Antennas and Wave Propagation
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Antennas and Wave Propagation By: Harish, A.R.; Sachidananda, M. Oxford University Press © 2007 Oxford University Press ISBN: 978‐0‐19‐568666‐1 Preface Antennas are a key component of all types of wireless communication—be it the television sets in our homes, the FM radios in our automobiles, or the mobile phones which have become an almost integral part of most people’s daily lives. All these devices require an antenna to function. In fact, it was an antenna which led Arno Penzias and Robert Wilson to their Nobel Prize winning discovery of cosmic background radiation. The study of antennas and their field patterns is an important aspect of understanding many applications of wireless transmission technology. Antennas vary widely in their shapes, sizes, and radiation characteristics. Depending on the usage requirements, an antenna can be a single piece of wire, a huge reflective disc, or a complex array of electrical and electronic components. The analysis of antennas is almost invariably concomitant with the study of the basic concepts of the propagation of electromagnetic waves through various propagation media and the discontinuities encoun- tered in the path of propagation. About the Book Evolved from the lecture notes of courses taught by the authors at the Indian Institute of Technology Kanpur over several years, Antennas and Wave Propagation is primarily meant to fulfil the requirements of a single-semester undergraduate course on antennas and propagation theory. It is assumed that the reader has already gone through a basic course on electromagnetics and is familiar with Maxwell’s equations, plane waves, reflection and refraction phenomena, transmission lines, and waveguides. The book provides a lucid overview of electromagnetic theory and a com- prehensive introduction to various types of antennas and their radiation characteristics. Further, a clear-cut presentation of the basic concepts of v vi Preface wave propagation, including ground wave and ionospheric propagation, goes on to make this text a useful and self-contained reference on antennas and radio wave propagation. While a rigorous analysis of an antenna is highly mathematical, often a simplified analysis is sufficient for understanding the basic principles of operation of an antenna. Keeping this fact in mind, this book emphasizes the conceptual understanding of the principles of radiation and wave prop- agation by keeping the mathematical analysis to a minimum. In most cases, the design of an antenna is system specific. Simplified design procedures, rather than a rigorous mathematical analysis, are useful and practical for designing and building antennas for many communication applications. Hence, several simple antenna design procedures have been included, which give an engineering flavour to the book. Content and Structure This book contains eight chapters which provide a comprehensive treatment of antennas and wave propagation. Chapter 1 is essentially a review of basic electromagnetic theory. It also introduces the vector potential approach to the solution of the wave equation and the concept of the Hertzian dipole. In Chapter 2, students are introduced to the terminology used for describ- ing the radiation and input characteristics of antennas. The terms used for characterizing an antenna as a receiver are also clearly explained. The calcu- lation of free space communication link budget is illustrated with examples. The development of antenna theory starts from a study of the radia- tion from an infinitesimal current element. In Chapter 3, the field computa- tion is extended to antennas carrying linear current distributions, e.g., short dipole, half-wave dipole, monopole, and loop antennas. Detailed procedures for the computation of the performance parameters of these antennas are also given. A class of antennas which can be looked at as radiation from an aperture is treated in Chapter 4. Various forms of the field equivalence principle and its applications in the computation of the radiation fields of an aperture are explained. Several aperture type antennas, such as a slot, an open-ended waveguide, horn, reflector, etc., are also discussed. Chapter 5 is devoted to the study of antenna arrays. It starts with the pattern multiplication principle and goes on to explain various pattern prop- erties using a two-element array as an example. Use of polynomial represen- tation of the array factor of a uniformly-spaced linear array and its pole-zero Preface vii representation on a circle diagram is explained. The chapter ends with a dis- cussion on the design of binomial and Chebyshev patterns. A large number of specially designed antennas exist for specific usage requirements. Chapter 6 details a select set of such antennas under the title Special Antennas. These antennas cover a wide range of applications in various frequency bands. Some of the antennas discussed are monopole, V antenna, Yagi–Uda array, turnstile antenna, helix, spiral, microstrip patch, etc. The radiation pattern properties and some simple design procedures are explained. Chapter 7 is focused on the techniques used to measure antenna parame- ters. Indoor and outdoor measurement ranges which provide free-space-like conditions for the antenna are explained. Schematic block diagrams of the measurement instrumentation are presented. Procedures for the measure- ment of the gain, directivity, radiation pattern, etc. are also discussed. Finally, Chapter 8 deals with the issues related to the propagation of radio waves. In this chapter, we study the interaction of the media and the discontinuities with electromagnetic waves. The effect of the earth and the troposphere on the propagation of electromagnetic waves is considered in detail. This is followed by an exposition of the nature of the ionosphere and its effect on sky wave propagation. Each chapter is divided into sections that are independent. A large number of solved problems are interspersed through the text to enable the student to comprehensively grasp concepts and their applications. Suitable figures and diagrams have been provided for easy understanding of the concepts involved. Relevant numerical problems with answers have been included as end-chapter exercises to test the understanding of the topics introduced in each chapter. Seven different appendices provide easy reference to important formulae that are used throughout the book. These are followed by a list of references for those interested in further reading. A special attempt has been made to include topics that are part of curricula of courses offered by a large cross-section of educational institutes. Acknowledgements It is a pleasure to thank our wives Radha and Shalini, and children Bhavana and Bharath for their love, care, and emotional support. We are grateful to them for enduring the countless hours of absence during the prepara- tion of the manuscript. We appreciate the advice and support from friends and colleagues, which helped us in the preparation of the manuscript. We would like to thank IIT Kanpur, and especially the Department of Electrical viii Preface Engineering, IIT Kanpur, for providing a conducive environment for writ- ing the book. We are grateful to the Centre for Development of Technical Education, IIT Kanpur, for the financial support. Prof. R. Nityananda, Centre Director, NCRA, TIFR, Pune, has been kind enough to permit us to use a photograph of the GMRT facility. We would like to thank him for his kind gesture. The editorial team at Oxford University Press India has done a commendable job in bringing out this book. We would like to express our gratitude for the excellent editing, graphics, and design of the book. Teaching the antenna theory course has given us an opportunity to interact with many students, which has helped in improving the presentation of the material. We thank all the students who have interacted with us. Although much care has been taken to ensure an error-free text, some errors may have crept in. Feedback from the readers regarding such errors will be highly appreciated and will go a long way in helping us improve the subsequent editions. A.R. Harish M. Sachidananda Contents Preface Symbols xv CHAPTER 1 Electromagnetic Radiation 1 Introduction 1 1.1 Review of Electromagnetic Theory 4 1.1.1 Vector Potential Approach 9 1.1.2 Solution of the Wave Equation 11 1.1.3 Solution Procedure 18 1.2 Hertzian Dipole 19 Exercises 30 CHAPTER 2 Antenna Characteristics 31 Introduction 31 2.1 Radiation Pattern 32 2.2 Beam Solid Angle, Directivity, and Gain 44 2.3 Input Impedance 49 2.4 Polarization 53 2.4.1 Linear Polarization 54 2.4.2 Circular Polarization 56 2.4.3 Elliptical Polarization 58 2.5 Bandwidth 59 ix x Contents 2.6 Receiving Antenna 60 2.6.1 Reciprocity 60 2.6.2 Equivalence of Radiation and Receive Patterns 66 2.6.3 Equivalence of Impedances 67 2.6.4 Effective Aperture 68 2.6.5 Vector Effective Length 73 2.6.6 Antenna Temperature 80 2.7 Wireless Systems and Friis Transmission Formula 85 Exercises 90 CHAPTER 3 Wire Antennas 94 Introduction 94 3.1 Short Dipole 94 3.1.1 Radiation Resistance and Directivity 103 3.2 Half-wave Dipole 106 3.3 Monopole 115 3.4 Small Loop Antenna 117 Exercises 127 CHAPTER 4 Aperture Antennas 129 Introduction 129 4.1 Magnetic Current and its Fields 130 4.2 Some Theorems and Principles 133 4.2.1 Uniqueness Theorem 134 4.2.2 Field Equivalence Principle 134 4.2.3 Duality Principle 136 4.2.4 Method of Images 137 4.3 Sheet Current Distribution in Free Space 139 4.3.1 Pattern Properties 143 4.3.2 Radiation Pattern as a Fourier Transform