONDUCTORd = OUTER DIAMETER OF INNER CONDUCTOR

Nomogram E. Characteristic Impedance of Air -Filled Coaxial Lines

240

230

220

210

200

190

180

170

160

150

140

130

120

110

100

90

80

70

60

50

40

30

20

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0

187

a

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400

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.LECTRICAL LENGTHS Ni-7( X ACTUAL LENGTHNHERE K DIELECTRIC CONSTANT

APPENDIX I


15,000

10,0 0 0 --=

5,00 0

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Nomogram F. Input Reactance for Open Wire and Coaxial Lines

189

APPENDIX I


Zs

- 1000

4

800

600

500

400

300

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100

8070

60

50

40

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800

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500

400

300

200

100

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60

50

40

30

20

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8

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Nomogram G. Characteristic Impedance of a Quarter Wave Section Used as an Impedance Transformer

191

-

11

r

r

0 z

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DISTANCE IN MILES FROM TRANSMITTER TO INTERCEPTING POINT (D1)

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FREQUENCY IN MEGACYCLES / SECOND

I

Ill

I

II

APPENDIX I


=_-- 2000 109.1 - -_ 126.5

1900

1800 120

1700 100

1600

1500It

I10

14001--90

- 1300100

- 1200

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800 70

700

600

500

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1900

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Nomogram J. Radio & Optical Line -of -Sight Distances

195

APPENDIX I


20,000 1.5

titi15

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GAIN IN db = 20 log f + 20 log D - 52.6f FREQUENCY IN MEGACYCLESD DIAMETER IN FEET

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197

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FORMULA

Y = 2/3(SX-X2)Y INCREMENT TO BE ADDED,

IN FEET.S DISTANCE BETWEEN ANTENNAS

X DISTANCE FROM NEARESTANTENNA TO POINT TO BECORRECTED.

7...---

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5

15 17.5

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/

APPENDIX 1


...------""

0

5

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15

20

25

30

35

40

45

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Nomogram M. Plane to Normal Curved Earth Conversion

201

41,

a

l

IP

APPENDIX I


60 120

_r-

FLAT SURFACES

36 120

ROUND SURFACES

11050 30

40

30

20

110

fi

100 100

90

80

20

-r_/-

90

ti

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70 - 70

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ti Th=

ti10 - 50

0.4

40

30

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PRESSURE = 0.0025 V2

PRESSURE = 0.0042 V2

0.25

50

40

30

20

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Nomogram N. Pressure vs Wind Velocity

203

I

v.

a

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205

d,.1...

APPENDIX I


1000

900

800

700

600

i-Lo 500wu.

400

300

200

100

0LO

0

S

10

10

20

15

30

MILES

Chart P. 4/3 Earth's Profile

207

2040 25

50

4000

3600

3200

2800

2400

I -la2000 wIL

1600

1200

800

400

030

60 ....j

APPENDIX I


FREQUENCY RANGE .MEGACYCLES 30 - 300 MC 300 - 3,000 MC 3,000 - 30,000 MC 30,000 - 300,000 MC

WAVELENGTH.CENTIMETERS

1,000 - 100 CM 100- 10 CM 10 - 1.0 CM I 0 - 0.1 CM

BANDSFP

L S X K 0 V

DESIGNATIONVERY -HIGHFREQUENCY

V H F

ULTRA -HIGHFREQUENCY

U H F

SUPER -HIGHFREQUENCY

S H F

EXTREMELY - HIGHFREQUENCY

E H F

cn0I-cr,

iiwI -uccccaz0

PROPAGATIONLIMITATIONS

4/3 EARTH RADIUS -SOME SPORADIC E AND

ATMOSPHERIC REFLECTION

4/3 EARTH RADIUS -

SPORADICATMOSPHERIC REFLECTION

4/3 EARTH RADIUS -SOME

ATMOSPHERIC ABSORPTION

4/3 EARTH RADIUS -EXTREME

ATMOSPHERIC ABSORPTION

PREDOMINANTNOISE

MAN - MADENATURAL

RECEIVER - NOISEMAN-MADE

RECEIVER -NOISE RECEIVER - NOISE

R.F. SOURCE VARIOUS TRIODEMAGNETRONSKLYSTRONS

MAGNETRONSKLYSTRONS

TRANSMISSIONLINES

WIRECOAXIAL

COAXIALWAVEGUIDE

WAVEGUIDECOAXIAL

WAVEGUIDE

DRIVENANTENNA DIPOLE DIPOLE

DIPOLEHORN

HORN

APPLICATIONS

COMMUNICATIONSNAVIGATIONTELEVISIONCONTROLRADAR'

SEARCHE.W.I.F.F.

COMMUNICATIONSNAVIGATIONTELEVISIONCONTROLRADAR-

SEARCHE.W.GUNLAYINGI F.F.

MICROWAVE RELAYSNAVIGATIONCONTROLRADAR .

SEARCHBOMBINGE. W.GUNLAYING

EXPERIMENTALI TACTICAL RADAR, ETC 1

Chart Q. High Frequency Spectrum

209

APPENDIX I

GLOSSARY

GLOSSARY

ABSORPTION LOSS. That part of the transmissionloss due to the dissipation or conversion of elec-trical energy into other forms of energy (e.g., heat),either within the medium or attendant upon areflection.

ABSORPTION MODULATION. A system for pro-ducing amplitude modulation of the output of aradio transmitter by means of a variable impe-dance device inserted in or coupled to the outputcircuit.

AMPLITUDE MODULATION (AM). Modulationin which, the amplitude of a carrier is the charac-teristic varied.

ANTENNA. A means of radiating or receiving radiowaves.

ANTENNA ARRAY. A system of antennas coupledtogether for the purpose of obtaining directionaleffects.

ANTENNA RESISTANCE. The quotient of thepower supplied to the entire antenna circuit by thesquare of the effective antenna current toa specified point.

NOTE. Antenna resistance is made up of suchcomponents as radiation resistance, ground resist-ance, radio -frequency resistance of conductors inthe antenna circuit, and equivalent resistance dueto corona, eddy currents, insulator leakage, anddielectric power loss.

APERTURE (of a unidirectional antenna). Thatportion of a plane surface near the antenna, per-pendicular to the direction of maximum radiation,through which the major part of the radiationpasses.

ATMOSPHERIC DUCT. An almost horizontallayer in the troposphere, extending from the levelof a local minimum of the modified refractive indexas a function of height, down to a level where theminimum value is again encountered, or down tothe earth's surface if the minimum value is notagain encountered.

ATTENUATION. Of a quantity associated wit ahtraveling wave in a homogeneous medium, thedecrease with distance in the direction of propa-gation.

NOTE. In a diverging wave, attenuation includesthe effect of divergence.

ATTENTUATION CONSTANT. For a travelingplane wave at a given frequency, the rate of ex-ponential decrease of the amplitude of a fieldcomponent (or of the voltage or current) in thedirection of the propagation, in nepers or decibelsper unit length.

AUTOMATIC FREQUENCY CONTROL (AFC).An arrangement whereby the frequency of anoscillator is automatically maintained within spe-cified limits.

AUTOMATIC GAIN CONTROL (AGC). A circuitarrangement which adjusts the gain in a specifiedmanner in response to changes in input.

BALANCED MODULATOR. A modulator, specifi-cally a push-pull circuit, in which the carrier andmodulating signal are so introduced that aftermodulation takes place the output contains thetwo sidebands without the carrier.

BANDWIDTH (of a wave). The least frequency in-terval outsibe of which the power spectrum of atime -varying quantity is everywhere less thansome specified fraction of its value at a referencefrequency.

CAUTION. This definition permits the spectrumto be less than the specified fraction within theinterval.

NOTE. Unless otherwise stated, the referencefrequency is that at which the spectrum has itsmaximum value.

(of a device). The range of frequencies withinwhich performance, with respect to some char-acteristic, falls within specific limits.

BASEBAND. The frequencips containing the intel-ligence used to modulate the carrier of a radiorelay system.

BINARY NUMBER SYSTEM. A number systemwhich uses two symbols (usually denoted by "0"and "1") and has two as its base, just as thedecimal system uses ten symbols ("0, 1, . . . , 9")and the base ten.

BOLOMETER. A specially constructed resistorwhich has a positive temperature coefficient andwhich is used for power measurements.

CARRIER WAVE. A wave generated at a point inthe transmitting system and modulated by thesignal.

211

APPENDIX I

GLOSSARY

CAVITY RESONATOR. A space normally boundedby an electrically conducting surface in whichoscillating electromagnetic energy is stored, andwhose resonant frequency is determined by thegeometry of the enclosure.

CHANNELING. The utilization of a modulation -frequency band for the simultaneous transmissionfrom two or more communication channels inwhich the separation therebetween is accomplishedby the use of carriers or subcarriers, each in adifferent discrete frequency band forming a sub-division of the main band.

NOTE. This covers a special case of multiplextransmissions.

CHARACTERISTIC IMPEDANCE (Z.). The ratioof the voltage to the current at every point alonga transmission line on which there are no standingwaves.

CLIPPER. A transducer which gives output onlywhen the input exceeds a critical value.

CLIPPER -LIMITER. A transducer which givesoutput only when the input lies above a criticalvalue and a constant output for all inputs abovea second higher critical value.

NOTE. This is sometimes called an amplitudegate, or slicer.

COEFFICIENT OF REFLECTION. The squareroot of the ratio of the reflected power leaving areflecting surface to the power incident to the samesurface.

CONDUCTION CURRENT. The power flow par-allel to the direction of propagation expressed inwatts per square meter.

CONDUCTIVITY. A measure of the ability of amaterial to act as a path for electron flow. It is thereciprocal of resistivity and is expressed in mhos/meter.

CONVERSION TRANSCONDUCTANCE (of aheterodyne conversion transducer). The quotientof the magnitude of the desired output -frequencycomponent of current by the magnitude of theinput -frequency component of voltage when theimpedance of the output external termination isnegligible for all of the frequencies which mayaffect the result.

NOTE. Unless otherwise stated, the term refersto the cases in which the input -frequency voltageis of infinitesimal magnitude. All direct electrodevoltages and the magnitude of the local -oscillatorvoltage must be specified, fixed values.

CONVERSION VOLTAGE GAIN (of a conversiontransducer). The ratio of (1) the magnitude ofthe output -frequency voltage across the outputtermination, with the transducer inserted betweenthe input -frequency generator and the outputtermination, to (2) the magnitude of the input -frequency voltage across the input termination ofthe transducer.

CONVERTER. A conversion transducer in whichthe output frequency is the sum or difference ofthe input frequency and an integral multiple ofthe local oscillator frequency.

NOTE. The frequency and voltage or power ofthe local oscillator are parameters of the conver-sion transducer. Ordinarily, the output signal am-plitude is a linear function of the input signalamplitude over its useful operating range.

CRITICAL FREQUENCY. The limiting frequencybelow which a magneto -ionic wave component isreflected by, and above which it penetrates through,an ionospheric layer at vertical incidence.

CROSS -MODULATION. Modulation of a desiredsignal by an undesired signal.

CROSSTALK. The sound heard in a receiver asso-ciated with a given telephone channel resultingfrom telephone currents in another telephonechannel.

NOTE. In practice, crosstalk may be measuredeither by the loudness of the overheard sounds orby the magnitude of the coupling between thedisturbed and disturbing channels. In the lattercase, to specify the loudness of the overheardsounds, the volume in the disturbing channel mustalso be given.

DECIBEL. The decibel is one -tenth of a bel, thenumber of decibels denoting the ratio of the twoamounts of power being ten times the logarithmto the base 10 of this ratio. The abbreviation dbis commonly used for the term decibel.

NOTE. With P1 and P2 designating two amountsof power and the number of decibels denoting theirratio,

n = 10 logio (P1 /P2) decibels.

When the conditions are such that ratios of cur-rents or ratios of voltage (or analogous quantitiesin other fields) are the square roots of the corres-ponding power ratios, the number of decibels bywhich the corresponding powers differ is expressedby the following equations:

n = 20 logio (I1/I2) decibels

212

n = 20 logio (Vi/V2) decibels

where II /IL, and VI ,N2 are the given current andvoltage ratios, respectively. By extension, theserelations between numbers of decibels and ratiosof currents or voltages are sometimes appliedwhere these ratios are not the square roots of thecorresponding power ratios; to avoid confusion,such usage should be accomplished by a specificstatement of this application.

DEMODULATION. The process of recovering themodulating wave from a modulated carrier.

DEVIATION RATIO. In a frequency -modulationsystem, the ratio of the maximum frequency devia-tion to the maximum modulating frequency of thesystem.

DEW POINT. The temperature at which the watervapor in the air begins to condense.

DIFFRACTION. The bending of a wave into theregion behind an obstacle.

DIPOLE ANTENNA. A straight radiator, usuallyfed in the center, and producing a maximum ofradiation in the plane normal to its axis. Thelength specified is the overall length.

NOTE. Common usage in microwave antennasconsiders a dipole to be a metal radiating structurewhich supports a line current distribution similarto that of a thin straight wire, a half wavelengthlong, so energized that the current has two nodes,one at each of the far ends.

DIRECT WAVE. A wave that is propagated directlythrough space.

DIRECTION OF PROPAGATION. At any pointin a homogeneous, isotropic medium, the directionof time average energy flow.

DIRECTIONAL ANTENNA. An antenna havingthe property of radiating or receiving radio wavesmore effectively in some directions than others.

DIRECTIVE GAIN. In a given direction, 47 timesthe ratio of the radiation intensity in that directionto the total power radiated by the antenna.

DISCRIMINATOR. A device in which amplitudevariations are derived in response to frequencyvariations.

DISPLACEMENT CURRENT. The current atright angles to the direction of propagation de-termined by the rate at which the field energychanges.

APPENDIX I

GLOSSARY

DISTORTION. An undesired change in wave form.

DISTRIBUTED CAPACITANCE. The capacitancethat exists between the turns in a coil or choke,or between adjacent conductors or circuits, as dis-tinguished from the capacitance which is concen-trated in a capacitor.

DISTRIBUTED INDUCTANCE. The inductancethat exists along the entire length of a conductor,as distinguished from the self-inductance which isconcentrated in a coil.

DUPLEX OPERATION. The operation of asso-ciated transmitting and receiving apparatus inwhich the processes of transmission and receptionare concurrent.

EFFECTIVE AREA. The square of the wavelengthmultiplied by the power gain (or directive gain)in that direction, and divided by 47r.

NOTE. When power gain is used, the effectivearea is that for power reception; when directivegain is used, the effective area is that for direc-tivity.

EFFECTIVE RADIUS OF THE EARTH. Aneffective value for the radius of the earth, which isused in place of the geometrical radius to correctfor atmospheric refraction when the index of re-fraction in the atmosphere changes, linearly withheight.

NOTE. Under conditions of standard refractionthe effective radius of the earth is 8.5 x 106 meters,or 4/3 the geometrical radius.

ELECTRIC FIELD STRENGTH. The magnitudeof the electric field vector.

ELECTRIC FIELD VECTOR. At a point in anelectric field, the force on a stationary positivecharge per unit charge.

NOTE. This may be measured either in newtonsper coulomb or in volts per meter. This term issometimes called the electric field intensity butsuch use of the word intensity is deprecated infavor of field strength since intensity connotespower in optics and radiation.

ELLIPTICALLY POLARIZED WAVE. An elec-tromagnetic wave for which the electric and/or themagnetic field vector at a point describes anellipse.

NOTE. This term is usually applied to transversewaves.

FADING. The variation of radio field strength

213

APPENDIX I

GLOSSARY

caused by changes in the transmission mediumwith time.

FRAUNHOFER REGION. That region of the fieldin which the energy flow from an antenna pro-ceeds essentially as though coming from a pointsource located in the vicinity of the antenna.

NOTE. If the antenna has a well-defined apertureD in a given aspect, the Fraunhofer region in thataspect is commonly taken to exist at distancesgreater than 2D2/ -y from the aperture, 7 beingthe wavelength.

FREQUENCY DEVIATION. In frequency modula-tion, the peak difference between the instantaneousfrequency of the modulated wave and the carrierfrequency.

FREQUENCY -DIVISION MULTIPLEX. The pro-cess or device in which each modulating wavemodulates a separate subcarrier and the sub -carriers are spaced in frequency.

NOTE. Frequency division permits the trans-mission of two or more signals over a commonpath by using different frequency bands for thetransmission of the intelligence of each messagesignal.

FREQUENCY MODULATION (FM). Angle mod-ulation of a sine -wave carrier in which the instan-taneous frequency of the modulated wave differsfrom the carrier frequency by an amount propor-tional to the instantaneous value of the modula-ting wave.

NOTE. Combinations of phase and frequencymodulation are commonly referred to as "fre-quency modulation".

FRESNEL REGION. The region between the an-tenna and the Fraunhofer region.

NOTE. If the antenna has a well-defined apertureD in a given aspect, the Fresnel region in thataspect is commonly taken to extend a distance2D2/X in that aspect, X being the wavelength.

FRESNEL ZONES. Zones of wave reinforcementand destructive interference caused by interactionof direct waves and those waves reflected from theearth.

GROUND WAVE. A radio wave that is propagatedover the earth and is ordinarily affected by thepresence of the ground and the troposphere. Theground wave includes all components of a radiowave over the earth except ionospheric and tropo-spheric waves.

NOTE. The ground wave is refracted because ofvariations in the dielectric constant of the tropo-sphere including the condition known as surfaceduct.

GROUNDED -CATHODE AMPLIFIER. An elec-tron -tube amplifier with the cathode at groundpotential at the operating frequency, with inputapplied between the control grid and ground, andthe output load connected between plate andground. (This is the conventional amplifier circuit.)

GROUNDED -GRID AMPLIFIER. An electron -tube amplifier circuit in which the control grid isat ground potential at the operating frequency,with input applied between cathode and ground,and output load connected between plate andground. The grid -to -plate impedance of the tubeis in parallel with the load instead of acting as afeedback path.

GROUP VELOCITY. Of a traveling plane wave, thevelocity of propagation of the envelope of a waveoccupying a frequency band over which the en-velope delay is approximately constant. It is equalto the reciprocal of the rate of change of phaseconstant with angular frequency.

NOTE. Group velocity differs from phase velocityin a medium in which the phase velocity varieswith frequency.

HALF - POWER WIDTH OF A RADIATIONLOBE. In a plane containing the direction of themaximum of the lobe, the full angle between thetwo directions in that plane about the maximumin which the radiation intensity is one-half themaximum value of the lobe.

HARMONIC. A sinusoidal component of a periodicwave or quantity having a frequency which is anintegral multiple of the fundamental frequency.For example, a component the frequency of whichis twice the fundamental frequency is called thesecond harmonic.

HETERODYNE. To beat or mix two frequencies ina non-linear component so as to produce differentfrequencies from those introduced.

HORIZONTALLY POLARIZED WAVE. A linearlypolarized wave whose electric field vector ishorizontal.

IMAGE FREQUENCY. In heterodyne frequencyconverters in which one of the two sidebands pro-duced by beating is selected; an undesired inputfrequency capable of producing the selectedfrequency by the same process.

214

NOTE. The word "image" implies the mirror-like symmetry of signal and image frequenciesabout the beating oscillator frequency or the in-termediate frequency, whichever is higher.

IMAGE RATIO. The ratio of (1) the field strengthat the image frequency to (2) the field strength atthe desired frequency, each field being appliedin turn, under specified conditions, to produceequal outputs.

IMPULSE NOISE. Noise characterized by tran-sient disturbances separated in time by quiescentintervals. The frequency spectrum of these dis-turbances must be substantially uniform over theuseful pass band of the transmission system.

INCIDENT WAVE. In a medium of certain propa-gation characteristics, a wave which impinges ona discontinuity or medium of different propagationcharacteristics.

INTERELECTRODE TRANSIT TIME. The timerequired for an electron to traverse the distancebetween two electrodes.

INTERFERENCE. In a signal transmission systemeither extraneous power which tends to interferewith the reception of the desired signals, or thedisturbance of signals which results.

INTERMEDIATE FREQUENCY (L -F). The fre-quency in superheterodyne reception resultingfrom a frequency conversion before demodulation.

INTERMEDIATE SUBCARRIER. A carrier whichmay be modulated by one or more subcarriers andwhich is used as a modulating wave to modulatea carrier or another intermediate subcarrier.

IONOSPHERE. The part of the earth's outer at-mosphere where ions and electrons are present inquantities sufficient to affect the propagation ofradio waves.

NOTE. According to current opinion, the lowestlevel is approximately 50 kilometers above theearth's surface.

ISOTROPIC ANTENNA (UNIPOLE). A hypo-thetical antenna radiating or receiving equally inall directions. A pulsating sphere is a unipole forsound waves. In the case of electromagnetic wavesunipoles do not exist physically but represent con-venient reference antennas for expressing directiveproperties of actual antennas.

KELVIN SCALE (ABSOLUTE SCALE). A tem-perature scale using the same divisions as the

APPENDIX I

GLOSSARY

centrigrade scale, but with the zero point estab-lished at absolute zero -273°C), theoreticallythe lowest possible temperature.

LEAKAGE RADIATION. In a transmitting system,radiation from anything other than the intendedradiating system.

LIMITER. A transducer whose output is constantfor all inputs above a critical value.

NOTE. A limiter may be used to remove ampli-tude modulation while transmitting angle modu-lation.

LINEARLY POLARIZED WAVE. At a point in ahomogeneous, isotropic medium, a transverse elec-tromagnetic wave whose electric field vector at alltimes lies along a fixed line.

LOWEST USEFUL HIGH FREQUENCY. Thelowest high frequency effective at a specified timefor ionospheric propagation of radio waves be-tween two specified points.

NOTE. This is determined by factors such asabsorption, transmitter power, antenna gain, re-ceiver characteristics, type of service, and noiseconditions.

MAGNETIC FIELD. A state of the medium inwhich moving electrified bodies are subject toforces by virtue of both their electrifications andmotion.

MAGNETO -IONIC WAVE COMPONENT. Eitherof the two elliptically polarized wave componentsinto which a linearly polarized wave incident onthe ionosphere is separated because of the earth'smagnetic field.

MAXIMUM USABLE FREQUENCY. The upperlimit of the frequencies that can be used at aspecified time for radio transmission between twopoints and involving propagation by reflectionfrom the regular ionized layers of the ionosphere.

NOTE. Higher frequencies may be transmittedby sporadic and scattered reflections.

MILLIBAR. A unit of pressure equal to 1000 dynesper square centimeter. Standard atmospheric pres-sure at sea level is equal to 1013 millibars.

MODIFIED INDEX OF REFRACTION. In thetroposphere, the index of refraction at any heightincreased by h a, where h is the height above sealevel and a is the mean geometrical radius of theearth. When the index of refraction in the tropo-sphere is horizontally stratified, propagation over

215

APPENDIX I

GLOSSARY

a hypothetical flat earth through an atmospherewith the modified index of refraction is substan-tially equivalent to propagation over a curvedearth through the real atmosphere.

MODULATING SIGNAL (MODULATINGWAVE). A wave which causes a variation of somecharacteristic of a carrier.

MODULATION. The process or result of the proc-ess whereby some characteristic of one wave isvaried in accordance with another wave.

MODULATION INDEX. For a sinusoidal modula-ting wave, the ratio of the frequency deviation tothe frequency of the modulating wave.

MULTIPATH TRANSMISSION. The propagationphenomenon which results in signals reaching theradio receiving antenna by two or more paths,usually having both amplitude and phase differ-ences between each path.

MULTIPLE MODULATION. A succession of proc-esses of modulation in which the modulated wavefrom one process becomes the modulating wavefor the next.

NOTE. In designating multiple -modulation sys-tems by their letter symbols, the processes arelisted in the order in which the signal intelligenceencounters them. For example, PPM -AM meansa system in which one or more signals are used toposition -modulate their respective pulse subcarrierswhich are spaced in time and are used to amplitude -modulate a carrier.

MULTIPLEX RADIO TRANSMISSION. The si-multaneous transmission of two or more signalsusing a common carrier wave.

NOISE. Any extraneous electrical disturbance tend-ing to interfere with the normal reception of atransmitted signal.

NOISE FIGURE. Of a linear system at a selectedinput frequency, the ratio of (1) the total noisepower per unit bandwidth (at a correspondingoutput frequency) available at the output term-inals, to (2) the portion thereof engendered at theinput frequency by the input termination, whosenoise temperature is standard (290°K) at all fre-quencies. (See NOISE TEMPERATURE.)

NOTE 1. For heterodyne systems there will be,in principle, more than one output frequency cor-responding to a single input frequency, and vice -versa; for each pair of corresponding frequenciesa noise factor is defined.

NOTE 2. The phrase, "available at the outputterminals", may be replaced by "delivered by thesystem into an output termination", withoutchanging the sense of the definition.

NOISE TEMPERATURE. At a pair of terminalsand at a specific frequency, the temperature of apassive system having an available noise powerper unit bandwidth equal to that of the actualterminals.

NOISE TEMPERATURE (STANDARD). Thestandard reference temperature T. for noisemeasurements is taken as 290°K.

NOTE. K To/e = 0.0250 volt where e is theelectron charge and K is Boltzmann's constant.

OPTICAL HORIZON. The locus of points at whicha straight line from the given point becomestangential to the earth's surface.

OPTIMUM WORKING FREQUENCY. The mosteffective frequency at a specified time for ion -spheric propagation of radio waves between twospecified points.

NOTE. In predictions of useful frequencies theoptimum working frequency is commonly takenas 15 percent below the monthly median valueof the maximum usable frequency, for the specifiedtime and path.

PATH ATTENUATION. The power loss betweentransmitter and receiver due to all causes. It isequal to 10 log P /P where P, is the powerto _ t, _ r

radiated from the transmitting antenna and P.is the power available at the output terminals ofthe receiving antenna and is expressed in decibels.

PERMEABILITY. A measure of the ability of amaterial to act as a path for magnetic lines offorce.

PHASE CONSTANT. For a traveling plane waveat a given frequency, the rate of linear increase ofphase lag of a field component (for the voltage orcurrent) in the direction of propagation, in radiansper unit length.

PHASE MODULATION (PM). Angle modulationin which the angle of a sine -wave carrier is causedto depart from the carrier angle by an amountproportional to the instantaneous value of themodulating wave.

NOTE. Combinations of phase and frequencymodulation are commonly referred to as "fre-quency modulation".

216

APPENDIX I

GLOSSARY

PHASE VELOCITY. Of a traveling plane wave ata single frequency, the velocity of an equiphasesurface along the wave normal.

PLANE WAVE. A wave whose equiphase surfacesform a family of parallel planes.

POLAR DIAGRAMS. A system of coordinates inwhich a point is determined by the length and theangle of a line connecting the center of the dia-gram and the point.

POWER GAIN. In a given direction, 4r times theratio of the radiation intensity in that directionto the total power delivered to the antenna.

PROPAGATION CONSTANT. For a travelingplane wave at a given frequency, the complexquantity whose real part is the attenuation con-stant in nepers per unit length and whose imaginarypart is the phase constant in radians per unitlength.

PULLING. A change in the resonant frequency of acircuit due to a change in the load.

PULSE. A single disturbance characterized by therise and decay in time or space or both of aquantity whose value is normally constant.

NOTE. In these definitions an r -f carrier, am-plitude -modulated by a pulse, is not consideredto be a pulse.

PULSE AMPLITUDE MODULATION (PAM)Modulation in which the modulating wave iscaused to amplitude -modulate a pulse carrier.

PULSE CARRIER. A carrier consisting of a seriesof pulses.

NOTE. Usually pulse carriers are employed assubcarriers.

PULSE CODE.(1) A pulse train modulated so as to represent

information.(2) Loosely, a code consisting of pulses, such as

Morse Code, Baudot Code, Binary Code.

PULSE -CODE MODULATION (PCM). Modula-tion which involves a pulse code.

NOTE. This is a generic term, and additionalspecification is required for a specific purpose.

PULSE -DURATION MODULATION (PDM).Pulse -time modulation in which the value of eachinstantaneous sample of the modulating wave iscaused to modulate the duration of the pulse.

NOTE. The terms "pulse -width modulation" and

"pulse -length modulation" also have been usedto designate this system of modulation.

NOTE. In pulse -duration modulation, the modu-lating wave may vary the time of occurrence of theleading edge, the trailing edge, or both edges ofthe pulse.

PULSE -POSITION MODULATION (PPM). Pulse -time modulation in which the value of each in-stantaneous sample of a modulating wave iscaused to modulate the position in time of a pulse.

PULSE SHAPER. Any transducer used for changingone or more characteristics of a pulse.

NOTE. This term includes pulse regenerators.

PULSE -TIME MODULATION (PTM). Modula-tion in which the values of instantaneous samplesof the modulating wave are called to modulate thetime of occurrence of some characteristic of apulse carrier.

NOTE. Pulse -duration modulation and pulse -position modulation are particular forms of pulse -time modulation.

PUSH -PUSH CIRCUIT. A circuit employing twosimilar tubes with grids connected in phase op-position and plates in parallel to a common load,and usually used as a frequency multiplier toemphasize even -order harmonics.

PUSHING. A change in the resonant frequency ofa circuit due to changes in the applied voltages.

Q. The figure of merit of efficiency of a circuit or coil.Numerically it is the ratio of the inductive re-actance to the resistance of the circuit or coil.

RADIATION EFFICIENCY. The ratio of thepower radiated to the total power supplied to theantenna at a given frequency.

RADIATION INTENSITY. In a given direction,the power radiated from an antenna per unit solidangle in that direction.

RADIATION RESISTANCE. The quotient of thepower radiated by an antenna divided by thesquare of the antenna current referred to a specificpoint.

RADIO -FREQUENCY PULSE. A radio -frequencycarrier amplitude -modulated by a pulse. Theamplitude of the modulated carrier is zero beforeand after the pulse.

NOTE. Coherence of the carrier (with itself) isnot implied.

217

APPENDIX I

GLOSSARY

RADIO HORIZON. The locus of points at whichdirect rays from the transmitter become tangentialto the earth's surface.

NOTE. On a spherical surface the horizon is acircle. The distance to the horizon is affected byatmospheric refraction.

RANDOM (OR FLUCTUATION) NOISE. Noisecharacterized by a large number of overlappingtransient disturbances occurring at random.

REACTANCE MODULATOR. A device, used forthe purpose of modulation, whose reactance maybe varied in accordance with the instantaneousamplitude of the modulating electromotive forceapplied thereto. This is normally an electron -tubecircuit and is commonly used to effect phase orfrequency modulation.

REFLECTION. That phenomenon which causes awave which strikes a medium of different char-acteristics to be returned into the original mediumwith the angles of incidence and of reflection equaland lying in the same plane.

REFRACTION. That phenomenon which causes awave which enters another medium obliquely toundergo an abrupt change in direction if thevelocity of the wave in the second medium isdifferent from that in the first.

REFRACTED WAVE. That part of an incidentwave which travels from one medium into asecond medium.

REFRACTIVE INDEX. Of a wave transmissionmedium, the ratio of the phase velocity in freespace to that in the medium.

REFRACTIVE MODULUS. In the troposphere,the excess over unity of the modified index ofrefraction, expressed in millionths. It is repre-sented by M and is given by the equation

M = (77 h/a -1) 106,

where 7/ is the index of refraction at a height habove sea level, and a is the radius of the earth.

RELATIVE DIELECTRIC CONSTANT. Theratio of the dielectric constant of a material to thedielectric constant of a vacuum.

SCATTERING. When radio waves encounter mat-ter, a disordered change in the direction of propa-gation of the waves.

SELECTIVE FADING. Fading in which the vari-ation of radio field intensity is not the same at all

frequencies in the frequency band of the receivedwave.

SELECTIVITY (of a receiver). That characteristicwhich determines the extent to which the receiveris capable of differentiating between the desiredsignal and disturbances of other frequencies.

SENSITIVITY. The least signal input capable ofcausing an output signal having desired char-acteristics.

SIDEBANDS. (1) The frequency bands on bothsides of the carrier frequency within which fall thefrequencies of the wave produced by the processof modulation. (2) The wave components lyingwithin such bands.

NOTE. In the process of amplitude modulationwith a sine -wave carrier, the upper sideband in-cludes the sum (carrier plus modulating) fre-quencies; the lower sideband includes the difference(carrier minus modulating) frequencies.

SIGNAL-TO-NOISE RATIO. The ratio of the valueof the signal to that of the noise.

NOTE. This ratio is usually in terms of peakvalues in the case of impulse noise and in terms ofthe root -mean -square values in the case of therandom noise.

NOTE. Where there is a possiblity of ambiguity,suitable definitions of the signal and noise shouldbe associated with the term; as, for example:peak -signal to peak -noise ratio; root -mean -squaresignal to root -mean -square noise ratio; peak -to -peak signal to peak -to -peak noise ratio, etc.

NOTE. This ratio is often expressed in decibels.NOTE. This ratio may be a function of the band-

width of the transmission system.

SIMPLEX OPERATION OF A RADIO SYSTEM.A method of operation in which communicationbetween two stations takes place in one directionat a time.

NOTE. This includes ordinary transmit -receiveoperation, press -to -talk operation, voice -operatedcarrier, and other forms of manual or automaticswitching from transmit to receive.

SINGLE-SIDEBAND MODULATION (SS). Mod-ulation whereby the spectrum of the modulatingwave is translated in frequency by a specifiedamount either with or without inversion.

SINGLE-SIDEBAND TRANSMISSION. Thatmethod of operation in which one sideband istransmitted and the other sideband is suppressed.

218

APPENDIX I

GLOSSARY

The carrier wave may be either transmitted orsuppressed.

SPHERICAL WAVE. A wave whose equiphase sur-faces form a family of concentric spheres.

STANDARD REFRACTION. The refraction whichwould occur in an idealized atmosphere in whichthe index of refraction decreases uniformly withheight at a rate of 39 x 10-6 per kilometer.

NOTE. Standard refraction may be included inground wave calculations by use of an effectiveearth radius of 8.5 x 106 meters, or 4/3 the geo-metrical radius of the earth.

STANDING WAVE. A wave in which, for anycomponent of the field, the ratio of its instantan-eous value at one point to that at any other pointdoes not vary with time.

SUBCARRIER. A carrier which is applied as amodulating wave to modulate another carrier oran intermediate subcarrier.

SURFACE DUCT. An atmospheric duct for whichthe lower boundary is the surface of the earth.

TENTH -POWER WIDTH. In a plane containingthe direction of the maximum of a lobe, the fullangle between the two directions in that planeabout the maximum in which the radiation in-tensity is one -tenth the maximum value of thelobe.

THERMISTOR. A specially constructed resistorwhich has a negative temperature coefficient, usedfor power measurements.

TIME -DIVISION MULTIPLEX. The process ordevice in which each modulating wave modulatesa separate pulse subcarrier, the pulse subcarriersbeing spaced in time so that no two pulses occupythe same time interval.

NOTE. Time division permits the transmissionof two or more signals over a common path byusing different time intervals for the transmissionof the intelligence of each message signal.

TRANSDUCER. A device by means of whichenergy can flow from one or more transmissionsystems to one or more other transmission systems.

NOTE. The energy transmitted by these systemsmay be of any form (for example, it may beelectric, mechanical, or acoustical), and it may beof the same form or different forms in the variousinput and output systems.

TRANSVERSE ELECTRIC WAVE. In a homo-geneous isotropic medium, an electro-magneticwave in which the electric field vector is every-where perpendicular to the direction of propa-gation.

NOTE. This is abbreviated "TE Wave".

TRANSVERSE ELECTROMAGNETIC WAVE.In a homogeneous isotropic medium, an electro-magnetic wave in which both the electric andmagnetic field vectors are everywhere perpen-dicular to the direction of propagation.

NOTE. This is abbreviated "TEM Wave".

TRANSVERSE MAGNETIC WAVE. In a homo-geneous isotropic medium, an electro-magneticwave in which the magnetic field vector is every-where perpendicular to the direction of propa-gation.

NOTE. This is abbreviated "TM Wave".

TRAVELING PLANE WAVE. A plane wave eachof whose frequency components has an exponentialvariation of amplitude and a linear variation ofphase in the direction of propagation.

TROPOSPHERE. That part of the earth's atmos-phere in which temperature generally decreaseswith altitude, clouds form, and convection is active.

NOTE. Experiments indicate that the tropo-sphere occupies the space above the earth's surfaceto a height of about 10 kilometers.

TROPOSPHERIC WAVE. A radio wave that ispropagated by reflection from a place of abruptchange in the dielectric constant or its gradientin the troposphere.

NOTE. In some cases the ground wave may beso altered that new components appear to arisefrom reflections in regions of rapidly changing die-lectric constants; when those components are dis-tinguishable from the other components, they arecalled tropospheric waves.

VECTOR. A quantity which has both magnitudeand direction or an arrow drawn in the directionand whose length is proportional to the magnitudeof the quantity.

VELOCITY -MODULATED OSCILLATOR (KLY-STRON). An electron -tube in which the velocityof an electron stream is varied (velocity -modu-lated in passing through a resonant cavity calleda buncher. Energy is extracted from the bunchedelectron stream at a higher energy level in passingthrough a second cavity resonator called the

219

APPENDIX I

GLOSSARY

catcher. Oscillations are sustained by couplingenergy from the catcher cavity back to the bunchercavity.

VERTICALLY POLARIZED WAVE. A linearlypolarized wave whose magnetic field vector ishorizontal.

VIDEO. A term pertaining to the bandwidth andspectrum position of the signal resulting fromtelevision scanning.

NOTE. In current usage, video means a band-width in the order of megacycles per second, anda spectrum position that goes with a d -c carrier.

WAVEGUIDE. A system of material boundariescapable of guiding waves.

WAVE INTERFERENCE. The variation of waveamplitude with distance or time, caused by thesuperposition of two or more waves.

NOTE. As most commonly used, the term refersto the interference of waves of the same or nearlythe same frequency.

WAVELENGTH. In a periodic wave, the distancebetween points of corresponding phase of twoconsecutive cycles. The wavelength X is related tothe phase velocity, v, and the frequency, f, by

= v/f.

220

APPENDIX I

MKS SYMBOLS

QUANTITY

VoltageCurrentResistancePowerCapacitanceInductance

GLOSSARY

(METERS, KILOGRAMS, SECONDS)

MKS

V, voltsI, amperesR, ohmsP, wattsC, faradsL, Henrys

Characteristic Impedance - Z., ohmsReactance - X, ohms XL = Inductive

X, = CapacitiveImpedance Z, ohmsAdmittance Y, mhosConductance G, mhosConductivity a, mhos/meterPermeability Ai, henrys/meter for free space llo

= 1.257 x 10-6 henrys/mDielectric constant - K, farads/meter

K = actual dielectric constantKo = dielectric constant of a vacuumKr = IC/ Ko = relative dielectric constantKo = 8.854 x 10-12 farads/m

Magnetic field intensity-H, ampere turns/meter oramp/meter

Electric field intensity-E, volts/meterPoynting Power Flow-p, watts/meter'Total current density-J, amp/meter2Propagation constant-r, hyperbolic radians/meterAttenuation constant-a, nepers/meter or db/meterPhase constant-p, circular radians/meterWavelength-A, meters or centimetersGuide wavelength-Xg, metersCut-off wavelength-X, metersFrequency-f, cps, mc, etc.Velocity of propagation-v, meters/secIndex of refraction -27, numericRefractive Modulus-M, numericReflection coefficient-p, numericBase of Natural log-e, 2.7182818, or loge

N = 2.302585 logioNImaginary unit-j = 1/-1Angular velocity-w, circular radians = 2,rf where f

is in cpsQuality, or figure of Merit-Q = coK/a for a wave

medium Q = X/R for a circuit

221

INDEX

A

Absorption, 22, 36Alternate Polarization, 41Amplifier Efficiency, 91Amplifiers, 90, 91

Buffer, 91Cascode, 95Grounded Grid, 91I -F, 97Klystron, 91Microwave, 91Push -Push, 91Transition, 91Traveling Wave, 91VHF, 90Video, 98

Amplitude, 2Antenna Bandwidth, 66Antenna Beamwidth, 70, 75, 78Antenna Dimensions, 67Antenna Directivity, 119Antenna Duplexers, 59Antenna Efficiency, 66Antenna Gain, 16, 44, 68, 69, 78, 79Antenna Height Frequency Dependence, 26Antenna Impedance, 66Antenna Length, 68Antenna Noise, 117Anti -cyclonic Movement, 135Anti -Resonance, 66Array Impedance, 71Atmospheric Conditions

Cold Fronts, 28Storms, 28Warm Fronts, 27Winds, 28

Atmospheric Noise, 22, 111, 119Attenuation, 15

Atmospheric, 15, 33Free Space, 15Precipitation, 36Rain, 17, 36Transmission Line, 51, 52, 53, 54Waveguide, 54, 56

Attenuation Constant, 12Attenuators, 61, 62

Cutoff, 61Dissipative, 61, 62Lossy Line, 62Modes, 62Pads, 62Polyiron, 62, 63

INDEX

Attenuators (Continued)Sand Load, 62Series, 62Shunt, 62Strip, 63

Automatic Frequency Control Systems, 86

B

Balance Converter, 62Bandwidth, 105Bazooka, 61Broadside Array, 72Bullington Nomograms, 125, 140

C

Carrier Noise, 117Cathode Resistance, 116Cathode Temperature, 115Cavity AFC, 86Cavity Resonators, 59

Coupling, 59Design, 59Impedance, 61Modes, 59Tuning, 59

Channel Width, Audio, 110Characteristic Impedance, 11, 60Coaxial Cable, 53

Coaxial Cavity Tuning, 96Coaxial Tuning, 59Delay Line, 60Fields, 54Phase Shifter, 60Stub Support, 60

Coefficient of Reflection, 5Conductivity, 4Convection Currents, 34Cool Air, 34Corona, 112, 114Cosmic and Solar Noise, 112Coupling, 85Critical Frequency, 93, 153Critical Frequency Determination, 153Cross Modulation, 114Current, 12

Conduction, 12Displacement, 12

Cutoff Frequency, 55Cyclonic Movement, 5

dbw, 136dbw to Microwatts, 139

D

223

INDEX

Decibel (db), 15Destructive Interference, 2, 9Detectors, 97

Gated Beam, 98Linear, 161Mixer, 93Phase, 98Ratio, 98Square Law, 163

Dew Point, 34Dew Point Temperature, 38, 39Diathermy Noise, 114, 122Dielectric Constant, 3, 4Diffraction, 7

Four Ray Path, 20Knife -Edge, 20

Diffuse Reflection, 22, 26Dipole Movement, 36Directive Gain, 69Directivity, 69Directivity Pattern, 69Director Elements, 71Discriminators, 97, 98Diurnal Changes, 35Diurnal Noise, 119Diversity Reception, 30, 31

Frequency Diversity, 31Space Diversity, 30, 31

Driven Elements, 71Ducts, 26, 27, 28

Elevated, 27Height, 28Partial Trapping, 28Strong Trapping, 28Surface, 28

E

Earth's Radius, 30Effective Antenna Area, 15, 16Effective Antenna Height, 26Effective Antenna Resistance, 65Effective Radiated Power, 18, 70, 71Electron Paths, 82, 83, 84, 85End Effect, 68End Fed Antenna, 66Endfire Array, 72Equipment Testing and Calibrating, 157Equivalent Noise Resistance, 115Equivalent Reflector Diameter, 75, 76

F

Fade Margin, 45Fading, 25, 45

Average Signal, 28

Fading (Continued)Dirunal Variations, 27Path Difference, 25Period and Amplitude, 30Phase Lag, 9, 25Sub -standard Signal, 28

Fading Types, 28Filters, 59Flange Joint, 64Fog, 36, 37Folded Dipole, 71Fraunhofer Region, 75Frequency, 1Frequency Characteristics, 20Frequency Control, 58, 86Frequency Division Multiplexing, 105Frequency Meter, 161, 162Frequency Multiplication, 91Fresnel, 7, 8Fresnel Region, 75Fresnel Zone Radius, 8Fresnel Zones, 8Front -to -Back Ratio, 70Fundamental Resonant Frequency, 65

Grid Resistance, 115Ground Grid Triode, 95Groundwave, 13Group Velocity, 55Guide Wavelength, 55

G

H

Hail, 37, 38Half wave Dipole, 16, 66, 68Harmonic Response, 59Homogenous Air, 34Hop, 155Horizon, 14, 22, 38Horn, 77, 78, 79Huygens, 7

I -F, 93Ignition Noise, 114, 121Impedance, 49, 60Impedance Matching, 60Impedance Transformer, 61Inductance, 48Induction Heating Interference, 114Inverse Beam Bending, 25Ionosphere, 151Ionosphere Layers, 151, 152, 153Ionospheric Propagation, 151Ionospheric Variations, 153

224

Ionospheric Waves, 20, 151Iso-Frequency Charts, 155Isotropic Antenna, 4, 15, 16, 69Isotropic Radiator, 4

Klystron, 82, 86Klystron AFC, 82, 86

K

L

Lens Antennas, 78, 79Lighthouse Tube, 82Limiters, 98Linear Array, 72Lobe Pattern, 69Lobing, 10Loss Resistance, 67Lowest Usable Frequency (LUF), 154

M

M Gradient, 38, 39Standard, 28, 38Substandard, 38, 39Superstandard, 38, 39Temperature. Relationship, 39

M Inversion, 35M Profile, 28, 38Magnetron, 86, 88Magnetron Stabilizers, 85, 86Maintenance, 91Man -Made Noise Sources, 120, 121Maximum Usable Frequency (MUF), 154,Maxwell, 2Median Field Strength, 128Metallic Insulator, 60Mixers, 93Modes, 54, 55, 56Modulation

Delta, 108Double, 109Index, 88Pulse Amplitude, 106, 107Pulse Clipping, 109Pulse Code, 108Pulse Duration, 107Pulse Position (Phase), 107, 108Pulse Time, 106Triple, 109

ModulatorsAM, 87, 88Armstrong, 88De -emphasis, 88Frequency Deviation, 88FM, 87, 90Grid, 87

Modulators (Continued)Phase, 88Plate, 87Pre -emphasis, 88Reactance Tube, 88Saturable Inductor, 88Single Sideband, 87, 88Tree Carrier, 90VHF, 87

Multipath, 25

N

Neper, 51Nocturnal Changes, 35Noise, 111

Atmospheric, 22, 111, 112Cosmic, 112, 120Impulsive, 111Location, 120Man -Made, 22, 111, 120Mixer, 115, 116, 123Precipitation, 112, 119Random, 111Required Field, 112Resistance, 114, 115Solar, 112, 120Sources, 111, 113Transmission Line, 117Tube, 96, 115

Noise Elimination, 119

156 Natural, 119, 120Suppression, 119, 120

Noise Figure, 116, 122, 123Noise Filters, 120

0Obstacle Gain, 18Obstructed Paths, 126, 127Optical Paths, 126Optimum Fresnel Zone Clearance, 8Optimum Traffic Frequency (FOT), 154Order Wire, 110Oscillation, Local Mixers, 96, 97Oscillators, 81

Microwave, 81, 82, 83, 84, 85Resonant Cavities, 82, 83UHF, 81, 82

P

Parallel Resonance, 58, 66Parasitic Elements, 71Partition Noise, 115Path Predictions, 125

Field Strength, 125, 126Optimum Frequency Range, 126

225

INDEX

Path Predictions (Continued)Reliability, 126System Performance, 126Threshold Level, 126

Paths, 139Beam Path, 38Beyond Radio Horizon, 126, 127Line of Sight, 139Non -optical, 140Obstructed Line of Sight, 139, 140Optical Path, 30

Period of Oscillation, 1Permeability, 4Phase Angle, 51Phase Constant, 12, 52Phase Opposition, 2Phase Relationship, 2Phase Velocity, 56Polar Air Masses, 34Polarization, 3Power Directivity, 17Power Gain, 16, 17Poynting Theorem, 12Pressure, 33, 34Pressurized Lines, 64Probability Law, 115Propagation Constant, 12, 51, 52Pulsating Interference, 2

"Q" Value, 12, 58, 590

R

R -F Amplifier, 94, 95R -F Power Measuring, 163, 164, 165, 166

Continuous Flow Calorimeter, 164Johnson Wattmeter, 165

Radiation Pattern, 10, 11Radiation Resistance, 67Radio -Optical Distance, 129Rain Absorption, 17Rain Drop Size Variations, 36, 37Rate of Rainfall, 36, 37Rayleigh, 36, 37Reactance, 85Received Power, 17Receiver, 93

Direct Detection, 99Superheterodyne, 93

Receiver CharacteristicsAGC, 94, 98Bandwidth, 93, 94Direct Detection, 99Image Ratio, 94

Receiver Characteristics (Continued)Internal Noise, 93, 94Lumped Constant Circuits, 94, 95Pulse Restoration, 99Pulse Shaping, 98Selectivity, 96Sensitivity, 44, 93

Receiver Noise, 22, 23, 93, 122, 123Receiver Tuning, 95, 96

Butterfly, 95, 96Lumped Constant, 94, 95Microwave, 96Parallel Rod, 95Stagger, 97

Reciprocity, 65Reflection, 4, 5, 6Reflection Areas, 8Reflection Coefficient, 5Reflector Elements, 71, 72Reflectors, 69, 71, 74, 75

Corner, 74Cylindrical Parabolic, 73Gratings, 77Parabolic, 74, 75, 76Passive, 75Plane, 74

Refraction, 4, 5, 6Index of, 6, 7, 14, 38k, 14Law of, 6, 7, 13Super-, 26, 27

Refractive Modulus, 35, 38Rejection Stub, 121, 122Relative Humidity, 33, 34Reliability, 44, 45Repeaters, 101, 102

Active, 101Baseband, 101Drop, 102, 110Heterodyne, 101Passive, 101, 103, 104Plane, 103, 104Terminal, 101, 102, 103Through, 101, 102

Reradiation, 65Roller Fading, 28

S

S/N Ratio, 93, 94, 109, 110, 116, 117Sampling, 106, 107Scattering, 17, 22, 36Scintillation, 28Selective Interference, 111, 114, 121, 122Self -capacitance, 48, 49

226

INDEX

Series Resonance, 58Service Units, 103Shielding, 122Shot Effect, 115Signals

Standard, 28Substandard, 28Superstandard, 28

Signal Skipping, 41Signal to External Noise Ratio, 116, 117Siting, 41, 42, 43, 44, 132

Access, 43Air Surveys, 41By Helicopters, 41, 42, 43Contour Maps, 41, 42, 132Field Trips, 41, 42Locations, 41Path Classification, 132, 134Power Supply, 43Profiles, 42, 132, 134

Skip Distance, 155Sky Wave, 13Sleet -Glaze, 38Snell's Law, 6Snow, 37Solar Flares (Sudden Ionospheric Disturbances), 153Space Charge, 115Sporadic E (Es), 22, 152, 155Standard Atmosphere, 33, 34Standard Atmospheric Gradients, 33Standing Wave, 49, 51Storms, 34Stratosphere, 151Subsidence, 35, 39Summary of Fading Causes, 30, 31Sunspot Eruptions, 120Sunspots, 153Superheterodyne, 93

ITemperature, 33Temperature Inversion, 34, 35Terminal Resistance, 67Terminal Station Transmitter, 81Thermal Agitation Noise, 112, 114, 115Thermal Radiation, 112, 114Threshold Level, 44Transmission Characteristics, 35Transmission Lines, 47, 58

Capacitance, 48, 49Characteristic Impedance, 50, 57Closed Circuited, 49Infinite, 49Line Length, 48

Transmission Lines (Continued)Losses, 51, 52Lumped Constants, 48Matching, 51Non -resonant, 49Open Circuited, 49, 50Short Circuited, 49, 50Spacing Methods, 50, 51, 53Terminations, 49, 50

Transmission Line Types, 52, 53, 54Four Wire, 52, 53Shielded Pair, 53Spiral Four, 52, 53Twisted Pair, 52Two Wire, 52

Transmitters, 81Traveling Wave Magnetron, 84Traveling Wave Tube, 82, 84, 85Tropic Air Masses, 34, 35Troposphere, 13, 157Tropospheric Wave, 13Tube Transconductance, 95Tuned Trap, 121, 122Types of Rains, 36

V

VSW Measurements, 161, 163, 164VSW Neon Tube Indicator, 163VSW Ratio, 163Vapor Pressure, 33, 34Velocity Constant, 52Voltage Standing Wave Ratio, 49, 66

wWavefronts, 4Waveguide Attenuation, 55, 57Waveguide Coupling, 59Waveguide Installation, 63, 64Waveguide Junctions, 64Waveguide Reflection Loss, 64Waveguides, 54

Circular, 57, 58Dielectric, 54E Plane, 55H Plane, 55Rectangular, 56, 57

Wavelengths, 2Wavemeters, 157, 158, 161Wave Reinforcement, 2Wave Velocity, 4, 82, 118Weather, 33

Yagi Arrays, 71

227

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