Fundamentals of Antennas: Concepts and Applications
Christos G. Christodoulou Parveen F. Wahid
Tutorial Tutor ial Texts in Optical Engineering Engineering Volume TT50
Bellingham, Washington USA
Library Library of Congress Congress Cataloging-in-Public Cataloging-in-Publication ation Data Christodoulou, Christodoulou, C. G. (Christos G.) Fundamentals of antennas : concepts and applications / by C.G. Christodoulou and P.F. Wahid p. cm . Includes bibliographical bibliographical references references and index. ISBN 0-8194-4112-0 (pbk.) 1.Antennas 1.Antennas (Electronics). (Electronics). I.Wahid, P. F. (Parveen F.) II. Title.
TK7871.6 .C48 2001 621.384'135–dc21 2001032207 CIP
Published by SPIE—The International International Society for Optical Engineering Engineering P.O. Box 10 Bellingham, Bellingham, Washington Washington 98227-0010 Phone: Phone: 360/676-3 360/676-3290 290 Fax: 360/647-1 360/647-1445 445 Email: Email:
[email protected] [email protected] WWW: www.spie.org
Copyright Copyright © 2001 The Society of Photo-Optical Instrumentation Instrumentation Engineers All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisher.
Printed in the United States of America.
Library Library of Congress Congress Cataloging-in-Public Cataloging-in-Publication ation Data Christodoulou, Christodoulou, C. G. (Christos G.) Fundamentals of antennas : concepts and applications / by C.G. Christodoulou and P.F. Wahid p. cm . Includes bibliographical bibliographical references references and index. ISBN 0-8194-4112-0 (pbk.) 1.Antennas 1.Antennas (Electronics). (Electronics). I.Wahid, P. F. (Parveen F.) II. Title.
TK7871.6 .C48 2001 621.384'135–dc21 2001032207 CIP
Published by SPIE—The International International Society for Optical Engineering Engineering P.O. Box 10 Bellingham, Bellingham, Washington Washington 98227-0010 Phone: Phone: 360/676-3 360/676-3290 290 Fax: 360/647-1 360/647-1445 445 Email: Email:
[email protected] [email protected] WWW: www.spie.org
Copyright Copyright © 2001 The Society of Photo-Optical Instrumentation Instrumentation Engineers All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisher.
Printed in the United States of America.
INTRODUCTION
The field of information science and technology incorporates several devices, incl includ udiing ante antenn nnaas, whic hich can can be used used to tran transm smit it,, coll colleect and and tran transf sfeer info inform rmat atio ion. n. Under Underst stand andin ing g how how these these ante antenn nnas as work work and how how they they can be utilized at different frequencies ranging from radio to terahertz requires some insi insigh ghtt into into the physi physics cs of ante antenn nnaa opera operati tion on and and a knowl knowled edge ge of the basi basicc parameters for their operation. This book, which is tutorial in nature, contains seven chapters. Chapter 1 outlines how antennas have evolved historically, and presents some important advances made in their design and applications. The chapter discusses the impact of antennas in various systems, to give the reader an idea of the range of their applications applications that include include communicati communications, ons, remote remote sensing, sensing, radar, biomedicin biomedicine, e, etc. In Chapter 2 the reader is introduced to the fundamentals of antennas. All of the the figu figures res of meri meritt and param paramet eter erss used used to evalu evaluat atee ante antenna nnass are are covere covered. d. Concepts Concepts such as radiation radiation pattern, directivi directivity, ty, gain, bandwidth, bandwidth, polarization, polarization, and others are explained in a very straightforward manner. The information provided in this chapter chapter forms forms the cornerstone cornerstone upon which which all the other chapters chapters are built. built. Chapter 3 introduces the most basic type of antenna, the wire antenna, and presents the analysis of this antenna for different configurations such as small dipoles, dipoles of finite length, and loop antennas. These antennas are still used today in a variety of applications such as communication, TV broadcasting, and navigation. In Chapter 4, array antennas are discussed. Several antennas can be arranged in space, in different geometrical configurations, to produce a highly directional pattern. Such a configuration of multiple antenna elements is referred to as an ante antenn nnaa arra array. y. In an arra array y ante antenn nna, a, the the fiel fields ds from from the the indi indivi vidu dual al elements can be made to interfere constructively in some directions and cancel in others. Phased array antennas offer the unique capability of scanning of the main beam (major lobe) by changing the phase of the excitation of o f each array element. Chapter 5 exposes the reader to a variety of antennas, such as reflectors, lenses, horns, and microstrip antennas. This chapter adds to the knowledge base provided by the previous chapters by explaining how different applications require different antennas and why a single antenna cannot be used successfully for all applications. Chapter 6 shows how an antenna can be integrated with a detector detector for successful successful operation in order to efficientl efficiently y collect collect terahertz terahertz radiation. These These inte integr grate ated d ante antenn nnas as have have severa severall appli applica cati tions ons in areas areas such such as remo remote te sensing sensing,, radio radio astrono astronomy my,, plasma plasma diagnost diagnostics ics,, atmosphe atmospheric ric studie studies, s, and space space commu communi nicat catio ions. ns. Howe Howeve ver, r, these these appl applic icat atio ions ns demand demand the the use use of lowlow-noi noise se rece receiv iver erss over over a rang rangee of abou aboutt 30 GHz GHz to more ore than than 1 THz. THz. The The seri seriou ouss tech techni nica call chal challe leng nges es on the the desi design gn and and use use of subm submil illi lim meter eter-w -wav avee loca locall oscillators and detectors that exist are presented and discussed in this chapter, which is a fusion between between optics optics and antenna concepts. concepts. ix
x
INTRODUCTION
In Chapter 7, antenna measurement techniques are described. Measurements often form an integral part of the antenna design process, with measurements on prototype antennas being conducted at various steps of the design process to check that the antenna meets the design specification. The key parameters that are often often measur measured ed are the the radiat radiatio ion n patter pattern, n, effici efficienc ency, y, gain, gain, and impeda impedance nce.. Depend Dependin ing g on the the ante antenn nnaa and and its its appl applic icat atio ion, n, othe otherr param paramete eters rs such such as the the polarization purity, power-handling capacity, etc., may also be measured. The use of sophi sophist stic icat ated ed comput computer eriz ized ed equip equipme ment nt has has made made it poss possib ible le to make ake accurate measurements of antenna parameters. The advantages and disadvantages of performing measurements indoors using anechoic chambers versus outdoor ranges are presented and discussed as well. This book is intended for students, engineers, and researchers who have not taken a formal antenna course and are interested in the basics of antenna theory and opera operati tion. on. The The auth author orss have have atte attemp mpte ted d to link link the the lowe lowerr-fre freque quency ncy (RF) (RF) concepts to the higher-frequency (optics) concepts with which the readers may be more familiar. The book is written in a modular fashion, so that readers can choose the chapters they are interested in without having to go through the entire book. It is the hope of the authors that readers find in this book the necessary tools and examples that can help them in incorporating antennas, as needed, in their research problems.
CONTENTS Introduction / ix / ix Chapter 1. History and Applications / 1 / 1 1.1 History and development of antennas / 1 / 1 1.2 Applications and impact on systems / 3 / 3 1.2.1 1.2.1 Antenna Antennass in commu communic nicati ation on systems systems / 4 1.2. 1.2.2 2 Ante Antenna nnass in remot remotee sensi sensing ng / 6 1.2.3 1.2.3 Antenna Antennass for biome biomedic dical al applic applicati ations ons / 7 1.2.4 1.2.4 Radio Radio astrono astronomy my applica applicatio tions ns / 9 1.2. 1.2.5 5 Rada Radarr ante antenn nnas as / 9 References References / 10
Chapter 2. Fundamental Parameters of Antennas / 13 2.1 Radiation pattern / 13 / 13 2.2 Power density / 15 / 15 2.3 Radiation intensity / 16 / 16 2.4 Directivity / 17 / 17 2.5 Gain / 17 / 17 2.6 Input impedance / 17 / 17 2.7 Bandwidth / 18 / 18 2.8 Polarization / 18 / 18 2.9 Friis equation / 19 / 19 References References / 20
Chapter 3. Wire Antennas / 21 3.1 Infinitesimal dipoles / 21 / 21 3.1.1 Directivity / 23 / 23 3.2 Small dipole / 24 / 24 3.3 Dipole of finite length / 25 / 25 3.3.1 Input impedance / 28 / 28 3.4 Effect of infinite conductors on the radiation pattern of linear wire antennas antennas / 29 3.5 Loop antennas / 32 / 32 3.5.1 Small circular loop antennas / 32 / 32 3.5.2 Large circular-loop antennas / 34 / 34 3.6 Radiated fields of a short dipole and a small loop / 34 / 34 References References / 36
vii
Chapter 4. Antenna Arrays / 37 4.1 Array factors / 38 / 38 4.2 Uniform N -element -element linear array / 42 / 42 4.2.1 Broadside array / 44 / 44 4.2.2 End-fire array / 44 / 44 4.3 Planar arrays / 46 / 46 4.4 Circular arrays / 48 / 48 References References / 49
Chapter 5. Types of Antennas / 51 5.1 Reflector antennas / 51 / 51 5.1.1 Plane and corner reflectors / 51 / 51 5.1.2 Parabolic reflector / 51 / 51 5.2 Lens antennas / 54 / 54 5.3 Horn antennas / 56 / 56 5.4 Microstrip antennas / 57 / 57 5.4.1 Analysis of microstrip antennas / 59 / 59 5.4.2 Multiple feeds for circular polarization / 65 / 65 5.4.3 Microstrip arrays / 66 / 66 5.5 Radome coverings / 68 / 68 References References / 68
Chapter 6. Antennas for Infrared Detectors / 71 6.1 Antennas for infrared detectors / 72 / 72 6.2 Design of helical helical antennas for terahertz terahertz applications applications / 74 / 74 6.3 Design of broadband FIR antennas / 76 / 76 References References / 81
Chapter 7. Antenna Measurements / 85 7.1 Radiation pattern measurements / 85 / 85 7.1.1. Outdoor ranges / 85 / 85 7.1.2 Anechoic chambers / 86 / 86 7.2 Gain measurement measurementss / 88 7.2.1 Comparison method / 88 / 88 7.2.2 Two-antenna method / 89 / 89 7.3 Impedance measurements / 90 / 90 References References / 90
Index / 91 / 91
viii
CHAPTER 1 HISTORY AND APPLICATIONS 1.1 History and development of antennas Since 1901, the time of Marconi’s first experiments with transmitting electromagnetic waves, antennas have found several important applications over the entire frequency range, and numerous designs of antennas now exist. Antennas are an integral part of our everyday lives and are used for a multitude of purposes. All antennas operate on the same basic principles of electromagnetic theory formulated by James Clark Maxwell. An antenna is used to either transmit or receive electromagnetic waves, and it serves as a transducer that converts guided waves into free-space waves in the transmitting mode, or vice-versa in the receiving mode. Maxwell put forth his unified theory of electricity and magnetism in 1873 [1] in his famous book A Treatise on Electricity and Magnetism, incorporating all previously known results on electricity and magnetism and expressing these mathematically through what we refer to as Maxwell’s equations, which hold over the entire electromagnetic spectrum. His theory was met with much skepticism, and it was not until 1886 that Heinrich Hertz [2], considered the Father of Radio, was able to validate this theory with his experiments. The first radio system, at a wavelength of 4 m, consisted of a λ /2 dipole (transmitting antenna) and a resonant loop (receiving antenna) [3]. By turning on the induction coil, sparks were induced across the gap and detected at the receiving antenna. Almost a decade later in 1901, Guglielmo Marconi was able to receive signals across the Atlantic in St. Johns, Newfoundland, that were sent from a station he had built in Poldhu, Cornwall, England. Marconi’s transmitting antenna was a fan antenna with 50 vertical wires supported by two 6-m guyed wooden poles. The receiving antenna was a 200-m wire pulled up with a kite [3]. For many years since Marconi’s experiment, antennas operated at low frequencies up to the UHF region and were primarily wire-type antennas. The demands for effective communication systems during World War II moved the field of antennas up into the higher frequencies, and led to the design of many new types of microwave antennas that were capable of producing highly directive beams with small-sized antennas. An excellent reference on the early work done in microwave antennas is the MIT Radiation Laboratory Series book by Silver [4]. Advances in computer architecture and technology moved the field into new directions and produced major advances, with microstrip antennas and arrays, in particular, being heavily investigated during the 1960–80 period for a wide range of applications. In addition, the use of numerical techniques to 1
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analyze complex antenna systems became prevalent, making the issues of reduced computational time and computer memory storage requirements an important part of antenna design. Sophisticated simulation tools are now an integral part of antenna research, and several commercial simulation packages such as IE3D, NEC, XFDTD, FIDELITY, etc. are used extensively, significantly reducing manufacturing costs and time. Research during the latter part of the twentieth century led us into the arena of wireless communications. This posed new and exciting challenges to antenna engineers, with stringent demands being placed on the size and performance of the antennas used for satellite and terrestrial communications. Research was directed toward the design of “smart” or “adaptive” antennas that can perform well in a mobile environment. Various topics related to these antennas can be found in the “Special Issue on Wireless Communications” [5]. More recently, microeletromechanical system (MEMS) devices have emerged as an attractive option for high-frequency systems. MEMS phase shifters, with the advantages of low loss and fast actuation, have been investigated for use in fast- scanning phased arrays [6]. Reconfigurable antennas, where several antennas share the same physical aperture, cover different frequency bands, and perform different functions, have now caught the attention of researchers. Some examples of research done on reconfigurable antennas are given in references [7] and [8]. The applications of antennas range from communications to astronomy, to various deep-space applications. These antennas have been discussed in several books, and some of these have been included in references [9-26]. Elaborate antennas or antenna systems require careful design and a thorough understanding of the radiation mechanism involved. The selection of the type of antenna to be used for a given application is determined by electrical and mechanical constraints and operating costs. The electrical parameters of the antenna are the frequency of operation, gain, polarization, radiation pattern, impedance, etc. The mechanical parameters of importance are the size, weight, reliability, manufacturing process, etc. In addition, the environment under which the antenna is to be used also needs to be taken into consideration; e.g., the effects of temperature, rain, wind vibrations, etc. For example, the 23 antennas on the Space Shuttle orbiter must have a useful life of 100,000 operational hours over a 10-year period or about 100 orbital missions. These antennas are required to operate at temperatures from -150ºF to 350ºF , during re-entry. They also have to withstand a substantial amount of pressure and possible direct lightning strikes. The designer will have to meet all of these constraints, along with the standard antenna problems of polarization, scan rates, frequency agility, etc. Antennas are shielded from the environment through the use of radomes, whose presence is taken into account while designing the antenna. Antennas can be classified broadly into the following categories: wire antennas, reflector antennas, lens antennas, traveling-wave antennas, frequencyindependent antennas, horn antennas, and conformal antennas. In addition,
HISTORY AND APPLICATIONS
3
antennas are very often used in array configurations to improve upon the characteristics of an individual antenna element.
1.2 Applications and impact on systems Antennas enjoy a very large range of applications, both in the military and commercial world. Most well known to the average person are those applications associated with radio, TV, and communication systems. Today, antennas find extensive use in biomedicine, radar, remote sensing, astronomy, collision avoidance, air traffic control, global positioning systems, pagers, wireless LANs, etc., and cover a very wide range of frequencies, as shown in Table 1.1. Table 1.1. Frequency bands and general usage. Band Designation
Frequency Range
Usage
Very Low Frequencies (VLF)
3–30 kHz
Low Frequency (LF)
30-300 kHz
Medium Frequency (MF) High Frequency (HF)
300-3000 kHz
Very High Frequency (VHF)
30-300 MHz
Surveillance, TV broadcasting (54–72 MHz), (76–88 MHz), and (174–216 MHz), FM radio (88–108 MHz), Wind profilers.
Ultrahigh Frequency (UHF)
300-1000 MHz
Cellular communications, surveillance TV (470–890 MHz).
L
1-2 GHz
Long-range surveillance, remote sensing.
S
2-4 GHz
C
4-8 GHz
Weather, traffic control, tracking, hyperthermia. Weather detection, long-range tracking.
X
8-12 GHz
Ku
12-18 GHz
K Ka
18-27 GHz 27-40 GHz
Submillimeter waves
3-30 MHz
Long-distance telegraphy, navigation. Antennas are physically large but electrically small. Propagation is accomplished using earth’s surface and the ionosphere. Vertically polarized waves. Aeronautical navigation services, long distance communications, radio broadcasting. Vertical polarization. Regional broadcasting and communication links. AM radio. Communications, broadcasting, surveillance, CB radio (26.965–27.225 MHz). Ionospheric propagation. Vertical and horizontal propagation.
Satellite communications, missile guidance, mapping. Satellite communications, altimetry, highresolution mapping. Very high resolution mapping. Airport surveillance. Experimental stage.
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1.2.1 Antennas in communication systems Antennas are one of the most critical components in a communication system, since they responsible for the proper transmission and reception of electromagnetic waves. A good design can help relax some of the complex system requirements involved in a communication link and increase overall system performance. The choice of an antenna for a specific application (cellular, satellite-based, ground-based, etc.), depends on the platform to be used (car, ship, building, spacecraft, etc.), the environment (sea, space, land ), the frequency of operation, and the nature of the application (video, audio data, etc.). Communication systems can be broken into several different categories: Direct (line-of-site) links . These are transmission links established between two highly directional antennas. The link can be between two land-based antennas (radio relays); between a tower and a mobile antenna (cellular communication); between a land-based antenna and a satellite antenna (satellite communication); between two satellite antennas (space communication). Usually these links operate at frequencies between 1 GHz and 25 GHz. A typical distance between two points in a high-capacity, digital microwave radio relay system is about 30 miles. Satellite Communications . Antennas on orbiting satellites are used to provide communications between various locations around the earth. They are used either to form a large area-of-coverage beam for broadcasting, or spot beams for point-to-point communications. Also, multibeam antennas are used to link mobile and fixed users who cannot be linked economically via radio, land-based relays [27-29]. In general, most telecommunication satellites are placed in geostationary orbit (GEO), about 22,235 miles above the earth, as shown in Fig. 1.1. There are also some satellites at lower earth orbits (LEOs) that are used for wireless communications. Modern satellites have several receiving and transmitting antennas that can offer services such as video, audio, and data transmission. The impact of antennas on satellite technology continues to grow. For example, very small aperture terminal dishes (VSATs) at Ku band that can transmit any combination of voice, data, and video using satellite networking, have become valuable tools for several small and large companies. Most satellites operate at the L, S, or Ku band, but increasing demand for mobile telephony and high-speed interactive data exchange is pushing the antenna and satellite technology into higher operational frequencies. For example, the ETSVI (a Japanese satellite comparable to NASA’s TDRS), caries five antennas: an S-band phased array, a 0.4-m reflector for 43/38 GHZ for up and down links, an 0.8-m reflector for 26/33 GHz, a 3.5-m reflector for 20 GHz, and a 2.5-m reflector for 30 GHz. In Fig. 1.2, the antennas used on NASA’s Advanced Communications Technology Sattellite (ACTS) are shown. It is anticipated that in the twenty-first century, millions of households worldwide will have access to
HISTORY AND APPLICATIONS
5
dual Ku/Ka-band dishes that provide greater bandwidth availability. These households will be able to enjoy hundreds of TV channels from around the world. Moreover, low-cost access to high-speed, voice, data and video communications will be available to a larger number of customers.
Figure 1.1. A satellite communication system.
Figure 1.2. Antennas on NASA’s ACTS satellite [Courtesy, NASA Langley].
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Personal/Mobile Communication Systems . The vehicular antennas used with mobile satellite communications constitute the weak link of the system. If the antenna has high gain, then tracking of the satellite becomes necessary. If the vehicle antenna has low gain, the capacity of the communication system link is diminished. Moreover, handheld telephone units require ingenious design due to a lack of “real estate” on the portable device. There is more emphasis now on enhancing antenna technologies for wireless communications, especially in cellular communications, which will improve the link performance and reduce the undesirable visual impact of antenna towers. Techniques that utilize “smart” antennas, fixed multiple beams, and neural networks are increasing the capacity of mobile communication systems, whether it is land-based or satellite-based [30]. It is anticipated that in the twenty-first century, the “wire” will no longer dictate where we must go to use the telephone, fax, e-mail, or computer. This will lead to the design of more compact, more sophisticated antennas.
1.2.2 Antennas in remote sensing Remote sensing is the process of obtaining information about a certain object without coming into direct physical contact with it. Antennas such as horns, reflectors, phased arrays, and synthetic apertures are used in remote sensing from an airplane or a satellite to infer the physical properties of planetary
atmosphere and surface, or to take images of objects. For most remote sensing applications, a radiometer (shown in Fig. 1.3) is used to observe a distributed target of large angular extent and warm in temperature [31, 32]. Most antennas associated with radiometers are downwardlooking, with radiation patterns that possess small, close-in sidelobes. Radiometer antennas require a very careful design to achieve high beam efficiency, low antenna losses, low sidelobes, and good polarization properties. The ohmic loss in the antenna is perhaps the most critical parameter, since it can modify the apparent temperature observed by the radiometer system. The degree of resolution of a remote map depends on the ability of the antenna system to separate closely space objects in range and azimuth. To increase the azimuth resolution, a technique called synthetic aperture is employed. As an aircraft flies over a target, the antenna transmits pulses assuming the value of a single radiating element in a long array. Each time a pulse is transmitted, the antenna, due to the aircraft’s motion, is further along the flight path. By storing and adding up the returned signals from many pulses, the single antenna element acts as the equivalent of a very large antenna, hundreds of feet long. This system can produce maps that approach the quality of good aerial photographs; the synthetic aperture antenna becomes a “radio camera” that can yield excellent remote imagery. Figure 1.4 shows the three-day average global brightness temperature for H polarization and V polarization.
HISTORY AND APPLICATIONS
7
Figure 1.3. A radiometer system.
Today, antennas are used for remote sensing applications in both military and civilian sectors. In the 1970s, remote sensing provided NASA with maps of the lunar surface before the Apollo landing. In 1985, British scientists noted the “ozone depletion” over Antarctica. In 1992, Hurricane Andrew, the most costly natural disaster in the history of the United States, was detected on time by very high resolution radar on satellites, which helped keep the casualties low. In 1993, during the flooding of the Mississippi River, antenna images were used to assist in emergency planning and locating the threatened areas. In 1997, NASA used a variety of antennas to receive signals from Mars, allowing the entire world to observe the Pathfinder maneuver itself through the rocky martian terrain.
1.2.3 Antennas for biomedical applications The antenna used in many biological applications operates under very different conditions than do its more traditional free-space, far-field counterparts. Near fields and mutual interaction with the body dominate; also, the antenna radiates in a lossy environment rather than free space. Several antennas, from microstrip antennas to phased arrays, operating at various frequencies, have been developed to couple electromagnetic energy in or out of the body. Most medical applications can be classified into two groups [33]: therapeutic and informational. Examples of therapeutic applications are hyperthermia for cancer therapy, enhancement of bone and wound healing, nerve simulation, neural prosthesis, microwave angioplasty, treatment of prostatic hyperlastia, and cardiac ablation. Examples of informational applications are tumor detection using microwave radiometry, imaging using microwave tomography, measurement of lung water content, and dosimetry.
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(a)
(b)
Figure 1.4. Three-day average global brightness temperature plots: (a) H polarization (b) V polarization [Courtesy NASA/JPL].
Therapeutic applications are further classified as invasive and noninvasive. Both applications require different types of antennas and different restrictions on their design. In the noninvasive applications (i.e., not penetrating the body), antennas are used to generate an electromagnetic field to heat some tissue. Antennas such as helical-coils, ring capacitors, dielectrically loaded waveguides,
HISTORY AND APPLICATIONS
9
and microstrip radiators are attractive because of their compactness. Phased arrays are also used to provide focusing and increase the depth of penetration [34-36]. The designer has to choose the right frequency, antenna size, and spot size that the beam has to cover in the body. The depth of penetration—since the medium of propagation is lossy—is determined by the total power applied or available to the antenna. Invasive applications require some kind of implantation in the tissue. Many single antennas and phased or nonphased arrays have been used extensively for treating certain tumors. A coaxial cable with an extended center conductor is a typical implanted antenna. This type of antenna has also been used in arteries to soften arterial plaque and enlarge the artery. Antennas have also been used to stimulate certain nerves in the human body. As the technology advances in the areas of materials and in the design of more compact antennas, more antenna applications will be found in the areas of biology and medicine.
1.2.4 Radio astronomy applications Another field where antennas have made a significant impact is astronomy. A radio telescope is an antenna system that astronomers use to detect radio frequency (RF) radiation emitted from extraterrestrial sources. Since radio wavelengths are much longer that those in the visible region, radio telescopes make use of very large antennas to obtain the resolution of optical telescopes. Today, the most powerful radio telescope is located in the Plains of San Augustin, near Sorocco, New Mexico. It is made of an array of 27 parabolic antennas, each about 25 m in diameter. Its collecting area is equivalent to a 130m antenna. This antenna is used by more than 500 astronomers to study the Solar System, the Milky Way galaxy, and extraterrestrial systems. Puerto Rico is the site of the world’s largest single-antenna radio telescope. It uses a 300-m spherical reflector consisting of perforated aluminum panels. These panels are used to focus the received radio waves on movable antennas placed about 168 m above the reflector surface. The movable antennas allow the astronomer to track a celestial object in various directions in the sky. Antennas have also been used in constructing a different type of a radio telescope, called a radio interferometer , which consists of two or more separate antennas that are capable of receiving radio waves simultaneously but are connected to one receiver. The radio waves reach the antennas at different times and are used to measure the distance or angular position of an object with a very high degree of accuracy.
1.2.5 Radar antennas Modern airplanes, both civilian and military, have several antennas on board that are used for altimetry, speed measurement, collision avoidance, communications, weather detection, navigation, and a variety of other functions [37-39]. Each function requires a certain type of antenna and makes the operation of a radar system feasible.
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Scientists in 1930 observed that electromagnetic waves emitted by a radio source were reflected back by aircraft (echoes) that could be detected by electronic equipment. In 1937, the first radar system, used in Britain for locating the direction of enemy guns, operated around 20–30 MHz. Since then, several technological developments have emerged in the area of radar antennas, and the desire to operate at different frequencies has led to the development of several very versatile and sophisticated antennas. Radar antennas can be ground-based, mobile, satellite-based, or placed on any aircraft or spacecraft. Today, radar antennas are used for coastal surveillance, air traffic control, weather prediction, surface detection (ground-penetrating radar), mine detection, tracking, air defense, speed detection (traffic radar), burglar alarms, missile guidance, mapping of the surface of the earth, reconnaissance, etc. Radar antennas are generally designed to be part of a very complex system that includes high-power klystrons, traveling wave tubes, solid-state devices, integrated circuits, computers, signal processing, and a myriad of mechanical parts. The requirements vary depending on the application (continuous wave, pulsed radar, Doppler, etc.) and the platform of operation. Advances in high-frequency systems, MEMS devices, and materials research will continue to push the field of antennas into new, unexplored areas and present challenges that will keep antenna design and analysis interesting and exciting.
References 1. J. C. Maxwell, A Treatise on Electricity and Magnetism, London, U.K.: Oxford Univ. Press, 1873; 1904. 2. H. R. Hertz, Electric Waves, London: McMillian, 1893; New York, Dover, 1962. 3. J. D. Kraus, “Antennas since Hertz and Marconi,” IEEE Trans. Antennas and Propagat., vol. AP-33, pp. 131–137, Feb. 1985. 4. S. Silver, Microwave Antenna Theory and Design, MIT Radiation Lab. Series, vol. 12, New York: McGraw-Hill, 1949. 5. Special Issue on Wireless Communications, IEEE Transactions on Antennas and Propagation, vol. 46, no. 6, June 1998. 6. E. Brown, “RF-MEMS switches for reconfigureable integrated circuits,” IEEE Trans. Microwave Theo. Tech., vol. 46, no. 11, pp. 1868, 1998. 7. J. Chiao, Y. Fu, I. M. Chio, M. DeLisio and L. Lin, “MEMS reconfigureable Vee antenna,” IEEE MTT Digest, pp. 1515–1518, 1999. 8. B. Elmaran, I. Chio, L. Chen and J. Chiao, “A beam-steerer using reconfigureable PBG ground plane,” IEEE MTT Digest, pp. 835-838, 2000. 9. S. A. Schelkunoff and H. T. Friis, Antenna Theory and Practice, New York: Wiley , 1952. 10. S. A. Schelkunoff, Advanced Antenna Theory, New York: Wiley, 1952. 11. E. A. Laport, Radio Antenna Engineering , New York: McGraw-Hill, 1952.
HISTORY AND APPLICATIONS
11
12. R. E. Collin and F. J. Zucker, Eds. Antenna Theory, Pts. 1 and 2, New York: McGraw-Hill, 1969. 13. R. S. Elliot, Antenna Theory and Design, New York: Prentice-Hall, 1981. 14. W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, New York: Wiley, 1981. 15. W. Rudge, K. Milne, A. D. Olver and P. Knight, Eds. The Handbook of Antenna Design, vols. 1 and 2, London: Peter Peregrinus, 1982. 16. R. C. Johnson and H. Jasik, Antenna Engineering Handbook , New York: McGraw-Hill, 1961; 1984. 17. K. F. Lee, Principles of Antenna Theory, New York: Wiley, 1984. 18. W. L. Weeks, Antenna Engineering , New York: McGraw-Hill, 1984. 19. R. E. Collin, Antennas and Radiowave Propagation, New York: McGrawHill, 1985. 20. J. R. Wait, Introduction to Antennas and Propagation, Hithin Herts, U.K.: IEE, 1986. 21. L. V. Blake, Antennas, New York: Wiley, 1966. 22. E. Wolff, Antenna Analysis, New York: Wiley, 1966. 23. Y. T. Lo and S. W. Lee, Eds., Antenna Handbook: Theory Applications and Design, New York: Van Nostrand Reinhold, 1988. 24. J. D. Kraus, Antennas, New York: McGraw-Hill, 1950; 1988. 25. F. R. Connor, Antennas, London: Edward Arnold, 1989. 26. C. A. Balanis, Antenna Theory: Analysis and Design, New York: Wiley 1982, 1996. 27. W. L. Pritchard and J. A. Sciulli, Satellite Communications Systems Engineering , New Jersey: Prentice-Hall, 1986. 28. L. H. Van Tress, Ed., Satellite Communication Systems, New York: IEEE Press, 1979. 29. S. D. Dorfman, “Satellite communications in the 21st century,” Strategies Summit, Telecom ’95 (IUT), Geneva, Switzerland, Oct. 10, 1995. 30. Jagoda and M. de Villepin, Mobile Communications, John Wiley and Sons, 1993. 31. G. W. Stimson, Introduction to Airborne Radar , Hughes Aircraft Company, Radar Systems Group, El Segundo, Calif., 1983. 32. C. T. Swift, “Passive microwave remote sensing of the ocean - a review,” Boundary Layer Meteorology, vol. 18, pp. 25–54, 1980. 33. C. H. Durney, “Antennas and other electromagnetic applicators in biology and medicine,” Proc. IEEE, vol. 80, no. 1, Jan. 1992. 34. F. Montecchia, “Microstrip antenna design for hyperthermia treatment of superficial tumors,” IEEE Trans. Biomed. Eng., vol. 30, pp. 580–588, June 1992. 35. J. Chen and O. P. Gandhi, “Numerical simulation of annular phased arrays of dipoles for hyperthermia of deep-seated tumors,” IEEE Trans. on Biomed. Eng., vol. 39, pp. 206–216, March 1992.
12
CHAPTER 1
36. R. L. Magin and A. F. Perterson, “Non-invasive microwave phased arrays for local hyperthermia–a review,” Int. J. Hyperthermia, vol. 5, pp. 429–450, 1989. 37. M. I. Skolnik, Introduction to Radar Systems, New York: McGraw-Hill. 38. F. Nathason, Radar Design Principles, New York: McGraw-Hill, 1969. 39. D. K. Barton, Radar Systems Analysis, Dedham, Mass.: Artech House, 1976.
CHAPTER 2 FUNDAMENTAL PARAMETERS OF ANTENNAS The most basic properties of an antenna are its radiation pattern, gain, impedance, and polarization. These properties are identical for linear passive antennas used either as a transmitter or receiver by virtue of the reciprocity theorem [1]. A complete definition of the terms used for antennas can be found in [2].
2.1 Radiation pattern The radiation pattern is defined in [2] as the spatial distribution of a quantity that characterizes the electromagnetic field generated by an antenna. The field intensity of the propagating wave decreases by 1/ R with distance R from the source. To understand how an antenna radiates, consider a pulse of electric charge moving along a straight conductor. A static electric charge or a charge moving with a uniform velocity does not radiate. However, when charges are accelerated along a conductor and are decelerated upon reflection from its end, radiated fields are produced along the wire and at each end. A detailed explanation of how an antenna radiates is given in [3-5]. The 3D spatial distribution of the radiated energy is displayed as a function of the observer’s position along a constant radius. Power patterns and field patterns are commonly used. The power pattern is a plot of the received power at a constant radius, and the field pattern is the spatial variation (function of and ) of the electric and magnetic fields at a constant radius. The space surrounding an antenna is divided radially into three regions: 1) the near-field (reactive) region, 2) the near-field (radiating) or Fresnel region, and 3) the far-field or Fraunhofer region. These regions are defined as follows [2]: The reactive near field is the portion of the near-field region immediately surrounding the antenna where the reactive field dominates. The radiating nearfield region is the portion of the near field of an antenna between the reactive near-field region and the far-field region, where the angular field distribution is dependent on the distance from the antenna. The far-field region is the region of the field of an antenna where the angular field distribution is essentially independent of the distance from a specified point in the antenna region. If D is the largest dimension of the antenna and is the wavelength, then the reactive near-field region extends to a distance R 0.62 between R 0.62 D 2 / and R < 2 D 2 13
,
D 2 / , the Fresnel region lies
and the Fraunhofer region extends
14
CHAPTER 2
from R 2 D 2
to
infinity. The minimum distance for the far field observations
is 2 D 2 . The radiation pattern of an antenna is commonly described in terms of its principal E-plane and H-plane patterns. For a linearly polarized antenna, the E plane pattern is defined as the plane containing the electric field vector and the direction of maximum radiation, and the H-plane pattern is the plane containing the magnetic field vector and the direction of the maximum radiation. Figure 2.1 shows a rectangular and a polar plot of a radiation pattern. Radiation intensity Major lobe
Minor lobes
HPBW
Sidelobe Back lobe
FNBW
/2
/2
0
(a)
0
0
30
30
-10 dB 60
60
-20 dB -30 dB 90
0
90
120
120
150
150
0
180
(b)
Figure 2.1. (a) Rectangular and (b) polar radiation patterns.
FUNDAMENTAL PARAMETERS OF ANTENNAS
15
Practical antennas are designed to have directional radiation patterns, i.e., they will radiate or receive radiation more effectively in one specified direction than in others. An isotropic radiator, often used as a reference for expressing an antenna’s directional properties, is a hypothetical lossless antenna radiating equally in all directions. An omnidirectional pattern is a special case of a directional pattern where the radiation is nondirectional in the azimuthal plane and directional in the elevation plane, as shown in Fig. 2.2.
Figure 2.2. An omnidirectional pattern.
From the rectangular radiation pattern shown in the Fig. 2.1 we can identify the major lobe in the ! = 0 direction and the minor lobes (sidelobes and back lobes) in the other directions. Some patterns may have more than one major lobe. The major lobe contains the direction of maximum radiation, and between the lobes there are nulls or directions of minimum radiation. Minor lobes levels are expressed relative to the major lobes level. Sidelobe levels of "20 dB or lower are acceptable for many applications. The half-power beamwidth is the width of the main lobe in degrees, at the half-power points. The first null beamwidth is the width of the main lobe between its first nulls. Generally, the beamwidth of an antenna refers to its half-power beamwidth, also known as the 3-dB beamwidth.
2.2 Power density The power density W of an antenna or the time average Poynting vector is given by
16
CHAPTER 2
1
W
Re[ E x H * ] W/m2
2
(2.1)
where and H are peak values in time. A time dependence of e j t has been assumed. The time average power radiated by an antenna is the total power crossing a closed surface in the normal direction, and is given by
Prad
W
W ds
(2.2)
S
For an isotropic radiator, the power density is only in the radial direction and is not a function of ! or # ; i.e.,
W
W0 aˆr W/m2
(2.3)
and the total radiated power is given by
Prad
2
W ds (W0 aˆr ) ( r 2 sin d d aˆr ) S
0 0
4r 2W 0
or W 0
P rad
W/m2
2
4 r
(2.4)
As can be seen, the power density is uniformly distributed over the surface of a sphere of radius r .
2.3 Radiation intensity The radiation intensity U ( !, #) of an antenna is the power radiated per unit solid angle, and is a far-field parameter. U = r 2 W
W/unit solid angle
(2.5)
where W is the radiated power density in W/m2. The total power can be obtained by integrating the radiation intensity over the entire solid angle
Prad U d
2
U sin dd 0 0
W
(2.6)
FUNDAMENTAL PARAMETERS OF ANTENNAS
17
2.4 Directivity The directivity of an antenna is the ratio of the radiation intensity in a given direction to the average radiation intensity, i.e, total radiated power/4 : D 4
U ( )
P rad
(2.7)
If the direction is not specified, the direction of the maximum radiation is implied. The directivity is an indication of the directional properties of the antenna. It does this by comparing the field intensity at any point to that of an isotropic radiator. The directivity is a dimensionless quantity and is usually expressed in decibels.
2.5 Gain The gain of an antenna is defined as the ratio of the radiation intensity in a given direction to the radiation intensity that would be obtained if the power accepted by the antenna were radiated isotropically [2]. The gain can be expressed as G 4
U ( )
P 0
(2.8)
where P 0 is the power input to the antenna. If the direction is not specified, the direction of maximum radiation is implied. The gain is a dimensionless quantity, expressed in decibels. The directivity is based on radiated power, whereas the gain is based on input power. The gain is related to the directivity through
G e D
(2.9)
where e is the antenna efficiency and takes into account losses due to mismatch at the antenna terminals and dielectric and conduction losses. For a perfectly matched lossless antenna, its gain and directivity are equal.
2.6 Input impedance The input impedance of an antenna is the impedance presented by an antenna at its terminals. The antenna impedance Z A can be expressed as Z A = RA + j X A
$
(2.10)
where R A is the antenna resistance in ohms and X A is the antenna reactance in ohms.The radiation resistance is expressed as
18
CHAPTER 2
A
= Rr + RL
$
(2.11)
where Rr is the radiation resistance and R L is the loss resistance. The radiation resistance is associated with the radiation of real power. For a lossless antenna, the input resistance reduces to the radiation resistance. The input impedance is also the ratio of the voltage to the current at its terminals or the ratio of the appropriate electric and magnetic fields at a point. The input impedance can be determined by using equivalent circuit representation for the antenna [4]. The impedance is a function of the geometry of the antenna, the method of excitation, and the frequency. It is generally determined experimentally, although in recent years, numerical electromagnetic techniques have been developed that allow one to determine the impedance accurately for many complex geometries.
2.7 Bandwidth The bandwidth of an antenna is defined as the range of frequencies within which the performance of an antenna conforms to a specific standard [2] with respect to some characteristic. The pattern bandwidth, expressed in terms of beamwidth, sidelobe levels, and pattern characteristics, is used to characterize the radiation pattern variations. The impedance bandwidth relates to the input impedance and radiation efficiency. The bandwidth is expressed as the ratio of the upper to lower frequencies of acceptable operation for broadband antennas. For narrowband antennas, the bandwidth is usually expressed as a percentage of the frequency difference over the center frequency.
2.8 Polarization
The polarization of a wave is the locus of the tip of the electric field vector, , as a function of time. For a linearly polarized wave, the locus is a straight line; it is a circle for a circularly polarized wave and an ellipse for an elliptically polarized wave. The linear and circularly polarized waves are special cases of the elliptically polarized wave. Right-hand polarization and left-hand polarizations refer to the clockwise (CW) and counterclockwise (CCW) movement,
respectively, of the tip of the vector as observed along the direction of propagation. A linearly polarized antenna is one that radiates a linearly polarized wave, and a circularly polarized antenna radiates a circularly polarized wave. Consider a uniform plane wave traveling in the z direction, given by
E E x aˆ x
E y aˆ y
i.e.,
E x 0 cos(t kx x ) aˆ x E y 0 cos( t kz y )aˆ y
(2.12)
FUNDAMENTAL PARAMETERS OF ANTENNAS
19
where E x0 and E y0 are constants, x and y are the phases, and k is the wave number. For linear polarization, = x = y = 0 or , and
E y 0 E x 0
E x
(2.13)
which represents a straight line. The + and – signs correspond to a phase of = 0 and , respectively. For circular polarization, = y " x = /2, and E y 0 E x 0 This gives E x2
E y2
1
(2.14)
1 , which represents a circle.
For the case of elliptical polarization, = " /2 and E y0 E xo. The shape of the path traced by the tip of the electric field vector in this case is an ellipse. These cases are illustrated in Fig. 3.3. The Poincaré sphere can also be used to represent the polarization of the wave radiated by an antenna [3]. Each point on the Poincaré sphere represents a unique polarization.
2.9 Friis equation The Friis equation relates the power received to the power transmitted between two antennas separated by a distance R > 2 D2/, D being the largest dimension of either antenna. For matched alignment along the maximum direction for radiation and reception, the equation is [3] 2
Gr Gt Pt 4R
P r
(2.15)
where P t is the power input at the transmitting antenna, P r is the power received by the receiving antenna, and Gr and Gt are the gains of the receiving and transmitting antennas, respectively.
20
CHAPTER 2
Ey
Ey (0,a) a
(a)
b
Ex (a,0
(a)
Ex
(b)
Ey
Ey
(0,2a)
Ex
(a,0
Ex
Figure 2.3. Polarization of an electromagnetic wave: (a) linear (b) right circular (c) left circular (d) elliptical.
References 1. S. Silver, Microwave Antenna Theory and Design, Radiation Laboratory Series, McGraw-Hill. 2. IEEE Standard Definitions of Terms for Antennas, 1983. 3. J. D. Kraus, Antennas, 2nd Ed., McGraw-Hill. 4. C. Balanis, Antenna Theory - Analysis and Design, 2nd Ed., John Wiley and Sons.
CHAPTER 3 WIRE ANTENNAS The dipole antenna, a linear wire antenna, is the most basic type of a radiator. A center-fed dipole of length l consists of two linear conductors of length l / 2 separated by a small gap. Dipole antennas can be grouped as infinitesimal dipoles, small dipoles, and finite-length dipoles.
3.1 Infinitesimal dipoles A linear wire antenna of length l << (usually at least l < /50) is considered to be an infinitesimal dipole. The radius a is assumed to be << and << l . The current on the antenna, assumed to be constant, can be represented by I ( z ) I 0 aˆ z
(3.1)
For an infinitesimal dipole situated at the origin as shown in Fig. 3.1, the fields at a distance r from the antenna are given in spherical coordinates by [1] z
θ
l/2
y
l/2
Ф
Figure 3.1. An infinitesimal dipole at the origin.
21
22
CHAPTER 3
I l cos 1 jkr Er 0 1 e 2 jkr 2r E
j
E
0
H
j
kI 0l sin 1 1 jkr 4r
jkr e kr 2 1
kI 0l sin
1
4r
H r H
(3.2)
jkr e jkr 1
0
The complex power density is
W
1
1
Re( ExH * ) ( E H *aˆr Er H *aˆ ) 2
2
(3.3)
and the total radiated power in the radial direction is 2 j I 0l Pr W ds 1 (kr )3 3 S
(3.4)
The real radiated power in the radial direction is
I 0l P rad 3
2
(3.5)
The imaginary component of the power in Eq. (3.4) along with the contributions of W from Eq. (3.3) determine the total reactive power of the antenna. The reactive power is dominant for small values of kr . For larger values of kr , the reactive power is negligible, and it is zero for kr . The far fields of the infinitesimal dipole ( kr 1) can be written as
E
j
4r
kI 0le jkr
sin
sin 4r Er E H r H 0 H
kI 0 le jkr
j
(3.6)
WIRE ANTENNAS
23
As can be seen, the far field is transverse or TEM with respect to the radial direction. The wave impedance E / H is equal to the intrinsic impedance of the medium. The radiation resistance of the infinitesimal dipole is obtained by setting
Prad
1 2
2
I 0 Rr
(3.7)
and obtaining 2
2 l 802 l Rr 3
2
(3.8)
3.1.1 Directivity Using the the far field expressions given in Eq. (3.6), the average power density can be written as Wav
1 2
Re( ExH )
1 2
2
E aˆr
2
kI 0l sin 2
2 4
2
r
aˆr
(3.9)
The radiation intensity is U
r 2W av
(3.10)
The maximum radiation intensity occurs in the broadside direction, with a half-power beamwidth of 90 degrees. The infinitesimal dipole has an omnidirectional pattern, as shown in Fig. 3.2. The directivity of an infinitesimal dipole is given by D0
4
U max P rad
3
2
(3.11)
The maximum effective aperture is
2 3 2 Aem D0 4 8
(3.12)
24
CHAPTER 3
Figure 3.2. Radiation pattern of an infinitesimal dipole.
Aem represents the area over which power is extracted from the incident wave and delivered to the load. When multiplied by the power density of the incident wave, it gives the maximum power that can be delivered to the load. In Eq. (3.12) it is assumed that there are no losses, the antenna is matched to the load and polarization matched to the incident wave.
3.2 Small dipole A small dipole is one whose length is /50 < l < /10. The current distribution can be approximated by a triangular representation. For the dipole shown in Fig. 3.3, the current can be represented as
2 I 0 1 l z aˆ z for 0 z l / 2 I e ( x , y , z ) I 1 2 z aˆ 0 l z for l/2 z l /2
(3.13)
where I 0 is a constant and the primed coordinates are points located on the dipole.
WIRE ANTENNAS
25
z P (r, , )
r
l/2
l/2
= x Figure 3.3. Small dipole located at the origin.
The far fields of the small dipole are given by [1,2] E
j
H j
kI 0 le jkr 8r
sin
kI 0le jkr sin
(3.14)
(3.15)
8r H r H E E r 0 The radiation resistance of the small dipole is Rr
2 P rad I 0
2
l 202
2
and is 1/4 that of the infinitesimal dipole. The relative shape of the radiation pattern is the same of that of the infinitesimal dipole, hence the directivity and the effective area of the small dipole are the same as in Eqs. (3.11) and (3.12).
3.3 Dipole of finite length The current distribution on a dipole of finite length can be assumed to be sinusoidal. The radius of the dipole can be assumed to be zero. For a center-fed dipole located at the origin, with the current going to zero at the ends, the current distribution can be represented as
26
CHAPTER 3
l I sin 0 k z a z 2 for 0 z / 2 I e ( x 0, y 0, z ) I sin k l z a z 0 2 for l / 2 z 0
(3.16)
The current distribution along the dipole for different lengths is shown in Fig. 3.4. For a dipole located at the origin along the z -axis, the far fields are given by
kl cos kl cos cos 2 2 I 0 e jkr E j 2r sin kl kl cos cos E I 0 e jkr 2 2 H j 2r sin
(3.17)
The average power density is
Wav
Wav aˆr
1 2
2
E aˆr
kl cos kl cos cos 2 2 I 0 2 2 sin 8 r
2
(3.18)
aˆr
and the radiation intensity is
kl cos kl cos 2 cos 2 I 0 2 2 U r W av 2 sin 8
2
(3.19)
WIRE ANTENNAS
27
Figure 3.5(a) shows the radiation pattern for dipoles of different lengths. For lengths up to l = , the pattern is omnidirectional, with the beamwidth decreasing as the length increases. For lengths l >, sidelobes begin to appear in the pattern. Figure 3.5(b) shows the radiation pattern of a l = 1.5 dipole. The 3-dB beamwidth for the infinitesimal dipole l << is 90 degrees, and for l = , it is 47.8 degrees. For a half-wavelength dipole, l = /2, the equation becomes
cos cos 2 I 0 e jkr E j 2 r sin cos cos 2 I 0 e jkr H j 2 r sin
(3.20)
The radiation resistance of the half-wave dipole is 73 Ω and can be calculated from the far fields. The directivity of the half-wave dipole is 1.643 and its effective area is 0.13 λ 2. Expressions for determining the radiation resistance and the directivity for a dipole of length l can be found in [1].
l/ 2
I 0
Current I e
l= 4 l= 2 l/ 2
l= l = 3 2 l = 2
Figure 3.4. Current distributions along a finite-length dipole.
28
CHAPTER 3
0
l<<
30
30
0
l= /2 l=
10 dB 60
0
60
0
20 dB
30 dB
90
0
90
0
0
120
0
120
150
150 180
0
0
0
Figure 3.5(a). Radiation patterns of dipoles of different lengths.
0 0 dB
10 dB
20 dB
30 dB
90
90
18 0 180
Figure 3.5(b). Radiation pattern of a l = 1.5 dipole.
WIRE ANTENNAS
29
3.3.1 Input impedance The real part of the antenna input impedance, which is the input resistance, reduces to the radiation resistance for the case of a lossless antenna. The radiation resistance can be referred to the maximum current or to the current at the input terminals. We set I in
2
2
Rin
I 0 2
2
Rr
(3.21)
where Rin is the radiation resistance at the input (feed) terminals, R r the radiation resistance at the current maximum, I 0, the current maximum and I in, the current at the input terminals. As can be seen, when the antenna length is a multiple of , l = n; for n = 1, 2, 3…., in is infinite. In practice, Rin has very high values because the current distribution is not purely sinusoidal and due to the effects of the finite radius of the dipole and the spacing at the terminals. For a l = /2 dipole, Rr Rin since the current maximum occurs at the input terminals. The input impedance of a half-wavelength dipole is Z in = 73 + j 42.5. The imaginary part can be reduced or eliminated through matching or by reducing the dipole length. The resonant length of the dipole is generally around l = 0.47 to 0.48 , depending on its radius [2].
3.4 Effect of infinite conductors on the radiation pattern of linear wire antennas The presence of an infinite conductor (ground plane) near a linear antenna affects its radiation characteristics significantly. For antennas near or on infinite perfect conductors, the analysis can be done using image theory; i.e., virtual sources are introduced at the appropriate locations to account for the reflections that occur at the conductor. Consider a vertical infinitesimal dipole placed at a height h above a flat infinite conductor, as shown in Fig. 3.6. The virtual source is located a distance h below the conductor. For this case, the polarity of the image source is the same as that of the actual source, and the reflection coefficient is 1. The fields arriving at the distant point after reflections from the ground appear to originate from the virtual source. The far field can be determined by summing the fields of the actual source and the image source. Referring to Fig. 3.6 and using the far fields of an infinitesimal dipole, we have E
j
kI 0le jkr 4r
sin [2 cos(kh cos )]z 0
30
CHAPTER 3
P1 Direct Reflected Actual source
Direct
P2
Reflected
h
r 1 i2
i1 R 1
r 2 R 2
σ = ∞
h
Virtual source (image)
Figure 3.6. Infinitesimal dipole above a perfect conductor.
E = 0, z < 0
(3.22)
As can be seen in the above equation, the pattern is a product of the field of a single infinitesimal dipole located symmetrically at the origin [Eq. (3.6)] and a term that is a function of the height h above the ground plane and the angle of the observation point. This is the concept of pattern multiplication that is discussed in more detail in the next chapter. The fields below the conductor are zero. Figure 3.7 shows the field patterns for different values of the height h above the conductor. A large number of sidelobes begin to appear in the pattern as h exceeds . A vertical quarter-wave monopole (l = /4) mounted on an infinite conductor appears as an equivalent /2 dipole. The far fields above the conductor will be the same as those of the half-wavelength dipole. The input impedance of the /4 monopole referred to as current maximum is one-half that of the /2 dipole. For the case of the horizontal infinitesimal dipole placed at a height h above an infinite conductor, we have a virtual source of opposite polarity as shown in Fig. 3.8. The far fields can be obtained by summing the fields from the source and its image [1]. In the far field, the direct component can be written as
WIRE ANTENNAS
31
Figure 3.7. Radiation patterns of an infinitesimal dipole above a perfect conductor.
Ed j
kI 0le jkr 1 4r 1
sin
(3.23)
and the reflected component as Er
jRh
kI 0 le
jkr 2
4r 2
sin
(3.24)
Here, Rh, the reflection coefficient, is = −1, cos aˆ y aˆr sin sin sin 1 sin 2 sin 2
and
(3.25)
The total far field, valid only above the ground plane, can be expressed using the approximations r 1 = r – h cos , r 2 = r + h cos for the phase terms, and r 1 = r 2 = r for the amplitude terms, as E
Ed E r j
kI 0 le jkr 4r
1 sin
2
sin [2 j sin(kh cos )] 2
(3.26)
32
CHAPTER 3
P1 Direct Reflected Actual source
Direct
P2
Reflected
h
r 1 2
i1 R 1
h
r 2 R 2
σ = ∞
Virtual source(image)
Figure 3.8. Horizontal infinitesimal dipole above a perfect conductor.
3.5 Loop antennas The loop antenna is another type of basic radiating element and another example of a wire antenna. Loop antennas can have shapes that are circular, square, elliptical, etc. Electrically small loop antennas with a radius that is small compared to its wavelength have radiation patterns that are of the same form as an infinitesimal dipole. These antennas are referred to as infinitesimal magnetic dipoles. Loop antennas that are electrically small have very low radiation resistance and hence are not efficient radiators, and they are usually used as receivers. In many instances, loop antennas with N turns rather than a single turn are used to increase the radiation efficiency.
3.5.1 Small circular loop antennas The single-turn circular loop is one of the simplest forms of the loop antenna. Consider a loop centered at the origin in the xy plane, as shown in Fig. 3.9. The radius a of the loop is small compared to the wavelength, and the radius of the wire is assumed to be negligible. Assuming a constant current distribution on the loop, we have current in the direction I = I 0, where I 0 is a constant.
WIRE ANTENNAS
33
z
θ
r
R θ'=π/2
IΦ
a
I
d Ф
Ф'
dl =a Ф
x
Figure 3.9. Small circular loop at the origin.
The far fields of the small loop are given by [1-3] E H
k 2a 2 I 0e jkr 4r
k 2a 2 I 0 e jkr
4r H r H Er E
sin sin
(3.27)
0
As in the case of the dipole antenna, the near fields are reactive and the far fields are real. The real radiated power is given by Prad
2 (ka)4 I 0 12
The radiation resistance, determined by setting Prad
(3.28)
I 0 2
2
Rr , is given by
34
CHAPTER 3
2 2 2 (k a ) 6
Rr
(3.29)
In terms of the area S of the loop and the circumference C , we have
C Rr 202
4
4
c Rr 20 2 S 2 Rr 31,171 4
(3.30)
The radiation resistance of a single-turn loop is in general larger than its loss resistance, making it a very poor radiator. For an N -turn linear-loop antenna, the radiation resistance is that given in Eq. (3.30) multiplied by a factor N 2. Hence, the radiation resistance can be increased by increasing the number of turns.
3.5.2 Large circular-loop antennas The current in a large-loop antenna can be considered to be uniform for radius a < 0.03 , and it is not necessarily uniform for loops with large radii. Assuming a constant current distribution, the far fields for a large loop are [4] E
ak I 0 e jkr 2r E
H r H 0 H
J1 (ka sin )
akI 0 e jkr 2r
J1 (ka sin )
(3.31)
where J 1(ka sin ) is the Bessel function of the first order. The radiation patterns are shown in Fig. 3.10 for different values of the radius a. The radiation patterns for loops with radius < /2 are similar to those of a linear dipole with length l << . They exhibit a null along = 0 degrees, the axis of the loop. As the radius increases, the field in the plane of the loop ( = 90 degrees ) begins to decrease, and a null appears at = 90 degrees [3].
WIRE ANTENNAS
35
0
a = 0.1 0
30
a = 0.2 a = 0.5
300
10 dB 60
600
-20 dB 30 dB
900
900
1200
120
1500
1500 1800
Figure 3.10. Radiation patterns of a large circular loop.
3.6 Radiated fields of a short dipole and a small loop Equations (3.6) and (3.31) give the far fields for an infinitesimal dipole and a small loop, respectively. The comparison between these fields is given in Table 3.1. For a loop and an electric dipole carrying a current I 0 of the same phase, the fields are in phase quadrature. The small loop can be considered equivalent to an infinitesimal magnetic dipole. A small loop carrying current I 0 placed at the origin in the xy plane can be replaced by an infinitesimal magnetic dipole at the origin oriented in the z direction, carrying a magnetic current I m [2,4]. Table 3.1. Comparison of the fields of a short dipole and a small loop.
Infinitesimal Dipole
Small Dipole
kI0le jkr
k 2a 2I 0e jkr
E j H j
4r
kI0le jkr
sin
sin
4r Er E Hr H 0
H E
4r k 2a 2I 0e jkr
sin
sin
4r Hr H Er E
0
36
CHAPTER 3
References 1. C. Balanis, Antenna Theory Analysis and Design, 2nd Ed. John Wiley and Sons. 2. K. F. Lee, Principles of Antenna Theory, John Wiley and Sons. 3. J. Kraus, Antennas, Second Edition, McGraw-Hill. 4. E. Wolff, Antenna Analysis, John Wiley and Sons.
CHAPTER 4 ANTENNA ARRAYS Several antennas can be arranged in space, in different geometrical configurations, to produce a highly directional pattern [1-5]. Such a configuration of multiple antenna elements is referred to as an antenna array. In an array antenna, the fields from the individual elements interfere constructively in some directions and cancel in others. Usually, arrays consist of identical elements, although it is possible to create an array of dissimilar radiating elements. Arrays offer the unique capability of electronic scanning of the main beam (major lobe) by changing the phase of the excitation current of each array element (phased-array antennas). Also, a large variety of radiation patterns and sidelobe levels can be achieved by controlling the magnitude of the excitation current as well. Phased-array antennas have many applications, such as radar, remote sensing, and communications. There are five main control mechanisms that affect the overall performance of an array antenna; the array geometry (linear, circular, planar, etc., arrangement of the radiating elements), the distance of separation between adjacent elements, the amplitude current excitation of each individual element, phase excitation of each individual element, and the radiation pattern of each individual element Figure 4.1 shows a two-dimensional planar array. The individual element consists of a stacked microstrip antenna as shown in Fig. 4.2. Each microstrip antenna is fed by an external phase shifter through a coaxial connection.
Figure 4.1. An array antenna of 6×9 microstrip elements.
37
38
CHAPTER 4
Figure 4.2. The configuration of a single element used for t he array.
4.1 Array factor Consider an array of two dipoles in free space, as shown in Fig. 4.3 below. Let the dipole at (0, 0, d /2) carry a current I 0 ( / 2) and the one at (0, 0, !d /2) carry a current I0 !( / 2) , where is the phase difference between the two dipoles. This phase difference can be achieved through a variety of phases shifters that employ microwave, semiconductor, or optical techniques. The total electric field at the observation point P is given as the vectorial sum of the fields due to the two individual antennas [1]:
z
P r 1
r
d
y r 2
Figure 4.3. Geometry of two dipoles of length l and separation
d.
ANTENNA ARRAYS
39
Etotal
E 1 E 2
e j ( kr / 2) l 4 r1 jkI o
1
r1 r
d 2
cos
cos 1 aˆ1
and
r2
cos 2 aˆ 2
e j ( kr 2 / 2)
r
r 2 d 2
(4.1)
cos
Hence, Eq. (4.1) becomes
Etotal E1 E 2 aˆ
j kI 0 4 r
l e
jkr
1 cos 2 cos ( kd cos ) 2
(4.2)
A close examination of Eqs. (4.1) and (4.2) shows that the total field is equal to the field of the single element (element factor) located at the origin, multiplied by an array factor (AF) that is given by EAF
1 2 cos (kd cos ) 2
(4.3)
In general, the far-field pattern of any array is given by the multiplication pattern of the field of the single element in the array and the array factor: Total Pattern= Element Factor (EF) × Array Factor (AF)
(4.4)
The array factor is a function of the geometrical arrangement of the radiating elements comprising the array, the current excitation of the elements, the phase shift between the elements, the distance of separation d between the elements and the frequency of operation. Example 4.1:
Find the total pattern of two identical horizontal dipoles shown in Fig. 4.4, with d 4 and 0 . Consider the normalized array factor in Eq. (4.3); i.e., AFn
1 cos (kd cos ) 2
(4.5)
40
CHAPTER 4
z r 1
r d r 2
Figure 4.4. Far-field geometry of two dipoles of length l separated by a distance
In this case,
1 2
( kd cos )
1 2
2
4
d.
cos . Thus, the array factor becomes
cos 4
AFn cos
(4.6)
No null is introduced by the array factor. The only null that occurs is the one due to the element factor (horizontal dipole) at 2 , as shown in Fig. 4.5 below. The total pattern, using the multiplication pattern procedure, is also shown in Fig. 4.5. If 2 then AFn cos 4 (cos 1) , which introduces a null at 0 deg. Figure 4.6 illustrates the principle of pattern multiplication in this case. If 2 , then the nulls would appear at =90 deg and =180 deg.
ANTENNA ARRAYS
41
×
Element pattern
Array factor of 2 sources spaced by 0.25 " . phase delta= 0 deg.
Multiplication pattern of 2 sources spaced by 0.25 " . phase delta=0 deg.
Figure 4.5. Element factor, array factor, and total pattern for a two-element array of infinitesimal horizontal dipoles with d 4 and 0 .
×
Element pattern
Array factor of 2 sources spaced by 0 25 " . phase delta= 0 deg.
Multiplication pattern of 2 sources spaced by 0.25 " . phase delta=0 deg.
Figure 4.6. Element factor, array factor, and total pattern for a two-element array of horizontal dipoles with d 4 and 2 .
42
CHAPTER 4
×
Array factor of 2 sources spaced by 0 25 " . phase delta= 0 deg.
Element pattern
Multiplication pattern of 2 sources spaced by 0.25 " . phase delta=0 deg.
Figure 4.7. Element factor, array factor, and total pattern for a two-element array of horizontal dipoles with d 4 and 2 .
4.2 Uniform
N -element
linear array
Consider an N -element array antenna of isotropic radiators shown in Fig. 4.8, which is a linear array, where each element is fed with a current of the same magnitude but with a progressive phase shift between the elements. The distance of separation between adjacent elements is d . The array factor can be expressed as the sum of the contributions from the elements of the array, i.e., AF 1 e j
e j 2
e j 3
... e j ( N 1)
(4.7)
where, kd cos . Equation (4 7) is a geometric series that can be expressed as
sin
N
AF sin
2
2
(4.8)
ANTENNA ARRAYS
43
r N
r 3
r 2 d r 1 d
Figure 4.8. Geometrical configuration of N isotropic elements along by a distance d and fed with a progressive phase of .
z
separated
Figure 4.9. An 8-element linear microstrip array antenna.
44
CHAPTER 4
From a close examination of the AF in Eq. (4.8), the following points can be made: 1. The principal maximum (major lobe) occurs when the denominator goes to zero, i.e., 0 .
kd cos major 0 or cos major
2d
2. The nulls occur when the numerator goes to zero, i.e., sin( N / 2) 0 or N / 2 n for n =1, 2, 3, … Figure 4.9 depicts a linear array of eight microstrip antennas. The entire antenna is mounted on a ground plane.
4.2.1 Broadside array A broadside array is an array that has its major lobe at # major = 90 deg, that is, in a direction normal to the axis of the array. Therefore, we have $ = kd cos90 + 0 , which gives 0 . Hence, in order to have the main beam at # = 90 deg, the progressive phase shift between the elements should be equal to zero, provided that the spacing d n for n = 1,2,3, …
4.2.2 End-fire array An end-fire array has its major lobe at # major = 0 deg or # major = 180 deg. For # major = 0 deg we set kd cos # + = kd cos 0 + , which indicates that the progressive phase shift should be = !kd . For # major = 180 deg, the condition is = kd . Example 4.2
To demonstrate the method of designing uniform array antennas and to introduce the concept of grating lobes, a 10-element uniform array with 0 is considered for two different values of the spacing d ( d 4 and d ) as shown in Fig. 4.10. Since 0 , a major lobe should appear at
90 deg.
However, when
d , two more maximum lobes appear at 0 deg and 180 deg. These two extra maximum lobes are called grating lobes. These lobes are usually undesired lobes that occur due to some constructive interference of the individual element fields. These grating lobes appear when the distance of separation d is greater than . Thus as a rule of thumb, d should always be less than to avoid any grating lobes.
ANTENNA ARRAYS
45
It should be mentioned here that nonuniform arrays are arrays where the elements are not fed with the same amplitude. Examples of these are the binomial array and Dolph-Tschebyscheff array. In the binomial array, the amplitude of each element is changed to maximize the beamwidth of the major lobe; and in the Dolph-Tschebyscheff array, the major beam to sidelobe ratio is maximized by changing the amplitude excitation to specific values given by formulas found in [1]. 90
10
120
60 8 6
150
30 4 2
180
0
210
330
240
300
270 Array Factor of 10 sources spaced by 0.25 lambda, phase delta= 0 deg
90
10
120
60 8 6
150
30 4 2
180
0
210
330
240
300
270 Array Factor of 10 sources spaced by 1 lambda, p hase delta= 0 deg
Figure 4.10. Array factor patterns for a 10-element, uniform broadside array with 0 .
46
CHAPTER 4
z r
1
1
2
3
2
x Figure 4.11. Planar array geometry.
4.3 Planar arrays Linear arrays can only scan the beam in one direction ( ). To also scan the main beam along the direction as well, two-dimensional arrays are employed. Twodimensional (planar) arrays provide more gain and lower sidelobes than linear arrays. The design principles for planar arrays are the same as those discussed earlier for the linear arrays. The array factor of a planar array can be expressed as the multiplication of the array factors of two linear arrays, one along the x direction and the other along the y direction [1]. The array factor can be written as AF planar
or
AF x AFy
sin( M x / 2) sin( N y / 2) AF M sin( / 2) N sin( / 2) x y
(4.9)
(4.10)
where x kd x sin cos x and y kd y sin cos y . Generally, array antennas are used at RF frequencies, at or below the gigahertz range. Array antennas that include photonic and optical interfaces can also be used at terahertz frequencies. Figure 4.12 shows the setup used for imaging purposes at terahertz frequencies using a 5×5 array of helical antennas. The antennas are approximately 300 m apart. The terahertz antenna structures
ANTENNA ARRAYS
47
terahertz Optics
terahertz source
object being scanned
THz Optics
processing electronics
30fps
LCVD Helical Antenna– Microbolometer Array with Parallel Output
Figure 4.12. Helical array antenna used as a terahertz imager.
were fabricated by using a laser chemical vapor deposition (LCVD) process to form fibers that can be grown into complex three-dimensional structures directly on semiconductor substrates. By focusing the laser through a diffractive optic, arrays of antennas can be fabricated at the same time. Terahertz radiation detection devices can be realized by combining the LCVD antennas with MEMS microbolometers that convert received terahertz radiation into a change in resistance. Arrays of these antenna-bolometer pairs can be fabricated on the same substrate to realize a terahertz-imaging device. Figure 4.13 shows a photograph of a 5-turn rectilinear helical antenna structure wound around a center post [6]. This is the antenna that was used as the
Figure 4.13. Photograph of a rectilinear 3D helical antenna structure designed for approximately 0.5 THz.
48
CHAPTER 4
P
Figure 4.14. Geometry of an
N -element
circular array.
array element in the planar array antenna in Figure 4.12. The spiral diameter was 200 m, the pitch angle is 13 deg, the loop height is 185 m, and the “wire” diameter is 18 m. Assuming that the useful frequency range of operation for the axial antenna mode is derived from the antenna circumference equaling 0.75 to 1.33 , the antenna would have a frequency range of 0.36 to 0.63 THz. The antenna stands approximately 1-mm tall, normal to the substrate surface.
4.4 Circular arrays In a circular-array configuration, the elements are placed in a circular ring. Applications of circular arrays can be found today in the areas of direction finding, GPS, space navigation, radar, sonar, etc. Figure 4.14 shows the geometry of an N -element circular array. The array factor in this case is given by [1]: jka sin cos( ) sin cos( n o o AF(, ) I e n n 1 N
where o and o are the angles of the main beam.
n )
(4.11)
ANTENNA ARRAYS
49
References 1. C. A. Balanis, Antenna Theory: Analysis and Design, New York: John Wiley & Sons, 1997. 2. R. E. Collin, Antennas and Radiowave Propagation, New York: McGrawHill, 1985. 3. J. D. Kraus, Antennas, 2nd ed., New York: McGraw-Hill, 1988. 4. K. F. Sander, G. A. L. Reed, Transmission and Propagation of Electromagnetic Waves, 2nd ed., Cambridge, England: Cambridge University Press, 1986. 5. W. L. Stutzman, G. A. Thiele, Antenna Theory and Design, New York: John Wiley & Sons, 1981. 6. R. N. Dean, Jr., P.C. Nordine and C. G. Christodoulou, “3-D helical THz antennas,” Microwave and Optical Technology Letters, pp. 106-111, Jan. 20, 2000.
CHAPTER 5 T YPES OF ANTENNAS In this chapter, several different types of antennas are discussed. The antennas presented are the reflector antenna, the lens antenna, the horn antenna, and the microstrip antenna. These antennas have distinct characteristics that make them suitable for a variety of applications.
5.1 Reflector antennas Since World War II, when reflector antennas gained prominence due to their use with radar systems, reflector antennas have played an important role in communication systems. Love [1] has published a collection of papers on reflector antennas. Reflector antennas can have a variety of geometrical shapes and require careful design and a full characterization of the field system. Silver [2] presents the technique for their analysis based on aperture theory and physical optics. Other methods such as the geometrical theory of diffraction and the fast Fourier transform, along with various optimization techniques, are used more often for the accurate design of these antennas [3].
5.1.1 Plane and corner reflectors The plane reflector, shown in Fig. 5.1(a), is the simplest type of reflector antenna [4]. The polarization of the feed and its position can be adjusted to obtain the desired radiation properties. The analysis of the system can be done using image theory. The corner reflector has been investigated by Kraus [4], and the 90-deg corner reflector is found to be the most effective. The feeds for the corner reflector are generally dipoles, which are placed parallel to the vertex. These antennas can be analyzed in a rather straightforward manner using the method of images. In Fig. 5.1(b), the antenna 1, which is the feed, is shown along with three images. For corner reflectors with infinite sides, the gain increases as the angle increases. 5.1.2 Parabolic reflector Among curved reflectors, the paraboloid is the most commonly used. The paraboloidal reflector is formed by rotating a parabolic reflector about its axis. The reflector transforms a spherical wave radiated from an antenna at its focus into a plane wave. The fields across the plane AA shown in Fig. 5.2 will be in phase. If the amplitudes are also constant, then the result is an antenna with a large aperture possessing a high gain. The plane BB where the reflector ends is 51
52
CHAPTER 5
the aperture plane. The use of directional antennas as the feed antenna helps to eliminate any significant direct radiation from the source. To avoid the blockage caused by the feed placed at the focal point, i.e. for a front-end arrangement, the feed is sometimes offset from the axis as shown in Fig. 5.3. A higher efficiency can be realized by modifying the reflector surfaces [5,6].
Figure 5.1. (a) Plane reflector; (b) Corner reflector.
B' A' Q
P
S
F
Axis
A B
Aperture plane
Figure 5.2 Parabolic reflector.
TYPES OF ANTENNAS
53
Figure 5.3. Parabolic reflector with an off-set feed.
Other types of reflectors used are the Cassegrain and the Gregorian reflectors. The Cassegrain reflector is a dual-reflector system that uses a parabola as the primary reflector and a hyperbola as the secondary reflector with a feed along the axis of the parabola. The Gregorian dual-reflector antenna uses an ellipse as the subreflector. The Cassegrain and the Gregorian reflectors are shown in Figs. 5.4 and 5.5, respectively.
Figure 5.4. A Cassegrain reflector antenna.
54
CHAPTER 5
Figure 5.5. A Gregorian dual-reflector antenna.
Most paraboloid reflectors use horn antennas (conical or pyramidal) as their feeds. With a parabolic reflector, feed scanning is limited. A spherical reflector provides greater scanning but requires more elaborate feed design since it fails to focus an incident plane wave to a point. Spherical reflectors can suffer from a loss in aperture and increased minor lobes due to blockage by the feed. The radiation characteristics of the paraboloidal reflector can be determined by the aperture method or the current distribution method [2,7]. In the aperture distribution method, fields reflected from the paraboloidal surface are found over the aperture plane normal to the reflector axis, using geometrical optics methods. Equivalent sources are then determined over this aperture plane within the projected area of the reflector. The equivalent sources outside this area are assumed to be zero. The radiated fields are computed using the equivalent sources and aperture techniques. In the current distribution method, the physical optics approximation of the induced surface current density is formulated over the illuminated surface of the reflector. The radiated field is then obtained by integrating the current density over the surface.
5.2 Lens antennas At high frequencies, lens antennas can be used to perform functions similar to reflector antennas. The collimating action of the lens antenna is shown in Fig. 5.6. Both lenses and parabolic reflectors use free space as a feed network to excite a large aperture. The feed of a lens remains out of the aperture, eliminating
TYPES OF ANTENNAS
55
(a)
(b)
Figure 5.6. Lens antenna. (a) Concave-Planar. (b) Convex-Planar.
aperture blockage and the resulting high sidelobe levels. Dielectric lens antennas are similar to the optical lens and the aperture of the antenna is equal to the projection of the rim shape. Lenses are divided into two categories, singlesurface and dual-surface. In the single-surface lens, one surface is an equiphase surface of the incident or emergent wave and the rays pass through normal to this surface without refraction. In a dual-surface lens, refraction occurs at both lens surfaces. Single-surface lenses convert either cylindrical or spherical waves to plane waves, as shown in Fig. 5.6. Cylindrical waves require a line source and a cylindrical lens surface, and spherical waves use a point source and a spherical lens surface. The far-field pattern is determined by diffraction from the aperture. Dual-surface lenses allow more control of the pattern characteristics. Both surfaces are used for focusing, and the second surface can be used to control the distribution in the aperture plane. These simple lenses are many wavelengths thick, if their focal length and aperture are large compared to a wavelength; in this case, the surface of the lens can be zoned by removing multiples of wavelengths from the thickness. The zoning can be done either in the refracting or nonrefracting surface. The zoned lens is frequency sensitive and can give rise to shadowing losses at transition regions. Figure 5.7 shows a zoned lens. Artificial dielectric lenses in which particles such as metal spheres, strips, disks, or rods are introduced in the dielectric have been investigated by Kock [7,8]. The size of the particles has to be small compared to the wavelength. Metal plate lenses using spaced conducting plates are used at microwave frequencies. Since the index of refraction of a metal plate medium depends on the ratio of wavelength to the spacing between the plates, these lenses are frequency sensitive. The Luneberg lens is a spherical symmetric lens with an index of refraction that varies as a function of the radius. A plane wave incident on this lens will be brought to a focus on the opposite side. These lenses can be made using a series of concentric spherical shells, each having a dielectric constant.
56
CHAPTER 5
Figure 5.7. Zoned lens.
5.3 Horn antennas The electromagnetic horn antenna is characterized by attractive qualities such as unidirectional pattern, high gain, and purity of polarization. Horn antennas are used as feeds for reflector and lenses antennas and as a laboratory standard for the calibration of other antennas. A good collection of papers on horn antennas can be found in [9]. Horn antennas can be of rectangular or circular type. The conical horn antenna is shown in Fig. 5.8. Circular horns, derived from circular waveguides, can be conical, biconical, or exponentially tapered. Rectangular horns, derived from a rectangular waveguide can be pyramidal or sectoral E-plane and H-plane horns. The E-planes sectoral horn has a flare in the direction of the field of the dominant TE 10 mode in the rectangular wave guide and the H-plane sectoral horn has a flare in the direction of the H field. The pyramidal horn has a flare in both directions. The radiation pattern of the horn antenna can be determined from a knowledge of the aperture dimensions and the
Figure 5.8. Conical horn antenna.
TYPES OF ANTENNAS
57
Figure 5.9. Sectoral and pyramidal horns. (a) E-plane sectoral, (b) H-plane sectoral, (c) pyramidal.
aperture field distribution. Figure 5.9 shows the geometry of the sectoral and pyramidal horns. The large aperture and single-mode excitation can be achieved by gradually flaring the waveguide to form a horn. Higher order modes are generated at the throat of the horn (the region between the waveguide and the horn). However, these will be attenuated in the throat region if the flare angle is not large. The flare angle of the horn and its dimension affect its radiation pattern and directivity. Maximum directivity can be achieved by optimizing the horn length and the flare angle. The radiation patterns for various horn antennas can be found in [10]. The dependence of the patterns on parameters such as the flare angle, aperture size, and length of the horn are also presented. The need for feed systems that provide low cross polarization and edge diffraction and more symmetrical patterns led to the design of the corrugated horn [11]. These horns have corrugations or grooves along the walls that are λ /4 to λ /2 deep. The conical corrugated horn, referred to as a scalar horn, has a larger bandwidth than its small flare angle corrugated horn. This horn is very suitable as a feed for reflector antennas.
5.4 Microstrip antennas Microstrip patch antennas appear in a variety of shapes, including rectangular, circular, elliptical, and triangular. They are planar and conformal structures that are also lightweight and can be used with integrated circuits [12-16]. Microstrip or printed antennas are used in several applications, including radar, GPS, mobile
58
CHAPTER 5
Figure 5.10. Geometry of a rectangular microstrip patch antenna.
Figure 5.11. Feed configurations for a microstrip patch antenna.
TYPES OF ANTENNAS
59
communications, aeronautical applications, medical applications, etc. Figure 5.10 shows the geometry of a rectangular microstrip patch antenna. The patch element shown in Fig. 5.10 uses a microstrip line feed. This particular feed is one of a number of feed arrangements that can be used with microstrip antennas. Figure 5.11 shows several popular feed mechanisms that can be utilized with microstrip antennas. Each feed configuration has its advantages and disadvantages. For impedance matching purposes, the offset microstrip line feed is the easiest to use since the offset depth controls the input impedance of the antenna. Moreover, this configuration is simple to fabricate and analyze as well. However, the feed line radiates and causes pattern and polarization degradation. The coaxial probe feed reduces spurious feed radiation, it is fairly easy to construct and match, but it tends to have a narrow bandwidth. The aperture-coupled feed isolates the feed mechanism from the radiating element through the use of a ground plane. Energy from the feed line is coupled to the element patch through the aperture slot. Finally, the proximity-coupled feed removes the ground plane so it is easier to manufacture than the aperture-coupled feed. It also exhibits low spurious radiation and provides the largest bandwidth of the feed configurations presented here.
5.4.1 Analysis of microstrip antennas Transmission line model
Several models have been developed to analyze and design microstrip antennas. Using the transmission-line model, shown in Fig. 5.12, the microstrip antenna is modeled as two radiating slots that are separated by a distance L. In reality, due
Figure 5.12. Transmission line model.
60
CHAPTER 5
to fringing effects the actual distance of separation is Leff (effective length or electrical length), which is the length of the patch, L, plus an additional distance, 2 L , that accounts for the fact that the patch looks electrically wider due to the fringing fields. This added distance can be calculated from [7]:
W 0.12 h L 0.412 h W r eff 0.258 0.8 h
r eff 0.3
where,
eff is
(5.1)
the effective dielectric constant of a microstrip transmission line
given by h 1 1 r eff r r 1 12 2 2 W
1/ 2
(5.2)
Thus, the effective distance separating the two radiating slots becomes Leff L 2 L
(5.3)
It is this adjusted length that is utilized in calculating the resonant frequency of the antenna, from [12]: ( f r )010
c 2 Leff
eff
(5.4)
with c being the speed of light . Since the transmission-line model takes into consideration fringing effects at the edges of the patch, it provides a good prediction of the resonant frequency. Moreover, it predicts the input impedance of the antenna fairly accurately. However, it does not account for the effects of a truncated dielectric substrate or a finite ground plane; nor does it provide insight into the radiation patterns of the antenna. Finally, the model breaks down as the height of the dielectric substrate, h, becomes a significant portion of the wavelength (.01, for example, or less). Cavity model
In order to gain some insight into the radiating mechanism of a microstrip antenna, one needs to first understand the near-field quantities that are present around the structure. The cavity model is very useful in achieving this goal since
TYPES OF ANTENNAS
61
Figure 5.13. Geometry of the cavity model.
it provides a mathematical solution for the electric and magnetic fields of a microstrip antenna. It does so by using a dielectric loaded cavity to represent the antenna, as shown in Fig. 5.13. This approach models the dielectric material by assuming that it is truncated at the edges of the patch. The patch and ground planes are assumed to be perfect electric conductors, and the edges of the substrate are modeled with perfectly conducting magnetic walls. It should be noted that the cavity model does not include feed effects; the feed is shown in the figure just for reference. If we assume that the dielectric is very thin, then the electric field is constant along the height of the substrate, h, and is nearly normal to the surface of the patch. In that case we can consider only the TM z modes inside the cavity. The electric and magnetic fields inside the cavity are given by [10] E x
j
E y
E z
k x k y
j
j
H x
Amnp sin(k x x)cos(k y y )sin(k z z ) k y k z
Amnp cos(k x x )sin(k y y )sin(k z z )
k z 2 ) Amnp cos(k x x )cos(k y y )cos(k z z )
(k 2
j
k y
Amnp cos(k x x )sin(k y y )cos(k z z )
(5.5)
62
CHAPTER 5
H y
j
k x
Amnpsin(k x x )cos(k y y )cos(k z z )
H z 0 with k x
k y
k z
m L n W p h
,
m 0,1, 2...
,
n 0,1, 2...
,
p 0,1, 2...
m n p
0
(5.6)
and Amnp is the amplitude coefficient. The resonant frequencies for the cavity are 2
m n p ( f r ) mnp 2 L W h 1
2
(5.7)
Examining the above fields for TM z 100 dominant mode excitation, we see that k y
k z 0
and the field components reduce to
E z jA100 cos x L H y
A100sin x L L
(5.8)
We obtain the equivalent electric and magnetic current densities on the patch using
nˆ H nˆ E
(5.9)
ˆ is the outward directed surface normal. where n The magnetic field is zero along the x = 0 and x = L walls, and it is normal to the surface along the y = 0 and y = W walls. Thus, no equivalent electric current density flows on the walls of the cavity. The electric field results in a nonzero magnetic current density on the walls of the cavity. Figure 5.14 depicts both the
TYPES OF ANTENNAS
63
Figure 5.14. Field configurations and current densities for microstrip patch.
electric field and the associated magnetic current densities for the microstrip antenna. The magnetic currents can be broken into a pair of radiating slots and a pair of non-radiating slots. The radiating slots are in phase so they will constructively interfere in the far-field. Therefore, these two slots form the primary radiation mechanism for the microstrip antenna. On the other hand, the nonradiating slots are out of phase so they will destructively interfere in the far field and will not contribute to the radiated fields. An effective loss tangent needs to be added to account for the power that is lost to radiation. Alternatively, the radiated energy can be modeled using an impedance boundary condition at the walls [10]. Although the cavity model is good at predicting the radiation patterns of a microstrip antenna, it does have some limitations. First, the cavity model does not model the feed effects, nor does it model the adverse effects introduced by a finite substrate and ground plane. One way to circumvent these limitations is to employ numerical techniques such as the finite difference method, the method of moments of the finite-element approach. Figure 5.15 shows a cross-section of a stacked microstrip antenna consisting of two square metal patches and a foam layer (r = 1.1) on top of a Rexolite substrate (r = 2.53, tan = 0.00066) with truncated dielectric layers. The coaxial probe is connected to the lower patch, and the upper patch (parasitic) is excited through coupling from the main radiating patch. The radiation patterns are shown in Figs. 5.16 and 5.17. The stacked microstrip antenna provides a wider bandwidth as compared to a single-layer patch antenna.
64
CHAPTER 5
Figure 5.15. Layout of a stacked antenna element.
0 0 ddB B
10 d 10 dB B
20 d 20 dB B
30 dB 30 d B
900 9
90
1 18 80 0
Figure 5.16. E-Plane radiation pattern of the stacked element phi-cut = 0 degrees, f = 4.75 GHz.
TYPES OF ANTENNAS
65
0 0 dB
10 dB
20 dB
30 dB
90
90
18 0
Figure 5.17. H-Plane radiation pattern of the stacked element phi-cut = 90 deg, f = 4.75 GHz.
5.4.2 Multiple feeds for circular polarization Rectangular and circular patches primarily radiate linearly polarized waves if conventional feeds are used without any changes. However, circular and elliptical polarizations can be achieved by utilizing several feed arrangements or making slight modifications to the elements [16, 17]. Circular polarization can be obtained if two orthogonal modes are excited, with a 90-deg time-phase difference between them. This is usually accomplished by adjusting the physical dimensions of the patch and using either one or more feeds. For a circular patch, circular polarization is obtained by using two feeds with proper angular separation. By making use of two coaxial probes, each probe is always positioned at a point where the field generated by the other probe exhibits a null so that there minimal mutual coupling between the two probes. To achieve circular polarization, the two feeds are fed in such a manner that there is 90-deg time-phase difference between the two fields; this can be achieved through the use of a 90-deg hybrid, as shown in Fig. 5.18. Sometimes a shorting pin is positioned at the center of the patch to connect the patch to the ground plane. For z
the z
dominant
mode
z
( TM110 )
and
for
higher-order
modes
z
( TM 210 , TM 010 , TM 310 …), the required spacing between the two feeds that yields circular polarization is different. Furthermore, as it is seen in Fig. 5.19, two additional feed probes located diametrically opposite to the original poles are usually recommended, in order to preserve symmetry. The additional probes are used to suppress the adjacent modes, which usually have the next highest
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Figure 5.18. Circular patch fed with two coaxial probes.
Figure 5.19. Circular patch feed arrangements for the dominant and higher-order modes.
magnitudes. For even modes ( TM z 210 and TM z 410 ), the four feed probes have phases of 0 deg, 90 deg, 0 deg, and 90 deg, while for the odd modes ( TM z 110 and TM z 310 ) they have phases of 0 deg, 90 deg, 180 deg and 270 deg.
5.4.3 Microstrip arrays Microstrip antennas can be easily integrated into arrays [18-24] and can be arranged in a rectangular lattice, shown in Fig. 5.20, or in a triangular lattice, shown in Fig. 5.25. Figure 5.22 shows an example of a 4×4-element subarray of circular microstrip patches along with the feed network, designed for use in a direct broadcast system [25]. It has circular polarization, as indicated by the two feeds for each patch. Note the difference in feed line lengths to create the required 90deg phase shift between the two feeds for each patch.
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Figure 5.20. Rectangular lattice configuration.
Figure 5.21. Triangular lattice configuration.
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Figure 5.22. A circular microstrip patch array for a direct broadcast system.
5.5 Radome coverings A radar dome, or radome, is a protective dielectric housing for antennas. The function of the radome is to protect the antenna from adverse environments in ground-based, shipboard, airborne and aerospace applications, while causing an insignificant effect on the electrical performance of the enclosed antenna or antennas. The frequency band of application for radomes is approximately 1 to 1000 GHz. Radomes [12] are generally composed of low-loss dielectrics of thickness comparable to a wavelength, which are shaped to cover the antenna and, if necessary, to conform to aerodynamic streamlining.
References 1. A.W. Love, Reflector Antennas, New York: IEEE Press, 1978. 2. S. Silver, Microwave Antennas Theory and Design, Radiation Lab Series, McGraw-Hill. 3. R. Collin, and F. J. Zucker, Antenna Theory Part II , McGraw-Hill, 1969. 4. J. D. Kraus, “The corner reflector antenna,” Proc. IRE, vol. 28, pp. 513–519, Nov. 1940. 5. P. J. Wood, Reflector Analysis and Design, London: Peter Peregrinus Press, 1980. 6. P. J. B. Clarricoats G. T. Poulton, “High efficiency microwave reflector antennas–A review,” Proc. IEEE, vol. 6J, no. 10, pp. 1470–1502, Oct. 1977. 7. W. E. Kock, “Metallic Delay Lens,” BSTJ, vol. 27, pp. 58–82, Jan 1948. 8. W. E. Kock, “Metal lens antennas,” Proc. IRE, vol. 34, pp. 828–836, Nov. 1946.
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9. A.W. Love, Electromagnetic Horn Antennas, IEEE Press, 1976. 10. A.Balanis, Antenna Theory – Analysis and Design, John Wiley & Sons. 11. P. J. B. Clarricoats and A. D. Olver, Corrugated Horns for Microwave Antennas, London: Peter Peregrinus Press, 1984. 12. R. C. Johnson, Antenna Engineering Handbook , 3rd ed., McGraw-Hill. 13. P. Bhartia, K. Rao, and R. S. Tomar, Millimeter-Wave Microstrip and Printed Circuit Antennas, Artech House, 1st ed., Boston, 1991. 14. K. R. Carver, Microstrip Antenna Technology, vol. 29, no. 1, Jan 1981. 15. D. M. Pozar and D. H. Schaubert, Microstrip Antennas, Piscataway, N.J.: IEEE Press, 1995. 16. D. M. Pozar, Microstrip Antennas, Proc. IEEE, pp. 79–91, vol. 80, no. 1, Jan. 1987. 17. J. Huang, “Circularly polarized conical patterns from circular microstrip antennas,” IEEE Trans. Antennas and Prop., vol. 32, no. 9, pp. 991–994, Sept. 1984. 18. J. T. Aberle and D. M. Pozar, “Analysis of infinite arrays of one and two probe fed circular patches,” IEEE Trans. Antennas Prop., vol. 38, no. 4, pp. 421–432, April 1990. 19. R. Telikepalli et al., “Wide band microstrip phased array for mobile satellite communications,” IEEE Trans. Microwave Theory Tech., vol. 43, no. 7, pp. 1758–1763, July 1995. 20. R. P. Jedlicka et al., “Measured mutual coupling between microstrip antennas,” IEEE Trans. Antennas Prop., vol. 29, no. 1, pp. 147–149, Jan. 1981. 21. D. M. Pozar, “Input impedance and mutual coupling of rectangular microstrip antennas,” IEEE Trans. Antennas Prop., vol. 30, no. 6, pp. 1191– 1196, Nov. 1982. 22. J. Gómez-Tagle, “Application of the FDTD method for the analysis of finitesized phased array microstrip antennas,”University of Central Florida, Electrical and Computer Engineering Department, Orlando, Florida, 1999. 23. R. C. Hansen, Phased Array Antennas, 1st ed., New York: John Wiley & Sons, 1998. 24. R. J. Mailloux, Phased Array Antenna Handbook , Artech House. 25. M. Rubelj, P. F. Wahid, C. G Christodoulou, “A microstrip antenna array for direct broadcast satellite receivers,” Microwave and Opt. Tech. Lett., vol. 15, no. 2, June 1997.
CHAPTER 6 ANTENNAS FOR INFRARED DETECTORS The last research frontier in high-frequency electronics is in the terahertz (or submillimeter-wave) region, between microwaves and the infrared (i.e., 0.3–15 THz). While the terahertz frequency region offers many technical advantages (e.g., wider bandwidth, improved spatial resolution, compactness), the solid state electronics capability within that frequency region has been very limited from a basic signal source and systems perspective (i.e., < milliwatts). This limited development is mainly due to two fundamental factors. First, extremely challenging engineering problems exist in this region where component size is on the order of λ . Second, applications of this shorter-wavelength microwave region have been restricted, so far, to a few specialized fields (e.g., molecular spectroscopy). On the lower-frequency side, electronic devices reach an upper frequency limit of several hundred gigahertz due to transient times and parasitic RC time constants. On the higher-frequency side, photonic devices such as interband laser diodes can only be used at approximately 10 THz. The other important component of a system working in the far-infrared region (FIR) regime, besides the FIR source, is the FIR detector. In the field of FIR detectors, specifically those based on resonant tunneling in quantum well heterostructures, a great deal of research has been conducted and some promising results have been published. Today, increasingly more important applications of terahertz technology are rapidly emerging that are relevant to civilian and military applications. For example, at frequencies above 300 GHz, the strong absorption of electromagnetic energy by atmospheric molecules makes any communication link impossible to achieve. On the other hand, this same fundamental interaction mechanism allows terahertz electronics to be a very promising tool for the identification and interrogation of chemical and biological (CB) agents. Recent developments in microwave remote-sensing techniques and submillimeter-wave heterodyne radiometric systems have led to the use of limb sounders to study the upper atmosphere of Earth [1]. The Antarctic ozone hole discovered in 1985 [2], and its effect in shielding life from solar ultraviolet radiation, shows that it is necessary to monitor the upper atmosphere in order to detect the change of the atmospheric ozone layer, which is being depleted systematically by pollution [3]. There is an urgent need to include local oscillators and detectors for radiometers at 2.5 THz in new satellites, for more accurate monitoring of ozone depletion and tropospheric chemistry in general. Several applications, in areas such as remote sensing, radio astronomy, plasma diagnostics, atmospheric studies, space communications, generally 71
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demand low-noise receivers from about 30 GHz to more than 1 THz. However, this region presents serious technical challenges on submillimeter-wave local oscillators and detectors[4-8]. For example, the frequency coverage of the NASA SMMM (Sub-Millimeter Moderate Mission) is from 400 GHz to 1.2 THz, and the minimum output power requirement of the local oscillator at 1 THz is 50 µW. The challenge here is to develop a small, lightweight, reliable device, that makes use of a low-voltage power supply but is capable of generating enough output power. In this chapter we show how an antenna can be integrated with the detector for successful operation to efficiently collect terahertz radiation.
6.1 Antennas for infrared detectors As the size of FIR detectors is reduced in order to improve performance, they cannot collect much of the terahertz radiation, and, therefore, the detection of such radiation becomes difficult. An antenna coupled to the detector can efficiently collect the radiation and feed it to the detector. Since high-frequency devices are fabricated using lithographic techniques, it is usual practice to integrate the feed antenna onto the same dielectric substrate as the detector. A complete review of lithographic and submillimeter FIR antennas can be found [913]. FIR antennas have been used in many applications. They have been used with GaAs Schottky diodes and superconducting junctions in the design of heterodyne receivers for astronomical and atmospheric spectroscopy. They have been used in conjunction with simple resistive bolometers and with thermocouples in imaging arrays. They have also been used in the design of photo mixers. In general, the size of FIR antennas is comparable to the wavelength of the radiation being detected, while the detector itself is simply a fraction of the wavelength, in order to achieve a fast response. The antenna collects the radiation and supplies an electrical signal to the detector to be processed. So far, several antenna configurations, such as dipole antennas [14], bowtie antennas [15,16], log-periodic antennas [15], spiral antennas [16,17], helical antennas [18], and microstrip antennas [19] have been used to feed various types of detectors. Infrared antennas are different than microwave antennas in that the surface impedance of the metals is much higher at terahertz frequencies than at microwave frequencies. This fundamental difference is due to the skin effect [20]. This high surface impedance causes losses that can slow the antenna currents so that the antenna does not radiate very efficiently. The surface impedance is not a constant, but depends on the characteristics of the incident waves and on the shape and thickness of the material. Usually, the antenna is chosen as a compromise between bandwidth and efficiency. To take advantage of the fast response of the detector, a broadband antenna must be used as the collecting area in order to achieve the detection of extremely narrow pulses of radiation. Broadband antennas can be easily realized by using electrically thick dielectric substrates. However, for good efficiency, the substrate thickness must
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be much smaller than the operating wavelength (usually λ /20 or less) to avoid substrate losses. At low frequencies, because the wavelength is large, it is easy to fabricate antennas with thin substrates. However, at terahertz frequencies, the substrate thickness becomes too small to handle. The substrate tends to be too fragile to support the antenna-detector circuit for reliable operation. It should be mentioned that for antennas deposited on dielectric substrates, they couple energy primarily into the dielectric substrate rather than into the air. When compared to a wave in air, the wave on the antenna is a slow wave and excites evanescent modes. Compared to a wave in the dielectric, it is a fast wave and excites radiation fields. Therefore, for materials with high dielectric constants, such as Si or GaAs, most of the energy (90% or more) is confined in the dielectric substrate instead of being radiated in free space. Also, the efficiency of an antenna is limited by the amount of power lost to surface waves. As the substrate becomes electrically thicker, more surface modes can exist, which can have a detrimental effect on antenna performance. Moreover, the finite size of the substrate diffracts these surface waves from the substrate edges, and this affects the sidelobe level, polarization, and main beam shape. To reduce loss due to dielectric heating, a special substrate geometry is required to achieve high efficiency. Several techniques have been employed over the years to reduce losses and enhance coupling of radiation from the antenna to free space. One of the earliest approaches was to utilize a lens of the same dielectric constant attached to the antenna substrate, called substrate lens. This technique completely reduces substrate mode losses and diffraction at the edges [21,22]. In order to reduce reflection losses at the air/dielectric interface, a matching layer is required with the design of the substrate lens. Many antenna systems were built on a substrate lens with a bowtie antenna, shown in Fig. 6.1, for imaging arrays in plasma diagnostics and two-dimensional tracking applications [23]. Bowtie antennas with a substrate lens have been integrated with a resonant tunneling diode (RTD) to study the stimulated emission and absorption in the terahertz range [24]. Other antenna structures have also been studied and used with a substrate lens, including Yagi-Uda imaging arrays, coupled slotlines, double-slot antennas, and double dipole antennas. Planar log-periodic, helical, and spiral antennas offer an attractive alternative to bowtie antennas on dielectric lenses for wideband applications [25,26]. The dielectrically filled parabola is another new design that is based on the substrate lens principle. In this case, a quartz substrate is machined as a parabola, and its curved edge is metallized to produce a parabolic reflector. The antenna is fabricated with its flat portion toward the dielectric lens and radiates most of its power into the substrate. The radiation is then reflected and collimated by the parabolic reflector. Measurements with dipole, spiral, log-periodic, and bowtie antennas placed at the focus of the parabola yield very good radiation patterns.
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Figure 6.1. A bowtie antenna used for wideband terahertz applications.
In [27], yet another approach was used to handle the substrate mode problem. The idea was to remove the substrate and integrate the antenna on a thin dielectric membrane. The membrane is so thin compared to the free-space wavelength that the antenna effectively radiates as if it were in free space. Other antenna structures have also been designed with membrane technology,m such as integrated horn antenna and reflector antennas [10]. Other techniques have also been developed to reduce or even eliminate surface waves. One of these techniques is based on the use of photonic bandgap (PBG) substrates. According to this technique, holes in certain arrangements are drilled in the substrate [28,29] to create certain periodic patterns that result in an increased efficiency and directivity.
6.2 Design of helical antennas for terahertz applications Figure 6.2 depicts an example of a helical antenna designed for the 0.1- to 2.7THz range. The terahertz antenna structure was fabricated by using laser chemical vapor deposition (LCVD) to form fibers that can be grown into complex three-dimensional structures directly on semiconductor substrates [18]. By focusing the laser through a diffractive optic, arrays of antennas can be fabricated at the same time. Terahertz radiation detection devices can be realized by combining the LCVD antennas with MEMS microbolometers that convert received terahertz radiation into a change in resistance. Arrays of these antenna bolometer pairs can be fabricated on the same substrate to realize a terahertz imaging device.
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Figure 6.2. SEM photograph of an antennalike structure consisting of 40-µm square spirals around a center post.
Figure 6.3 depicts a helical antenna as a conductor coiled around an imaginary cylinder. The conductor can be coiled in the clockwise or counterclockwise direction depending on the polarization requirements. The pitch angle, α, provides a measure of how tightly the helix is wound. For a given circumference, smaller values of α imply closer turn spacing. The operation of a helical antenna can be described in terms of transmission and radiation modes. Transmission modes describe how an electromagnetic wave propagates along the helix. At low frequencies, where the wavelength is much longer than the helix circumference, regions of positive and negative charge in the current distribution are separated by many turns. Because of this separation, the electric field becomes directed mainly along the axis of the helix. At frequencies where the wavelength approaches the value of the helix circumference, higher order transmission modes occur. The radiation field pattern depends on the radiation modes excited. There are mainly two modes: the normal mode and the axial mode. The axial mode antenna is the most widely used mode. Actually, the axial mode helical antenna is the most widely used circularly polarized antenna, either in space or on the ground. For the axial mode to occur, the frequency of operation must be such that the helix circumference is within the range 0.75 to 1.33 λ. The axial mode is characterized by a symmetric main lobe directed along the axis of the helix. On the other hand, for the normal mode the maximum field strength occurs in the direction perpendicular (normal) to the helix axis. The radiation resistance in this
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D= diameter of C =circumference helix π tan α = /C = π L = S 2 + C 2 length of α = pitch = number of d =diameter of helix
Figure 6.3. Helical antenna geometry.
case is very low and hence the normal mode helix is not a very efficient antenna. For this discussion, only the axial mode helical antenna is considered. The input impedance of the axial mode antenna is mostly resistive and is given by
Χ λ
R = 140
Ω
This is an empirical formula used for calculating the impedance of a helical antenna. It does not take into account the effect of skin depth, but since no closed-form solution exists, it is a reasonable approximation. It is this impedance that can be used for matching purposes with a waveguide or bolometer. More specifically, the dimensions of the helix at 1 THz ( λ =300 µm) are C =341.307 µm s=81.3 µm d =15 µm N =5 turns α= 13 deg.
6.3 Design of broadband FIR antennas Consider the device shown in Fig. 6.4. It consists of a bow-tie antenna integrated with a double quantum well (DQW), photon-assisted tunneling (PAT) terahertz detector. The radiation can be detected by observing the current-voltage characteristic of the detector with and without the terahertz radiation. A detailed discussion on the detector’s principle of operation can be found in [30-34].
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Figure 6.4. DQW FIR detector integrated with bowtie antenna.
The basic structure of this terahertz detector is similar to that of the recently demonstrated double electron layer-tunneling transistor (DELTT) [32], the first quantum tunneling transistor whose behavior is not sensitive to any lateral dimensions of the device. To take full advantage of the electrically tunable DQW PAT FIR detector, any antenna fabricated with this detector should be broadband and efficient in collecting the terahertz radiation. There are many possibilities of broadband antenna structures to choose from such as the bowtie, log-periodic, and spiral antennas. According to the theory of the DQW PAT FIR detectors, photons from the laser beam with the correct amount of energy at terahertz frequencies, push the device beyond threshold to produce a tunneling current that flows in the detector. One of the fundamental issues in this design is the matching of the DQW detector to the input impedance of the bowtie antenna. A bad impedance match between the detector and the antenna causes the incoming terahertz radiation to be reflected instead of being collected and fed to the active area of the detector. Therefore, a better understanding of how the bowtie and other broadband antennas behave at these terahertz frequencies is very important in the realization of the terahertz detector. Also, a quasi-static analysis of the antenna-detector structure is important in studying the effects of the dc bias on the electric field and potential distributions inside the detector structure. Another important issue is the development of an equivalent circuit model for the terahertz detector. This is very crucial in achieving the required impedance matching between the antenna and the detector. The input reflection coefficient of the antenna obtained though simulation is shown in Fig. 6.5. The results show that the bowtie antenna with the
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configuration shown in Fig. 6.4 is well suited to work in the 45- to 95-GHz frequency band. This gives a 70% bandwidth around the 70-GHz center frequency, based on the −10-dB criterion (or equivalently 2:1 VSWR). The computed directivity of the bowtie antenna in the broadside direction as a function of frequency is shown in Fig. 6.6. The dips in the directivity at 70 and 90 GHz are due to nonfundamental mode current distributions that tend to radiate off the broadside direction. Also, these dips might result due to losses contributed by substrate and surface-wave modes. [35] Since the main goal of the antenna here is to efficiently couple radiation from free space and feed it to the active region of the detector, it is desirable to have
Figure 6.5. Reflection 6.5. Reflection coefficient vs. frequency of the bowtie antenna shown in Fig. 6.4.
Figure 6.6. Directivity in the broadside direction of the original bowtie antenna as a function of frequency. frequency.
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79
Figure 6.7. Radar cross section (RCS) of the original bowtie antenna vs. frequency at different elevation angles. The antenna is illuminated by a plane wave incident normally in the –z -direction -direction with the electric field polarized in the x -direction. -direction.
the effective collecting aperture of the antenna as large as possible at the frequency of radiation. By illuminating the antenna structure with an electromagnetic plane wave incident at some angle and measuring the backscattered fields, the radar cross-section (RCS) of the antenna can be calculated. The effective aperture is then proportional to RCS. In the present case, the antenna is illuminated by a plane wave normally incident in the – z -direction, -direction, with an electric field polarized in the x-direction, x-direction, and the simulation results for the RCS as a function of frequency and at different elevation angles in the x-z the x-z plane, plane, are shown in Fig. 6.7. [35] A new bowtie antenna with dimensions designed to operate around the 1.6THz frequency band is shown in Fig. 6.8. The bowtie antenna is designed to have a length of approximately half a wavelength (inside the substrate) at 1.6 THz and a bow angle of 60 deg. The simulated results for the input reflection coefficient as a function of frequency are shown in Fig. 6.9, and a clear resonance is observed at 1.6 THz. In the 1.45- to 2-THz frequency band, the reflection coefficient magnitude is less than –10 dB, giving a bandwidth of 34% around 1.6 THz. The bowtie antenna in the present design behaves much like a half-wave dipole, but with a broader bandwidth. [35]
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15.6µm
28.2µm Figure 6.8. Modified bowtie antenna design.
Figure 6.9. Reflection 6.9. Reflection coefficient vs. frequency of the modified bowtie antenna with a center frequency of 1.6 THz.
References 1. J. W. Waters and P. H. Siegel, “Applications “Applications of millimeter millimeter and sub millimeter technology to earth’s upper atmosphere: results to date and potential for the future,” the 4 th International Symposium on Space Terahertz Technology, Los Angeles, Calif., March 1993. 2. J. Farman, B. Gardiner, and J. Shanklin, “Large losses of total ozone in Antarctica reveal seasonal ClO x/NO x,” Nature, ,” Nature, vol. vol. 315, p. 207, 1985.
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3. P. B. Hays and H. E. Snell, “Atmospheric remote sensing in the terahertz regions,” Proceedings of the 1st International Symposium on Space Terahertz Technology, p. 482, 1990.T. G. Phillips, “Developments in submillimeterwave astronomy,” The 19th International Conference on Infrared and Millimeter Waves , Sendai, Japan, 1994. 4. S. Gulkis, “Submillimeter wavelength astronomy missions for the 1990s,” Proceedings of the 1st International Symposium on Space Terahertz Technology, pp. 454–457, 1990. 5. N. C. Luhmann, “Instrumentation and techniques for plasma diagnostics: an overview,” Infrared and Millimeter Waves, vol. 2, pp. 1–65, K. J. Button, Ed., New York: Academic Press, 1979. 6. P. E. Young, D. F. Neikirk, P. P. Tong, and N. C. Luhmann, “Multi-channel far-infrared phase imaging for fusion plasma,” Rev. Sci. Instrum., vol. 56, pp. 81–89, 1985. 7. P. F. Goldsmith, “Coherent systems in the terahertz frequency range: elements, operation and examples,” Proceedings of the 3rd International Symposium on Space Terahertz Technology, pp. 1–23, 1992. 8. D. B. Rutledge, D. P. Neikirk, and D. P. Kasilingham, “Integrated-circuit antennas”, Infrared and Millimeter Waves, vol. 10, New York Academic Press, 1983, pp. 1–90. 9. M. Rebiez, “Millimeter-wave and terahertz integrated circuit antennas,” Proc. of the IEEE , vol. 80, pp. 1748–1770, Nov. 1992. 10. E. N. Grossman, “Lithographic antennas for submillimeter and infrared frequencies,” IEEE International Symposium on Electromagnetic Compatibility, pp. 102–107, 1995. 11. D. S. Hernandez and I. Robertson, “Integrated antennas for terahertz circuits,” IEE Colloquium on Terahertz Technology, pp. 1–7, 1995. 12. Mizuno, Y. Daiku and S. Ono, “Design of printed resonant antennas for monolithic-diode detectors,” IEEE Trans. on Microwave Theory Techn., vol. 25, pp. 470–472, June 1977. 13. I.Wike, W. Herrmann and F. K. Kneubuhl, “Integrated nanostrip dipole antennas for coherent 30 THz infrared detection,” Appl. Phys. B, vol. 58(2), pp. 87–95, 1994. 14. N. Chong and H. Ahmed, “Antenna-coupled polycrystalline silicon air bridge thermal detector for mid-infrared radiation,” Appl. Phys. Lett., Vol. 71(12), pp. 1607–1609, 1997. 15. C. Fumeaux et al, “Nanometer thin-film Ni-NiO-Ni diodes for detection and mixing of 30 THz radiation,” Infrared Phys. Technol., Vol. 39(3), pp. 123– 183, 1998. 16. E. N. Grossman, J. E. Sauvageau and D. G. McDonald, “Lithographic spiral antennas at short wavelengths,” Appl. Phys. Lett. 59 (25), pp. 3225–3227, Dec. 1991. 17. R. N. Dean, Jr., P.C. Nordine and C. G. Christodoulou, “ 3-D helical THz antennas”, Microwave and Optical Technology Letters, pp. 106–111, Jan. 20, 2000.
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18. Codreanu, C. Fumeaux, D. F. Spencer and G. D. Boreman, “Microstrip antenna-coupled infrared detector,” IEE Electronics Lett., vol. 35, pp. 2166– 2167, Dec. 1999. 19. D. B. Rutledge, S. E. Schwarz and A. T. Adams, “Infrared and submillimeter antennas,” Infrared Physics, vol. 18, pp. 713–729, Pergamon Press Ltd, 1978. 20. R. C. Compton et al, “Bow-tie antennas on a dielectric half-space: theory and experiment,” IEEE Trans. Antennas and Propagat., vol. 35, pp. 622–630, June 1987. 21. E. N. Grossman, D. G. McDonald and J. E. Sauvageau, “Far-infrared kineticinductance detectors,” IEEE Trans. on Magnetics, vol. 27, pp. 2677–2680, March 1991. 22. D. P. Neikirk et al, “Imaging antenna array at 119 µm,” Appl. Phys. Lett., vol. 41(4), pp. 329–331, Aug. 1982. 23. H. Drexler, J. S. Scott and S. J. Allen, “Photon-assisted tunneling in a resonant tunneling diode: stimulated emission and absorption in the THz range,” Appl. Phys. Lett., Vol. 67(19), pp. 2816–2818, Nov. 1995. 24. D. B. Rutledge and M. S. Muha, “Imaging antenna arrays,” IEEE Trans. Antennas and Propagat., vol. 30, pp. 535–540, July 1982. 25. I.Wike, W. Herrmann and F. K. Kneubuhl, “Submicron thin-film MOM diodes for the detection of 10 µm infrared laser radiation,” Fourth International Conference on Advanced Infrared Detectors and Systems, pp. 116–119, 1990. 26. G. M. Rebeiz et al, “Monolithic millimeter-wave two-dimensional horn imaging array,” IEEE Trans. Antennas Propagat., vol. 28, pp. 1473–1482, Sept. 1990. 27. M. J. Vaughan, K. Y. Hur, and R. C. Compton, “Improvements of microstrip patch antenna radiation patterns,” IEEE Trans. Antennas Propagat , vol. 42, pp. 882–885, June 1994. 28. R. A. York and Z. B. Popovic, Ed., Active and Quasi-Optical Arrays for Solid-State Power Combining, New York: John Wiley & Sons, 1997. 29. Sanchez, C. F. Davis, K. C. Liu and A. Javan, “The MOM tunneling diode: theoretical estimate of its performance at microwave and infrared frequencies, ” J. Appl. Phys., vol. 49(10), pp. 5270–5277, Oct. 1978. 30. J. A. Simmons et al, “Planar quantum transistor based on 2D-2D tunneling in double quantum well heterostructure,” J. Appl. Phys., vol. 84(10), pp. 5626– 5634, Nov. 1998. 31. M. A. Blout et al, “Double electron layer tunneling transistor (DELTT),” Semicond. Sci. Technol., vol. 13, pp. A180–A183, 1998. 32. J. S. Moon et al, “Unipolar complementary circuits using double electron layer tunneling transistor,” Appl. Phys. Lett., vol. 74, pp. 314–316, Jan. 1999. 33. P. J. Burke, I. B. Spielman and J. P. Eisenstein, “High frequency conductivity of the high-mobility two-dimensional electron gas,” Appl. Phys. Lett ., vol. 76, pp. 745–747, Feb. 2000.
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34. M. Khodier, C.G. Christodoulou, and J. Simmons, “An integrated broadband bowtie antenna for THz detection with a double quantum well,” IEEE AP/URSI Symposium in Boston, Mass., July 2001.
CHAPTER 7 ANTENNA MEASUREMENTS Antenna measurements are an important part of the antenna design process. Measurements on prototype antennas are often done at various steps of the design process to check that the antenna meets the design specification. The key parameters of an antenna that are measured are the radiation pattern, efficiency, gain, and impedance. Depending on the antenna and its application, other parameters such as the polarization purity, power handling capacity, etc. may also be measured. The use of sophisticated computerized equipment has made it possible to make accurate measurements of the important antenna parameters. Detailed discussion on measurement techniques can be found in the IEEE Standard Test Procedure for Antennas.
7.1 Radiation pattern measurements To obtain a complete 3D space pattern, measurements of the field intensity have to be made in all directions. The field components E θ and E φ are measured as a function of θ ( φ constant) and φ ( θ constant). The measurements can be taken by keeping the antenna under test fixed and moving the measuring antenna, or by rotating the antenna under test about its vertical axis and keeping the measuring antenna fixed. In most cases, pattern measurements are taken along the principal planes; i.e., the E-plane and the H-plane patterns of the antenna are measured. Consider an antenna located at the origin along the z-axis, as shown in Fig. 7.1. The requirement for the accurate measurement of the far-field radiation pattern is that the antenna under test be illuminated by a uniform plane wave. Reflection from the ground or obstacles surrounding the antenna can cause unwanted reflections and errors in the measurements [1].
7.1.1. Outdoor ranges The problem encountered with outdoor measuring ranges is reflection from the ground, surrounding obstacles, and a lack of protection from the environment. The effect of the ground is reduced by placing the antennas on towers or adjacent buildings. In cases where the range is on irregular terrain, slant ranges are designed such that the test antenna is at a fixed height on a tower and the source is located at the ground. Ground reflections may be minimized using a source antenna with high directivity [2].
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Figure 7.1. Geometry for radiation pattern measurements.
7.1.2 Anechoic chambers An anechoic chamber is an enclosed room with the walls, floor, and ceiling covered with absorbing material to minimize reflections. These chambers provide a controlled environment for antenna testing. The absorbing materials used generally come in the form of wedges or pyramids, as shown in Fig. 7.2, with a thickness on the order of a few wavelengths. Reflection coefficients of –20 to –40 dB are obtainable over a range of incident angles and frequencies [1,2]. The region within the chamber where phase errors are about ± 5 deg and the amplitude errors are about ± 0.5 dB is referred to as the quiet zone.
Figure 7.2. Sections of absorbing material: (a) pyramid, (b) wedge.
ANTENNA MEASUREMENTS
87
In a tapered chamber, shown in Fig. 7.3, the tapered section of the chamber ends in a rectangular section at the test region [3]. The antenna under test is generally the receiving antenna. As the frequency gets higher and the antenna under test gets larger, it becomes more difficult to obtain plane wave illumination. The tapered chamber presents a more uniform plane wave at the test antenna than a rectangular chamber. Compact ranges [4] use as an off-set reflector to obtain plane wave illumination over much smaller distances as compared to conventional ranges. The reflector usually has edges that are serrated or rolled to minimize diffraction from the edges. Different reflector antenna configurations such as parabolic, Gregorian, Cassegrain, etc. are used to further improve performance. An illustration of a compact test range is given in Fig. 7.4. The far-field patterns can also be obtained from measurements of the near field [2,5]. This allows the use of a smaller chamber; however, it requires very accurate near-field measurements, with extra care taken to ensure that the probe does not disturb the field being measured. Depending on the type of antenna being measured, one of the three techniques below is used.
Figure 7.3. Tapered chamber.
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CHAPTER 7
Figure 7.4. Compact test range.
In planar near-field scanning, the probe is moved over the antenna aperture plane and the amplitude and phase are recorded. In a cylindrical near-field scanning system, the probe is moved vertically while the antenna under test is rotated; and for spherical near-field scanning, the probe is moved around the antenna over a spherical surface. The near-field values are transformed to farfield data using Fourier transforms. Computer software packages are available that carry out this transformation. The equipment used for measuring and recording the data is placed outside the anechoic chamber. The measurement is generally computerized and radiation plots in either rectangular or polar form can be generated.
7.2 Gain measurements 7.2.1 Comparison method The gain of an antenna can be measured by comparison with a reference antenna whose gain is known. Commonly used reference antennas are the halfwavelength dipole and the pyramidal horn. In an anechoic chamber or test range, a known amount of power is radiated by a source antenna and received by the antenna under test, and the received signal level P R is noted. The test antenna is then replaced with reference antenna, and the received signal level P R is noted. The gain of the antenna is given by G=
P A P R
GR
ANTENNA MEASUREMENTS
89
where GR is the gain of the reference antenna. It is assumed that both antennas are properly matched and are located at a suitable distance from the source such that the incident wave is a uniform plane wave.
7.2.2 Two-antenna method Two identical test antennas can be used for measuring the gain, using one as the transmitter and one as the receiver. Using the Friis transmission equation, the power received by the antenna under test is Pr = P t
G 2 λ 2 2
2
(4 π) r
(7.1)
where P t is the transmitted power (W), G is the gain of the identical antennas, λ is the wavelength (m), and r is the distance between the antennas (m). From the above equation we have G=
4πr P r
λ
P t
(7.2)
The gain can thus be determined by measuring the ratio of the received to transmitted power, the distance between the antennas, and the wavelength. If the gain of the two antennas differs considerably, then we write
G =
G01G02
(7.3)
where G01 is the gain of one antenna and G02 the gain of the second antenna. A third reference antenna, whose gain need not be known, can be used for comparison [1]. We obtain the ratio
G′ =
G1 G2
(7.4)
where G1 is the gain of one antenna above the reference and G2 that of the second antenna; then we have
G′ = and, therefore,
G01 G02
(7.5)
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CHAPTER 7
G01 = G G ′ G02 =
G
(7.6)
G′
7.3 Impedance measurements The antenna impedance can be derived by measuring the complex reflection coefficient using a vector network analyzer. In many instances, the return loss of the antenna is measured from which the voltage standing wave ratio (VSWR) can be obtained. The VSWR is related to the reflection coefficient, ρ, through the relation VSWR =
1+ ρ 1− ρ
(7.7)
The return loss is given by the equation below and is generally expressed in decibels: 2
VSWR + 1 = RL = 2 VSWR − 1 ρ 1
(7.8)
VSWR values of 2 or less correspond to an acceptable match for many applications.
References 1. J. Kraus, Antennas, 2nd ed., McGraw-Hill. 2. S. Drabowitch, A. Papiernik, H. Griffiths, J. Encinas, B. L. Smith, Modern Antennas, ITP Chapman and Hill. 3. C. Balanis, Antenna Theory, Analysis and Design, John Wiley and Sons. 4. R. C. Johnson, H. A. Ecker, R. A. Moore, “Compact range techniques and measurements,” IEEE Trans. Ant. and Prop., vol. AP-17, pp. 568–576, Sep. 1969. 5. R. C. Johnson, H. Ecker, J. S. Hollis, “Determination of far field antenna patterns from near field measurements,” Proc. IEEE, vol. 61, no. 2, pp. 1668–1694, Dec. 1973.
Christos G. Christodoulou received
the B.Sc. degree in physics and math from the American University of Cairo in 1979, and the M.S. and Ph.D. degrees in Electrical Engineering from North Carolina State University, Raleigh, in 1981 and 1985, respectively. He served as a faculty member at the University of Central Florida, Orlando, from 1985 to 1998, where he received numerous teaching and research awards. In 1999, he joined the faculty of the Electrical and Computer Engineering Department of the University of New Mexico, Albuquerque. In 1991 he was selected as the AP/MTT Engineer of the Year (Orlando Section). He is a senior member of IEEE and a member of URSI (Commission B). He served as the general Chair of the IEEE Antennas and Propagation Society/URSI 1999 Symposium in Orlando, Florida. He has published more than 150 papers in journals and conference proceedings. He is also the co-author of a book, Applications of Neural Networks in Electromagnetics. He is currently the co-editor for a column on "Wireless Communications" for the IEEE AP Magazine and the associate editor for the IEEE Transactions on Antennas and Propagation. His research interests are in the areas of wireless communications, modeling of electromagnetic systems, smart antennas, neural network applications in electromagnetics, and reconfigurable/ MEMS antennas. Parveen F. Wahid received
her B.Sc. degree in mathematics and physics in 1969, her M.Sc. degree in physics in 1971 from the University of Mysore, India, and her Ph.D. in electrical communication engineering from the Indian Institute of Science in 1979. She was a research associate in the Electrical Engineering Department, University of Utah, from 1980 to 1982 and at the Electrical Engineering Department, University of Nebraska/Lincoln from 1982 to 1983. Since 1984 she has been with the University of Central Florida, where she is now a professor in the Department of Electrical Engineering. She teaches electromagnetics, antenna theory and design, and microwave engineering courses. Her research interests are in the area of the design of microstrip antennas and arrays and adaptive arrays for wireless applications. Dr. Wahid has more than 50 technical publications in journals and conference proceedings. She is the recipient of the 2000 IEEE Third Millennium award, the 1996 Orlando Section Engineer of the Year award, and the 1998 IEEE Orlando Section Professional Service award. She is a member of the IEEE AP-S ADCOM. She served as the General Chair for the 1998 IEEE Region 3 Southeastcon conference and was the Technical Program Chair for the 1999 IEEE International AP/URSI symposium.
INDEX
Index Terms
Links
# 90-degree hybrid
63
A absorbing material adaptive
84 2
air/dielectric interface
71
analysis of microstrip antennas
58
anechoic chamber
84
antenna array
37
antenna efficiency
17
antenna measurements
83
aperture plane
50
aperture theory
49
aperture-coupled feed
57
array factor
38
artificial dielectric lenses
54
B bandwidth
17
beamwidth
15
Bessel function
33
bowtie antenna
71
broadband FIR antennas
75
broadside array
44
78
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Index Terms
Links
C Cassegrain
51
Cassegrain reflector
51
cavity model
59
cellular communications
6
circular patch
63
circular polarization
18
circular-array
48
coaxial probe feed
57
compact ranges
85
conformal structures
56
corner reflector
50
63
D DELTT
75
dielectric heating
71
dielectric loaded cavity
59
dielectric substrate
71
dipole
21
dipole of finite length
25
directional pattern
15
directivity
16
double quantum well (DQW) photon-assisted tunneling (PAT) dual-surface lens
75 53
E element factor
39
elliptical polarization
18
end-fire array
44
E-plane
14
63
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Index Terms
Links
equivalent electric and magnetic current densities
60
F far-field
39
far-field region
13
fast Fourier transform
49
feed
57
field patterns
13
FIR detector
69
FIR source
69
Fraunhofer region
13
Fresnel region
13
Friis equation
18
fringing effects
59
G gain
13
gain measurements
86
geometrical theory of diffraction
49
grating lobes
44
Gregorian dual-reflector antenna
52
ground plane
28
17
H half-power beamwidth
15
half-wavelength dipole
26
helical antennas
71
higher-order modes
63
horn antenna
54
H-plane
14
72
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Index Terms
hyperthermia
Links
7
I image theory
29
impedance
13
impedance measurements
87
infinitesimal dipole
21
infrared
69
infrared detectors
69
input impedance
17
isotropic radiator
15
59
L large circular-loop
33
LCVD
72
LCVD antennas
47
left-hand polarization
18
lens
71
lens antennas
53
linear array
42
linear wire antenna
21
linearly polarized
18
linearly polarized waves
63
log-periodic antennas
71
loop antenna
31
Luneberg lens
54
M major lobe
15
maximum effective aperture
23
measurement techniques
83
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75
Index Terms
Links
MEMS
47
microstrip antennas
56
microstrip arrays
64
minor lobes
15
mobile satellite communications
72
6
multiple feeds for circular polarization
63
multiplication pattern
39
N near-field region
13
nonuniform arrays
45
null
40
O offset microstrip line feed
57
omnidirectional pattern
15
outdoor ranges
83
P parabolic reflector
50
phased-array
37
physical optics
49
planar arrays
46
plane reflector
50
polarization
13
power density
15
power patterns
13
principal maximum
43
printed antennas
56
proximity-coupled feed
57
pyramidal horn
55
18
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Index Terms
Links
Q quarter-wave monopole
30
quasi-static analysis
76
R radar
9
radar antennas
10
radiating region
13
radiation intensity
16
radiation pattern
13
radiation resistance
17
radio astronomy
9
radio interferometer
9
radio telescope
9
radiometer
6
radiometer antennas
6
radome
66
reactive region
13
reciprocity theorem
13
reconfigurable antennas
2
rectangular lattice
64
reflection coefficient
29
reflector antennas
49
remote sensing
28
84
6
resonant frequency
59
resonant length
28
return loss
88
right-hand polarization
18
S satellite communications
4
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Index Terms
Links
scalar horn
56
scanning
37
sectoral E-plane and H-plane horns
55
sectoral horn
55
single-layer patch antenna
61
single-surface lens
53
small circular loop
31
small dipole
24
smart
2
spiral antennas
71
stacked microstrip antenna
61
surface impedance
70
synthetic aperture
6
synthetic aperture antenna
6
T tapered chamber
85
TEM
22
terahertz antenna
46
therapeutic applications
8
time average Poynting vector
15
total radiated power
16
transmission line model
58
transmission modes
73
triangular lattice
64
tunneling current
75
U uniform array
44
uniform N-element linear array
42
This page has been reformatted by Knovel to provide easier navigation.
