Small Antenna Design
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Small Antenna Design
by Douglas B. Miron, Ph.D.
AMSTERDAM • BOSTON • HEIDELBERG • LONDON
NEW YORK • OXFORD • PARIS • SAN DIEGO
SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO
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ISBN-13: 978-0-7506-7861-2
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Printed in the United States of America.
I dedicate this work to my mother,
Florence Ethel Coolidge.
She gave me love, liberty, and a backbone.
Contents
Preface.........................................................................................xi
About the Author........................................................................ xiii
What’s on the CD-ROM?.............................................................. xv
Chapter 1: Introduction.................................................................. 1
1.1 What Is Small?...................................................................................................1
1.2 What Are the Problems?....................................................................................2
1.3 Some Historical Small Antenna Types and Applications..................................2
1.4 Some Present and Future Small Antennas.........................................................5
References................................................................................................................8
Chapter 2: Antenna Fundamentals I................................................ 9
2.1 Electromagnetic Waves......................................................................................9
2.1.1 Waves in Space................................................................................11
2.1.2 Waves in Transmission Lines...........................................................14
2.1.3 Power in Waves................................................................................18
2.2 Polarization......................................................................................................20
2.3 The Short Dipole..............................................................................................23
2.3.1 Radiation Pattern.............................................................................24
2.3.2 Circuit Behavior...............................................................................28
2.4 The Small Loop...............................................................................................31
2.4.1 Circuit Behavior...............................................................................32
2.5 Directionality, Efficiency, and Gain.................................................................35
References..............................................................................................................37
Chapter 2 Problems................................................................................................38
Chapter 3: Antenna Fundamentals II............................................. 43
3.1 Bandwidth and Quality Factor, Q....................................................................43
3.2 Impedance Matching and System Efficiency...................................................51
3.2.1 Narrow-Band Matching...................................................................52
3.2.2 Wideband Matching.........................................................................53
3.2.3 System Efficiency............................................................................55
3.3 Reception.........................................................................................................56
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Contents
3.3.1 Effective Height...............................................................................57
3.3.2 Effective Area..................................................................................58
3.3.3 Reception Pattern.............................................................................58
3.4 Ground Effects.................................................................................................59
3.4.1 Image Theory...................................................................................59
3.4.2 Vertical Dipole Above a Perfect Ground Plane................................60
3.4.3 Horizontal Dipole Above a PEC Plane............................................63
3.4.4 Grounded-Source Antennas.............................................................66
3.4.5 Counterpoise....................................................................................67
3.4.6 Summary of Ground Effects............................................................68
3.5 Improvements..................................................................................................68
References..............................................................................................................69
Chapter 3 Problems................................................................................................71
Chapter 4: Introduction to Numerical Modeling of Wire Antennas..... 75
4.1 General Concepts.............................................................................................75
4.2 The Mathematical Basics of the Numerical Electromagnetic
Code (NEC)....................................................................................................77
4.2.1 Basis Functions................................................................................79
4.2.2 Applied Field Models......................................................................88
4.2.3 Solving the Integral Equation..........................................................91
4.3 Using NEC in the Command Window.............................................................92
4.4 Modeling Guidelines........................................................................................99
4.5 NEC in a Graphical User Interface (GUI).....................................................103
4.6 Examples from Chapters 2 and 3...................................................................105
4.6.1 The Short Dipole............................................................................105
4.6.2 Small Loop in Free Space..............................................................106
4.6.3 End-Loaded Short Dipole..............................................................108
References............................................................................................................109
Chapter 4 Problems..............................................................................................110
Chapter 5: Programmed Modeling............................................... 113
5.0 Introduction....................................................................................................113
5.1 Using Wire-List Generators in NEC..............................................................113
5.2 Using Code to Generate a Wire List..............................................................118
Chapter 5 Problems..............................................................................................131
Chapter 6: Open-Ended Antennas............................................... 133
6.0 Introduction....................................................................................................133
6.1 Thick Monopoles...........................................................................................135
6.1.1 Modeling Thick Monopoles...........................................................136
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Contents
6.2 Top Loading...................................................................................................140
6.2.1 The Inverted-L...............................................................................140
6.2.2 Top-Loading with Radials.............................................................146
6.2.3 Volume Loading.............................................................................149
6.3 Coil Loading..................................................................................................152
6.4 Using Resonance............................................................................................165
6.5 Summary........................................................................................................172
References............................................................................................................174
Chapter 6 Problems..............................................................................................175
Chapter 7: Loops and Other Closed-Wire Antennas....................... 179
7.0 Introduction....................................................................................................179
7.1 Thick Loops...................................................................................................180
7.1.1 The Doughnut................................................................................180
7.1.2 The Barrel Loop.............................................................................185
7.2 Solenoid Antennas.........................................................................................194
7.3 The Contrawound Toroidal Helix Antenna (CTHA).....................................198
7.4 The Folded Spherical Helix Monopole..........................................................202
7.5 Final Comments.............................................................................................205
References............................................................................................................206
Chapter 7 Problems..............................................................................................207
Chapter 8: Receiving Antennas.................................................... 211
8.0 Introduction....................................................................................................211
8.1 External Noise................................................................................................212
8.2 The Ferrite Rod Antenna................................................................................213
8.2.1 Antenna Parameters.......................................................................214
8.2.2 Circuit Applications.......................................................................219
8.3 Active Receiving Antennas............................................................................223
8.3.1 The Active Whip............................................................................224
8.3.2 The Active Loop............................................................................225
8.3.3 General Considerations..................................................................225
References............................................................................................................230
Chapter 8 Problems..............................................................................................231
Chapter 9: Measurements.......................................................... 235
9.1 What Are You Measuring?.............................................................................235
9.2 Measurements Through a Transmission Line................................................236
9.2.1 If I Only Have an SWR Meter.......................................................237
9.2.2 Impedance Measured Through a Transmission Line.....................239
9.3 Ranges and Test Enclosures...........................................................................240
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Contents
9.4 The Wheeler Cap and Variations....................................................................242
9.4.1 Series and Parallel Effects.............................................................243
References............................................................................................................246
Chapter 9 Problems..............................................................................................247
Appendix A: The Mathematics of Antenna Orientation.................. 249
A.1 Unit-Vector and Coordinate Variable Relations............................................249
A.2 The Horizontal Dipole..................................................................................251
A.3 The Vertical Loop..........................................................................................252
Appendix A Problems..........................................................................................253
Appendix B: The Parallel-Ray Approximation................................ 255
Appendix B Problems..........................................................................................257
Appendix C: The Small Loop....................................................... 259
Appendix C Problems..........................................................................................262
Appendix D: The Proximity Effect................................................ 263
D.1 Current Distribution......................................................................................263
D.1.1 Problem Formulation and Reduction to a System of
Linear Equations...........................................................................263
D.1.2 Solution for the Current Coefficients............................................267
D.2 Power and Resistance....................................................................................269
References............................................................................................................270
Appendix E: What Every EE Student Should Know About Mathematics
by the Senior Year............................................................ 271
E.1 What Is Mathematics to an Engineer?...........................................................271
E.2 The Process Is as Important as the Result.....................................................271
E.3 Facts and Idioms............................................................................................272
E.3.1 Special Numbers...........................................................................272
E.3.2 Identities and Formulas.................................................................273
E.3.3 Approximations.............................................................................273
E.4 Integrals and Derivatives...............................................................................273
E.5 Radians or Degrees?......................................................................................274
E.6 Matrix Notation and Operations....................................................................274
E.7 Answers for Section E.3................................................................................275
Index........................................................................................ 277
Preface
Miniaturization of electronic systems has accelerated over the last few decades
and this process feeds expectations for even smaller components and systems
in each new generation of equipment. Antennas have not been exempt from this
pressure to be made smaller. Often, the result has been the use of antennas that
are reduced in size without regard to their performance. This has led to needlessly
poor system efficiency and reduced range. In this text we discuss the limitations
on small antenna performance, possible trade-offs, recent developments, detailed
design and optimization.
Antenna performance is fundamentally a function of size measured in wavelengths at the operating frequency. “Electrically small” antennas are those that are
small compared to the wavelength, not necessarily small compared to the people
who use them. The wavelength at the middle of the AM broadcast band is 300 m,
so a tower 30 m tall is called electrically small even though it’s 15 times the
height of a tall man. Small in the antenna business can mean “electrically small,”
“low profile,” or “physically small.” Historical applications have included mine
communications, broadcast transmission and reception, and mobile radio communication for both military and civilian uses. Present and future applications
include the historical ones plus mobile telephones and handheld combinations of
telephones and wireless data links for video and computer mobile networks, and
wireless data networks that include both stationary and mobile elements. Versions
of these networks are being designed and deployed in the obvious area of personal
communications, and areas as diverse as medical monitoring and industrial production. The performance and efficiency (battery life, for example) of any of these
systems depend in a very basic way on each device’s ability to get its signal out
and capture the signals from the other elements in the network. The antenna is the
component that does it.
The intended reader for this book is the design engineer with a B.S.E.E.
­degree. Chapter-end problems have been written so that the book can also be
used in a senior-level elective course. Most people graduating from such a program have an exposure to electromagnetic theory but no experience in RF circuits
or actual antennas. Some mathematics is necessary to understand the concepts
xi
Preface
presented, but few derivations are given. Each topic will begin with a discussion
of the physical principles involved. The simplest possible illustration will be used
first, one with analytic results available if possible. Then more complex and more
practical versions of the topic will be presented. The emphasis is on the intelligent
use of formulas where available and applicable, and numerical modeling. The analytic results for simple structures not only provide useful guidance in themselves,
but they also serve as checks or standards for the numerical modeling process.
The ideal situation is achieved when analysis, numerical simulation, and experimental results all agree, and published results are used whenever possible.
A major concern of this work is to bring small antenna design into the current
computational environment. Familiarity with the Windows operating systems,
C++, and MATLAB® is assumed, but not entirely essential. A reader familiar with
C will not find it difficult to read the program listings in the book. Some historically important data has been converted from graphical form to curve-fit equations
so that the entire design process can be done on the computer. Many original
modeling programs have been written for both traditional and novel antennas and
supporting structures.
Teaching is the third way of learning. First, one learns as a student, then as a
practitioner. To teach, one has to understand even better to pass the art and science on to another. Unlike this Preface, the book is written mostly in the style of
informal lecture and conversation. It is as much a story as a textbook.
xii
About the Author
Doug Miron earned his degrees from Yale and the University of ­Connecticut.
He was educated as a general-purpose EE, later specializing in control ­systems.
He has worked, taught, and published in nearly every area of ­electrical engineering. He began his professional interest in radio frequency systems, ­circuits,
and antennas at Hermes Electronics Ltd, Dartmouth, Nova Scotia, in 1974. He
­continued research on RF circuits and small antennas while teaching at South
­Dakota State University from 1979–1996. Among other activities, he has published several articles and papers on numerical impedance matching, LC and
microstrip circuits, numerical antenna simulation, and also discovered the ­
volume-loaded small dipole.
xiii
What’s on the CD-ROM?
Numerical methods are the main tool used in this book. The main numerical
tool is NEC2, the U.S. Government-developed code for modeling wire antennas.
The folder nec has source code and executables for the current user-modified
version of this code. The root folder also has a public-domain GUI in a .zip file.
In addition, the nec folder has many C++ programs to generate NEC input files
for various antennas and structures. These programs read text files with numbers
describing the geometry and operating conditions for each antenna and structure.
Examples of such text files and other utility programs are also in the nec folder.
MATLAB was used for data analysis in many of the examples in the book.
Utility programs to find the equivalent circuit Q, bandwidth, resistance components, and antenna voltage for a given power input are in the matrf folder. This
folder also contains programs for impedance-matching design, both narrow-band
and wide-band. Also, there are programs for generating data used in some of the
book’s examples, including the NEC basis functions and curve-fitting with these
functions.
xv