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Antennas in Practice

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Antennas in Practice Antennas in Practice EM fundamentals and antenna selection Alan Robert Clark Andr´eP C Fourie Version 1.4, December 23, 2002 ii Titles in this series: Antennas in Practice: EM fundamentals and antenna selection (ISBN 0-620-27619-3) Wireless Technology Overview: Modulation, access methods, standards and systems (ISBN 0-620-27620-7) Wireless Installation Engineering: Link planning, EMC, site planning, lightning and grounding (ISBN 0-620-27621-5) Copyright °c 2001 by Alan Robert Clark and Poynting Innovations (Pty) Ltd. 33 Thora Crescent Wynberg Johannesburg South Africa. www.poynting.co.za Typesetting, graphics and design by Alan Robert Clark. Published by Poynting Innovations (Pty) Ltd. This book is set in 10pt Computer Modern Roman with a 12 pt leading by LATEX 2". All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of Poynting Innovations (Pty) Ltd. Printed in South Africa. ISBN 0-620-27619-3 Contents 1 Electromagnetics 1 1.1 Transmission line theory . 1 1.1.1 Impedance . 3 1.1.2 Characteristic impedance & Velocity of propagation . 3 Two-wire line . 4 One conductor over ground plane . 5 Twisted Pair . 5 Coaxial line . 5 Microstrip Line . 6 Slotline . 6 1.1.3 Impedance transformation . 6 1.1.4 Standing Waves, Impedance Matching and Power Transfer 8 1.2 The Smith Chart . 9 1.3 Field Theory . 10 1.3.1 Frequency and wavelength . 10 1.3.2 Characteristic impedance & Velocity of propagation . 11 1.3.3 EM waves in free space . 12 1.3.4 Reflection from the Earth’s Surface . 14 1.3.5 EM waves in a conductor . 16 2 Antenna Fundamentals 17 2.1 Directivity, Gain and Pattern . 17 2.1.1 Solid angles . 17 2.1.2 Directivity . 18 Isotropic source . 18 Decibels . 19 2.1.3 Efficiency . 19 2.1.4 Radiation pattern . 20 Directivity estimation from beamwidth . 22 2.2 Reciprocity . 22 2.3 Polarization . 23 2.4 Effective aperture . 24 2.5 Free-space link equation and system calulations . 25 3 Matching Techniques 29 3.1 Balun action . 29 3.1.1 Unbalance and its effect . 29 iii iv CONTENTS 3.1.2 Balanced and unbalanced lines—a definition . 30 3.2 Impedance Transformation . 30 3.2.1 Angle Correction . 32 3.3 Common baluns/balun transfomers . 33 3.3.1 Sleeve Balun . 33 3.3.2 Half-wave balun . 33 3.3.3 Transformers . 34 3.3.4 LC Networks . 34 3.3.5 Resistive Networks . 34 3.3.6 Quarter wavelength transformer . 35 3.3.7 Stub matching . 36 3.3.8 Shifting the Feedpoint . 36 3.3.9 Ferrite loading . 38 3.4 Impedance versus Gain Bandwidth . 38 4 Simple Linear Antennas 41 4.1 The Ideal Dipole . 41 4.1.1 Fields . 41 4.1.2 Radiation resistance . 43 4.1.3 Directivity . 43 4.1.4 Concept of current moment . 44 4.2 The Short Dipole . 44 4.2.1 Fields . 45 4.2.2 Radiation resistance . 45 4.2.3 Reactance . 45 4.2.4 Directivity . 46 4.3 The Short Monopole . 47 4.3.1 Input impedance . 47 4.4 The Half Wave Dipole . 48 4.4.1 Radiation pattern . 48 4.4.2 Directivity . 48 4.4.3 Input impedance . 49 4.5 The Folded Dipole . 50 4.6 Dipoles Above a Ground Plane . 52 4.7 Mutual Impedance . 53 5 Arrays and Reflector Antennas 57 5.1 Array Theory . 57 5.1.1 Isotropic arrays . 57 5.1.2 Pattern multiplication . 58 5.1.3 Binomial arrays . 59 5.1.4 Uniform arrays . 60 Beamwidth . 62 Interferometer . 63 5.2 Dipole Arrays . 64 5.2.1 The Franklin array . 65 5.2.2 Series fed collinear array . 65 5.2.3 Collinear folded dipoles on masts . 67 5.3 Yagi-Uda array . 67 5.3.1 Pattern formation and gain considerations . 68 CONTENTS v 5.3.2 Impedance and matching . 69 5.3.3 Design . 69 Element correction . 69 Stacking and Spacing . 70 5.4 Log Periodic Dipole Array . 71 5.4.1 Design procedure . 75 5.4.2 Feeding LPDA’s . 75 5.5 Loop Antennas . 76 5.5.1 The small loop . 76 Radiation pattern . 77 Input impedance . 77 5.6 Helical Antennas . 78 5.6.1 Normal-mode . 78 5.6.2 Axial mode . 80 Original Kraus design . 81 King and Wong design . 81 5.7 Patch antennas . 82 5.8 Phased arrays and Multi-beam “Smart Antennas” . 87 5.9 Flat reflectors . 89 5.10 Corner Reflectors . 91 5.11 Parabolic Reflectors . 91 A Smith Chart 95 vi CONTENTS List of Figures 1.1 A transmission line connects a generator to a load. 1 1.2 2-wire; Coax; ¹strip; waveguide; fibre; RF; 50Hz! . 2 1.3 A “Lumpy” model of the TxLn, discretizing the distributed pa- rameters. 3 1.4 Twisted-Pair geometry . 5 1.5 Impedance values plotted on the Smith Chart . 9 1.6 Electromagnetic Wave in free-space . 13 1.7 Radio Horizon due to earth curvature. 13 1.8 Geometry of Interference between Direct Path and Reflected Waves 14 1.9 Interference pattern field strength contours for h=¸ = 1:44 . 15 2.1 Standard coordinate system. 17 2.2 concept of a solid angle . 18 2.3 Three-dimensional pattern of a 10 director Yagi-Uda array . 21 2.4 xy plane cut of the 10 director Yagi-Uda . 21 2.5 Rectanglar radiation patterns of the 10-director Yagi-Uda in the two principle planes . 22 2.6 Reciprocity concepts . 23 2.7 Polarization possibilities—wave out of page . 23 2.8 Aperture efficiency of a parabolic dish . 25 2.9 Effective aperture of dipole À physical aperture . 25 2.10 Apertures must not overlap! . 25 2.11 Point-to-point link parameters . 26 3.1 The reason for unbalanced currents . 29 3.2 Balanced and Unbalanced Transmission lines . 30 3.3 Power loss in dB versus VSWR on the line. 31 3.4 Increase in Line Loss because of High VSWR . 32 3.5 VSWR at Input to Transmission Line versus VSWR at Antenna 32 3.6 The Bazooka or Sleeve balun. 33 3.7 A HalfWave 4:1 transformer balun. 33 3.8 Transmission-line transformer. 34 3.9 L-Match network. 35 3.10 Quarter wavelength transformer . 35 3.11 Single Matching Stub . 36 3.12 Smith Chart of Single Stub Tuner Arrangement . 37 3.13 T and Gamma Matching Sections . ..
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