Bellingham, Washington USA

Tutorial Texts in Optical EngineeringVolume TT50

Fundamentals of Antennas:

Concepts and Applications

Christos G. ChristodoulouParveen F. Wahid

Library of Congress Cataloging-in-Publication Data

Christodoulou, C. G. (Christos G.)Fundamentals of antennas : concepts and applications / by C.G. Christodoulou and P.F. Wahid

p. cm .Includes bibliographical references and index.ISBN 0-8194-4112-0 (pbk.)

1.Antennas (Electronics). I.Wahid, P. F. (Parveen F.) II. Title.

TK7871.6 .C48 2001621.384'135dc21

2001032207CIP

Published by

SPIEThe International Society for Optical EngineeringP.O. Box 10Bellingham, Washington 98227-0010Phone: 360/676-3290Fax: 360/647-1445Email: spie@spie.orgWWW: www.spie.org

Copyright © 2001 The Society of Photo-Optical Instrumentation Engineers

All rights reserved. No part of this publication may be reproduced or distributedin any form or by any means without written permission of the publisher.

Printed in the United States of America.

ix

INTRODUCTION

The field of information science and technology incorporates several devices,including antennas, which can be used to transmit, collect and transferinformation. Understanding how these antennas work and how they can beutilized at different frequencies ranging from radio to terahertz requires someinsight into the physics of antenna operation and a knowledge of the basicparameters for their operation.

This book, which is tutorial in nature, contains seven chapters. Chapter 1outlines how antennas have evolved historically, and presents some importantadvances made in their design and applications. The chapter discusses the impactof antennas in various systems, to give the reader an idea of the range of theirapplications that include communications, remote sensing, radar, biomedicine,etc. In Chapter 2 the reader is introduced to the fundamentals of antennas. All ofthe figures of merit and parameters used to evaluate antennas are covered.Concepts such as radiation pattern, directivity, gain, bandwidth, polarization, andothers are explained in a very straightforward manner. The information providedin this chapter forms the cornerstone upon which all the other chapters are built.

Chapter 3 introduces the most basic type of antenna, the wire antenna, andpresents the analysis of this antenna for different configurations such as smalldipoles, dipoles of finite length, and loop antennas. These antennas are still usedtoday in a variety of applications such as communication, TV broadcasting, andnavigation. In Chapter 4, array antennas are discussed. Several antennas can bearranged in space, in different geometrical configurations, to produce a highlydirectional pattern. Such a configuration of multiple antenna elements is referredto as an antenna array. In an array antenna, the fields from the individualelements can be made to interfere constructively in some directions and cancel inothers. Phased array antennas offer the unique capability of scanning of the mainbeam (major lobe) by changing the phase of the excitation of 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 baseprovided by the previous chapters by explaining how different applicationsrequire different antennas and why a single antenna cannot be used successfullyfor all applications. Chapter 6 shows how an antenna can be integrated with adetector for successful operation in order to efficiently collect terahertz radiation.These integrated antennas have several applications in areas such as remotesensing, radio astronomy, plasma diagnostics, atmospheric studies, and spacecommunications. However, these applications demand the use of low-noisereceivers over a range of about 30 GHz to more than 1 THz. The serioustechnical challenges on the design and use of submillimeter-wave localoscillators and detectors that exist are presented and discussed in this chapter,which is a fusion between optics and antenna concepts.

x INTRODUCTION

In Chapter 7, antenna measurement techniques are described. Measurementsoften form an integral part of the antenna design process, with measurements onprototype antennas being conducted at various steps of the design process tocheck that the antenna meets the design specification. The key parameters thatare often measured are the radiation pattern, efficiency, gain, and impedance.Depending on the antenna and its application, other parameters such as thepolarization purity, power-handling capacity, etc., may also be measured. Theuse of sophisticated computerized equipment has made it possible to makeaccurate measurements of antenna parameters. The advantages and disadvantagesof performing measurements indoors using anechoic chambers versus outdoorranges are presented and discussed as well.

This book is intended for students, engineers, and researchers who have nottaken a formal antenna course and are interested in the basics of antenna theoryand operation. The authors have attempted to link the lower-frequency (RF)concepts to the higher-frequency (optics) concepts with which the readers may bemore familiar. The book is written in a modular fashion, so that readers canchoose the chapters they are interested in without having to go through the entirebook. It is the hope of the authors that readers find in this book the necessarytools and examples that can help them in incorporating antennas, as needed, intheir research problems.

vii

CONTENTS

Introduction / ix

Chapter 1. History and Applications / 11.1 History and development of antennas / 11.2 Applications and impact on systems / 3

1.2.1 Antennas in communication systems / 41.2.2 Antennas in remote sensing / 61.2.3 Antennas for biomedical applications / 71.2.4 Radio astronomy applications / 91.2.5 Radar antennas / 9

References / 10

Chapter 2. Fundamental Parameters of Antennas / 132.1 Radiation pattern / 132.2 Power density / 152.3 Radiation intensity / 162.4 Directivity / 172.5 Gain / 172.6 Input impedance / 172.7 Bandwidth / 182.8 Polarization / 182.9 Friis equation / 19References / 20

Chapter 3. Wire Antennas / 213.1 Infinitesimal dipoles / 21

3.1.1 Directivity / 233.2 Small dipole / 243.3 Dipole of finite length / 25

3.3.1 Input impedance / 283.4 Effect of infinite conductors on the radiation pattern of linear wire

antennas / 293.5 Loop antennas / 32

3.5.1 Small circular loop antennas / 323.5.2 Large circular-loop antennas / 34

3.6 Radiated fields of a short dipole and a small loop / 34References / 36

viii

Chapter 4. Antenna Arrays / 374.1 Array factors / 384.2 Uniform N-element linear array / 42

4.2.1 Broadside array / 444.2.2 End-fire array / 44

4.3 Planar arrays / 464.4 Circular arrays / 48References / 49

Chapter 5. Types of Antennas / 515.1 Reflector antennas / 51

5.1.1 Plane and corner reflectors / 515.1.2 Parabolic reflector / 51

5.2 Lens antennas / 545.3 Horn antennas / 565.4 Microstrip antennas / 57

5.4.1 Analysis of microstrip antennas / 595.4.2 Multiple feeds for circular polarization / 655.4.3 Microstrip arrays / 66

5.5 Radome coverings / 68References / 68

Chapter 6. Antennas for Infrared Detectors / 716.1 Antennas for infrared detectors / 726.2 Design of helical antennas for terahertz applications / 746.3 Design of broadband FIR antennas / 76References / 81

Chapter 7. Antenna Measurements / 857.1 Radiation pattern measurements / 85

7.1.1. Outdoor ranges / 857.1.2 Anechoic chambers / 86

7.2 Gain measurements / 887.2.1 Comparison method / 887.2.2 Two-antenna method / 89

7.3 Impedance measurements / 90References / 90

Index / 91

1

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

2 CHAPTER 1

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, frequency-independent 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 Long-distance telegraphy, navigation. Antennas are physically large but electrically small. Propagation is accomplished using earth’s surface and the ionosphere. Vertically polarized waves.

Low Frequency (LF) 30-300 kHz Aeronautical navigation services, long distance communications, radio broadcasting. Vertical polarization.

Medium Frequency (MF)

300-3000 kHz Regional broadcasting and communication links. AM radio.

High Frequency (HF) 3-30 MHz Communications, broadcasting, surveillance, CB radio (26.965–27.225 MHz). Ionospheric propagation. Vertical and horizontal propagation.

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 Weather, traffic control, tracking, hyperthermia.

C 4-8 GHz Weather detection, long-range tracking. X 8-12 GHz Satellite communications, missile guidance,

mapping. Ku 12-18 GHz Satellite communications, altimetry, high-

resolution mapping. K 18-27 GHz Very high resolution mapping. Ka 27-40 GHz Airport surveillance. Submillimeter waves Experimental stage.

4 CHAPTER 1

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 ETS-VI (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].

6 CHAPTER 1

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 downward-looking, 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.

8 CHAPTER 1

(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 130-m 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.

10 CHAPTER 1

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: McGraw-

Hill, 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.

13

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 passiveantennas used either as a transmitter or receiver by virtue of the reciprocitytheorem [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 thatcharacterizes the electromagnetic field generated by an antenna. The fieldintensity of the propagating wave decreases by 1/R with distance R from thesource.

To understand how an antenna radiates, consider a pulse of electric chargemoving along a straight conductor. A static electric charge or a charge movingwith a uniform velocity does not radiate. However, when charges are acceleratedalong a conductor and are decelerated upon reflection from its end, radiatedfields are produced along the wire and at each end. A detailed explanation of howan antenna radiates is given in [3-5].

The 3D spatial distribution of the radiated energy is displayed as a functionof the observers position along a constant radius. Power patterns and fieldpatterns are commonly used. The power pattern is a plot of the received power ata 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 surroundingan 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 orFraunhofer region. These regions are defined as follows [2]:

The reactive near field is the portion of the near-field region immediatelysurrounding the antenna where the reactive field dominates. The radiating near-field region is the portion of the near field of an antenna between the reactivenear-field region and the far-field region, where the angular field distribution isdependent on the distance from the antenna. The far-field region is the region ofthe field of an antenna where the angular field distribution is essentiallyindependent of the distance from a specified point in the antenna region. If D isthe largest dimension of the antenna and is the wavelength, then the reactivenear-field region extends to a distance R 0.62 2 /D , the Fresnel region lies

between R 0.62 2 /D and R < 22D , and the Fraunhofer region extends

14 CHAPTER 2

FNBW

HPBWMinor lobes

Radiationintensity

Major lobe

SidelobeBack lobe

/2 0 /2

from 22R D to infinity. The minimum distance for the far field observationsis 22D .

The radiation pattern of an antenna is commonly described in terms of itsprincipal 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 thedirection of maximum radiation, and the H-plane pattern is the plane containingthe magnetic field vector and the direction of the maximum radiation. Figure 2.1shows a rectangular and a polar plot of a radiation pattern.

(a)

0 dB

-10 dB

-20 dB

-30 dB

0 dB

-10 dB

-20 dB

-30 dB

600600

300 300

1200 1200

900

1500 1500

1800

00

900

(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 directionthan in others. An isotropic radiator, often used as a reference for expressing anantennas directional properties, is a hypothetical lossless antenna radiatingequally in all directions. An omnidirectional pattern is a special case of adirectional pattern where the radiation is nondirectional in the azimuthal planeand 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 identifythe major lobe in the θ = 0 direction and the minor lobes (sidelobes and backlobes) in the other directions. Some patterns may have more than one major lobe.The major lobe contains the direction of maximum radiation, and between thelobes there are nulls or directions of minimum radiation. Minor lobes levels areexpressed relative to the major lobes level. Sidelobe levels of −20 dB or lowerare acceptable for many applications. The half-power beamwidth is the width ofthe main lobe in degrees, at the half-power points. The first null beamwidth is thewidth of the main lobe between its first nulls. Generally, the beamwidth of anantenna 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 givenby

16 CHAPTER 2

]Re[21 *HxEW

W/m2 (2.1)

where E

and H

are peak values in time. A time dependence of ejt has beenassumed. The time average power radiated by an antenna is the total powercrossing a closed surface in the normal direction, and is given by

radS

P W ds

W (2.2)

For an isotropic radiator, the power density is only in the radial direction and isnot a function of θ or Φ; i.e.,

0 rW W a

W/m2 (2.3)

and the total radiated power is given by

22

rad 00 0

20

)

4

( ) ( sinr rS

r W

P W ds W a r d d a

or

rad0 24

PWr

W/m2 (2.4)

As can be seen, the power density is uniformly distributed over the surface of asphere of radius r.

2.3 Radiation intensity The radiation intensity U (θ, Φ) of an antenna is the power radiated per unit solidangle, and is a far-field parameter.

U = r2 W W/unit solid angle (2.5)

where W is the radiated power density in W/m2. The total power can be obtainedby integrating the radiation intensity over the entire solid angle

2

rad0 0

sinP U d U d d

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 givendirection to the average radiation intensity, i.e, total radiated power/4:

rad

( )4 UDP

(2.7)

If the direction is not specified, the direction of the maximum radiation isimplied. The directivity is an indication of the directional properties of theantenna. It does this by comparing the field intensity at any point to that of anisotropic radiator. The directivity is a dimensionless quantity and is usuallyexpressed in decibels.

2.5 Gain The gain of an antenna is defined as the ratio of the radiation intensity in a givendirection to the radiation intensity that would be obtained if the power acceptedby the antenna were radiated isotropically [2]. The gain can be expressed as

0

( )4 UGP

(2.8)

where P0 is the power input to the antenna. If the direction is not specified, thedirection of maximum radiation is implied. The gain is a dimensionless quantity,expressed in decibels. The directivity is based on radiated power, whereas thegain is based on input power. The gain is related to the directivity through

eG D (2.9)

where e is the antenna efficiency and takes into account losses due to mismatchat the antenna terminals and dielectric and conduction losses. For a perfectlymatched 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 atits terminals. The antenna impedance ZA can be expressed as

= +A A AZ R j X Ω (2.10)

where RA is the antenna resistance in ohms and XA is the antenna reactance inohms.The radiation resistance is expressed as

18 CHAPTER 2

= +A r LR R R Ω (2.11)

where Rr is the radiation resistance and RL is the loss resistance. The radiationresistance is associated with the radiation of real power. For a lossless antenna,the input resistance reduces to the radiation resistance. The input impedance isalso the ratio of the voltage to the current at its terminals or the ratio of theappropriate electric and magnetic fields at a point. The input impedance can bedetermined by using equivalent circuit representation for the antenna [4]. Theimpedance is a function of the geometry of the antenna, the method of excitation,and the frequency. It is generally determined experimentally, although in recentyears, numerical electromagnetic techniques have been developed that allow oneto determine the impedance accurately for many complex geometries.

2.7 Bandwidth The bandwidth of an antenna is defined as the range of frequencies within whichthe performance of an antenna conforms to a specific standard [2] with respect tosome characteristic. The pattern bandwidth, expressed in terms of beamwidth,sidelobe levels, and pattern characteristics, is used to characterize the radiationpattern variations. The impedance bandwidth relates to the input impedance andradiation efficiency. The bandwidth is expressed as the ratio of the upper to lowerfrequencies of acceptable operation for broadband antennas. For narrowbandantennas, the bandwidth is usually expressed as a percentage of the frequencydifference over the center frequency.

2.8 Polarization The polarization of a wave is the locus of the tip of the electric field vector, E

,as a function of time. For a linearly polarized wave, the locus is a straight line; itis a circle for a circularly polarized wave and an ellipse for an ellipticallypolarized wave. The linear and circularly polarized waves are special cases of theelliptically polarized wave. Right-hand polarization and left-hand polarizationsrefer to the clockwise (CW) and counterclockwise (CCW) movement,respectively, of the tip of the E

vector as observed along the direction ofpropagation. A linearly polarized antenna is one that radiates a linearly polarizedwave, and a circularly polarized antenna radiates a circularly polarized wave.

Consider a uniform plane wave traveling in the z direction, given by

x x y yE E a E a

i.e.,

0 0 cos( ) cos( )x x x y y yE E t kx a E t kz a

(2.12)

FUNDAMENTAL PARAMETERS OF ANTENNAS 19

where Ex0 and Ey0 are constants, x and y are the phases, and k is the wavenumber. For linear polarization, = x = y = 0 or, and

0

0

yy x

x

EE E

E (2.13)

which represents a straight line. The + and signs correspond to a phase of = 0and , respectively. For circular polarization, = y− x = /2, and

0

01y

x

EE

(2.14)

This gives 2 2 1x yE E , which represents a circle.For the case of elliptical polarization, = − /2 and Ey0 Exo. 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 torepresent the polarization of the wave radiated by an antenna [3]. Each point onthe Poincaré sphere represents a unique polarization.

2.9 Friis equation The Friis equation relates the power received to the power transmitted betweentwo antennas separated by a distance R > 2D2/, D being the largest dimension ofeither antenna. For matched alignment along the maximum direction for radiationand reception, the equation is [3]

2

4r

r tt

P G GP R

(2.15)

where Pt is the power input at the transmitting antenna, Pr is the power receivedby the receiving antenna, and Gr and Gt are the gains of the receiving andtransmitting antennas, respectively.

20 CHAPTER 2

(a)

(a) (b)

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.

Ex

Ey

ba

Ex

Ey

(a,0

(0,a)

Ex

Ey

(a,0

(0,2a)

Ex

Ey

21

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 / 2l 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

0 ˆ( ) zI z I a (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]

Figure 3.1. An infinitesimal dipole at the origin.

z

y

x

θ

l/2

l/2

Ф

22 CHAPTER 3

02

02

0

cos 11

2

sin 1 11

4

0

sin 11

4

0

jkrr

jkr

jkr

r

I lE e

jkrr

kI lE j e

r jkr kr

E

kI lH j e

r jkr

H H

(3.2)

The complex power density is

* **1 1ˆ ˆRe( ) ( )

2 2 r rW ExH E H a E H a

(3.3)

and the total radiated power in the radial direction is

20

31

3 ( )r

S

I l jP W ds

kr

(3.4)

The real radiated power in the radial direction is

2

0rad 3

I lP

(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

0

0

sin4

sin4

0

jkr

jkr

r r

kI leE j

r

kI leH j

rE E H H

(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

2

rad 0

1

2 rP I R (3.7)

and obtaining

2 2

2280

3r

l lR

(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

2 22 0

av 2

1 1 sinˆ ˆRe( )

2 2 2 4r r

kI lW ExH E a a

r

(3.9)

The radiation intensity is

2avU r W (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

max0

rad

34

2

UD

P (3.11)

The maximum effective aperture is

2 2

em 0

3

4 8A D

(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

0

0

2ˆ1

for 0 / 2( , , )

2ˆ1

for /2 z /2

z

e

z

I z al

z lI x y z

I z al

l l

(3.13)

where I0 is a constant and the primed coordinates are points located on the dipole.

WIRE ANTENNAS 25

Figure 3.3. Small dipole located at the origin.

The far fields of the small dipole are given by [1,2]

0

0

sin8

sin

80

jkr

jkr

r r

kI leE j

r

kI leH j

rH H E E

(3.14)

The radiation resistance of the small dipole is

2

2rad2

0

220r

P lR

I

(3.15)

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

dz l/2

zP (r, , )

r

y

x

l/2

=

26 CHAPTER 3

0

0

sin2

for 0 / 2( 0, 0, )

sin2

for / 2 0

z

e

z

lI k z a

zI x y z

lI k z a

l z

(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

0

0

cos cos cos2 2

2 sin

cos cos2 2

2 sin

jkr

jkr

kl kl

I eE j

r

kl klE I e

H jr

(3.17)

The average power density is

2av av

02 2

2

1ˆ ˆ

2

cos cos cos2 2 ˆ

sin8

r r

r

W W a E a

kl klI

ar

(3.18)

and the radiation intensity is

202

av 2

2

cos cos cos2 2

sin8

kl klI

U r W

(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

0

0

cos cos2

2 sin

cos cos2

2 sin

jkr

jkr

I eE j

r

I eH j

r

(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 λ2. Expressions for determining the radiation resistance and the directivity for a dipole of length l can be found in [1].

I0 Current I e

l = l = 3 /2 l = 2

l = /4 l = /2

l/2

l/2

Figure 3.4. Current distributions along a finite-length dipole.

28 CHAPTER 3

Figure 3.5(a). Radiation patterns of dipoles of different lengths.

0 dB

10 dB

20 dB

30 dB

0

90

180

90

0 dB

10 dB

20 dB

30 dB

0

90

180

90

Figure 3.5(b). Radiation pattern of a l = 1.5 dipole.

0 dB

10 dB

20 dB

30 dB

0 dB

10 dB

20 dB

30 dB

0 dB

10 dB

20 dB

30 dB

0 dB

10 dB

20 dB

30 dB

0 dB

10 dB

20 dB

30 dB

0 dB

10 dB

20 dB

30 dB

l<< l=/2 l=

600 600

300 300

00

1200 1200

900

1500 1500

1800

900 900

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

2 2

in 0in2 2 r

I IR R (3.21)

where Rin is the radiation resistance at the input (feed) terminals, rR the radiation resistance at the current maximum, I0, the current maximum and Iin, 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…., inR is infinite. In practice, inR 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, inrR R since the current maximum occurs at the input terminals. The input impedance of a half-wavelength dipole is inZ = 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

0 sin [2cos( cos )] 04

jkrkI leE j kh z

r

30 CHAPTER 3

R2 R1

i1 r

2r1

i2

h

h

Actual source

Direct

ReflectedDirect

Reflected

P1

P2

Virtual source (image)

σ = ∞

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.

1

0

1

sin4

jkr

d

kI leE j

r

(3.23)

and the reflected component as

2

0

2

sin4

jkr

r h

kI leE j R

r

(3.24)

Here, Rh, the reflection coefficient, is = −1,

ˆ ˆcos sin siny ra a

and 2 2sin 1 sin sin (3.25)

The total far field, valid only above the ground plane, can be expressed using the approximations r1 = r – h cos , r2 = r + h cos for the phase terms, and r1 = r2 = r for the amplitude terms, as

220 1 sin sin [2 sin( cos )]4

d r

jkr

E E E

kI lej j kh

r

(3.26)

32 CHAPTER 3

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 = I0, where I0 is a constant.

R2 R1

i1 r

2 r1 2

h

h

Actual source

Direct

ReflectedDirect

Reflected

P1

P2

Virtual source(image)

σ = ∞

WIRE ANTENNAS 33

Figure 3.9. Small circular loop at the origin.

The far fields of the small loop are given by [1-3]

2 20

2 20

sin4

sin4

0

jkr

jkr

r r

k a I eE

r

k a I eH

rH H E E

(3.27)

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

24

rad 0( )12

P ka I

(3.28)

The radiation resistance, determined by setting2

0rad 2 r

IP R , is given by

Rr

z

y

x

θ

θ'=π/2

Ф' a dФ IФ

dl=a

l

Ф

IΦ

34 CHAPTER 3

2 2 2( )6rR k a

(3.29) In terms of the area S of the loop and the circumference C, we have

4

220r

CR

42

2

4

20

31,171

r

r

cR

SR

(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 N2. 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]

01

01

( sin )2

( sin )2

0

jkr

jkr

r

ak I eE J ka

rE akI e

H J kar

H H

(3.31)

where J1(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 dB

10 dB

-20 dB

30 dB

0 dB

10 dB

-20 dB

30 dB

0 dB

10 dB

-20 dB

30 dB

0 dB

10 dB

-20 dB

30 dB

0 dB

10 dB

-20 dB

30 dB

0 dB

10 dB

-20 dB

30 dB

a = 0.1

900

a = 0.2a = 0.5

1800

1500 1500

1200

900

600 600

00

300300

1200

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 I0 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 I0 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 Im [2,4].

Table 3.1. Comparison of the fields of a short dipole and a small loop.

Infinitesimal Dipole Small Dipole

2 20

2 20

sin4

sin4

0

jkr

jkr

r r

k a I eH

r

k a I eE

rH H E E

0

0

sin4

sin4

0

jkr

jkr

r r

kI leE j

r

kI leH j

rE E H H

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.

37

CHAPTER 4 ANTENNA ARRAYS

Several antennas can be arranged in space, in different geometricalconfigurations, to produce a highly directional pattern [1-5]. Such a configurationof multiple antenna elements is referred to as an antenna array. In an arrayantenna, the fields from the individual elements interfere constructively in somedirections 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 arrayelement (phased-array antennas). Also, a large variety of radiation patterns andsidelobe levels can be achieved by controlling the magnitude of the excitationcurrent 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 performanceof an array antenna; the array geometry (linear, circular, planar, etc., arrangementof the radiating elements), the distance of separation between adjacent elements,the amplitude current excitation of each individual element, phase excitation ofeach individual element, and the radiation pattern of each individual element

Figure 4.1 shows a two-dimensional planar array. The individual elementconsists of a stacked microstrip antenna as shown in Fig. 4.2. Each microstripantenna is fed by an external phase shifter through a coaxial connection.

Figure 4.1. An array antenna of 6×9 microstrip elements.

38 CHAPTER 4

Figure 4.2. The configuration of a single element used for the array.

4.1 Array factor Consider an array of two dipoles in free space, as shown in Fig. 4.3 below. Letthe dipole at (0, 0, d/2) carry a current I0 ( / 2) and the one at (0, 0, −d/2) carrya current I0 −( / 2) , where is the phase difference between the two dipoles.This phase difference can be achieved through a variety of phases shifters thatemploy microwave, semiconductor, or optical techniques.

The total electric field at the observation point P is given as the vectorial sumof the fields due to the two individual antennas [1]:

Figure 4.3. Geometry of two dipoles of length l and separation d.

r

y

r1

P

d

r2

z

ANTENNA ARRAYS 39

1 2

total 1 2

( / 2) ( / 2)

1 1 2 21 2

cos cos4

j kr j kro

E E E

j kI e el a ar r

(4.1)

1 cos2dr r and 2 cos

2dr r

Hence, Eq. (4.1) becomes

total 1 2

0 1 cos 2cos ( cos )4 2

E E E

j kI jkra e kdr

l

(4.2)

A close examination of Eqs. (4.1) and (4.2) shows that the total field is equalto the field of the single element (element factor) located at the origin, multipliedby an array factor (AF) that is given by

AF12cos ( cos )2

E kd (4.3)

In general, the far-field pattern of any array is given by the multiplication patternof 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 radiatingelements comprising the array, the current excitation of the elements, the phaseshift between the elements, the distance of separation d between the elementsand the frequency of operation.

Example 4.1:Find the total pattern of two identical horizontal dipoles shown in Fig. 4.4, with

4d and 0 .Consider the normalized array factor in Eq. (4.3); i.e.,

1AF cos ( cos )2n kd

(4.5)

40 CHAPTER 4

Figure 4.4. Far-field geometry of two dipoles of length l separated by a distance d.

In this case, 1 1 2( cos ) cos2 2 4

kd . Thus, the array factor becomes

AF cos cos4n

(4.6)

No null is introduced by the array factor. The only null that occurs is the one dueto 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 AF cos 4(cos 1)n , which introduces a null at 0

deg. Figure 4.6 illustrates the principle of pattern multiplication in this case. If2 , then the nulls would appear at =90 deg and =180 deg.

r2

r

y

r1

d

z

ANTENNA ARRAYS 41

Figure 4.5. Element factor, array factor, and total pattern for a two-element array of

infinitesimal horizontal dipoles with 4d and 0 .

Figure 4.6. Element factor, array factor, and total pattern for a two-element array of horizontal dipoles with 4d and 2 .

×

×

Element pattern

Multiplication pattern of 2 sources spaced by 0.25 λ. phase delta=0 deg.

Multiplication pattern of 2 sources spaced by 0.25 λ. phase delta=0 deg.

Array factor of 2 sources spaced by0 25 λ. phase delta= 0 deg.

Array factor of 2 sources spacedby 0.25 λ. phase delta= 0 deg.

Element pattern

42 CHAPTER 4

Figure 4.7. Element factor, array factor, and total pattern for a two-element array of horizontal dipoles with 4d 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 samemagnitude but with a progressive phase shift between the elements. Thedistance of separation between adjacent elements is d.

The array factor can be expressed as the sum of the contributions from theelements of the array, i.e.,

2 3 ( 1)AF 1 ...j j j j Ne e e e (4.7)

where, coskd .Equation (4 7) is a geometric series that can be expressed as

sin2AF

sin2

N

(4.8)

Multiplication pattern of 2 sources spaced by 0.25 λ. phase delta=0 deg.

×

Element pattern Array factor of 2 sources spaced by0 25 λ. phase delta= 0 deg.

ANTENNA ARRAYS 43

Figure 4.8. Geometrical configuration of N isotropic elements along z separated by a distance d and fed with a progressive phase of .

Figure 4.9. An 8-element linear microstrip array antenna.

rN

r3

r2

r1

d

d

44 CHAPTER 4

From a close examination of the AF in Eq. (4.8), the following points can bemade:

1. The principal maximum (major lobe) occurs when the denominator goesto zero, i.e., 0 .

majorcos 0kd or majorcos2 d

2. The nulls occur when the numerator goes to zero, i.e.,

sin( / 2) 0N or / 2N n for n =1, 2, 3,

Figure 4.9 depicts a linear array of eight microstrip antennas. The entire antennais mounted on a ground plane.

4.2.1 Broadside array A broadside array is an array that has its major lobe at θmajor = 90 deg, that is, in adirection normal to the axis of the array. Therefore, we have ψ = kd cos90+ 0 , which gives 0 . Hence, in order to have the main beam at θ = 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 θmajor = 0 deg or θmajor = 180 deg. For θmajor= 0 deg we set kd cos θ += kd cos 0 + , which indicates that the progressivephase shift should be = −kd. For θmajor = 180 deg, the condition is = kd.

Example 4.2To demonstrate the method of designing uniform array antennas and to introducethe concept of grating lobes, a 10-element uniform array with 0 is consideredfor two different values of the spacing d ( 4d and d ) as shown in Fig.4.10. Since 0 , a major lobe should appear at 90 deg. However, whend , two more maximum lobes appear at 0 deg and 180 deg. These twoextra maximum lobes are called grating lobes. These lobes are usually undesiredlobes that occur due to some constructive interference of the individual elementfields. These grating lobes appear when the distance of separation d is greaterthan . Thus as a rule of thumb, d should always be less than to avoid anygrating lobes.

ANTENNA ARRAYS 45

It should be mentioned here that nonuniform arrays are arrays where theelements are not fed with the same amplitude. Examples of these are the binomialarray and Dolph-Tschebyscheff array. In the binomial array, the amplitude ofeach element is changed to maximize the beamwidth of the major lobe; and in theDolph-Tschebyscheff array, the major beam to sidelobe ratio is maximized bychanging the amplitude excitation to specific values given by formulas found in[1].

Array Factor of 10 sources spaced by 0.25 lambda, phase delta= 0 deg

2

4

6

8

10

30

210

60

240

90

270

120

300

150

330

180 0

Array Factor of 10 sources spaced by 1 l ambda, phase delta= 0 deg

2

4

6

8

10

30

210

60

240

90

270

120

300

150

330

180 0

Figure 4.10. Array factor patterns for a 10-element, uniform broadside array with 0 .

46 CHAPTER 4

Figure 4.11. Planar array geometry.

4.3 Planar arrays Linear arrays can only scan the beam in one direction ( ). To also scan the mainbeam along the direction as well, two-dimensional arrays are employed. Two-dimensional (planar) arrays provide more gain and lower sidelobes than lineararrays. The design principles for planar arrays are the same as those discussedearlier for the linear arrays.

The array factor of a planar array can be expressed as the multiplication ofthe array factors of two linear arrays, one along the x direction and the otheralong the y direction [1]. The array factor can be written as

planarAF AF AFx y (4.9)

orsin( / 2)sin( / 2)AF

sin( / 2) sin( / 2)yx

x y

NMM N

(4.10)

where sin cosx x xkd and sin cosy y ykd .Generally, array antennas are used at RF frequencies, at or below the

gigahertz range. Array antennas that include photonic and optical interfaces canalso be used at terahertz frequencies. Figure 4.12 shows the setup used forimaging purposes at terahertz frequencies using a 5×5 array of helical antennas.The antennas are approximately 300 m apart. The terahertz antenna structures

y321 N

2

M

1

r

z

x

ANTENNA ARRAYS 47

Figure 4.12. Helical array antenna used as a terahertz imager.

were fabricated by using a laser chemical vapor deposition (LCVD) process toform fibers that can be grown into complex three-dimensional structures directlyon semiconductor substrates. By focusing the laser through a diffractive optic,arrays of antennas can be fabricated at the same time. Terahertz radiationdetection devices can be realized by combining the LCVD antennas with MEMSmicrobolometers that convert received terahertz radiation into a change inresistance. Arrays of these antenna-bolometer pairs can be fabricated on the samesubstrate to realize a terahertz-imaging device.

Figure 4.13 shows a photograph of a 5-turn rectilinear helical antennastructure 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.

terahertzOptics

object beingscanned

LCVD Helical AntennaMicrobolometer Array with Parallel Output

terahertzsource

processingelectronics 30fps

THzOptics

48 CHAPTER 4

Figure 4.14. Geometry of an N-element circular array.

array element in the planar array antenna in Figure 4.12. The spiral diameter was200 m, the pitch angle is 13 deg, the loop height is 185 m, and the wirediameter is 18 m. Assuming that the useful frequency range of operation for theaxial antenna mode is derived from the antenna circumference equaling 0.75 to1.33 , the antenna would have a frequency range of 0.36 to 0.63 THz. Theantenna 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 directionfinding, GPS, space navigation, radar, sonar, etc. Figure 4.14 shows the geometryof an N-element circular array. The array factor in this case is given by [1]:

sin cos( ) sin cos( )AF( , )

1

jkaN n o o nI enn

(4.11)

where o and o are the angles of the main beam.

P

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: McGraw-

Hill, 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: CambridgeUniversity Press, 1986.

5. W. L. Stutzman, G. A. Thiele, Antenna Theory and Design, New York: JohnWiley & Sons, 1981.

6. R. N. Dean, Jr., P.C. Nordine and C. G. Christodoulou, 3-D helical THzantennas, Microwave and Optical Technology Letters, pp. 106-111, Jan. 20,2000.

51

CHAPTER 5

TYPES 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

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.

Figure 5.2 Parabolic reflector.

S

Aperture plane

B

A

P

A'

F Axis

B'

Q

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, single-surface 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 TE10 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 effL (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]:

eff

eff

0.3 0.120.412

0.258 0.8

r

r

Wh

L hW

h

(5.1)

where, eff is the effective dielectric constant of a microstrip transmission line given by

1/ 2

eff

1 11 12

2 2r r

r

h

W

(5.2)

Thus, the effective distance separating the two radiating slots becomes

eff 2L L L (5.3)

It is this adjusted length that is utilized in calculating the resonant frequency of the antenna, from [12]:

010eff eff

( )2

r

cf

L

(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]

sin( )cos( )sin( )x yx mnp x y z

k kE j A k x k y k z

cos( )sin( )sin( )y zy mnp x y z

k kE j A k x k y k z

22( )cos( )cos( )cos( )z

z mnp x y z

k kE j A k x k y k z

(5.5)

cos( )sin( )cos( )yx mnp x y z

kH j A k x k y k z

62 CHAPTER 5

sin( )cos( )cos( )xy mnp x y z

kH j A k x k y k z

0zH

with

, 0,1,2...

, 0,1,2...

, 0,1,2...

x

y

z

mk m

Ln

k nWp

k ph

0pnm (5.6)

and mnpA is the amplitude coefficient. The resonant frequencies for the cavity are

2 2

1( )

2r mnp

m n pf

L W h

(5.7)

Examining the above fields for 100TM z dominant mode excitation, we see that

0y zk k and the field components reduce to

100

100

cos

sin

z

y

E j A xL

H A xL L

(5.8)

We obtain the equivalent electric and magnetic current densities on the patch using

ˆ

ˆ

J n H

M n E

(5.9)

where n is the outward directed surface normal. 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 dB

10 dB

20 dB

30 dB

0

90

180

90

0 dB

10 dB

20 dB

30 dB

0

90

180

90

Figure 5.16. E-Plane radiation pattern of the stacked element phi-cut = 0 degrees, f = 4.75 GHz.

TYPES OF ANTENNAS 65

0 dB

10 dB

20 dB

30 dB

0

90

180

90

0 dB

10 dB

20 dB

30 dB

0

90

180

90

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 the dominant mode ( 110TM z ) and for higher-order modes

( 210TM z , 010TM z , 310TM z …), 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

66 CHAPTER 5

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 ( 210TM z and 410TM z ), the four feed probes have

phases of 0 deg, 90 deg, 0 deg, and 90 deg, while for the odd modes ( 110TM z and

310TM z ) 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 90-deg phase shift between the two feeds for each patch.

TYPES OF ANTENNAS 67

Figure 5.20. Rectangular lattice configuration.

Figure 5.21. Triangular lattice configuration.

68 CHAPTER 5

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.

TYPES OF ANTENNAS 69

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 finite-sized 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.

71

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

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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 [9-13]. 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

ANTENNAS FOR INFRARED DETECTORS 73

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 2.7-THz 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.

ANTENNAS FOR INFRARED DETECTORS 75

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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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

140R Χ = λ 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].

D= diameter of C=circumference helix π tan α = s/C = πL S C= +2 2 length of

α = pitch N= number of d=diameter of helix

ANTENNAS FOR INFRARED DETECTORS 77

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 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.

ANTENNAS FOR INFRARED DETECTORS 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 with the electric field polarized in the x-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 back-scattered 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, with an electric field polarized in the x-direction, and the simulation results for the RCS as a function of frequency and at different elevation angles in the x-z plane, are shown in Fig. 6.7. [35]

A new bowtie antenna with dimensions designed to operate around the 1.6-THz 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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Figure 6.8. Modified bowtie antenna design.

Figure 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 of millimeter and sub millimeter technology to earth’s upper atmosphere: results to date and potential for the future,” the 4th 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 ClOx/NOx,” Nature, vol. 315, p. 207, 1985.

x

y

28.2µm

15.6µm

ANTENNAS FOR INFRARED DETECTORS 81

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 submillimeter-wave 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 kinetic-inductance 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.

ANTENNAS FOR INFRARED DETECTORS 83

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.

85

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 Eθ and Eφ 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].

86 CHAPTER 7

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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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 far-field 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 half-wavelength 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 PR is noted. The test antenna is then replaced with reference antenna, and the received signal level PR is noted. The gain of the antenna is given by

AR

R

PG GP

=

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

2 2

2 2(4 )r tGP P

rλ=

π (7.1)

where Pt 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

4 r

t

PrGP

π=λ

(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

0201GGG = (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

2

1

GGG =′ (7.4)

where G1 is the gain of one antenna above the reference and G2 that of the second antenna; then we have

02

01

GG

G =′ (7.5)

and, therefore,

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GGG

GGG

′=

′=

02

01

(7.6)

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

1

VSWR1

+ ρ=

− ρ (7.7)

The return loss is given by the equation below and is generally expressed in decibels:

RL = 2

21 VSWR 1

VSWR 1+ = − ρ

(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.

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INDEX

Index Terms Links

#

90-degree hybrid 63

A

absorbing material 84

adaptive 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 78

broadband FIR antennas 75

broadside array 44

Index Terms Links

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C

Cassegrain 51

Cassegrain reflector 51

cavity model 59

cellular communications 6

circular patch 63

circular polarization 18 63

circular-array 48

coaxial probe feed 57

compact ranges 85

conformal structures 56

corner reflector 50

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) 75

dual-surface lens 53

E

element factor 39

elliptical polarization 18 63

end-fire array 44

E-plane 14

Index Terms Links

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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 17

gain measurements 86

geometrical theory of diffraction 49

grating lobes 44

Gregorian dual-reflector antenna 52

ground plane 28

H

half-power beamwidth 15

half-wavelength dipole 26

helical antennas 71 72

higher-order modes 63

horn antenna 54

H-plane 14

Index Terms Links

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hyperthermia 7

I

image theory 29

impedance 13

impedance measurements 87

infinitesimal dipole 21

infrared 69

infrared detectors 69

input impedance 17 59 75

isotropic radiator 15

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

Index Terms Links

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MEMS 47 72

microstrip antennas 56

microstrip arrays 64

minor lobes 15

mobile satellite communications 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 18

power density 15

power patterns 13

principal maximum 43

printed antennas 56

proximity-coupled feed 57

pyramidal horn 55

Index Terms Links

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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 28

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 84

reflector antennas 49

remote sensing 6

resonant frequency 59

resonant length 28

return loss 88

right-hand polarization 18

S

satellite communications 4

Index Terms Links

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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

Index Terms Links

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V

voltage standing wave ratio 87

W

wire antenna 31

wireless communications 2 6

Y

Yagi-Uda imaging arrays 71