Spiral Antenna Miniaturization with High-contrast Dielectrics
A Thesis
Presented in Partial Fulfillment of the Requirements for the Degree Master of
Science in the Graduate School of The Ohio State University
By
Bradley Allen Kramer, B.Sc.
*****
The Ohio State University
2004
Approved by Master's Examination Committee:
Prof. John L. Volakis, Adviser Adviser Adj. Asst. Prof. Chi-Chih Chen Department of Electrical and Computer Engineering ii ABSTRACT
There is a great interest in the automotive and military sectors for small broadband antennas that meet modem communication needs. These needs require ultra- wide bandwidth (>10:1) broadband antennas, such as the spiral antenna. However, the physical size of the antenna at the low-frequency end becomes prohibitively large for many applications. To reduce the size of the antenna, miniaturization techniques such as high-contrast (εr>l and/or μr> 1) material loading or reactive loading must be employed. The concept of antenna miniaturization is to increase the electrical size of the antenna without increasing its physical size by slowing down the current flowing on the antenna structure. A common approach is to use dielectric materials to reduce the propagation constant of the current. This approach has received considerable attention in the past but has been limited by the lack of quality dielectrics which exhibit low-loss and high permittivity. However, there has recently been a renewed interest because of the currently available low-loss high-contrast dielectrics. In addition, size reduction using high- contrast dielectrics has already been demonstrated for narrowband antennas, such as patch antennas, but not for broadband antennas. Therefore, the concept of miniaturizing a broadband spiral antenna using dielectric materials is investigated experimentally and numerically. To investigate the miniaturization of the spiral antenna, a previously developed shallow cavity backed spiral antenna is used as the starting point. This design was then altered to facilitate the dielectric loading by using only a single resistor to terminate the spiral arm instead of multiple resistors. In addition, the previous balun which occupied the surface of the antenna was removed in favor of a hybrid balun. The performance of iii the new balun and termination are evaluated and compared to the previous balun and termination methods. Following the discussion of these modifications and improvements the miniaturization of a spiral antenna is studied using a 2” square spiral. It is shown that by loading the spiral with high-contrast dielectrics it can achieve sufficient operation down to 574 MHz where its size is only λ/10. As a consequence of dielectric loading there are issues that arise such as impedance reduction. This issue is examined using simulations and is addressed by introducing the concept of dielectric tapering. In addition to demonstrating the practicality of broadband antenna miniaturization using high-contrast materials, it is also observed that there are limitations associated with the miniaturization and that these limitations require further examination.
iv ACKNOWLEDGMENTS
I wish to thank Prof. John. L. Volakis and Dr. Chi-Chih Chen, for their advice, intellectual support, encouragement, and enthusiasm during the course of this research. Thanks is also due to Ming Lee for the valuable discussions and his alternative approach to antenna miniaturization which led to further and invaluable insights into the problem.
v VITA
August 19, 1978 ...... Born - Newark, Ohio, United States of America
2002 ...... B.Sc. Electrical and Computer Engineering The Ohio State University
2002 - present ...... Graduate Research Associate, The Ohio State University
PUBLICATIONS
Research Publication
1. Brad A. Kramer, Ming Lee, Chi-Chih Chen and John L. Volakis, "Design and Performance of an Ultra Wideband Ceramic-Loaded Slot Spiral," Accepted by IEEE Transactions on Antennas and Propagation. 2. Brad A. Kramer, Chi-Chih Chen and John L. Volakis, "The Development of a Mini-UWB Antenna," AMTA 2004 Conference Proceedings, Oct. 2004.
FIELDS OF STUDY
Major Field: Electrical and Computer Engineering
vi Table of Contents
ABSTRACT ...... •...... •.•...... •...... •....•...... •.•.••..••.•.••.•.••.••••.••.•.•..•.•...... III
ACKNOWLEDGMENTS •.•.••.•..•.•.••.•.••.•.••.•.•.••.•.••...•..•.•..•.••.•.••....•..•...... •..•...... •.....•••.••• V
VITA ...... ••.•.••.••••.•.••••.•.••••.•.•.•. VI
PUBLICATIONS ••.•.••.•..•.•.•.•..•.••.•.••.•.••.•.•..•.•.••.••••.••••••.••.••.•.••••.•..•.••.•.••.••.•.••••.••.••.••••.•.••.•...... ••.....•• VI
FIELDS OF STUDY ...... •...... •...... •..•...•..•....•.••.•...... •...... VI
TABLE OF CONTENTS .•....•....•.•....•.••.•...... •...... •.....•.•.•..••....•...•..•..••••..•...... •...... • VII
LIST OF TABLES ...... •..•...... •.....•...... •...... •...•...... •...... •..•.....•••..•••.••.•.••.•.••••••.•••.•. IX
LIST OF FIGURES ...•••••.•.••.••••.•.••.•.•.••••.•.•.••.•.•••••••.•.•••••••.••.•.••.•.••.•..•.••.•.••.••.••••.•••••••.••.•.•••...•.•.••...... •.... X
LIST OF FIGURES ...... •...... •...... •...•..•..•...... •.•...... •...... •...• X
CHAPTER I •.•..••.•.•..••...... •....•.••.•...... •.....•....••.•...•..•.•.•.•.•.•.....•...... •.....•...... ••...... •..•.••.•.•..••••.•.••••.•.•.•.•.• 1
INTRODUCTION ..•.••.•..•...... •..•.••.•.•.••...... •.....•....••.•.•..•.•...... •.•....•.••.•...••.• 1
1.1 MOTIVATION ...... 1 1.2 OBJECTIVE ...... 2 1.3 TECHNOLOGY DESCRIPTION ...... 3 1.4 TECHNICAL ISSUES ...... 7 1.5 TECHNICAL APPROACH ...... 8 CHAPTER 2 ...... •...... •.••.••••.••.•..•.••.••.•.••.•..•.•••••.•.•.•••....•.•...•.••....•.• 10
BASELINE DESIGN - ARCHIMEDEAN SLOT SPIRAL ANTENNA .....•...... •...... 10
2.1 SPIRAL ANTENNA ...... 10 2.2 GENERAL SPIRAL ANTENNA DESIGN ISSUES ...... 14 2.3 BASELINE DESIGN ...... 20 2.4 DESIGN IMPROVEMENTS ...... 22 CHAPTER 3 •.••.•.•.••.•..••.•..•.•.••.••.•.••.•.••••..•...•.••.•..•.•...... •.•..•.•.•...... •...... 30
ANTENNA MINIATURIZATION USING DIELECTRICS ...... •...... •.•.•....•...... •...... 30
3.1 CONCEPT ...... 30
vii 3.2 MINIATURIZATION CRITERIA FOR BROADBAND ANTENNAS ...... 34 3.3 DIELECTRIC LoADING OF THE SPIRAL ANTENNA ...... 35 3.4 DIELECTRIC LoADING ISSUES ...... 38 CHAPTER 4 ...... 50
SUMMARY...... 50
CHAPTER 5 ...... 52
FUTURE WORK ...... 52
5.1 DIELECTRIC LoADING ...... 52 5.2 AN ALTERNATIVE APPROACH TO Low FREQUENCY GAIN IMPROVEMENT ...... 53 BIBLIOGRAPHY ...... 57
Vlll List of Tables
TABLE 1.1 FREQUENCY BANDS OF MILITARY COMMUNICATION SYSTEMS ...... 2 TABLE 3.1 Two INCH SQUARE SPIRAL SUMMARY FOR THE FREQUENCY SHIFf OF THE -15DBI GAIN POINT (THE UNLOADED SPIRAL'S-15 DBI GAIN POINT OCCURS AT 887 MHz) ...... 37
ix List of Figures
FIGURE 1.1 ILLUSTRATION OF THE CONCEPT OF MINIATURIZATION USING MATERIALS ...... 5 FIGURE 1.2 ILLUSTRATION OF THE REACTIVE LOADING MINIATURIZATION APPROACH USING A TWO- CONDUCTOR TRANSMISSION LINE ...... 6 FIGURE 2.1 THE TWO ARM LOG-SPIRAL ANTENNA GEOMETRY ...... 12 FIGURE 2.2 CURRENT PHASE PROGRESSION (DEGREES) FOR A TWO ARM CIRCULAR ARCHIMEDEAN SPIRAL. 13 FIGURE 2.3 THE EFFECT OF CAVITY DEPTH, D ON THE INPUT IMPEDANCE FOR A 2" SQUARE SPIRAL (SIMULATION) ...... 18 FIGURE 2.4 THE EFFECT OF CAVITY DEPTH, DON TOTAL GAIN FOR A 2" SQUARE SPIRAL (SIMULATION) ...... 18 FIGURE 2.5 THE EFFECT OF CAVITY MODES ON THE PERFORMANCE OF A 2" SQUARE SPIRAL...... 19 FIGURE 2.6 CAVITY BACKED 18" CIRCULAR SLOT SPIRAL...... 20 FIGURE 2.7 SQUARE SPIRAL ILLUSTRATING THE RESISTIVE TERMINATION AND INFINITE COAXIAL BALUN USED IN THE ORIGINAL DESIGN ...... 21 FIGURE 2.8 GEOMETRY FOR A 2"X2" SLOT-LINE SPIRAL ...... 23 FIGURE 2.9 MEASURED AND CALCULATED GAIN FOR A 2"X2" SLOT-LINE SPIRAL ...... 23 FIGURE 2.10 NEW 0°-180° HYBRID BALUN ...... 25 FIGURE 2.11 MEASURED GAIN OF THE 2"X2" SPIRAL ANTENNAS FED WITH THE PREVIOUS INFINITE BALUN AND WITH THE NEW 0°-180° HYBRID BALUN ...... 25 FIGURE 2.12 MEASURED GAIN OF THE 2"X2" SPIRAL ANTENNAS FED WITH THE PREVIOUS INFINITE BALUN AND WITH THE NEW 0°-180° HYBRID BALUN ...... 26 FIGURE 2.13 SINGLE-RESISTOR VS. MULTIPLE-RESISTOR TERMINATION OF SPIRAL ARMS ...... 27 FIGURE 2.14 MEASURED AXIAL RATIO COMPARISON OF SINGLE-RESISTOR TERMINATION VS. TAPERED RESISTOR TERMINATION ...... 27 FIGURE 2.15 GAIN DECOMPOSITION INTO LHCP AND RHCP COMPONENTS ...... 28 FIGURE 2.16 MEASURED GAIN OF A 2"X2" SPIRAL WITH AND WITHOUT CAVITY TREATMENT...... 29 FIGURE 3.1 ILLUSTRATION OF MATERIAL LOADING OF A DIPOLE ...... 31 FIGURE 3.2 MINIATURIZATION (SIMULATION) FOR SINGLE SIDE LOADING WITH CONSTANT WAVE NUMBER K ...... 33 FIGURE 3 .3 MINIATURIZATION (SIMULATION) FOR DOUBLE SIDE LOADING WITH CONSTANT WA VE NUMBER K ...... 33 FIGURE 3 .4 ILLUSTRATION OF THE DIFFERENCE BETWEEN THE MINIATURIZATION CRITERIA USED FOR NARROWBAND AND BROADBAND ANTENNAS ...... 35 FIGURE 3.5 A CROSS SECTION OF THE FINITE SINGLE-SIDED LOADING GEOMETRY ...... 36 FIGURE 3.6 MEASURED TOTAL CIRCULARLY POLARIZED GAIN OF A 2" SQUARE SPIRAL WITH AND WITHOUT A DIELECTRIC SUPERSTRATE (MEASURED WITHOUT CAVITY AND RESISTIVE TERMINATION) ...... 3 7 FIGURE 3. 7 IMPACT OF SUPERSTRATE THICKNESS ON INPUT RESISTANCE REDUCTION FOR SINGLE-SIDED LOADING ...... 39 FIGURE 3.8 TOP VIEW OF A DIELECTRIC SLAB WHICH HAS A LINEAR TAPERING OF ITS DIELECTRIC CONSTANT ...... 40 FIGURE 3.9 EFFECT OF DIELECTRIC TAPERING ON INPUT IMPEDANCE REDUCTION ...... 41 FIGURE 3 .10 EFFECT OF DIELECTRIC TAPERING ON MINIATURIZATION ...... 41 FIGURE 3.11 MEASURED RETURN LOSS (DASH-DOT LINE) AND WITHOUT (SOLID LINE) A UNIFORM SUPERSTRATE (eR= 30) ...... 42 FIGURE 3 .12 CROSS SECTION AND PICTURE OF THE THICKNESS TAPERS DIELECTRIC SUPERSTRATE FOR THE 6" SQUARE ARCHIMEDEAN SPIRAL...... 43
x FIGURE 3.13 MEASURED RETURN LOSS WITH (DASH-DOT LINE) AND WITHOUT(SOLID LINE) A TAPERED SUPERSTRATE (ER= 30) ...... 44 FIGURE 3.14 MEASURED GAIN OF A 6"X6" SQUARE SLOT SPIRAL ANTENNA WITH AND WITHOUT HIGH DIELECTRIC SUPERSTRATE LOADING (ER= 30, THICKNESS= 0.5 INCHES) ...... 44 FIGURE 3 .15 INFLUENCE OF MAGNETIC MATERIAL LOADING ON INPUT IMPEDANCE ...... 45 FIGURE 3 .16 COMPARISON OF THE CP GAIN FOR AN UNLOADED AND LOADED SPIRAL ...... 46 FIGURE 3.17 THE CP GAIN COMPONENTS OF A LOADED SPIRAL (T = 2MM, ER= 9) WITH AND WITHOUT A TERMINATING LOAD ...... 47 FIGURE 3.18 COMPARISON OF THE INPUT IMPEDANCE FOR AN UNLOADED AND LOADED SPIRAL ...... 4 7 FIGURE 3.19 THE PERCENTAGE OF INPUT POWER THAT IS EITHER RADIATED OR DISSIPATED IN THE TERMINATION FOR THE 2" SPIRAL...... 48 FIGURE 3 .20 MINIATURIZATION FACTOR LIMITATIONS AS A FUNCTION OF DIELECTRIC CONSTANT FOR SINGLE-SIDED LOADING (THICKNESS= 0.11\,) ...... 49 FIGURE 5 .1 INPUT IMPEDANCE FOR A 2" SQUARE SPIRAL...... 54 FIGURE 5.2 TRANSMISSION LINE MODELS FOR IMPEDANCE MATCHING ...... 55 FIGURE 5.3 UNWRAPPED INPUT IMPEDANCE OF A 2" SQUARE SPIRAL...... 55
xi Chapter 1
Introduction
1.1 Motivation
A common approach in multifunctional radio frequency systems is to employ a different antenna for each system. The advantage of this approach is that it allows each antenna to be designed to meet the specific needs of each communication system. However, when the number of communication systems is large, this leads to numerous antennas that must be integrated onto platforms such as airplanes, ships and automobiles. This creates several problems such as space, payload, cost and EMC/EMI. Therefore, there is a significant interest in the military and commercial sectors in reducing the number of antennas and their size. For instance, in the commercial sector the need originates from consumer demand for multimedia and wireless applications. This is evident in the automotive industry where consumers expect automobiles to be enabled with the latest multimedia and wireless products [ 1]. This means that future automobiles will need to incorporate a multitude of embedded antenna systems that will operate from the AM radio broadcast :frequencies up to 2.5 GHz for Bluetooth applications [l]. Antennas must also be aesthetically pleasing implying a need for small and concealable antennas. Besides the commercial interest, there is also a significant military interest in small broadband antennas. This is motivated by the desire to "digitize the battlefield" in an attempt to further increase connectivity and enable high speed data transfer. A notable example of this application is the Joint Tactical Radio System (JTRS), a family of software programmable and modular communication systems [2]. The goal of JTRS is to migrate from hardware intensive communication system architectures that are specific to each system and move towards a software oriented system that can implement the architecture for a variety of communication systems by loading the appropriate software. For the antenna engineer such a system creates a challenging problem because the communication systems cover a broad frequency range as shown in Table 1.1. Therefore, the antenna needs to be able to operate sufficiently over each communication band. To further complicate the issue the antenna must be as small as possible to facilitate mobility and enable its application on smaller platforms such as unmanned autonomous vehicles (UAVs). Currently, there are no single antenna elements that can support operation across the required JTRS frequency band of 2 MHz to 2 GHZ. Thus, there exists a strong need for a single antenna element that can cover the entire operational band or at least a significant portion of it.
Freauencv Range Aoolication <2MHz Very Low Frequency/Low Frequency (VLF/LF) 2-30MHz Military High Frequency (HF) 30-88 MHz SINCGARS, Militarv Very High Frequency (VHF) 118-136MHz Air Traffic Control 156-174 MHz Maritime 225-400 MHz HAVE QUICK, Militarv Ultra High Frequency (UHF) 240-270 MHz UHF SATCOM Downlink 290-320 MHz UHF SATCOM Uplink 420-450 MHz Position Location (EPLRS) 960 - 1215 MHz Joint Tactical Information Distribution System (JTIDS) 1030/1090 MHz Identification Friend or Foe (IFF) 1220 - 1850 MHz GPS,MSE >2000MHz Microwave, Millimeter Wave, SHF/EHF SATCOM, Telemetry Table 1.1 Frequency bands of military communication systems.
1.2 Objective
The number of antenna systems can be reduced by using multi-band or broadband antennas to cover several or all of the communication bands within a specified frequency range. Since the frequency ranges of interest have bandwidths greater than 10: 1 ultra wide band antennas are needed. The first challenge in obtaining such a bandwidth is finding an antenna element that is extremely broadband. With such a large bandwidth requirement, antenna elements that belong to the class of frequency independent antennas
2 come to mind. This class of antennas is theoretically capable of covering any desired frequency range. As V. H. Rumsey has well established, if the geometry of an antenna is defined entirely by angles then its performance will be frequency independent [3]. However, such antennas are not finite in size. Therefore, it is necessary to specify at least one length. This length or dimension ultimately determines the lowest operating frequency of the antenna and thereby limits its bandwidth. One of the most commonly used frequency independent antennas is the spiral antenna. For the spiral antenna, frequency independent operation is achieved when its outer circumference or perimeter is greater than one wavelength. However, the physical size at the low frequency end becomes prohibitively large for many applications. To reduce its size, miniaturization techniques must be employed which involve the use of dielectric materials or reactive loading. Size reduction using high-contrast materials has been demonstrated for narrowband antennas [4], such as patch antennas, but not so for broadband antennas. As such, the objective of this work is to investigate and demonstrate the extent to which the spiral antenna can be miniaturized using high-contrast dielectric materials.
1.3 Technology Description
1.3.1 UWB Slot Spiral Antenna The spiral antenna is currently used in a variety of applications that require a conformal broadband circularly polarized antenna. The spiral antenna's planar structure makes is well suited for conformal mounting and it is easily capable of achieving a 9: 1 bandwidth which makes it very attractive for broadband applications. In addition, for a given operational frequency fo, the aperture of a spiral antenna is a factor of 7t smaller than that of a half wavelength dipole. For conformal mounting, a spiral antenna requires a metal backing. Much effort in the development of such a backing has been carried out by Nurnberger and Volakis [5-9] and Filipovic and Volakis [10], [11]. The two most popular types of spiral antennas are the log-spiral (equiangular) and the Archimedean spiral. Currently, most spiral antennas that appear in the literature are circular spirals that are of the Archimedean type. However, both spiral types exhibit very broadband behavior as
3 long as they as are tightly wound. It is also remarked that the log-spiral is technically the only spiral type which is frequency independent since its geometry can be completely specified in terms of angles.
1.3.2 Antenna Miniaturization Techniques The purpose of antenna miniaturization is to make the antenna operate at lower frequencies by effectively increasing its electrical size without increasing its physical size. That is, an antenna which is physically too small to operate at a given frequency can do so if it is miniaturized. Miniaturization can be explained by considering the propagation velocity of the current(s) flowing on the antenna. Essentially, loading the antenna slows down the current flow on the antenna which in turn causes the phase variation in the antenna structure to increase. This makes the antenna appear electrically larger than before. As a result, the initial operating frequency of the antenna is lowered according to the effectiveness of the loading. The two most common techniques used for antenna miniaturization are the use of materials and reactive (inductive and capacitive) loading. The approach using materials is readily explained by the reduction in wavelength within the antenna structure that occurs when the antenna is embedded in a material with a permittivity and/or permeability greater than free space. The wavelength reduction makes the antenna larger in terms of wavelengths, thus reducing its initial operating frequency. This approach is illustrated by the k-fJ diagram in Figure 1.1 where k and fJ are defined as follows:
k =2~ (1.1)
p = 2~g (1.2) with A. being the free space wave length and 'Ag the guided wavelength. Also, using k and fJ, the phase velocity normalized to the speed oflight, c, can be defined as:
VP k -=- (1.3) c p The k-fJ diagram shown in Figure 1.1 is for a homogeneous isotropic material which has broadband behavior due to the linear relationship between k and /J. Fork= fJ, the phase
4 velocity is equal to the speed of light and the k-/J relationship follows the dashed line. However, for a wave propagating in a medium with a permittivity and/or permeability greater than free space, there will be an increase in the phase variation. This leads to a k-/J relationship as illustrated by the red line in Figure 1.1. Therefore, the k-/J relationship for an antenna loaded with high-contrast material will follow a line which is below the dashed line and can be obtained using dielectric material, magnetic material, or a combination of them. However, due to the high losses associated with magnetic materials, we are practically restricted to using only dielectrics.
Figure 1.1 Illustration of the concept of miniaturization using materials.
The reactive loading approach relies on the fact that the phase velocity can be controlled by manipulating the equivalent inductance and capacitance per unit length of the antenna structure in the same way as a transmission line. This is readily illustrated by considering a lossless two-conductor transmission line that supports a propagating TEM mode (see Figure 1.2). The characteristic impedance and wave velocity for the transmission line are given by
(1.4)
1 1 v ------(1.5) p - J;;i - ~LeCe where G is a geometry factor and (Le, Ce) are the equivalent inductance and capacitance per unit length. Therefore, the phase velocity can be controlled by manipulating the 5 inductance and capacitance of the transmission line [12], [13]. Consequently, the challenge in slowing down the wave is based on the ability to represent the antenna structure as a transmission line so that it can be properly loaded. For antennas, this method is typically implemented using lumped elements [13] or by shape design such as meandering [10], [14] to enhance the inductance and capacitance of the structure. This approach is able to realize both the L and C to effectively emulate µ and E in a two dimensional sense. Therefore, not only can the phase velocity be controlled but conceptually so can the local transmission line impedance of the antenna structure. However, it is remarked that the equivalent transmission line impedance is related to the antenna impedance but not directly. Since both the L and C can be realized, the main advantage of this approach is that it could replace the effect of magnetic material. Also, this approach doesn't add additional weight and does not increase the profile of the antenna. However, it is remarked that the LC enhancement can be frequency dependent (meandering) or frequency limited (lumped elements limited to use in L-band or lower) and therefore its effectiveness is limited.
• • • • ••
L L
Figure 1.2 Illustration of the reactive loading miniaturization approach using a two conductor transmission line.
1.3 .3 Dielectric Materials The idea of using dielectric materials to reduce antennas size is widely known. However, these is a renewed interest in the use of dielectric materials due to the recent availability of low-loss (loss tangent, tana < 0.001) and high-contrast (1 < Er <150) dielectrics. These dielectric materials are usually high-temperature ceramics, low-
6 temperature cold fired ceramics or epoxy bonded ceramics. In addition, there are even dielectric materials made from plastic stock which exhibit low-loss (tano < 0.002). All of these materials are readily available from a variety of companies such as TransTech, Emerson and Cumming, PicoFarad, and Dielectric Laboratories. However, the weight of these materials can be significant when used in large quantities. Also, these materials are typically not available with dimensions greater than two inches due to the fact that most sources currently produce these materials as substrates for microwave circuit components. Modifying these materials is also difficult due to the need for special tools (carbide or diamond tipped) to machine them in their finished form
1.4 Technical Issues
1.4.1 Antenna Design In general, the presence of high-contrast materials affects radiation characteristics by changing the antenna impedance, bandwidth and radiation pattern. Higher order surface wave modes can also be introduced when high-contrast or a thick loading is employed. Using a high-contrast material loading without paying attention to such tradeoffs could result in disappointing performance due to the adverse effects introduced by the material. Physical constraints that require a low-profile antenna makes it even more challenging to reach an acceptable tradeoff in the design. The termination of the spiral arms ultimately determines the trade-off between radiation efficiency and axial ratio/cross-polarization. Resistive terminations are necessary to reduce currents reflected from the end of the spiral arms, which in turn improves bandwidth and polarization at the expense of antenna efficiency. Material loading of the spiral implies that stronger currents would reach the end of the spiral arms, causing further reduction in efficiency. Therefore, proper antenna design and material loading topologies must be investigated to address this issue. A good impedance matching scheme is also important for a miniaturized ultra wide band (UWB) antenna. Dielectric loading of the antenna will reduce the antenna impedance and could cause an increase in mismatch losses unless proper steps are taken.
7 To address this issue the spiral geometry must be altered to increase its impedance or the balun must be redesigned to compensate for the lower impedance value. Therefore, the effects of various parameters of the loading geometry on the input impedance need to be characterized so that adjustments can be made to the antenna geometry or balun to minimize mismatch loss. A small UWB balun design is another challenge for UWB miniaturization. Such a balun must be able to provide a nearly constant 180° phase shift over a wide range of frequencies to prevent squinted patterns and excitation of undesired modes. In addition, the balun must not create unwanted radiation at low frequencies, be unobtrusive and provide impedance matching over a large bandwidth. Therefore, care must be taken in choosing a balun to be used with the dielectric loaded spiral.
1.4 .2 Loading Scheme There is an important trade-off between miniaturization and practical considerations (cost, size, weight, etc.) that must be addressed. The optimal selection of the loading material (composition, texture, shaping, etc.) also needs to be determined. Although, the idea of using dielectric loading to lower the antenna's operating frequency has existed for quite some time, it usually consisted of a low dielectric constant and a homogeneous layer. The lack of proper material and efficient optimization tools were obvious limitations. Since most conventional high-contrast dielectric materials are ceramics which are difficult to machine, fabrication of special shapes or profiles that might be required for UWB antenna designs is also difficult. For instance, as the operational frequency decreases, the "resonant ring" moves outward away from the center. This suggests that a dielectric constant of the superstrate should be a function of distance from the center and should increase as the distance increases from the center. Such an approach is desirable for many reasons such as cost, weight, impedance, etc.
1.5 Technical Approach
To study the miniaturization of a broadband antenna, a previously developed [6], [ 1O] circular spiral antenna was used as the starting point. This design was first altered by
8 making it into a square spiral to better utilize the aperture area and thus lower its operational frequency. Additional improvements were also made to the balun and arm termination to facilitate the dielectric loading of the antenna. Low loss, high-contrast dielectric loadings with simnle dielectric profiles were then placed on the antenna to demonstrate the concept of antenna miniaturization using high-contrast materials. The impact of the high-contrast materials was then investigated using both numerical simulations and measurements on the 2" and 6" diameter prototypes. The study finally led to a good understanding of the miniaturization issues associated with high-contrast dielectric profiles. Insights were obtained from these initial investigations and such insights will provide important directions towards improving the amount of miniaturization. The remainder of the thesis is organized as follows. The following chapter starts out by introducing the reader to the spiral antenna and its theory of operation. The main design issues associated with the spiral antenna are then discussed. To facilitate dielectric loading, modifications were made to the previously developed baseline design and they are discussed at the end of chapter 2. In chapter 3, the dielectric loading of the spiral antenna is discussed by first introducing the concept of spiral antenna miniaturization using dielectrics. This is followed by a discussion of the experimental results obtained by loading the spiral with high-contrast material. As a result of the high-contrast material loading, many issues arise and some of these are addressed in this chapter. To conclude the thesis, chapter 4 summarizes the finding and chapter 5 outlines a plan for further extension of this work.
9 Chapter 2
Baseline Design - Archimedean Slot Spiral Antenna
There are four main issues associated with the design of a spiral antenna. The first is about making the antenna an efficient radiator by proper design of the spiral geometry. The other issues relate to the cavity backing for unidirectional radiation, the balun for broadband impedance matching and the arm termination. The major challenge associated with the later issues is making them as broadband as the spiral antenna itself. Before these issues can be discussed further, it is necessary to introduce the theory of operation of the spiral and the geometrical parameters that influence its performance. The first section serves to introduce the reader to theory of operation and the geometrical parameters which play a major role in the performance of the antenna. The following two sections will then discuss the design issues and methods used to address them. In the last section, we present improvements and modifications that were necessary for the material loading of the spiral antenna.
2.1 Spiral Antenna
2.1.1 Important Geometrical Parameters
The two most common spiral antenna types are the logarithmic and Archimedean. Although the Archimedean spiral is a broadband antenna, it is considered to be quasi frequency independent because its geometry cannot be completely defined by angles alone [3], [15]. However, an Archimedean spiral is just as broadband as a logarithmic
10 spiral as long as it is wound sufficiently tight so that it is a close approximation to a tightly wound log-spiral. The performance of both spiral types is mainly determined by two parameters which are the expansion ratio 't and the angle of angular rotation cS. The remainder of this section will define these parameters and characterize their affects for both spiral types. For the log-spiral, the equation that defines one edge of the log-spiral curve in polar coordinates is (2.1) where ro determines the initial radius and a is the growth which is defined using the pitch angle 'I' as follows (see Figure 2.1) 1 tan'!'= (2.2) a It is remarked that the entire geometry of the log-spiral can be defined in terms of the pitch angle, thus making the log-spiral a frequency independent structure. The expansion ratio 't is the radius increase factor for one turn of the spiral and is defined as the ratio of OA/OB as shown in Figure 2.1. It also can be defined using the pitch angle as follows -2rrlal -(2rr iltanlf/I} r =e =e (2.3)
The value of 't is always less than one and plays a role in determining the active region attenuation (radiation efficiency) and a major role in the axial ratio or polarization purity.
As 't approaches unity the spiral winding becomes tighter and this translates into better the axial ratio. The other edge of the log-spiral arm is obtained by rotating the curve (2.1) by the angle cS (angle of angular rotation). That is, the edge location is given by (2.4)
The input impedance of the spiral is high dependent upon the angle cS. When cS = 90° we have a self-complementary structure which has an impedance of 607t Qin free space [15], [16]. For cS > 90°, the spiral impedance is greater than 607t Q and, in this case, the spiral geometry takes the shape of a wire since the width of the arm is less than the spacing between adjacent arms. For cS < 90°, the spiral impedance is less than 607t Q and it is considered to be a slot spiral since width of the arm is greater than the spacing between adjacent arms. A large range of impedances can thus be obtained by varying cS. However,
11 it is not desired to deviate far from o = 90° because insufficient attenuation of the current through the active region will occur [15]. The importance of this attenuation will be discussed in the next section. ------' ' ' ' ' ' ' ' ' ' ' \ \ \ \ \ \ I I I
I I I \
\ \ ' ' ' ' ' ' ' ...... ------Figure 2.1 The two arm log-spiral antenna geometry.
For the Archimedean spiral, the edges of the arm are defined by the equation
(2.5)
It is remarked that the equivalent pitch angle 'If varies with radius. Nevertheless, an equivalent expansion ratio -r can be defined as
'f=e -2rriltan ll'I =e -2rrla ! rl (2.7)
However, in this case, 't is not constant and usually varies from 0.3 to 0.9 across the aperture. As with the log-spiral, the parameters 't and o affect the performance of the Archimedean spiral in the same manner. Generally speaking, the performance of the
Archimedean spiral for a given -r is the same as for a log spiral with the same 't. It is remarked that the geometry for the square Archimedean or log spiral can be obtained by sampling the corresponding circular spiral at 90° intervals. The difference between square and circular is discussed later in this chapter.
12 2.1.2 Theory of Operation Regardless of the shape of the spiral (circular or square) or its type, the theory of operation applies to all as long as they are tightly wound ('t > 0.25) [15]. The operation of the spiral antenna is usually based on "radiation band" theory which states that the spiral predominately radiates from annular bands whose circumference is an integer multiple of a wavelength [17], [18]. For a circular spiral the radiation bands occur when the diameter D = n/Jrt whereas for a square spiral it will occur when the width W = n/J4 [18]. Radiation occurs from these regions because the currents flowing in adjacent arms become in phase leading to coherent/constructive radiation from these adjacent currents on the arms. Outside these regions the currents are not in phase and therefore the local fields tend to completely cancel each other. This is illustrated in Figure 2.2 for a two arm spiral where each arm is fed 180° out of phase with respect to the other. Figure 2.2 shows the phase progression of the current flowing on each arm and the expected location of the first "radiation band" which has a circumference equal to IA.. It is evident from this figure that the currents in adjacent arms are nearly in phase at the first radiation band just as expected.
Figure 2.2 Current phase progression (degrees) for a two arm circular Archimedean spiral.
Typically, the two arm spiral is excited so that the current on each arm is 180° out of phase with respect to the other. For such an excitation the spiral can only radiate from
13 regions where the circumference is an odd integer multiple of a wavelength (first mode). Specifically, radiation from the lA.-circumference region will produce an omni-directional radiation pattern with the maximum at boresight. The first mode is the only one that has a maximum at boresight and is therefore the most commonly used mode. However, if a two arm spiral is excited such that the currents on each arm are in phase, the coherent condition occurs when the circumference is an even integer multiple of a wavelength (second mode). The corresponding radiation pattern has a null at boresight and a maximum at an elevation angle of 38° from boresight (which can be predicted from array theory [ 11 ]). All other radiation modes excited using spirals having more than two arms are similar to the second mode and are not discussed here. For further discussion of the radiation properties of these modes the reader is referred to [lS], [19].
2.2 General Spiral Antenna Design Issues
2.2.1 Active Region Attenuation Since the spiral is a traveling wave antenna it is not a 100% efficient radiator which means that not all of the energy that enters the 1A.-circumf erence region will be radiated. Some energy is still confined to the antenna and continues to travel outwards where it can radiate from higher order regions (3A., SA., etc.), if the antenna is large enough. Since the total pattern of the spiral is the weighted sum of the radiation from the regions at IA, 3A., SA., radiation from the higher order regions is undesired since the resulting patterns may have grating lobes that causes frequency dependent pattern distortion and boresight gain loss. Additionally, if the traveling wave is reflected from the end of the spiral arm, it will travel inwards and will radiate for a second time when it reaches a radiation band. However, the resulting radiation is cross-polarized with respect to the first and will cause the total radiated field to be elliptically polarized. To prevent radiation from higher order regions and re-radiation from the IA region the spiral must radiate as much energy as possible when it first encounters the lA.-circumference region and any energy left over must then be absorbed by the arm termination. This means that the spiral must be designed properly so that the amount of radiation from the IA region
14 sufficiently attenuates the current. The amount of attenuation needed is determined by the desired ratio of the 3A. to the IA. pattern at some elevation angle 0. This ratio is commonly referred to as the WOW and is usually desired to be no more than 6dB [15]. Therefore, it has been found that the required attenuation due to radiation through the 1A. region needs to be more than 13.4 dB [7], [15]. A proper choice of 8 and tis critical to accomplishing this. In the case of an Archimedean or logarithmic spiral, 8 should be between 40 and 140 degrees while t should be greater than 0.3 [15]. Generally speaking, both spiral types are relative insensitive to the choice oft except in the outer regions where a larger t has been shown to result in less gain loss [15]. While proper design of the spiral geometry is the most effective method in eliminating the effects of radiation from higher order radiation regions, there is another approach which can be used. By increasing the number of arms one can eliminate some
of the higher order regions. For an excitation of a single mode M (M = 1 being the first or normal mode) the first higher order radiation region that can exist will be (M+N)A. where
N is the number of arms [15], [19]. Therefore, if M = 1 and N = 2 the 3A. ring is the next region from which the spiral can radiate. If one desires to prevent radiation from this region the number of arms can be increased to four thereby making the next radiation ring at SA. instead of 3A.. Thus, the bandwidth, over which the (M+N)A. region does not exist, increases with N at the expense of increasing the complexity of the feed network [15], [19].
2.2.2 Arm Termination Proper design of the spiral geometry effectively reduces the amount of energy re radiated from the 1A. region at high frequencies. However, at low frequencies where the 1A. region is located near or overlaps with the end of the antenna, this approach is not enough. Thus, a broadband termination is needed to deal with the energy reaching the end of the spiral arm. Otherwise, the reflected current will lead to an increase in the cross polarization and axial ratio. There are several techniques which can be used to terminate the spiral such as resistive paints, absorbers, and resistive cards [15]. For these techniques to be effective, they must be applied to a length of the spiral arm which is at least AJ2 long. For cavity 15 backed spirals, absorber can be used to line the side walls of the cavity creating an effective termination [6], [7]. Additionally, the arms of the spiral can be grounded to the cavity side walls through a resistor or adjacent arms may be connected together at the periphery using resistors. The most important aspect of terminating the spiral is for the termination to be well matched over a broad range of frequencies.
2.2.3 Balun To obtain axial or normal mode radiation, the spiral antenna must be fed in a balance transmission line mode with each arm being excited with equal magnitude and 360/N degrees out of phase (N is the number of arms). Therefore, a balun is needed to feed the antenna. The challenge with designing the balun is that it must concurrently have constant impedance over the entire bandwidth while also being well balanced to prevent squinted patterns and radiation from the feed structure. Also, if the balun is to be integrated onto the spiral aperture, it must not disturb the antenna fields. Since the balun can limit the bandwidth of the spiral and significantly affect its radiation pattern and impedance, it is often considered to be the most important design parameter. Therefore, great care must be taken in selecting and implementing the balun. There are many baluns that could be used to feed the antenna. An integrated hybrid microstrip line can be used as in [20]. For applications that require extreme bandwidths and low profile, the infinite coaxial balun can be used [21]. For wide-band applications the Marchand balun, capable of 10: 1 bandwidths, can be adopted [22]. In addition, power dividers (hybrids) or small impedance transformers can also be used as a balun. In choosing a balun the most important characteristics are its bandwidth, loss and physical profile. Essentially, it is desired that the balun be very broadband, low loss and have a low profile.
2.2.4 Unidirectional Operation The spiral antenna radiates a symmetric pattern equally well to the front and to the back. For applications that require conformal mounting, this is undesirable since the antenna must radiate in only one direction. A spiral antenna becomes unidirectional when it is placed on a ground plane or cavity backing. Typically the cavity is used since
16 diffraction from the finite size ground plane can lead to significant radiation to the backside of the antenna. While the use of a cavity or ground plane achieves unidirectional radiation it also further complicates the design of the spiral. There are several problems that arise when combining a PEC backing with the spiral. The first is the excitation of cavity modes or resonances. The second issue is its impact on the antenna impedance and in turn on the gain, axial ratio, and cross-polarization. All of these issues are affected by one parameter which is the spacing between the backing structure and the spiral. Ideally, one would like to make the spacing as small as possible to reduce its profile. However, as the spacing is made smaller, the effects of the cavity or ground plane on antenna performance become significant due to the excitation of a parallel plate transmission line mode and shorting of the antenna fields [7], [15], and [23]. Excitation of the parallel plate mode causes most of the energy accepted by the antenna to be guided along the spiral arm to the end of the structure. If the arm has been terminated sufficiently, the guided wave will be dissipated in the termination thus reducing the efficiency. If the arm is not terminated sufficiently, the wave will be reflected and return to the input which will cause an oscillatory behavior in the input impedance that increases mismatch loss. It is also remarked that the input impedance is reduced as the spacing is reduced. This is due to the antenna fields being shorted out by the presence of the PEC backing. Figure 2.3 and Figure 2.4 illustrates how the total boresight gain and impedance are affected for a 2 inch diameter square spiral backed by a cavity with the same diameter. For this case, the spiral is purposely not terminated so that the effect of cavity depth on the gain and input impedance can be clearly seen. It is apparent that both parameters are significantly affected at lower frequencies by the cavity depth. It is also noted that with decreasing cavity depth the gain loss increases due to increasing mismatch loss.
17 0.5 1.5 2 2.5 3 3.5 frequency (GHz)
Figure 2.3 The effect of cavity depth, D on the input impedance for a 2" square spiral (simulation).
5 ...... ) ...... +...... !.. -..,,~ :-:d:·.:;~_:·;:~:·:.:.::..--~---""~
!~ : •••••• • ••L•·it>:t~-J••••••I•••••••I••••••: '// - '~" : ~ : : '.t': -10 ------~- ----_;-'-+------:------~------;------:------
~ I / : : : : : - -15 ------I. - --;i.~ -----:------~ ------~ ------.:. ------~ ------(ii I ' I I • ' ' • ., / :/ : : : : : 0:: -20 -----) -;~------+ ------; ...... ; ...... ;...... ; ...... s::. / / : : : : : : G I , • ' • I I I ~ .25 ~7 >i---i ·------·t------~ ------~------+------~------0 ' • • • • - Without Cavity '° -30 .. ------1------1-----·····t ··------1 D .. 25mm -35 ...... ; ...... ;...... ;...... ; D=6.25mm ; ; ; ; D=0.78125mm .JO __ __.!._ _ _j__ _L __ .....t:======:::'.J 0.5 1.5 2 2.5 3 3.5 frequency {GHz)
Figure 2.4 The effect of cavity depth, Don total gain for a 2" square spiral (simulation).
Therefore, the cavity depth should needs to be large at low frequencies to avoid impedance mismatch problems. However, a spacing which is sufficient at low frequencies becomes too large at high frequencies leading to undesired cavity modes. This causes gain drop near resonant frequencies, thus limiting the bandwidth of the spiral (see Figure 2.5). The larger the cavity is made, the smaller the bandwidth because the cavity mode resonances occur at lower frequencies. Therefore, there is a trade-off
18 between the cavity depth and the low frequency antenna performance. Since the performance at low frequencies is of the most interest, the cavity is made as deep as possible and it is treated so that cavity modes are suppressed.
' ' 5 ---~------~------~------~------~------:------+ ---- :-- ' ' ' iXi ' ' : . : . . : ~ 0 ---:---- -:------:------:------:------: ------:------:--- -- c ' ' ' . ' . ' ' "ii : : : : : : I : : <.!> -5 ---{------f------{------f------{------1--- -- :------!------:------
:!:Cl :• :• :' :• :• :. : ' : :' (;) -10 ---~------~------~------~------~------i---- -:------i------:------~ i i i ! ! /! ! ! ~ -15 --- ·------+--- Effect of Cavity Mode !------+------!------:!! : : ; ; ; : : ' :II ' ' • ' • ' ' = -20 -- ~------~------~------~------~------!------+------!------+----- : : : : : : : :E.. : : : : : : : -25 - ~------~ ------~------~ ------~------~ ------~ ------~ ------~ -- --- I I I I I I I 0 I I I I I I f I I I I I I l I I I I I I I I I I > I I I -3o~~-~~~~-~-~-~-~-~~ 2 3 .. 5 6 7 8 9 10 frequency (GHz)
Figure 2.5 The effect of cavity modes on the performance of a 2" square spiral.
The most common technique used to deal with cavity modes is to load the cavity with absorber. However, loading the cavity with absorber results in gain loss of up to 3dB when compared to the unloaded cavity. The amount of gain loss depends on how close the absorber is to the spiral, the depth of the cavity and the characteristics of the absorber. Typically, the characteristic impedance of the absorber is made to be as close to free space as possible. Doing so causes equal power to be radiated into the cavity and free space because the power is inversely proportional to the characteristic impedances of the media. That is, the ratio of power radiated into free-space and into the cavity is given by p,rad 0 '11cavity prad = (2.10) cavity '170 where Po is the power radiated into free-space, Pcavity is the power radiated into the cavity,
170 is the characteristic impedance of free-space and 1'/cavity is the characteristic impedance of the medium inside the cavity [15]. From (2.10) it is apparent that it would be advantageous to have 1'/cavity greater than 110. However, this would require use of a material
19 that has a permeability greater than its permittivity, but such materials are narrowband.
Therefore, the best and most practical option is to have Y/cavity equal to Y/O·
2.3 Baseline Design
The issues presented in the previous section will be discussed for the baseline design shown in Figure 2.6. As can be seen, the baseline Archimedean spiral design has multiple growth rates. The purpose of the multiple growth rates is to provide sufficient attenuation of the current through the IA region for a wide range of frequencies [5], [ 1OJ, and [11]. In [10] it was found that for Archimedean spirals, a smaller growth rate improved high frequency performance whereas a larger growth rate improved the low frequency performance. Therefore, the growth rate should be varied across the aperture to achieve optimal performance. This amounts to controlling/varying the expansion ratio 't across the aperture of the antenna.
Balun--_ £ Slot Spira I / Feed \ I - -~iY~l~~-+ Substrate High e / Lcavlty Bottom Loading
Figure 2.6 Cavity Backed 18" Circular Slot Spiral.
To suppress energy reaching the end of the spiral arm, a broadband Klopfenstein resistive taper was employed [7], [8], and [24]. This termination, shown in Figure 2.7, greatly reduces the cross-polarization and the axial ratio of the antenna by slowly attenuating the current as it reaches the end of the spiral arm. This can be achieved by
20 using resistive elements to connect the spiral arms together over a given length of the arm. It is noted that for optimal efficiency, it is important to minimize the length of the taper. For this reason, the Klopfenstein taper is used since it provides the minimum required taper length to achieve a given reflection coefficient.
Klopfenstein Resistive Taper
Infinite Coaxial Balun
Figure 2. 7 Square spiral illustrating the resistive termination and inrmite coaxial balun used in the original design.
This design also employs an infinite coaxial balun because of its extremely broad bandwidth and ease of implementation. Additionally, it can be mounted on the surface of the antenna without affecting the antenna fields (i.e. it has a very low profile). The infinite coaxial balun consists of a piece of coaxial cable soldered to the surface of the spiral along one of the spiral arms as shown in Figure 2.7. The balun then feeds the spiral at its center by using the center conductor to excite the center slot. This is done by stripping away the outer conductor in the feed region and extending the center conductor across the slot where it is then soldered on the other arm. A shorted dummy cable is usually soldered on the other arm to provide both physical and electrical symmetry. To address the possibility of exciting cavity modes a thin absorber layer is used to line the walls of the cavity and thus eliminate cavity modes. Typically, many layers of absorber are used to attenuate the cavity modes. This causes an attenuation of the field radiated from the backside which reduces the antenna efficiency. Additional efficiency reduction is possible from the interaction of the antenna fields with the absorber if it is placed to close to the antenna. However, efficiency reduction is minimized by using a thin layer of absorber to only suppress cavity modes [7], (1 O] .
21 2.4 Design Improvements
The purpose of this sub section is to discuss the modifications made to the balun and arm termination to facilitate dielectric loading. In addition, a lossless cavity mode suppression technique is presented. Before these modifications are discussed, our motivation for converting from a circular spiral to a square spiral is presented.
2.4.1 Square or Circular Spiral The choice between using a square or a circular spiral depends upon the shape of the aperture. For instance, if the aperture is square, a square spiral should be used since is maximizes the utilization of the entire aperture. That is, given a square aperture with width W, the initial operating frequency of a square spiral will be 22% less than a circular that fits within the aperture. For this reason, the square spiral is preferred since most size constraints are based on square apertures. The spiral antenna considered throughout much of the remaining chapters will be an Archimedean square spiral with a constant growth rate as shown in Figure 2.8. The following geometrical parameters apply to this spiral: slot width w = 0.0762cm (30 mils), conductor width S = 0.2286cm and aperture dimensions of 5.715x 5.715cm (2.25"x2.25"). The actual spiral has dimensions of 4.6482 x 4.9530cm (1.83"x 1.95") and will be referred to as the 2" spiral from here on. For this case, unidirectional radiation was achieved by using a square cavity having an inner diameter of 5.08cm (2") and a depth of2.54 cm (l"). The actual square slot spiral was printed on a 0.06096cm (24 mils) thick FR4 substrate (s = 4.25-j0.0595). Further, for the data given in Figure 2.9, the slot spiral was fed and terminated using newly developed methods to be discussed in the following sections. The curves in Figure 2.9 demonstrate the performance of the square spiral and provide a good validation of the analysis tool to be used for analysis. We remark that all analyses to be presented here were done using a previously developed finite element-boundary integral (FE-BI) code [25-27] and the measurements were done at the Ohio State University ElectroScience Laboratory compact range.
22 s iii
Figure 2.8 Geometry for a 2"x2" slot-line spiral
- Measured o ~ Simulated . . -5 ·······················:·········· ···········:······················
c : "iii -1 5 ...... ·f·······················!······················ (!) • :
~ -20 •..•...... -----r------••••••,.•• ••••------• ' ·; ' ' C) . ' . ' 5 -25 •••••••••••L••••. ••••••••••••••••••••••••••••••••••••• • •• • • . ' co .' '
-35 ------~ ------~------
-40 0.5 1 1.5 2 frequency (GHz)
Figure 2.9 Measured and calculated gain for a 2"x2" slot-line spiral
2.4.2 Balun In preparation for the dielectric loading, a new feeding scheme was needed since the previous balun (shown in Figure 2.7) occupied the surface of the spiral which must now be left bare for superstrate loading. Otherwise, the spiral must be printed directly onto the dielectric and the balun must be embedded within the dielectric. Both of these
23 difficulties were avoided by freeing the antenna surface from the spiraling cable. To do so, a 0°-180° broadband hybrid or power divider/combiner was employed. This hybrid uses a standard coax at the input, and its output is in the form of two coaxial cables with their outer conductors soldered together as shown in Figure 2.10. The hybrid serves to make the center conductors of the output cables opposite in polarity whereas the outer conductor provides the means for shielding, thus suppressing secondary radiation. Using this hybrid, the antenna can be fed from the substrate side through the use of two vias located on opposite sides of the slot at the center of the spiral (feed point). Therefore, the surface of the spiral is made free from the feeding structure allowing for loading of the spiral using a superstrate. In addition, it was found that the feeding cable arrangement adopted previously (see Figure 2.7) caused unstable gain values at very low frequencies. It was suspected that this was caused by cable radiation since the infinite coaxial balun is only balanced as long as the antenna currents have decayed to a negligible value by the time they reach the end of the spiral arm [28], [29]. Therefore, the number of resistors used to terminate the spiral arm will affect the radiation observed from the feeding cable. Obviously, if the arm is well terminated, the current can be significantly reduced before its reaches the end of the spiral arm and the cable radiation can be suppressed to a certain degree. Nevertheless, no matter how well the arm is terminated, the fact remains that the infinite coaxial balun is unbalanced at low frequencies for the spiral antenna. This problem has been overcome with the new balanced feeding arrangement via a 0°- 1800 Hybrid located at the spiral center. The measured gain of a 2"x2" spiral antenna (without arm termination) using these two different feeding arrangements is shown in Figure 2.11. We observe that the gain variations at low frequencies have been greatly reduced by using the hybrid feed. The higher axial ratio (resulting from the cable scattering/radiation) is significantly improved as demonstrated in Figure 2.12. Another distinct advantage of the hybrid balun in that it does not suffer from cable losses. This is because the hybrid balun requires a section of cable which is only slightly longer than the depth of the cavity (only a couple of inches). However, the length of the cable required for the coaxial balun it typically on the order of a couple feet resulting in significantly more cable loss.
24 Outer Conductor 500 o· Input
Conductor
Figure 2.10 New 0°-180° Hybrid Balun.
',~--..--~~-'Ii : _,r: '" ~-~ ... --~ 0------~ ------~~~------: ,, : ,;'" . :=- ..s ------~------~------·------co ' ' ~ c Ci -10 l-'.c ------___ ------;------!? -15 ,.4:'~~~' ' (I) , ' ' ,, ' ~ 1 ' 0 t : ' co -20 ------_J. _- ----~ ------! ------/J i i ,.r i · -25 -/V~------t ------~--~-P-re-v-io_u_s_B -al_u_n~ ,i; I ' r: J' i ---- Improved Balun J o ~'~----~------~-----~ 0_5 1 15 2 frequency (GHz}
Figure 2.11 Measured Gain of the 2"x2" spiral antennas fed with the previous infinite balun and with the new 0°-180° hybrid balun.
25 5 r-~~~~-,~~~~~~======~ - Infinite Balun 4.5 ------· Hybrid Balun
4 ------i------
3.5 ------:------
Q5 1 1E 2 frequency (GHz) Figure 2.12 Measured Gain of the 2"x2" spiral antennas fed with the previous infinite balun and with the new 0°-180° hybrid balun.
2.4.3 Arm Termination The previously employed termination was based on a Klopfenstein resistive taper which employed multiple chip resistors placed along a properly chosen length of the arm (see Figure 2.13). As mentioned previously, this served to slowly attenuate the current before it reached the end of the spiral arm. It has been shown to be very effective in minimizing reflections from the end of the spiral arm without a priori knowledge of the slot impedance. However, this termination occupies a significant length of the spiral arm, limiting a portion of the aperture's utility and the dielectric loading of that same portion. An improved (not optimal) alternative would be to use a single termination resistor located at the end of the slot line and matches the slot line impedance. This new arrangement is shown in Figure 2.13 and allows for greater utilization of the spiral aperture. Additionally, as shown in Figure 2.14, it provides better axial ratio (polarization purity) at low frequencies compared to the previous termination method. Another way of examining the effectiveness of the arm termination 1s to decompose the radiated field of the spiral into a right-hand (RHCP) and a left-hand (LHCP) circularly polarized component. Since the winding sense of the spiral determines
26 the polarization of the radiated wave from the outward flowing current any radiation with the opposite polarization is due to an inward flowing current. Of course the magnitude of this inward flowing current depends upon the effectiveness of the termination to attenuate it. Therefore, by comparing the two circular polarized components, we can evaluate the termination effectiveness. Figure 2.15 shows the decomposition of the gain into its left hand component (GL) and the right hand component (GR). For the winding sense of this spiral, the GR component is the desired polarization and the GL component is undesired component and contributes to cross-polarization. From Figure 2.15 it is evident that the single resistor termination improves the cross-polarization at low frequencies.
gle Chip Rlllllor / '
Figure 2.13 Single-resistor vs. multiple-resistor termination of spiral arms.
- Resistive Taper 9 ------+------· Single Chip Resistor ' 8 ------~------\------' .' .' .' ' 7 ------~------: ------' ' ' ' en ' ' :!:!. 6 ------~ ------· ------0 ~ 5 0::: ' ~ 4 ------~ ------!------>< . ' < , : : 3 \------~------:------'\ I\ : ' 2 ---« ---1 - \------~- - -- .. f \ I
------~l---~---,.~ ----~-J!.._-=-~·------,;... .' , ...... , l ...... '_:i.: \ ------~-=('_~:'(;# ' . ' , \ v I - I .- ... .,,...... ,., 1 1.5 2 frequency (GHz)
Figure 2.14 Measured axial ratio comparison of single-resistor termination vs. tapered resistor termination.
27 0 ------~.------.... ------: J# : ~ -5 ------r ------t------m : / : ~ -10 -- ••• •• ------)r'°':A.~:!".!""••• •••••••...... ~ ...... -----·········· .5 I: : ~ ••:•:::·;~··<-t• -~ .,;? · · ·: :· ,_: :?F~ ~· ~i~,, :••· i0 : (-.; .: : ., tJ : ':i ' . m ' . . • : : ,, ~o -- -f ------.r-.:.. r.: --- -i-·r ··------~ - --- :-- ~ ·· ·· : ------~ -- · ~ :·l .. r~· : · · · ~ -35 - ---·,,-:'------'- ~------Resistive Taper: GRHCP : -=~= • • : ...... Resistive Taper: GLHCP ::: _.o ~~ -{ '\: ------;,-> ----:------Single Resistor: GRHCP ;: lr ------,~ --r·------Single Resistor: GLHcP
0.5 1 1.5 2 frequency (GHz) Figure 2.15 Gain decomposition into LHCP and RHCP components.
2.4.4 Cavity Mode Suppression Several techniques for suppressing cavity resonances were investigated previously [7]. One of them is to add absorber lining inside the cavity to damp the resonance. This approach was shown to be quite effective for suppressing the undesired cavity modes. However, it also reduces antenna efficiency (and therefore gain) in the process. A new cavity mode suppression method was investigated without the lossy wall absorber. This approach introduces a layer of radial wires into the cavity at an optimal distance from the antenna aperture as shown in the inset of Figure 2.16. Away from the center, the spacing of the radial wires is large enough to have no impact on the low frequency operation (effectively making the cavity deeper). Near the center, the depth of the cavity is reduced to where the radial wire is located. The improvements obtained by using this new approach can be clearly seen in Figure 2.16. From this figure it is evident that this new technique works by shifting the cavity modes to higher frequencies instead of attenuating them. Thus, gain reduction does not occur at high frequencies as seen with the absorber treatment. This is readily observed from the region in Figure 2.16 which is highlighted by the dashed circle.
28 10 _.; ..... ~ ..... 5
0 as ::!:?. -5 ·i \.!) -10 ~--}--- ···+ ·· ·· · .=.. l:J) :' ~. .' Effect of Cavity "ii... -1 5 0 Resonance CD -20
-25 .. - Empty Cavity Radial Wire Treatment r Absorber Treatment -30 2 3 4 5 6 7 8 9 10 frequency (GHz)
Figure 2.16 Measured gain of a 2"x2" spiral with and without cavity treatment.
29 Chapter 3
Antenna Miniaturization using Dielectrics
The purpose of this chapter is to provide an understanding of how the spiral antenna can be miniaturized using materials with simple profiles or topologies. In addition, this chapter serves to experimentally quantify the amount of miniaturization that can be achieved and discusses some of the issues that arise from the dielectric loading. The first section discusses the concept of miniaturizing the spiral antenna with the subsequent section discussing the criteria used to measure the amount of miniaturization. The remaining sections focus on the miniaturization, issues and limitations of using dielectric materials.
3.1 Concept
The concept of miniaturizing the spiral antenna is readily explained by the radiation mechanism of the spiral antenna. Recall that the spiral antenna radiates because the current flowing in adjacent arms naturally becomes in phase in the regions (active region) where the circumference is an integer multiple of one wavelength. For a circular spiral with diameter D this occurs at integer multiples of /Jn and for the square spiral when the diameter is around IJ4. Therefore, the location of the active region depends entirely upon the phase velocity and by using high-contrast materials to reduce the phase velocity the diameter of the active region can be reduced. Thus, spiral antenna miniaturization is about reducing the diameter of the active region which occurs at A.g A. D--- 0 (3.1) - 4 - 4~µe&e
30 where ~and Ee are the effective relative permeability and permittivity. From (3.1) it is apparent that miniaturization results in a reduction of the active region diameter and is proportional to the effective permeability and permittivity obtained by loading the antenna. Therefore, the factor~µ e e e can be interpreted as the reduction or miniaturization factor. The relationship between (µe, Ee) and the (µr, Er) of the loading material depends upon how the antenna fields interact with the material around it. For an antenna that lies in the plane separating two infinite mediums, the relationship is
erl + 8 r2 (3.2) where (µr1. £r1) and (µr2. Er2) are the relative permeability and permittivity of medium 1 and 2 respectively [30], [31]. This relationship can be explained by considering the physical picture of the fields as shown in Figure 3.1 for any PEC antenna. For simplicity, a dipole is depicted in Figure 3.1.
Figure 3.1 Illustration of material loading of a dipole.
From an inspection of 3.2 it is observed that Ee is equal to the series combination of er1 and Er2 whereas µe is equal to the parallel combination of µr 1 and µr2. These relationships can be shown by using the usual analogy between(µ, E) and (L, C). It is apparent from this figure that the capacitance associated with the electric fields in medium 1 is in parallel with the capacitance due to the electric fields in medium 2. Since the capacitors are parallel and Ci ~ Ei, we have:
erl + er2 e =--- (3.3) e 2 which is just the average of the series combination of Erl and Er2. The effective permeability is similarly determined by using the average reluctance to the magnetic flux
31 around the antenna. As shown in Figure 3 .1, the path of the magnetic field H is always half in medium 1 and half in medium 2. Therefore, the effective µ can be determined by noting that the average reluctance to the magnetic flux around this path is the average of the reluctances in medium 1 and 2. Since the reluctance is inversely proportional to the inductance, we have the following relationship:
R =RI+ R2 => _l_ = _!_(_l +-1J (3.4) avg 2 Lavg 2 LI L2 and since ~ - µi, we therefore have
(3.5)
It is noted that these relationships are only true for the given loading configuration and the interaction of the fields with the material. To further verify (3.2) a 2" spiral was simulated with and without material loading. The spiral was first loaded on only one side with a 2mm thick slab of material. The relative permittivity and permeability were then varied while maintaining a constant wave number k. Figure 3.2 shows the shifting in the gain curve when only one side is loaded with µrEr= 9 and µrEr= 25. It is apparent that using only dielectric always results in the largest frequency shift in the gain curve whereas using all magnetic results in the smallest shift just as expected from equation (3.2). However, (3.2) predicts that when both sides are loaded the same amount of shifting occurs if the loading is purely dielectric or magnetic. Figure 3.3 verifies this by showing the shifting in the gain curve for the loading of both sides. It is clearly seen that at low frequencies the gain curves are nearly identical for the loaded cases.
32 . . ~ .: ,A?~-~~-~-~t~ :,O"-:: ~ -15 ------/~ ~·: · _____ ; ______1______0 ,.. I I ~ /~··.. : : ! : :: ~~~~'.<- · ::::_:::::t::::::::::::::::::::::-1= - ~: -~ - ~ -. - ~: -~ - ~ -- /l 1 --- - '• - 9. I', • 1 .JO ~~~· ------~------•.•...•. ••• 3. P.,. 3 . i •,•1. 11,•9 -35 -35 L.L____ .L_...... ':::======~ 0-5 1 1-5 0-5 1 1-5 frequency {GHz) frequency {GHz)
Figure 3.2 Miniaturization (simulation) for single side loading with constant wave number k.
-·-·-·-·-·-· 0 ------1.-.;.-;.-..... '--·-'":;;;==~,, ;~:.... /.~~~-~:~:-::~ ,,.. ,,, . ·'' ~...... ,,,' : '° ~ ------~-~ ·,"':··"""'r--·--~::_____ ------;------~ ,. , ' ' ~ -10 ______,,:.,.c ______f------!------(,!) ,.~/ : : / ~' : : '! -15 ------·'~------' ------~------0 ,.~~ : : I- •/ . ~ -20 · :;{:: . ------~------f------~ ; I ' I (0: 1/ : ,...______~ ~ -25 / ~ ------·------~------er• 1 111 =1 ---- er • 9 111 = 1
-30 ------~------·-·- e1 • 3 111 • 3 e •111 •9 1 1 -35 L_L_____ L______:======::::::'...J 0.5 1 1.5 2 frequency (GHz)
Figure 3.3 Miniaturization (simulation) for double side loading with constant wave number k.
Even though Figure 3 .2 and Figure 3 .3 illustrate the validity of the relation (3 .2), the use of magnetic materials is not practical at this time due to high losses associated with such material. Therefore, for the remainder of the thesis only miniaturization using dielectric material is considered. For only dielectric loading the effective permeability is unity and the relation reduces
8 = {(8 r + 1)/2 ' for infinte half - space (3.6) e 8 r ' for infinte full - space
33 However, these expressions refer to semi-infinite half-spaces above or below the antenna. For practical layers with a finite thickness and width, the miniaturization is much less than this and is discussed in the following sections.
3.2 Miniaturization Criteria for Broadband Antennas
One challenge associated with the miniaturization of a broadband antenna is how to define a measure of the attained miniaturization. The reason for this can be clearly illustrated by considering a narrowband antenna. For narrowband antennas the amount of miniaturization is very straightforward and is proportional to shifting of the resonant frequency. This measure is very straightforward because the resonant frequency can be easily defined in terms of return loss, gain or input impedance. As a result, it is easily distinguishable. Therefore, the effects of material loading are easily observed by comparing the location of the resonant frequency for the loaded and unloaded cases. For broadband antennas the choice of a reference point is not as obvious (see Figure 3.4). This is because broadband antennas lack a distinguishable frequency of operation. For the spiral antenna, one would ideally like to use the lowest acceptable operational frequency. However, the parameters such as gain, return loss and impedance used to characterize this point are sensitive to changes in the spiral' s geometry even if the diameter of the spiral is held constant. Therefore, using this point to measure the loading affect is not an optimal choice. What is needed is a reference point that is insensitive to such changes. One such point is the frequency at which the spiral antenna first achieves a gain of -1 SdBi. The only factors that influence its location besides material loading are the physical size of the spiral, radiation efficiency (arm termination), and mismatch losses. As long as the arm termination remains the same for all cases and mismatch losses are minimized by proper matching, then only dielectric loading and the physical size affect this point. Here on, the -1 SdBi gain point will be used as the reference with the miniaturization factor (MF) defined as:
34 MF= f unloaded ,-15dBi (3.7) fioaded ,-15dBi where !unloaded is the -15dBi gain point of the unloaded antenna and ftoaded is the -l 5dBi gain point of the loaded antenna.
' .' . ' ' ! ! : resonant frequency i : -r r:t~ ---±::~----F
Figure 3.4 Illustration of the difference between the miniaturization criteria used for narrowband and broadband antennas.
3.3 Dielectric Loading of the Spiral Antenna
In this section, the miniaturization of a square spiral is investigated experimentally by loading it with a uniform dielectric slab. The dielectric constant of the slab was varied from 9 to 85 while maintaining its electrical thickness. The obtained MF as a function of Br and other results are then discussed.
3.3.1 Initial Experimental Results for Dielectric Loading To experimentally demonstrate the concept of miniaturization using high-contrast material loading, a 2" square spiral was initially used due to its convenient size. High contrast dielectric layers of thickness 0.1 A.g with various dielectric constants were then individually placed on top of the spiral antenna as depicted in Figure 3.5. In addition, the width of the slab L is fixed to be equal to the diameter D of the spiral. It is remarked that
35 the guided wavelength Ag is defined with respect to the first frequency supported by the unloaded spiral (for square A.o = 4D, for circular A.o = 1tD) and is given by
A. _ A- _ 4D g-F-F0 (3.8)
""-.Spiral
+----L----+
Figure 3.5 A cross section of the tlnite single-sided loading geometry.
The total gain of the dielectric loaded antenna was then measured and is shown in Figure
3.6. The gain curves refer to the cases where Br = 9, 16, 30 and 85 respectively. The superstrates with Br= 9, 16 and 30 are made from a low-loss plastic stock (tan8<0.002) which was obtained from Emerson & Cumming Microwave. The ceramic superstrate with Br = 85 was obtained from picoFarad and is made from rare earth titanate (tan8<0.001). From Figure 3.6 it is evident that the dielectric loading shifts the gain curve to lower frequencies as the dielectric constant is increased. More specifically, using the miniaturization factor MF defined earlier, the corresponding -15 dBi point shifts from
887 MHz down to 574 MHz using a dielectric layer having Br= 85 (see Table 3.1 for more details). For this case, the MF is 1.55 and corresponds to a size reduction of 35%. It is also noted that the size of the spiral at 574 MHz is only )JlO. Although this reduction in size is significant, it is important to note that the maximum achievable MF for infinite half-space loading with Br= 85 is as large as 6.55.
36 ,.~ ··, .... ~ . -:( "'"'.6' ••' '\ I 1 •• 0 ------~------/~-~~·~· ~· - ~~~1~~~-~ ·::· : ·! u :.~..... ;~ .: : ''·· - al · ~· If""'\-···'' •• :... .. ~ -/! _,...... • .."' .... "'· ...... : / . : . ,~ ~ -5 ------~··----,..-;.·: ______-"'------:------, ••------.,,-- <.!> : #/ /: : ~ : i:J • ,,. / : : • 4.l •• / ••.. .-' : : •• ..... ~ -1 0 ------;l;'",'i!/ ------. ------:------~•• - ..'! ____ _ 1 (IJ ..... ' # ..7' I I ~ : ~ i i i:J ..... l',i : : - I! •1 C> -15 ••.... ·--- .. --/-i ------~------:---- I ___ ;. ~. :; ._, / :' : : ...... I! =9 (j) • /t' 1i-:-~ ; I : ,llf "\./ ---- I! = 16 :: ..20 ------+------:-- -- I r-- -- - 6. 30 I •••• s, =85 -25 r:______L______L__.:::======::'.J 0.5 1 1.5 2 frequency (GHz) Figure 3.6 Measured total circularly polarized gain of a 2" square spiral with and without a dielectric superstrate (measured without cavity and resistive termination).
£, t ti~ fL(-15 dBi) MF=foffL 9 7.3 mm 0.101 752 MHz 1.179 16 6.15 mm 0.113 718 MHz 1.235 30 4.3 mm 0.109 650MHz 1.365 85 2mm 0.089 574MHz 1.545 Table 3.1 Two inch square spiral summary for the frequency shift of the -15dBi gain point (the unloaded spiral's -15 dBi gain point occurs at 887 MHz).
Since no steps were taken to improve the impedance match for each measured case, the gain reduction seen in Figure 3.6 at high frequencies is mainly associated with mismatch losses. With better matching, the gain will be recovered and the low frequency gain will also improve, thus further increasing the MF. It is also believed that the gain drop for the Er = 85 case is a result of the spiral growth rate being too large in terms of wavelengths. That is, the high-contrast loading has effectively increased the growth rate such that it is now too coarse for the Archimedean spiral to maintain a broadband response. Therefore, gain reductions or fluctuations should be expected since any Archimedean spiral needs to be tightly wound to prevent gain fluctuations. This also implies that the growth rate of the spiral should be a function of the material loading to maintain a broadband response.
37 3.4 Dielectric Loading Issues
It was shown in the previous section that dielectric loading can reduce the initial operating frequency of the spiral antenna. However, there are issues and limitations associated with dielectric loading. The purpose of this section is to introduce these issues and limitations and discuss some possible solutions. The first issue that will be discussed is the reduction of the input impedance. This will be followed by a discussion on the affect dielectric loading has on the cross-polarization. This section is then concluded by introducing the limitations associated with antenna miniaturization.
3.4.1 Input Resistance Reduction A well known consequence of dielectric loading is the associated reduction in the input resistance of the antenna. Since dielectric loading reduces the antenna impedance, it is appropriate to quantify the amount of reduction as a function of the superstrates thickness and dielectric constant. To examine the impedance reduction, a two inch square spiral was simulated by loading it with a dielectric slab having Er= 9 and 16. For each of the dielectric constants, the thickness of the slab was varied and the effect on the input impedance was observed. As shown in Figure 3.7, increasing the thickness of the dielectric slab leads to an increasing reduction in the input resistance. In fact, the input resistance asymptotically approaches a value which is equal to the unloaded value divided by the square root of the effective dielectric constant. In this case, the effective dielectric constant is equal to~(er + 1)/2. From this observation, it can be inferred that loading both sides of the antenna will result in even more reduction due to the larger effective dielectric constant obtained by loading both sides.
38 100,---~,--~.-~.-~--.--~---.-~--;i:::======::::;-i : : : -a- s _=9 9Q ------~------+------i------:------I . . . . -e- g "'16 ' , I 80 ------f------f------i------i------1------1------. ' ' . ' .• 'I '0 .0 'I 7 ------~------~------1------1------1------1------, I I I I I t I I I I I I I I I t I
------•.. ------..I ------··yI ··------..I ------·------·------t t 0 I I I I I I I I I I g I I I I I 50 ------~------~------t ------t------t------t------ri.i : : : : : : ..io - ----~------~------t------t------t------t------, ' ' ' . . . . .' • + • ' • 30 ------:-. ____ .: _ ------.:. ------•. ------:------7 : 7 -7 -7 -7 -!-"'-":::::_- ---~----~---~----~----~---~------20 ------~------~ ------~ ------t------t ------t------t------t I • I I + o O I I I I 0 0 I I I I I t 0 10 ------~------~ ------~ ------t------t------t------t------• 0 I I I I I • 0 I I I I I I < I I I I I 0 o 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 thickness. t/l. II
Figure 3.7 Impact of superstrate thickness on input resistance reduction for single sided loading.
The reduction in the input resistance is undesirable for several reasons. First of all, it leads to mismatch losses unless the impedance of the balun is changed accordingly. For the spiral, it is not desired to alter the impedance significantly since it reduces the amount of attenuation of the traveling wave through the first active region. Therefore, changing the impedance of the spiral can only provide limited compensation. That is, if the loading reduces the impedance significantly then the balun must be redesigned or the profile of the material could be altered to help alleviate the problem. Another reason why a small input resistance is undesired is that it implies a small radiation resistance. Basically, a lower radiation resistance means the antenna will deliver less power if the gain and input power remain unchanged. This may or may not be an issue if the power delivered to the antenna can be increased as desired to compensate for the drop in radiation resistance. Whether or not the drop in radiation resistance is a problem, the use of high contrast materials presents a challenge from an impedance matching viewpoint. However, this becomes less of a problem if the antenna is loaded in an intelligent way to minimize impedance reduction. One possible approach is to use a tapered profile (thickness or dielectric constant) of the dielectric material. Another approach is to use magnetic material to increase the impedance and thereby counteract the effect of dielectric material
39 loading. Both of these methods will be discussed in the following sub section starting with dielectric tapering.
3.4.2 Solution Methods for Input Resistance Reduction
3.4.2.1 !Jielectric 1'a]Jerin15 When the spiral is loaded using a uniform dielectric slab with constant thickness the electrical thickness of the slab varies with frequency. Therefore, the slab will be electrically thicker at higher frequencies than at lower frequencies. This results in more scaling at high frequencies and, as a consequence, the antenna impedance associated with these frequencies is reduced more. This is undesired and unnecessary since it is the low frequency components that we wish to scale. The concept of dielectric tapering is to maintain the same electric thickness across the aperture of the spiral. Thus, uniform loading is achieved and the reduction of the input resistance constant and is minimized but not eliminated. An example of dielectric tapering is shown in Figure 3.8. In this figure the dielectric constant of the slab has been varied linearly starting with Er= 3 at its center and ending with Er= 9.
s.-7 E, = 8
Figure 3.8 Top view of a dielectric slab which has a linear tapering of its dielectric constant.
A two inch square spiral antenna was simulated using a uniform dielectric slab with Er = 9 and one having the profile shown in Figure 3.8. Figure 3.9 shows the comparison of the computed input resistance. From this figure, it is evident that the 40 dielectric tapering treatment results in less reduction of the input resistance for the same thickness (53Q versus 33Q for the uniform case). However, this treatment is only useful if miniaturization is not compromised. Indeed, Figure 3 .10 shows that the gain curves for the uniform slab and tapered slab are almost identical. Therefore, the graded dielectric allows for impedance control without effecting miniaturization or gain performance.
100,----.-~--.~.-----.--;:::=====r===c:=====::r::==;i : -e- Uniform Dielectric. e • 9 90 ____ T' ____ T' _____ r' ____ "f"' o Linear Dielectric TaperI
I I t I 80 -----1------1------: ------~------1------i------:------:------f----- ' 0 t I 0 I I I I I t I I + I I I I I I I t I I I 7 --- --:------:------:------~------:-----+--- --~------~ ------~ ----- ' + I I t I 0 I I I t I I 0 0 I I I -~~-!------1------:------L------!------~------L------L ------~ ----- ,. ' ' ' . ' . ' . [_~-~-t~-~::~~-~-~-t-~-~-~::_-:_-:~~-~-~-t-~-~--=~~-~-~-r-~~ ___ I I I I + · I I I I f I I I I • - - - •t ______,,I ______....I ______1..I ______1I ______,,I ______J 0 ______1,.I ______+ _ __ _ ' ' ' ' I I .t I I .I .I .t . . . t I I t I 30 -----: ------~ ------7------~ ------·------~ ------.... ------~ ------~ ----- I I + I I I + I I I I I I I I I I 20 ------t------1------~ ------~------t------~------~------~------~- - --- • I 0 I I I I I I I I I I t I I I I 1 0 • I 0 I I I I 10 ------+------~ ------:------~------+------1------:------~ ------~ ----- ' . ' ' . . ' ' ' ' . ' ' . . . ' ' 6 8 10 12 14 16 18 20 thickness. t (mm)
Figure 3.9 Effect of dielectric tapering on input impedance reduction.
' . . ' 5 ------~ ------:------1------...... ;;-- : ~-~-- - : --- - ... : : o ------~--- .":. -.:&,~;;-!.. ---L ------~------L------:/'"""" : : : 1V : : : iii .5 ------1~ ~------~ ------~------~ ------~ ,r": : : : .E -10 -- -- -. -.: . ---i------:------i------. ------:-- -. ------~ l : : : : ~ -15 ····/·-· ·· i-·------+------i------~------N ,/' .I ' ' .' Ci f I l I 1 .. -20 ··/------i------~---······· ·· ·i------~------0:: :I :' :' :' :' -25 /------E • 1, Z • 72.710 I 0 .JO __ --······· ...... Dielectric Taper. t • 10mm.; • 53.180 ---- Uniform. t • 10mm.; • 33.140 -3 51.L_~~_.'.:I:======::i:::====:=::i======::r:====:::::J 05 15 2 25 3 frequency (GHz)
Figure 3.10 Effect of dielectric tapering on miniaturization.
41 3.4.2.2 Initial Experimental Results for Dielectric Tapering
Since it is very challenging to combine several different materials to achieve a graded material, an easier way to implement the dielectric taper is to use a single material and taper its thickness. This approach is not only simple to fabricate but also reduces the weight of the dielectric slab. To experimentally verify the dielectric tapering concept, a 6" square spiral was used. The geometry of the 6" spiral is a scaled version of the 2" spiral used previously. To establish a baseline for the 6" spiral, it was loaded with a piece of plastic stock having er = 30 and dimensions of 6" by 6" by 0.5'' (0.11..g). The corresponding measured return loss is shown in Figure 3 .11 for both the unloaded and the loaded case. The curves in Figure 3.11 clearly show that the uniform dielectric slab causes a significant deterioration in the return loss.
0.------~----.----.----r----,,-----,
-5
-10 iii :!:!.. -15 en en .3 -20
____ ,, ______,, ______-30 ------;------______---,. ------' ' ' ' ' ' ' ' ' ' ' ' ' -35 ------+------·------.------_._--~ - Without Superstrate ---· Uniform Superstrate -40 L___ J___L___L __ _L_~====C:::::::==:::r-' 0 0.5 1 1.5 2 2.5 3 frequency (GHz}
Figure 3.11 Measured return loss (dash-dot line) and without (solid line) a uniform superstrate (sr= 30).
To improve the return loss, the uniform dielectric slab was altered by tapering the thickness of the slab. The slab was tapered by first cutting the square section into four triangular pieces using a diamond blade. Then, each smaller piece was further machined using a carbide milling bit into a section having a triangular cross section as shown in
42 Figure 3.12. The four pieces were then assembled and placed on the square slot spiral aperture using a very thin layer of low loss epoxy. It is remarked that the tapering of the dielectric slab reduced its weight by 25%.
o .~oo~ o · ~._ a----2.6100 '
Figure 3.12 Cross section and picture of the thickness tapers dielectric superstrate for the 6" square Archimedean spiral.
As shown in Figure 3.13, the tapered superstrate significantly improved the return loss by limiting the amount of input impedance reduction as demonstrated in the previous simulation. Nonetheless, it did not eliminate the mismatch losses. To completely eliminate mismatch losses, the impedance of the balun or antenna must also be changed. Additionally, one can see from Figure 3.14 that the tapering does improve the gain at higher frequencies in addition to not effecting the :frequency reduction. This is also in agreement with the earlier simulated results.
43 0
-5
-10 iii E -15 II) II) _,0 -20 .....c ~., -25 a:: -30
-35 - Without Superstrate ---· Tapered Superstrate -40 0 0.5 1 1.5 2 2.5 3 frequency (GHz)
Figure 3.13 Measured return loss with (dash-dot line) and without (solid line) a tapered superstrate (Er= 30).
5
0
-5
- Without Superstrate ' ' ' -35 ------~------: ------}------With Uniform Superstrate ' ' ' ' ' ' ...... With Tapered Superstrate -40~~~~~~~~~~~~~~~~~~~~~~~ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 frequency (GHz) Figure 3.14 Measured gain of a 6"x6" square slot spiral antenna with and without high dielectric superstrate loading (Er= 30, thickness= 0.5 inches).
3.4.2.3 Magnetic Material Loading for Impedance Improvements
Since dielectric tapering still results in a reduction of the input resistance, it is desired to investigate methods that would maintain input resistance. The use of magnetic
44 material provides a means for maintaining input impedance by essentially counteracting the effects of dielectric material. This is illustrated in Figure 3.15 where it can be seen that using the same µr and er to load the antenna results in less reduction than dielectric tapering alone. However, there is still a reduction in the input resistance. This is likely due to only one side of the antenna being loaded. That is, the magnetic material should be equally applied to each side of the antenna to completely eliminate the reduction in the input impedance.
150r-~~-,, ., ,, "TT~-r::======:l:=====::::::ii::::::====~ : l l i - e • 1. IL, = 1. Ri = 71.77 42 : '• 1 1 : l l ,~ i ---- e • 3. IL, • 3. Ri • 61.9104 : :: :: 1 1 :I ••'• ,11•
: : : : ~ I I I '• 1' . I t 100 ------~- .-: - ~ - - --rt·:------~------:------: :: : : : : : : : : : ~ : : : I I ~ ! 1 " : ,.: : ', : ' I I ' j ~\ : : : : l : J : \ _. ... - ...... _ _., : ' l \ : : I I ~ : \ : : ,_; : \ : \. so ------:-'Irt · - - I: - --'~.r' f ---- \:·l' ---:------' ""' ----,\ :,..----I : : : : : : ! 1 I r : : ~ ~ : I 'I I ! I \ ' I :'.J' oo---c..c...... ~~~--'--~~~-'--~~--'~~~-' 0.5 1.5 2 2. 3 frequency (GHz)
Figure 3.15 Influence of magnetic material loading on input impedance.
Nevertheless, as mentioned before, magnetic materials is narrowband and lossy, particularly at high frequencies. Thus, their use is not practical unless the frequency is less than I 00 MHz. Therefore, the best choice and most practical approach is dielectric tapering.
3.4.3 Polarization Purity The spiral antenna supports a fast leaky wave mode. This is a loosely coupled wave and will therefore radiate significantly upon encountering discontinuities or experiences charge acceleration or deceleration. Dielectric loading slows down the traveling wave which naturally leads to a more tightly bound wave. Therefore, the outward flowing wave radiates less and more energy reaches the spiral termination.
45 Therefore, at any frequency, more energy reaches the end of the spiral and is reflected if it is not dissipated in the termination. As noted before, this leads to an increase in cross polarization. Furthermore, this wave also returns to the input producing an oscillatory behavior in the input impedance. Figure 3 .16 shows the effect of loading on the cross polarization for an un terminated spiral. For the unloaded spiral the desired right-hand circular polarization (RHCP) component is much stronger than the left-hand circular polarized (LHCP) component. However, when the spiral is loaded the RHCP component is reduced on average by 2dB and the LHCP component increases significantly. This signifies that dielectric loading leads to more energy reaching the truncation.
5 r------:------:-::=:=:r. ====::::i:. ====~ 0 •..••••••. ··+·· ...... ~ :~:... -.-.·::.·~~r:~:~:..... ,._~:~:t\:./\.- r . ~ . -- :.~-~ '•t.. : ~ :- ---~ .. : .... ::.- ...... -,.. ~ _...... , ..... : ...... ___ , -5 ------~ .~- -- -- ~ - -- - ~ - - -~. ;------~------~ ------.... .( : \ : : ~ -10 ...... / j...... j...... \.:··+··········· ·l············· c I : : \ : : . ~ -15 ••••.•• / ••• j ·············~·-········· :·:-~: ·: ~· "·• .. ;,;:··· - ~·- ·· ·····.. / ~ / : : : ·· .... : / ~ -20 --- -f-- -- -~------+------~------~\t_ --- -- i··____ _ Q: / i i i .. .. -25 ··/ ···· . .•.• : ...... ~ ------· - - .. - - ~ -- - GRHCP' s, • 1 I • • • G 1 I : : : ...... LHCP' 61 • -30 '------~------~------~ - - ---·- GRHCP• e, • 9 ~ j j ---- GLHcP· s, • 9 ~5LL~~...L.~~-1~~~..L.'.====:=I=====:::J 0.5 1.5 2 2.5 3 frequency (GHz}
Figure 3.16 Comparison of the CP gain for an unloaded and loaded spiral.
The issue of cross-polarization can be alleviated by terminating the spiral with a single resistor (ZL = 50Q) as shown in Figure 3.17. From this figure it is apparent that the termination does not reduce the desired gain component (RHCP). However, it reduces the cross polarization component (LHCP) as desired.
46 . . ~JC: ... ••·••••.. •"t••••••••••••••"''•••• ~ ,,, ,,u•••• ' •'''•,,..,,: ..5 --·------• ·------:------:------:------'-> ' : : : l' - I ; ' I ' ' I l al ' / \ ' ,, ... \ I ' I ' ~ -10 ------·-· -~---.,,----r·--:-·T---•.-----~------·--7~"'\---r - -\--' c: : / ~ : l \ : ,,--~, / : \ : ~ l (; : I \ : I 1 : J \ I : l I ~: e> -15 ------·--H-· · -----~---:t·-···--· - \- - -,(------..--1---~-- - H·---..- "l';:J : ,' \ , \.J : ,,. : •J y cu I ,, ' JI ' I ~ -20 --;f. ------~ ------\·[~------~------+------: i /: 1.1: ' ' 0::: • I ' ' -25 -~ ·-··-· /-+-···-----·· ·-~--· ··- ··--·- - GRHC P'~ •Oa ! / ! ! ...... GLHCP'~ •Oa -30 ····-/- ····· j --·····---·---~------····-- -·-·- GRHCP' ~ • 500 / i i ---- GLHCP' ~ = 50a -35 L....[....' ___l._ ___ ..l__ __ _:::r:::=:=:=x::::::=:==.J 0.5 1.5 2 2.5 3 frequency {GHz}
Figure 3.17 The CP gain components of a loaded spiral (t = 2mm, Er= 9) with and without a terminating load.
However, a single terminating resistor cannot completely eliminate the oscillation in the input impedance as shown in Figure 3.18.
100 ,--,,-"'lr--.----;c:======:::::;i - •, - 9. 1t_ - 00 ------.. ------...... •, • 9. 1t_ - 220 30 ...... ;
------:-.------·-·- •, - 9. 1t_ - 400 60 · ··-· - ... . e • 9.z.._ • SOa ______.. ______1
40
30 ' 20 \ ·i · 10 .....
1.5 2 2.5 -11M/,. 5 1.5 2 2.5 frequency (GHz) frequency (GHz)
Figure 3.18 Comparison of the input impedance for an unloaded and loaded spiral.
Nonetheless, the main issue with using a resistive termination is that it reduces efficiency, particularly at lower frequencies. This is clearly observed by comparing the power radiated by the antenna to the power dissipated in the termination. Figure 3.19 shows this relationship by showing the percentage of the accepted power which is either
47
Chapter 4
Summary
The miniaturization of a broadband antenna using high-contrast dielectrics was investigated in this thesis. Specifically, the miniaturization of a square spiral was investigated numerically using the finite element boundary integral method and experimentally using the measurement facilities at the ElectroScience laboratory. A previously developed shallow cavity backed spiral antenna, discussed in chapter 2, was used as the starting point. The design was altered to facilitate the loading of the spiral antenna by removing any objects which occupied the surface of the antenna. The first alteration involved replacing the resistive taper termination, which is composed of numerous resistors, with a single resistor termination. Therefore, the new termination occupied significantly less space while maintaining similar axial ratio performance. In addition, it also improved the efficiency of the antenna at lower frequencies. The second alteration involved the elimination of the previous infinite coaxial cable balun. This balun greatly hindered the loading of the spiral because it occupied a portion of the spiral arm over the entire spiral aperture. To overcome this problem a hybrid balun was used to feed the antenna. Also, the hybrid balun eliminated unwanted radiation from the feeding cable at low frequencies that was an issue with the previous infinite balun. In addition to these design alterations, the design was modified to better utilize the square aperture by converting the previous circular spiral to a square spiral. In chapter 3, the miniaturization of a spiral antenna was studied experimentally and numerically. Specifically, a 2" square spiral was used because of its convenient size and frequency range of operation. The antenna was loaded using superstrates with various dielectric constants but with the same electrical thickness. The high-contrast material loading resulted in a significant improvement in the low frequency performance
50 of the loaded spiral. The improvement was such that a maximum MF of 1.55 (35% size reduction) was achieved using a dielectric constant of 85. Such an improvement provided sufficient operation of the spiral down to a frequency of 574 MHz where the size of the spiral is only All 0. As a consequence of dielectric loading the impedance of the antenna is reduced. It was found that the amount of reduction is nearly equal to ~(er+ 1)/2 for single side loading and Ji: when both sides are loaded. To minimize this reduction the concept of dielectric tapering was introduced. It was shown using simulations that linearly varying the dielectric constant of the slab from the center outwards effectively minimized the amount of reduction. That is, a low dielectric constant was used starting at the center of the spiral and was linearly increased outwards in the radial direction. This was also verified experimentally and implemented by linearly tapering the thickness of a dielectric slab instead of the dielectric constant due to fabrication limitations. In addition to demonstrating the practicality of broadband antenna miniaturization using high contrast materials, it was observed that there are limitations associated with the miniaturization and that these limitations require further examination.
51 Chapter 5
Future Work
This chapter outlines a plan for the extending this work. The first section discusses the continuing study of broadband antenna miniaturization using high-contrast materials. This section presents a plan to study the limitations of dielectric loading both numerically and theoretically. In addition, it presents some issues which have yet to be addressed or even initially studied. To conclude this chapter, the last section introduces a possible approach to overcoming the limitations of antenna miniaturization.
5.1 Dielectric Loading
5 .1.1 Characterization of the Miniaturization Factor It has been shown that high-contrast dielectric loading can be used to miniaturize a broadband antenna. However, it is not yet known to what extent dielectric material can miniaturize a broadband antenna and how the various parameters of the dielectric slab affect the miniaturization. Therefore, a simulation based study that will completely characterize the MF in terms of the thickness, width and dielectric constant is needed. This will not only characterize the MF but it will also provide validation for the experimental results. More importantly it will quantify the limitations of dielectric loading. However, a simulation based study can only provide a qualitative explanation of these limitations. To provide a physical explanation theoretical analysis is needed and is discussed next.
52 5.1.2 Theoretical Limitations of Dielectric Loading It has been shown experimentally in Chapter 3 that there are limitations associated with dielectric loading. To better understand these limitations, it is necessary to determine how the electrical size of the antenna is affected by the dielectric slab thickness, width, and dielectric constant. To do this requires a way of determining the effective wavelength or the effective e of the space surrounding the dielectric loaded spiral. This can be accomplished by the conformal mapping of the spiral and its surrounding medium into a parallel plate structure. Such a conformal mapping will allow the effective e to be calculated for a given loading configuration (i.e. slab thickness, width, dielectric constant, etc.) by simple analysis of the parallel plate structure. This approach is very similar to the approach used to analyze the TEM horn [32]. To accomplish this conformal mapping it will be necessary to develop a mapping of a logarithmic spiral to a bowtie antenna. Since the bowtie antenna is a special case for the general TEM horn the existing conformal mapping of the TEM horn to the parallel plate transmission line can be used to complete the process.
5 .1.3 Dielectric Loading Effects at High Frequencies Most of the work presented here has focused on the effect of dielectric loading at lower frequencies. However, there are issues at higher frequencies that will need to be addressed such as surface wave excitation and radiation from higher order regions (31.., 51.., etc.). Such affects require further examination in order to for the antenna to perform sufficiently over a large bandwidth.
5.2 An Alternative Approach to Low Frequency Gain Improvement
Since there are limitations associated with dielectric loading it may be necessary to use other means to improve the low frequency performance of the spiral. One approach is to use broadband impedance matching to improve the low frequency performance. However, to achieve broadband matching of the spiral antenna at low frequencies will
53 require an external matching network which will be composed of many stages. To avoid using such a complicated matching network another approach which may simplify the problem is introduced in the following section.
5.2.1 Impedance Matching Figure 5.1 shows the typical impedance behavior of a 2" diameter spiral antenna over an extensive range of frequencies. Notice that at high frequencies the impedance is concentrated at the center of the Smith chart which implies that the impedance is predominately real and has a small imaginary part. This behavior is typical for any broadband antenna and makes broadband impedance matching easy. However, as the frequency is lowered the spiral starts to become electrically small and the impedance moves to the outer rim of the Smith chart where it remains. This low frequency behavior is typical for an electrically small antenna and is why it is difficult to implement broadband matching without resorting to very complicated matching networks.
Figure 5.1 Input impedance for a 2" square spiral.
However, it is noted that the low frequency behavior of the spiral is very similar to the impedance of a fixed length of transmission line terminated with a constant impedance
load as shown in Figure 5.2. Using this observation the impedance Zin in Figure 5.1 can be transformed using the transmission line equation to the load impedance Zm.
54 I I I ·--~~~~~~~--·
ZIN Figure 5.2 Transmission line models for impedance matching.
By applying the transmission line equation the impedance shown in Figure 5.3 is obtained. Note that this behavior is more conducive to broadband matching because the real part is slowly varying (decreasing) while the imaginary part is relatively constant compared to the previous impedance curve. Therefore, further investigation is needed to see if it is possible to take advantage of this behavior and achieve broadband impedance matching without resorting to complicated matching networks.
Figure 5.3 Unwrapped input impedance of a 2" square spiral.
5 .2.2 Combining Dielectric Loading with Impedance Matching The purpose of the impedance matching approach is not to replace dielectric loading but to enhance and improve upon the achieved results. Therefore, the goal is to combine the two approaches to achieve maximal improvement in the low frequency spiral performance. Thus, subject to the success of the impedance matching approach for the free space case, the next step would be to combine it with dielectric loading.
55
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