HARE KRISHNA

ANTENNA AND WAVEPROPAGATION

[For B.Tech./B.E. (1st Semester),Rajasthan Technical University, Kota]

Prabhakar SharmaShilpa Sharma

Prabhat Sharma

As per the latest syllabus prescribed byGBTU, MTU (Formerly UPTU)

For B.Tech. Students of• ECE Vth Semester• EI (Elective)

SyllabusANTENNA AND WAVE PROPAGATION

EEC 504

UNIT-I• Antennas BasicsIntroduction, Basic Antenna Parameters, Patterns, Beam Area (or Beam Solid Angle) WA, Radiation Intensity, BeamEfficiency, Directivity D and Gain G, Directivity and Resolution, Antenna Apertures, Effective Height, The radioCommunication link, Fields from Oscillating Dipole, Single-to-Noise Ratio(SNR), Antenna Temperature, Antenna Impedance,Retarded Potential, Far Field due to an alternating current element, Power radiated by a current element, Field variation dueto sinusoidal current distribution.

UNIT-II• Points Sources and Their ArraysIntroduction, Point Source, Power Theorem and its Application to an Isotropic Source, Radiation Intensity, Arrays of TwoIsotropic Point Sources, Non-isotropic but Similar Point Sources and the Principle of Pattern Multiplication, PatternSynthesis by Pattern Multiplication, Linear Arrays of n Isotropic Point Sources of Equal Amplitude and Spacing, LinearBroadside Arrays with Non-uniform Amplitude Distributio. General Considerations.• Electric Dipoles, Thin Liner Antennas and Arrays of Dipoles and AperturesThe Short Electric Dipole, The Fields of a Short Dipole, Radiation Resistane of Short Electric Dipole, Thin Linear Antenna,Radiation Resistance of λ/2 Antenna. Array of Two Driven λ/2 Elements: Broadside Case and End-Fire Case, HorizontalAntennas Above a Plane Ground, Vertical Antennas Above a Plane Ground, Vertical Antennas Above a Plane Ground, Yagi-Uda Antenna Design, Long-Wire Antennas, Folded Dipole Antennas.

UNIT-IIIThe Loop Antenna. Design and its Characteristics Properties, Application of Loop Antenna, Far Field Patterns of CircularLoop Antennas with Uniform Current, Slot Antennas, Horn Antennas, Helical Antennas, The Log-Periodic Antenna, Microstrip Antennas.

UNIT-IV• Reflector AntennasFlat sheet Reflectors, Corner Reflector, The Parabola-General Properties, A comparison Between Parabolic and CornerReflectors, The Paraboloidal Reflector, Patterns of Large Circular Apertures with Uniform Illumination, Reflector Types(summarized), Feed Methods for Parabolic Reflectors,

• Antenna MeasurementsIntroduction, Antenna Measurement ranges, Radiation pattern Measurements, Gain and Directivity Measurements, SpectrumAnalyzer.

UNIT-V• Ground Wave PropagationPlane Earth Reflection, Space Wave and Surface Wave

• Space Wave PropagationIntroduction, Field Strength Relation, Effects of Imperfect Earth, Effects of Curvature of Earth

• Sky Wave PropagationIntroduction, Structural Details of the Ionosphere, Wave Propagation Mechanism, Refraction and Reflection of Sky Waveby Ionosphere, Ray path, Critical frequency, MUF, LUF, OF, Virtual Height and Skip distance Relation Between MUF andthe Skip distance, Multi-hop Propagation, Wave Characteristics.

ANTENNA AND WAVEPROPAGATION

Nandani Prakashan Pvt. Ltd.7/22 1st Floor, Ansari Road, Daryaganj, Delhi-110002.

E-mail: nandaniprakashan@gmail.comPh. 011-43522135, 011-43512467

Prabhakar SharmaB.Tech, M.Tech (CDAC-Mohali)

Assistant ProfesserAnand Engineering College, Agra

Shilpa SharmaB.Tech, M.Tech.

(Banasthali Jaipur)

Prabhat SharmaB.Tech(Hons.) M.Tech (NIT Jaipur)

Assistant ProfessorAnand Engineering College, Agra

ANTENNA AND WAVE PROPAGATIONPrabhakar SharmaShilpa SharmaPrabhat Sharma

Published by:NANDANI PRAKASHAN PVT. LTD.7/22, 1st Floor, Ansari Road, Daryaganj, New Delhi-110002E-mail: nandaniprakashan@gmail.comPhone : 011-43522135, 011-43512467

© Publisher

First Edition : 2011

All rights reserved, No part of this publication may be reproduced, translated ortransmitted (except for review or criticism), without the written permission of thepublishers.

ISBN: 978-93-81126-22-6

Printed at:Durga Offset Printers, Haryana.

Dedicated in the Lotus feet of

My Parents

Er. B. N. SharmaMrs. Sumitra Sharma

&My Loving Son Master Lakshya

This book is a gradual development of our lecture notes on Antenna and wave propagation used for last five plus years orso. Our teaching experience tells us that a text book, which is meant for leading a student, who is trying to understand thesubject for the first time, must clarify all the basic features of the subject in a most lucid and systematic manner. This bookis written with the same central idea, so that students can be benifitted from this book with a greater sense of ease.

Illustrative examples along with the previous year university questions are interspersed throughout the book at theirnatural locations. These have been selected so that apart from illustrating the concepts involved, they help to take the readerto a upper level of applications. For the basics, some appendices are given at the end of book which cover the mathematicalexpressions used in the book.

All comments and criticism regarding this book would be acknowledged by the authors at prabhakar.sh@gmail.com.

Prabhakar SharmaShilpa Sharma

Prabhat Sharma

PREFACE

ACKNOWLEDGMENTS

I am obliged to my parents Er. B.N. Sharma and Mrs. Sumitra Sharma for everything that I have. How can I acknowlege myteachers who made me what I am today, still my great regards will forever be there in their lotus feet.

I wish to express my profound thanks to all those who helped in making this book a reality. I thank to my colleaguesMr. Sumit Tripathi, Mr. R.S. Parmar, Ms. Pooja Japra and Mr. Ravi Singh for extending their cooperation while writing thisbook.

I would like to my sincere thanks to the entire management of SGI, Mr. P.K. Gupta (Chairman) and Mr. Y.K. Gupta(Vice-Chairman) specially. I forward my regards to Dr. B.D Gupta (Director, AEC Agra), Dr. Jai Prakash Aggarwal (VC,GLA University), Rahul Aggrawal (Head, ECE, AEC), Prof. R. Kumar (DG, VGI, Gr. Noida), Dr. Sanjay Sood (Head, R &D Deptt. CDAC Mohali) and to all my colleegues for their support throughout the work.

I am greatly thankful of Mrs Shimsa Verma, Mr Ishwar Mishra and all other staff members of Nandani Prakashan PvtLtd for making this book a great reality.

Thanks to you my students, enjoy learning ‘Antenna and Wave Propagation’.

Prabhakar Sharma

We are Thankful toMr. V.K. Deolia GLA University, MathuraDr. Sanjay Jain HCST, MathuraDr. Himanshu Vijay AEC, AgraDr. Vandana Thakrey AEC, AgraMr. Nagesh Sharma JPS Group, GurgaonMr. Abhay Chaturvedi GLA University, MathuraMr. A.N. Mishra BITS, GhaziabadMr. Ayub Khan AEC, AgraMr. Manoj Garg GL Bajaj, MathuraMr. Ravindra Sharma BSACET, MathuraMr. K.K. Upadhyay IVS, MathuraMr. R. Sharma AEC, AgraMr. R.S. Tomar AEC, AgraMr. Vikas Raina AEC, AgraMr. Kapil Kumawat JNU, JaipurMr. Akhilesh Gupta VIET, Gr. NoidaMr. Manish Sharma AEC, AgraMr. K.K. Singh BMAS, AgraMr. Manish Gupta BMAS, AgraMr. Rishi Sikka Sanjay Institute, MathuraMr. M.K. Agarwal GLA University, MathuraMr. V.K Tomar GLNA, MathuraMr. Chandra Shankar Porwal JSS, NoidaMr. A.S. Katiyar Galgotias UniversityMr. Abhay Gupta VIET, Gr. Noida

Mr. Harish Saraswat VIET, Gr. NoidaMr. R.K. Pachauri RKGIT, GhaziabadMr. Ravi Kumar Fairwealth Security Ltd.Mr. Manish Saraswat ABES, GhaziabadMr. Devendra Gautam Vodafone, GurgaonMrs. Reena Rani BSACET, MathuraAnd all others who taught us, suggested us and helped us directly or indirectly.

Prabhakar SharmaShilpa Sharma

Prabhat Sharma

Acknowledgmentsxii

ABOUT THE AUTHORS

Mr. Prabhakar SharmaReceived his M.Tech. (VLSI Design) from CDAC Mohali, and B.Tech. in ECE from UPTU, Lucknow. At presenthe is working as an Assistant Professor with the department of ECE at Anand Engineering College, Agra. He has theteaching experience of more than six years. In past he has taught at GLA institute of Technology and Management,Mathura and VIT Gr. Noida.

He has published several research papers in national and international conferences and journals. Areas of hisinterest include Microwave Engineering, Antennas and Electromagnetic Fields.

Mrs. Shilpa Sharma

Received her M.Tech. (VLSI Design) from Banasthali University, Banasthali and B.Tech. in ECE from UPTU,Lucknow.She has worked as an Assistant Professor with the department of ECE at VIT, Gr. Noida. She has the teachingexperience of more than five years.

Areas of her interest include Microwave Engineering, Electronics circuits and Electromagnetic Fields.

Mr. Prabhat Sharma

Received his M.Tech. (VLSI Design) from National Institute of Technology, Jaipur and B.Tech. (Hons.) in ECE fromUPTU, Lucknow. At present he is working as an Assistant Professor with the department of ECE at Anand EngineeringCollege, Agra. Previously He was with the Department of Computer Science and Electronics at Banasthali University,Banasthali. He has taught various courses at UG and PG level and published several research papers of national andinternational repute. Areas of his interest include Signal Processing, Digital Design and communication Systems.

The Salient Feature of the book.1. The book is strictly as per the latest syllabus prescribed by the GBTU, MTU (Formerly UPTU).2. Unnecessary text matter, questions and explanations have been avoided in an attempt to make this book precise

and concise. This makes the book student friendly and apt for slef study.3. The text has been presented in simple and easy language and in the form of lecture notes.4. Every topic is followed by large number of illstrative solved examples.5. Previous years university questions are given at the end of each chapter.6. Set of unsolved problems do appear in each chapter, whenever necessary hints and solutions are also given.7. Important formule and tips in the end of each unit helps to memorise the unit quickly.

CONTENTS

1. ANTENNA BASICS 1–62

1.1 Introduction ................................................................................................................................................. 11.2 Classification of Antennas ......................................................................................................................... 21.3 Antenna in Operation ................................................................................................................................ 41.4 Basic antenna parameters ............................................................................................................................. 5

1.4.1 Radiation Patterns ........................................................................................................................ 51.4.2 Beam Area (or Beam Solid Angle) BA ....................................................................................... 61.4.3 Radiation Intensity ..................................................................................................................... 101.4.4 Beam Efficiency .......................................................................................................................... 111.4.5 Directivity (D) and Gain (G) .................................................................................................... 121.4.6 Directivity and Resolution ......................................................................................................... 151.4.7 Antenna Apertures ..................................................................................................................... 161.4.8 Effective Height .......................................................................................................................... 18

1.5 The radio Communication Link ................................................................................................................. 201.6 Fields from oscillating dipole .................................................................................................................... 221.7 Antenna Temperature ................................................................................................................................. 241.8 Signal to Noise ratio (SNR) ...................................................................................................................... 251.9 Antenna Impedance .................................................................................................................................... 261.10 Retarded Potential ...................................................................................................................................... 291.11 Far field due to an alternating current element ........................................................................................ 311.12 Induction (Near) Field and Radiation (Far) Field .................................................................................... 371.13 Power Radiated by a Current Element ..................................................................................................... 381.14 Field Variation due to sinusoidal current distribution ............................................................................. 421.15 Important formulae and Tips .................................................................................................................... 471.16 University Questions ................................................................................................................................. 501.17 Solved Problems ......................................................................................................................................... 51

2. (I) POINT SOURCES AND THEIR ARRAYS 63–131

2.1 Introduction ............................................................................................................................................... 632.2 Classification of Antenna Arrays .............................................................................................................. 652.3 Point Source ................................................................................................................................................ 652.4 A Power Theorem and its Application to an Isotropic Source ............................................................. 662.5 Radiation Intensity ..................................................................................................................................... 662.6 Advantages of Antenna Arrays ................................................................................................................. 672.7 Various Forms of Antenna Arrays ............................................................................................................ 672.8 Arrays of Two Isotropic Point Sources ................................................................................................... 702.9 Non-isotropic but Similar Point Sources and the Principle of Pattern Multiplication ......................... 78

Contentsxvi

2.10 Linear arrays of n-Isotropic Point Sources of Equal Amplitude and Spacing ...................................... 822.10.1 Directivity ................................................................................................................................... 91

2.11 Linear Broadside Arrays with Non-Uniform Amplitude DistributionGeneral Considration .................................................................................................................................. 92

(II) ELECTRIC DIPOLES, THIN LINEAR ANTEENAS AND ARRAYS OF DIPOLES ANDAPERTURES

2.12 The Short Electric Dipole .......................................................................................................................... 942.13 The Fields of a Short Dipole .................................................................................................................... 942.14 Radiation Resistance of short Electric Dipole ....................................................................................... 1002.15 The Thin Linear Antenna ........................................................................................................................ 1022.16 Radiation Resistance of λ/2 Antenna ...................................................................................................... 1042.17 Array to Two driven λ/2 Elements: Broad-Side Case and End-Fire Case .......................................... 1052.18 Horizontal Antennas above a Plane Ground .......................................................................................... 1102.19 Vertical Antennas above a Plane Ground ............................................................................................... 1112.20 Yagi-Uda Antenna Design ........................................................................................................................ 1122.21 Long Wire Antennas ................................................................................................................................. 1142.22 Folded Dipole Antennas .......................................................................................................................... 1192.23 Important Formulae and Tips ................................................................................................................. 1212.24 University Questions ............................................................................................................................... 1222.25 Solved Problems ....................................................................................................................................... 125

3. PRACTICAL ANTENNAS 132–168

3.1 Introduction ............................................................................................................................................... 1323.2 The Loop Antenna ................................................................................................................................. 133

3.2.1 EMF Equation of Loop Antenna ............................................................................................ 1353.2.2 Conclusion ................................................................................................................................. 1373.2.3 As a Direction Finder .............................................................................................................. 1373.2.4 The Loop antenna, in General (Far Field of loop Antenna) ................................................ 1383.2.5 Far Field Pattern of Circular Loop Antennas with Uniform Current .................................. 1413.2.6 Application of Loop Antenna ................................................................................................. 142

3.3 Slot Antenna ........................................................................................................................................... 1443.4 The Log Periodic Antenna ....................................................................................................................... 147

3.4.1 Geometry of Log-periodic Antennas ....................................................................................... 1473.4.2 Operation of Log Periodic Antenna ........................................................................................ 1483.4.3 Impedance ................................................................................................................................. 1483.4.4 Radiation Pattern ...................................................................................................................... 1493.4.5 Design of Log Periodic Antenna ............................................................................................. 149

3.5 Helical Antenna ......................................................................................................................................... 1513.5.1 Radiation Pattern ...................................................................................................................... 1523.5.2 Two Modes of Operation ....................................................................................................... 1523.5.3 Applications .............................................................................................................................. 1533.5.4 Advantages ................................................................................................................................ 153

3.6 Horn Antenna ......................................................................................................................................... 1543.6.1 The Principle of Equality of Path Length (Fermat’s Principle) ........................................... 1563.6.2 Rectangular Horn Antenna ....................................................................................................... 1573.6.3 Directivity ................................................................................................................................. 159

Contents xvii

3.7 Microstrip Antenna (Patch Antenna) .................................................................................................... 1603.7.1 Impedance ................................................................................................................................. 1613.7.2 Patch Directivity ...................................................................................................................... 1623.7.3 Effective Height ........................................................................................................................ 1623.7.4 Limitations (Bandwidth) .......................................................................................................... 162

3.8 Important Formulae and Tips ................................................................................................................. 1633.9 University Questions ............................................................................................................................... 1633.10 Solved Problems ..................................................................................................................................... 166

4. (I) REFLECTOR ANTENNAS 169–210

4.1 Introduction ............................................................................................................................................... 1694.2 Flat Sheet Reflectors ................................................................................................................................ 1704.3 Corner Reflector ....................................................................................................................................... 173

4.3.1 Spacing vs Field Pattern of Corner Reflector ............................................................................ 1744.4 The Parabola–General Properties ............................................................................................................ 1764.5 The Paraboloidal Reflector ....................................................................................................................... 177

4.5.1 Designing of Paraboloid Reflector ........................................................................................... 1794.5.2 Field-distribution Across the Aperture of a Parabolic Reflector .......................................... 180

4.6 Patterns of Large Circular Apertures with Uniform .............................................................................. 1814.7 Comparison of Parabolic Reflectors with Corner .................................................................................. 1834.8 Reflector Types (Summarized) ................................................................................................................ 1834.9 Feed Methods for Parabolic Reflectors .................................................................................................. 186

(II) ANTENNA MEASUREMENTS

4.10 Introduction ............................................................................................................................................... 1874.11 Near-field and Far-field ............................................................................................................................ 1874.12 Measurement Ranges ................................................................................................................................ 1884.13 Differences Between Indoor and Outdoor Ranges ................................................................................. 1914.14 Radiation Pattern Measurements ............................................................................................................. 1924.15 Gain and Directivity Measurements ....................................................................................................... 193

4.15.1 Direct Comparison Method ..................................................................................................... 1944.15.2 Absolute Gain Method ............................................................................................................ 196

4.16 Spectrum Analyzer ................................................................................................................................... 1974.17 Important Formulae and Tips ................................................................................................................. 1994.18 University Questions ............................................................................................................................... 2014.19 Solved Examples ....................................................................................................................................... 202

5. GROUND, SPACE AND SKY WAVE PROPAGATION 211–269

5.1 Introduction ............................................................................................................................................... 2115.1.1 Propagation Characteristics of EM Waves .................................................................................... 2125.1.2 Propagation of Radio Waves ......................................................................................................... 2125.1.3 Factor Influencing the Propagation of Radio Wave ....................................................................... 2135.1.4 Important Terminology About the Wave Propagation .................................................................. 214

5.2 Fundamental Equation for free space propagation .................................................................................... 2165.3 Modes of Propagation ............................................................................................................................... 217

Contentsxviii

5.4 Ground wave or surface wave (30-3000 KHz) ......................................................................................... 2185.4.1 Wave Tilting of the Ground Wave ............................................................................................. 2195.4.2 Field Strength of Ground Wave ................................................................................................. 2205.4.3 Plane Earth Reflection ............................................................................................................... 2205.4.4 Space Wave and Surface Wave ................................................................................................... 224

5.4.4.1 Transition Between Surface and Space Wave ............................................................. 2255.5 Space wave or tropospheric wave propagation ........................................................................................ 225

5.5.1 Introduction ............................................................................................................................... 2255.5.2 Field Strength Due to Space Wave ............................................................................................ 2265.5.3 Nature of Space Wave Communication ..................................................................................... 2265.5.4 Importance of Space Wave Communication .............................................................................. 2275.5.5 Field Strength Relation of Space Wave ...................................................................................... 2285.5.6 Effects of Imperfect Earth ......................................................................................................... 2315.5.7 Effects of Curvature of Earth .................................................................................................... 231

5.6 Sky wave or Ionospheric wave propagation ............................................................................................. 2335.6.1 Structural Details of the Ionosphere ......................................................................................... 2345.6.2 Wave Propagation Mechanism .................................................................................................. 235

5.6.2.1 Refraction in the Absence of Earth’s Magnetic Field ................................................. 2355.6.2.2 Refraction in the Presence of the Earth’s Magnetic Field .......................................... 236

5.6.3 Refraction and Reflection of Sky Waves by Ionosphere ........................................................... 2375.6.4 Mechanism of Radio Wave Bending by the Ionosphere ........................................................... 2405.6.5 Ray Path .................................................................................................................................... 2425.6.6 Critical Frequency ..................................................................................................................... 2435.6.7 Maximum Usable Frequency .................................................................................................... 2445.6.8 Lowest Usable Frequency (LUF) ............................................................................................. 2445.6.9 Optimum Frequency ................................................................................................................. 2445.6.10 Virtual Height ............................................................................................................................ 2455.6.11 Skip Distance ............................................................................................................................ 2455.6.12 Wave Characteristics ................................................................................................................. 2465.6.13 Relation Between MUF and the Skip Distance ........................................................................ 2485.6.14 Multihop Propagation ............................................................................................................... 252

5.7 Important Formulae and Tips ................................................................................................................... 2545.8 University Questions ................................................................................................................................ 2565.9 Solved Problems ........................................................................................................................................ 257

Appendix ..................................................................................................................................................... 270-271Previous Years University Papers ................................................................................................................. 272-277Index ............................................................................................................................................................ 278-280

1. HPBW – Half power beamwidth2. FNBW – First Null Beamwidth3. En – Normalised field pattern4. Emax – Maximum field pattern value5. Ω – Steradian (Solid angle)6. D – Directivity7. ΩA – Beam Area (Beam Solid Angle)8. U – Radiation Intensity9. Pr – Radiated power

10. Pn (θ, φ) – Normalised power pattern11. ε – Efficiency12. Uav – Average radiatio intensity13. U(θ, φ)max– Maximum radiation intensity14. Uiso – Radiation intensity of isotropic

Antenna15. G – Gain16. GP – Power gain17. Gd – Directive gain18. Ae – Antenna aperture19. S – Power density20. εap – Aperture efficiency21. he – Effective height22. hp – Physical height23. Zo – Intrinsic impedance of free space (η)24. Pt – Transmitting power25. TA – Noise temperature26. K – Boltzman’s constant27. SNR – Signal to Noise ratio28. Te – Effective noise temperature29. RA – Antenna resistance30. XA – Antenna reactance31. µ – Permeability of free space32. [ J ] – Retarded current density33. [I] – Retarded current34. Az – Vector potential along Z direction35. B – Magnetic flux density36. H – Magnetic field intensity37. PTR – Total radiated power38. c – Velocity of light/e.m wave39. Rr – Radiation resistance40. Im – Maximum current value

41. β – Phase constant42. P – Poynting vector43. Sav – Average poynting vector44. ψ – Phase difference45. ET – Total electric field value46. HPPD – Half power-point direction47. ρ – Retarded charge density48. φ – Phase difference49. Ao – Capture area50. df – Far-field distance51. AUT – Antenna under test52. HAUT – Height of antenna under test53. Go – Gain with respect to isotropic antenna54. α – Effectiveness ratio55. FSPL – Free space path loss56. LOS – Line of sight57. PTant – Test antenna power density58. Piso – Isotropic antenna power density59. WT – Transmitted power60. AER – Effective aperture of antenna61. GR – Maximum directional gain of receiver62. GT – Transmitter gain63. Gr – Receiver gain64. Eflat – Electric field of flat earth65. σ – Standard deviation66. RH – Reflection coefficient for horizontal

polarization67. RV – Reflection coefficient for vertical po

larization68. fg – Gyro frequency69. B – Earth's magnetic flux density70. ω – Angular velocity71. Em – Maximum amplitude of electric field72. µ – Refractive index73. N – Electron density74. fc – Critical frequency75. fMUF – Maximum usable frequency76. φi – Incident angle77. φr – Reflected angle78. Nm – Maximum electron density.79. e – Charge of an electron80. emf – Electro magnetic field.

NOTATIONS