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Antennas From Theory to Practice

Comprehensive coverage of the fundamentals and latest developments in antennas and antenna design

In the newly revised Second Edition of Antennas: From Theory to Practice, renowned researcher, engineer, and author Professor Yi Huang delivers comprehensive and timely coverage of issues in modern antenna design and theory. Practical and accessible, the book is written for engineers, researchers, and students who work with radio frequency/microwave engineering, radar, and radio communications.

The book details the basics of transmission lines, radiowaves and propagation, antenna theory, antenna analysis and design using industrial standard design software tools and the theory of characteristic modes, antenna measurement equipment, facilities, and techniques. It also covers the latest developments in special topics, like small and mobile antennas, wide- and multi-band antennas, automotive antennas, RFID, UWB, metamaterials, reconfigurable and MIMO antennas, and more.

The new edition includes up to date information on a wide variety of newly relevant topics and trends, like adaptive impedance matching, the theory of characteristic modes, antenna materials and fabrication processes, and over-the-air (OTA) antenna system measurements. Many questions and examples are provided which enhances the ­learning experience.

The book covers:

  • An introduction to circuit concepts and transmission lines, including lumped and distributed element systems, transmission line theory, and the Smith Chart
  • An exploration of field concepts and radiowaves, including wave equations and solutions and radiowave propagation mechanisms, characteristics, and models
  • Discussions of antenna basics and popular antennas, including wire-type antennas, aperture-type antennas, and antenna arrays
  • Information about antenna manufacturing and measurements, including antenna measurement facilities and methods
  • The use of industrial standard simulation tools for antenna design and analysis

Perfect for engineers and researchers who work in RF engineering or radar and radio communications, Antennas: From Theory to Practice, Second Edition will also earn a place on the bookshelves of university students seeking a concise and practical introduction to the basics of antennas and antenna design.

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Antennas

From Theory to Practice

 

Second Edition

 

Yi Huang

Professor of Wireless EngineeringThe University of Liverpool, UK

This edition first published 2021© 2021 John Wiley & Sons Ltd

Edition HistoryJohn Wiley & Sons, Ltd. (1e 2008)

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, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Yi Huang to be identified as the author of this work has been asserted in accordance with law.

Registered OfficesJohn Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USAJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK

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Wiley also publishes its books in a variety of electronic formats and by print‐on‐demand. Some content that appears in standard print versions of this book may not be available in other formats.

Limit of Liability/Disclaimer of WarrantyIn view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials, or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging‐in‐Publication Data

Names: Huang, Yi, 1964- author.Title: Antennas : from theory to practice / Yi Huang, Professor of Wireless Engineering, The University of Liverpool, UK.Description: Second edition. | Hoboken, NJ, USA : Wiley, 2021. | Includes  bibliographical references and index.Identifiers: LCCN 2021007217 (print) | LCCN 2021007218 (ebook) | ISBN  9781119092322 (cloth) | ISBN 9781119092339 (adobe pdf) | ISBN  9781119092346 (epub)Subjects: LCSH: Antennas (Electronics)Classification: LCC TK7871.6 .H79 2021 (print) | LCC TK7871.6 (ebook) | DDC 621.382/4–dc23LC record available at https://lccn.loc.gov/2021007217LC ebook record available at https://lccn.loc.gov/2021007218

Cover Design: WileyCover Image: © bluebay2014/Getty Images

Preface to the Second Edition

Since the publication of the first edition of this book in 2008, it has attracted a lot of attention from university students, professors, researchers as well as engineers in the industry. The book has been adopted by many universities around the world as a textbook for undergraduate and postgraduate teaching and used as a reference book for antenna research and designs. It was translated to Korean as a major antenna book in 2014. The main attraction and success of the book are its distinct and unique feature from other well‐known antenna books: it has integrated the antenna theory with real‐world examples from the past to the present into one volume without excessive mathematics. This feature has been maintained in this new edition.

Based on the success of the first edition, this edition has provided a better coverage in many important areas and added some recent and latest developments in antenna theory and practice. In particular, the theory of characteristic modes (Section 6.5) for antenna design and analysis, new materials (e.g. composite materials, metamaterials, and meta‐surfaces in Section 7.1), fabrication processes (Section 7.2), and advanced measurement methods for antennas (Section 7.3). MIMO antennas, automotive antennas, and reflector antennas have been added to Special Topics in Chapter 8 to reflect some of the current hot topics. Every chapter has been updated with the latest information. Of course, the mistakes and errors identified in the first edition have also been corrected. As a result, the number of pages is increased significantly from 360 to over 500.

As an essential element of a radio system, the antenna has always been an interesting but difficult subject for radio‐frequency (RF) engineering students and engineers. Many good books on antennas have been published over the years, and some of them were used as our major references.

This book is different from other antenna books. It is especially designed for the people who are relatively new to antennas but would like to learn this subject from the basics to advanced antenna analyses, designs, and measurements within a relatively short period of time. In order to gain a comprehensive understanding of antennas, one must also know transmission lines and radio propagation. At the moment, people often have to read a number of different books, which may not be well correlated. Thus, it is not the most efficient way to study this subject. In this book, we put all the necessary information about antennas into a single manuscript and try to examine the antenna from both the circuit point of view and the field point of view. The book covers the basic transmission line and radio propagation theories, which are then used to gain a good understanding of antenna basics and theory. Various antennas are examined, and design examples are presented. Particular attention is given to modern computer‐aided antenna designs. Both basic and advanced computer software packages are used as examples to illustrate how they can be used for antenna analysis and design. Antenna materials, fabrication processes, measurement theory, and techniques are also addressed. Some special topics on the latest antenna development are covered in the final chapter.

The book material is mainly based on a successful short course on antennas for practicing professionals at the University of Oxford and the Antennas module for the students at the University of Liverpool. The book covers almost all aspects about antennas, especially important and timely issues involving modern practical antenna design and theory. Many examples and questions are given in each chapter. It is an ideal textbook for university antenna course, professional training course, and self‐study. It is also a valuable reference for engineers and researchers who work with RF engineering, radar and radio communications. The organization of this book is as follows:

Chapter 1

: Introduction

. The objective of this chapter is to introduce the concept of antenna and review essential mathematics and electromagnetics, especially Maxwell’s equations. Material properties (permittivity, permeability, and conductivity) are discussed, and some common ones are presented in tables.

Chapter 2

: Circuit Concepts and Transmission Lines

. The concepts of lumped and distributed systems are established. The focus is placed on the fundamentals and characteristics of transmission lines. A comprehensive coverage on Smith chart, bandwidth, and impedance match techniques is provided in this edition. A wide range of conventional and new transmission lines and connectors are introduced and compared.

Chapter 3

: Field Concepts and Radiowaves

. Field concepts, including plane wave, intrinsic impedance, and polarization, are introduced and followed by a discussion on radio propagation mechanisms and radiowave propagation characteristics in various media. Some basic radio propagation models are introduced, and circuit concepts and field concepts are compared at the end of this chapter.

Chapter 4

: Antenna Basics

. The essential and important parameters of an antenna (such as the radiation pattern, gain, and input impedance) are addressed from both the circuit point of view and field point of view. Through this chapter, you will become familiar with antenna language, understand how antennas work, and know what the main design considerations are.

Chapter 5

: Popular Antennas

. In this long chapter, some of the most popular antennas (wire‐type, aperture‐type, and array antennas) are introduced and analyzed using relevant antenna theories. The aim is to see why they have become popular, what their major features and properties are (including advantages and disadvantages), and how they should be designed.

Chapter 6

: Computer‐Aided Antenna Design and Analysis

. The aim of this special and unique chapter is to give a good review of antenna modeling methods and software development, introduce the basic theory behind computer simulation tools, and demonstrate how to use industry standard software to analyze and design antennas. Two software packages (one is simple and free) are presented with step‐by‐step illustrations. The theory of characteristic modes (TCM) is introduced, and a patch antenna is employed as an example to illustrate how to use TCM for antenna design and analysis.

Chapter 7

: Antenna Materials, Fabrication

,

and Measurements

. This is another practical chapter to address three important issues: what materials are suitable for antennas, how to make an antenna, and then how to conduct antenna measurements accurately and efficiently. Some popular measurement equipment and facilities are introduced and discussed. A good overview of antenna measurement systems is provided with real‐world examples. Some latest measurement techniques and problems are also presented and discussed.

Chapter 8

: Special Topics

. This final chapter presents some of the latest important developments in antennas. It covers electrically small antennas, mobile terminal and base‐station antennas, diversity and MIMO antennas, RFID antennas, multiband and broadband antennas, reconfigurable antennas, automotive antennas, and reflector antennas. Relevant theory, design techniques, and practical examples are provided for in‐depth understanding.

On completion of this book, the reader should be ready to conduct advanced antenna design, analysis, and measurements and ready to become an antenna researcher and engineer.

I am very grateful to the many individuals who have provided great contributions, comments, suggestions, and assistance to make this much improved second edition a reality. In particular, I would like to extend my sincere appreciation to:

Dr Kevin Boyle from Qualcomm, who has contributed significantly to the first edition as coauthor and provided many good suggestions, corrections, and references to the second edition. It is a pity that his new job has made it impossible for him to directly contribute to the second edition;

Mr Lars Foged, Scientific Director of MVG, who is a well‐known measurement expert and has contributed to various parts and a section on antenna measurements in

Chapter 7

;

Prof Tony Brown, a leading antenna expert from Manchester University, who has contributed a new section on reflector antennas in

Chapter 8

;

Prof Tae‐Hoon Yoo at Dongyang Mirae University for having translated the book into Korean and provided many great suggestions and feedbacks on how to make the second edition better;

Dr Hanyang Wang, Chief Antenna Expert of Huawei, for inspiring discussions on industrial practices in antenna designs, fabrication, and measurements.

My students: Ahmed Alieldin, Lyuwei Chen, Qian Xu, Sheng Yuan, Chaoyun Song, Jiayou Wang, Shahzad Maqbool, Barry Cheeseman, Yang Lu, and many other current and past students at the University of Liverpool for constructive feedbacks and production of figures;

The individuals and organizations who have provided us with their figures or allowed us to reproduce their figures;

A special one who has kindly provided a list of corrections of the first edition via John Wiley, but I was not given his/her name;

The team at John Wiley who have provided the guidance and great support throughout the process.

Prof Yi Huang

Chair in Wireless Engineering

The University of Liverpool, UK

[email protected]

January 2021

Preface to the First Edition

As an essential element of a radio system, the antenna has always been an interesting but difficult subject for radio‐frequency (RF) engineering students and engineers. Many good books on antennas have been published over the years, and some of them were used as our major references.

This book is different from other antenna books. It is especially designed for people who know little about antennas but would like to learn this subject from the very basics to practical antenna analysis, design, and measurement within a relatively short period of time. In order to gain a comprehensive understanding of antennas, one must know about transmission lines and radio propagation. At the moment, people often have to read a number of different books, which may not be well correlated. Thus, it is not the most efficient way to study the subject. In this book, we put all the necessary information about antennas into a single volume and try to examine antennas from both the circuit point of view and the field point of view. The book covers the basic transmission line and radio propagation theories, which are then used to gain a good understanding of antenna basics and theory. Various antennas are examined and design examples are presented. Particular attention is given to modern computer‐aided antenna design. Both basic and advanced computer software packages are used in examples to illustrate how they can be used for antenna analysis and design. Antenna measurement theory and techniques are also addressed. Some special topics on the latest antenna development are covered in the final chapter.

The material covered in the book is mainly based on a successful short course on antennas for practicing professionals at the University of Oxford and the Antennas module for students at the University of Liverpool. The book covers important and timely issues involving modern practical antenna design and theory. Many examples and questions are given in each chapter. It is an ideal textbook for university antenna courses, professional training courses, and self‐study. It is also a valuable reference for engineers and designers who work with RF engineering, radar and radio communications.

The book is organized as follows:

Chapter 1

: Introduction

. The objective of this chapter is to introduce the concept of antennas and review essential mathematics and electromagnetics, especially Maxwell’s equations. Material properties (permittivity, permeability, and conductivity) are discussed, and some common ones are tabulated.

Chapter 2

: Circuit Concepts and Transmission Lines

. The concepts of lumped and distributed systems are established. The focus is placed on the fundamentals and characteristics of transmission lines. A comparison of various transmission lines and connectors is presented. The Smith Chart, impedance matching, and bandwidth are also addressed in this chapter.

Chapter 3

: Field Concepts and Radio Waves

. Field concepts, including the plane wave, intrinsic impedance, and polarization, are introduced and followed by a discussion on radio propagation mechanisms and radio wave propagation characteristics in various media. Some basic radio propagation models are introduced, and circuit concepts and field concepts are compared at the end of this chapter.

Chapter 4

: Antenna Basics

. The essential and important parameters of an antenna (such as the radiation pattern, gain, and input impedance) are addressed from both the circuit point of view and field point of view. Through this chapter, you will become familiar with antenna language, understand how antennas work, and know what design considerations are.

Chapter 5

: Popular Antennas

. In this long chapter, some of the most popular antennas (wire‐type, aperture‐type, and array antennas) are examined and analyzed using relevant antenna theories. The aim is to see why they have become popular, what their major features and properties are (including advantages and disadvantages), and how they should be designed.

Chapter 6

: Computer‐Aided Antenna Design and Analysis

. The aim of this special and unique chapter is to give a brief review of antenna‐modeling methods and software development, introduce the basic theory behind computer simulation tools, and demonstrate how to use industry standard software to analyze and design antennas. Two software packages (one is simple and free) are presented with step‐by‐step illustrations.

Chapter 7

: Antenna Manufacturing and Measurements

. This is another practical chapter to address two important issues: how to make an antenna and how to conduct antenna measurement, with a focus placed on the measurement. It introduces S‐parameters and equipment. A good overview of the possible measurement systems is provided with an in‐depth example. Some measurement techniques and problems are also presented.

Chapter 8

: Special Topics

. This final chapter presents some of the latest important developments in antennas. It covers mobile antennas and antenna diversity, RFID antennas, multiband and broadband antennas, reconfigurable antennas, and electrically small antennas. Both the theory and practical examples are given.

The authors are indebted to the many individuals who provided useful comments, suggestions, and assistance to make this book a reality. In particular, we would like to thank Shahzad Maqbool, Barry Cheeseman, and Yang Lu at the University of Liverpool for constructive feedback and producing figures, Staff at Wiley for their help and critical review of the book, Lars Foged at SATIMO and Mike Hillbun at Diamond Engineering for their contribution to Chapter 7, and the individuals and organizations who have provided us with their figures or allowed us to reproduce their figures.

Yi Huang and Kevin Boyle

Acronyms and Constants

ε

0

8.85419×10

−12

F/m

μ

0

4

μ

×10

−7

H/m

η

0

377 Ω

h

Planck’s constant =

6.63 × 10

−34

Js

j

2D

Two‐dimensional

3D

Three‐dimensional

2G

Second generation (mobile system)

3G

Third generation (mobile system)

3GPP

The 3rd Generation Partnership Project (for mobile)

4G

Fourth generation (mobile system)

5G

Fifth generation (mobile system)

AC

Alternating current

ACC

Automatic cruise control

ADAS

Advanced driver assistance systems

AF

Antenna factor

AiP

Antenna in package

AM

Amplitude modulation

AMC

Artificial magnetic conductor

AR

Axial ratio

AUT

Antenna under test

BER

Bit error rate

BNC

Baby N connector

BPR

Branch power ratio

CA

Characteristic angle

CAD

Computer aided design

CAM

Computer‐aided manufacturing

CATR

Compact antenna test range

CDF

Cumulative distribution function

CEM

Computational electromagnetics

CFC

Carbon‐fiber composite

CM

Common mode

CNT

Carbon nanotube

CP

Circular polarization

CPU

Central processing unit

CPW

Co‐planar waveguide

CSRR

Complementary split ring resonator

CST

Computer simulation technology (a simulation tool)

CTIA

Cellular Telecommunications Industry Association

DAB

Digital audio broadcasting

dB

Decibel

DC

Direct current

DCS

Digital cellular system

DECT

Digital enhanced cordless telecommunications

DG

Diversity gain

DM

Differential mode

DNG

Double negative (material)

DPS

Double positive (material)

DRA

Dielectric resonant antenna

DUT

Device under test

EBG

Electromagnetic bandgap (material)

ECC

Envelope correlation coefficient

EGC

Equal gain combining

EIRP

Effective isotropic radiated power

EIS

Effective isotropic sensitivity

EM

Electromagnetic

EMC

Electromagnetic compatibility

EMI

Electromagnetic interference

ENG

Epsilon negative (material)

ENZ

Epsilon near zero (material)

EQC

Equivalent current

ERP

Effective radiated power

FCC

Federal Communications Commission

FDTD

Finite‐difference time domain

FEM

Finite element method

FET

Field effect transistor

FM

Frequency modulation

FMCW

Frequency modulated continuous wave

FNBW

First null beamwidth

FoM

Figure of merit

FPC

Flexible printed circuit

FSS

Frequency selective surface

GaAs

Gallium Arsenide

GO

Geometrical optics

GPS

Global positioning system

GSM

Global system for mobile communications

GTD

Geometrical theory of diffraction

HF

High frequency

HFSS

High‐frequency structure simulator (a simulation tool)

HIS

High impedance surface

HPBW

Half‐power beamwidth

HPBW

Half‐power bandwidth

HW

Hansen–Woodyard (condition)

IEEE

Institute of Electrical and Electronics Engineers

IFA

Inverted F antenna

InP

Indium Phosphide

IoT

Internet of Things

ISI

Inter symbol interference

ISM

Industrial, scientific and medical (frequency band)

LCP

Left‐hand circular polarization

LCP

Liquid crystal polymer

LDS

Laser direct structuring

LF

Low frequency

LHM

Left‐handed materials

LNA

Low‐noise amplifier

LPDA

Log‐periodic dipole antenna

LRR

Long‐range radar

LTCC

Low‐temperature co‐fired ceramic

LTE

Long‐term evolution (4G mobile system)

LUF

Lowest usable frequency

MCX

Miniature coaxial (connector)

MEG

Mean effective gain

MF

Medium frequency

MEMS

Microelectromechanical systems

MID

Moulded interconnect devices

MIMO

Multiple input and multiple output

MMIC

Monolithic microwave integrated circuits

mm‐Wave

Millimeter wave

MNG

Mu‐negative

MoM

Method of moments

MRC

Maximal ratio combining

MRR

Medium range radar

MS

Modal significance

MSTL

Mode‐selective transmission line

MVG

Microwave Vision Group

NEC

Numerical electromagnetic code

NFC

Near‐field coupling

NZI

Near‐zero refractive index

OATS

Open area test site

OTA

Over‐the‐air (test/measurement)

PCB

Printed circuit board

PCS

Personal communications system

PDF

Power density function

PDF

Probability density function

PET

Polyethylene terephthalate

PIFA

Planar inverted F antenna

PIM

Passive inter‐modulation

PTD

Physical theory of diffraction

PTFE

Polytetrafluoroethylene

PO

Physical optics

PVC

PolyVinyl Chloride

PWG

Plane wave generator

QZ

Quiet zone

RAM

Radio absorbing material

RC

Reverberation chamber

RCP

Right‐hand circular polarisation

RCS

Radar cross section

RF

Radio frequency

RFID

Radio‐frequency identification

RMS

Root mean square

SAR

Specific absorption rate

SC

Selection combining

SDR

Software defined radio

SI

International system of units (metric system)

SiP

System in package

SISO

Single‐input single‐output

SIW

Substrate integrated waveguide

SLL

Side lobe level

SMA

Sub‐miniature version A (connector)

SNR

Signal‐to‐noise ratio

SoC

System on chip

SRR

Split ring resonator

SRR

Short‐range radar

SSC

Source stirred chamber (or cap or cavity)

SWC

Switch combing

SWR

Standing wave ratio

TCM

Theory of characteristic modes

TDR

Time‐domain reflectometer

TE

Transverse electric (mode/field)

TEM

Transverse electro‐magnetic (mode/field)

THz

Terahertz, 10

12

Hz

TIS

Total isotropic sensitivity

TLM

transmission line modelling/matrix (method)

TM

Transverse magnetic (mode/field)

TMM

Thermoset microwave material

TPMS

Tire pressure monitor system

TRP

Total radiated power

TV

Television

UE

User equipment

UHF

Ultrahigh frequency

UMTS

Universal mobile telecommunications system (3G mobile system)

UTD

Uniform theory of diffraction

UWB

Ultrawide band

VHF

Very high frequency

VNA

Vector network analyzer

VSWR

Voltage standing wave ratio

Wi‐Fi

Wireless fidelity, a WLAN

WLAN

Wireless local area network

About the Author

Prof Yi Huang received BSc in Physics (Wuhan, China) in 1984, MSc (Eng) in Microwave Engineering (Nanjing, China) in 1987, and DPhil in Communications from the University of Oxford, United Kingdom, in 1994. He has been conducting research in the areas of antennas, wireless communications, applied electromagnetics, and radar since 1987. More recently, he is focused on mobile antennas, wireless energy harvesting, and power transfer. His experience includes three years spent with NRIET (China) as a Radar Engineer and various periods with the Universities of Birmingham, Oxford, and Essex in the United Kingdom as a member of research staff. He worked as a Research Fellow at British Telecom Labs in 1994 and then joined the Department of Electrical Engineering & Electronics, the University of Liverpool, United Kingdom, as a Faculty in 1995, where he is now a Chair Professor in Wireless Engineering, the Head of High Frequency Engineering Group.

Dr Huang has published over 400 refereed papers in leading international journals and conference proceedings and authored three books. He has received many patents, research grants from research councils, government agencies, charity, EU, and industry and is a recipient of over 10 awards (e.g. BAE Systems Chairman’s Award 2017 for Innovation for Next Generation GNSS Antenna, Highly Recommended IET Innovation Award 2018, and Best Paper Awards). He has served on a number of national and international technical committees and been an Editor, Associate Editor, or Guest Editor of five international journals. In addition, he has been a keynote/invited speaker and organizer of many conferences and workshops (e.g. IEEE iWAT2010, LAPC2012, and EuCAP2018). He is at present the Editor‐in‐Chief of Wireless Engineering and Technology, Associate Editor of IEEE Antennas and Wireless Propagation Letters, United Kingdom, and Ireland Rep to European Association of Antenna and Propagation (EurAAP), a Fellow of IET and IEEE, and Senior Fellow of HEA.

More information about him can be found from:

https://www.liverpool.ac.uk/electrical‐engineering‐and‐electronics/staff/yi‐huang/

About the Companion Website

Antennas: From Theory to Practice, Second Edition is accompanied by a companion website:

www.wiley.com//legacy/wileychi/huang_antennas2e/

The website includes:

Lecture PowerPoint Slides

Answers to questions

1Introduction

1.1 A Brief History of Antennas

Work on antennas started many years ago. The first well‐known satisfactory antenna experiment was conducted by the German physicist Heinrich Rudolf Hertz (1857–1894), pictured in Figure 1.1. The SI (International Standard) frequency unit, Hertz, is named after him. In 1888, he built a system, as shown in Figure 1.2, to produce and detect radio waves. The original intention of his experiment was to demonstrate the existence of electromagnetic radiation. In the transmitter, a variable voltage source was connected to a dipole (a pair of 1 m wires) with two conducting balls (capacity spheres) at the ends.

Figure 1.1 Heinrich Rudolf Hertz

Figure 1.2 1887 experimental setup of Hertz's apparatus