PATTERN RECONFIGURABLE PRINTED ANTENNAS AND TIME DOMAIN METHOD OF CHARACTERISTIC MODES FOR THE ANTENNA ANALYSIS AND DESIGN

Transcription

1 PATTERN RECONFIGURABLE PRINTED ANTENNAS AND TIME DOMAIN METHOD OF CHARACTERISTIC MODES FOR THE ANTENNA ANALYSIS AND DESIGN DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Nuttawit Surittikul, M.S., B.S. * * * * * The Ohio State University 26 Dissertation Committee: Approved by Prof. Roberto G. Rojas, Ph.D., Adviser Prof. Fernando Teixeira, Ph.D. Prof. Patrick Roblin, Ph.D. Adviser Graduate Program in Electrical and Computer Engineering

2 ABSTRACT The work considered here discusses two related topics. First, the development of a novel pattern reconfigurable printed antenna element for Global Positioning System (GPS) applications is presented. This antenna element consists of a microstrip patch, fed by four probes, and surrounded by a parasitic octagonal metallic ring loaded with diode switches. The patch and ring are located on top of a thick dielectric substrate. This novel concept is based on controlling the propagation characteristics of surfaces waves within the substrate by using a metallic parasitic ring. If properly designed, this ring can control the radiated surface waves that interact with the main beam radiated by the patch itself. It is shown through computer simulations and measurements that the beamwidth of the antenna can be changed by turning the diode switches on and off. This dissertation discusses the complete design of the radiating patch, diode switches and biasing circuitry. The effect of these additional structures on the radiation pattern is also discussed since our computer models do include these components. This antenna concept was developed to minimize the effect of interfering signals incident on the antenna along the horizon. This dissertation also shows that microstrip antennas can be fabricated with a thick substrate without the usual surface wave problem. The second topic considered in this dissertation is the development of the theory of characteristic modes using a time domain Maxwell equations solver. This method ii

3 can provide a clear physical insight to the behavior of antennas. The conventional approach for computing the characteristic modes has been in the frequency domain in conjunction with the Method of Moments. The method described here uses the finite difference time domain (FDTD) technique. The proposed method provides a major advantage over previous frequency domain algorithms because the resonances of the structure can be captured in a single FDTD run. To illustrate the method, we compute the resonances as well as the characteristic modes for several structures, such as, a printed dipole antenna, a reconfigurable printed antenna for application in the global positioning system (GPS) and a log-periodic antenna which is a wideband structure. To access the validation of our proposed method, we compare the simulated results to the analytical solutions, and discover an excellent agreement between the resonances predicted by both methods. iii

4 VITA August 22, Born - Phichit, Thailand May B.S., Electrical Engineering, Chulalongkorn University, Bangkok, Thailand December M.S., Electrical Engineering, The Ohio State University, Columbus, Ohio July 2-present Graduate Research Associate, The ElectroScience Laboratory, The Ohio State University. PUBLICATIONS Research Publications Journal Articles N. Surittikul, S. Iyer, R. G. Rojas and K. W. Lee, Pattern Reconfigurable Printed Antenna for GPS Applications, submitted to IEEE Transactions on Antennas and Propagation. K. W. Lee, R. G. Rojas and N. Surittikul, A Pattern Reconfigurable Microstrip Antenna Element, to be published on Microwave and Optical Technology Letters. N. Surittikul and R. G. Rojas, Time Domain Method of Characteristic Modes for the Analysis and Design of Antennas, to be submitted to IEEE Transactions on Antennas and Propagation. iv

5 N. Surittikul, and R. G. Rojas, Dual Band Reconfigurable Stacked Microstrip Antenna for GPS Applications, to be submitted to IEEE Transactions on Antennas and Propagation. Conference Papers N. Surittikul and R. G. Rojas, Time Domain Method to compute Quality Factors and Bandwidths of characteristic modes of antennas, IEEE AP-S International Symposium, USNC/URSI National Radio Science Meetings and AMEREM Meeting, Albuquerque, NM, July 9-14, 26. N. Surittikul and R. G. Rojas, Time Domain Method of Characteristic Modes for the Analysis/Design of Antennas, IEEE AP-S International Symposium and USNC/URSI National Radio Science Meetings, Washington, DC, July 3-8, 25. N. Surittikul and R. G. Rojas, Analysis of Reconfigurable Printed Antennas using Characteristic Modes: FDTD Approach, IEEE AP-S International Symposium and USNC/URSI National Radio Science Meetings, Monterey, CA, June 2-25, 24. N. Surittikul, R. G. Rojas and K. W. Lee, Reconfigurable Circularly Polarized Dual Band Stacked Microstrip Antenna, IEEE AP-S International Symposium and USNC/URSI National Radio Science Meetings, Columbus, OH, June 22-27, 23. N. Surittikul and R. G. Rojas, Reconfigurable Circularly Polarized Dual Band Stacked Microstrip Antenna, EM Measurements Consortium Meeting, Columbus, OH, July 31-August 1, 23. K. W. Lee, R. G. Rojas and N. Surittikul, Surface Wave Control for Reconfigurable Printed Antenna Applications, IEEE AP-S International Symposium and USNC/URSI National Radio Science Meetings, San Antonio, TX, June 16-21, 22 (invited). v

6 R. G. Rojas, K. W. Lee, and N. Surittikul, Reconfigurable GPS Antenna, National Radio Science Meeting (URSI), Boulder, CO, January 9-12, 22 (invited). R. G. Rojas, K. W. Lee, and N. Surittikul, Reconfigurable GPS Antenna, EM Measurements Consortium Meeting, Columbus, OH, July 31-August 1, 21. Academic Reports R. G. Rojas and N. Surittikul, Reconfigurable Printed Antenna for GPS Applications, The Ohio State University, The ElectroScience Laboratory, Department of Electrical and Computer Engineering, Columbus, Ohio, April 21, Technical Report R. G. Rojas, K. W. Lee and N. Surittikul, Reconfigurable Printed Antenna for GPS Applications, The Ohio State University, The ElectroScience Laboratory, Department of Electrical and Computer Engineering, Columbus, Ohio, September 21, Technical Report R. G. Rojas, N. Surittikul and K. W. Lee, Reconfigurable Printed Antenna for GPS Applications, The Ohio State University, The ElectroScience Laboratory, Department of Electrical and Computer Engineering, Columbus, Ohio, August 22, Technical Report R. G. Rojas and N. Surittikul, Reconfigurable Dual Band Stacked Microstrip Antenna for GPS Applications, The Ohio State University, The ElectroScience Laboratory, Department of Electrical and Computer Engineering, Columbus, Ohio, August 23, Technical Report R. G. Rojas, N. Surittikul and S. Iyer, Multilayer Reconfigurable GPS Antennas and Platform Effects, The Ohio State University, The ElectroScience Laboratory, Department of Electrical and Computer Engineering, Columbus, Ohio, October 24, Technical Report vi

7 R. G. Rojas, N. Surittikul and S. Iyer, Multilayer Reconfigurable GPS Antennas and Platform Effects, The Ohio State University, The ElectroScience Laboratory, Department of Electrical and Computer Engineering, Columbus, Ohio, November 24, Technical Report N. Surittikul, Reconfigurable Printed Antennas: Design and Analysis, Ph.D Research Proposal, The Ohio State University, The ElectroScience Laboratory, Department of Electrical and Computer Engineering, Columbus, Ohio, March 24. N. Surittikul, Ph.D. Candidacy Examination, The Ohio State University, The ElectroScience Laboratory, Department of Electrical and Computer Engineering, Columbus, Ohio, May 24. R. G. Rojas, and N. Surittikul, Time Domain Method of Characteristic Modes for the Analysis and Design of Antennas, The Ohio State University, The ElectroScience Laboratory, Department of Electrical and Computer Engineering, Columbus, Ohio, December 25, Technical Report FIELDS OF STUDY Major Field: Electrical Engineering Studies in: Electromagnetic Microwave Circuits: Design and Analysis Mathematics Prof. Roberto Rojas Prof. Fernando Teixeira Prof. Edward Newman Prof. Patrick Roblin Prof. Ulrich Gerlach vii

8 TABLE OF CONTENTS Page Abstract Vita List of Tables ii iv xi List of Figures xii Chapters: 1. Introduction Background and Motivation Literature Review Organization of This Dissertation Development of the Single Band Radiation Pattern Reconfigurable Antenna for GPS Application Introduction Motivation Principle of Operation Previous Works st Prototype nd Prototype Asymmetry Consideration of the Radiation Pattern on the Azimuth Plane Identification of the Cause of an Asymmetry in Radiation Pattern on the Azimuth Plane Description of New Antenna Geometry viii

9 2.5 Design Procedure Design of Parasitic Ring Design of the Switching Circuit Microstrip Feed Network for Circular Polarization Measured Results and Discussions Impedance Characteristics Radiation Characteristics A Summary and Conclusions Development of the Dual Band Radiation Pattern Reconfigurable Antenna for GPS Application Introduction Basic Antenna Geometry Feed Configuration Input Impedance Microstrip Feed Network for Circular Polarization Design of Parasitic Structures (Strips/Rings) D Strip/Ring Parametric Study D Strip/Ring Parametric Study Asymmetry Consideration of the Radiation Pattern on the Azimuth Plane Description of New Antenna Geometry Basic Geometry Parasitic Structure and Switching Circuitry Design Measured Results and Discussions Impedance Characteristics Radiation Characteristics A Summary and Conclusions Development of the Time Domain Method of Characteristic Modes for the Analysis and Design of Antennas Introduction Characteristic Modes Computation of Characteristic Modes Conventional Method Proposed Method Numerical Results Rectangular Cross Section Waveguide ix

10 5.2 Printed Dipole Antenna Air Dielectric Patch Antenna Pattern Reconfigurable Antenna Log-Periodic Antenna A Summary and Conclusions Conclusions A Summary and Conclusion of This Dissertation Future Works RF MEMS Switches Antenna Feed Technique Reconfigurable Array GPS Antenna with Excellent Axial Ratio Characteristic Modes for Material Body Bibliography x

11 LIST OF TABLES Table Page 5.1 Comparison of the resonances of the rectangular waveguide obtained from the analytical solution and the proposed method Comparison of the resonances of the air dielectric patch antenna obtained from the cavity model and the proposed method xi

12 LIST OF FIGURES Figure Page 1.1 Top views of a 3 3 patch antenna array fabricated on a substrate [47]. The rectangular patches are connected by the RF MEMS switches. The antenna operating frequency could be modified by activating the RF MEMS switches. (a) antenna geometry when switches are turned off (b) antenna geometry when switches are turned on Geometry of a frequency reconfigurable leaky mode/multifunction printed antenna [22] Geometry of a radiation pattern reconfigurable patch antenna surrounded by a switch-loaded parasitic structure [23]. This reconfigurable scheme is based on the modification of the characteristics of the surface waves, and thus the radiation pattern, through the use the switch loaded parasitic structure. The surface waves are modified simply by activating the switches Geometry of a RF MEMS reconfigurable Vee antenna [3] Geometry of a reconfigurable single turn square spiral printed antenna capable of both radiation pattern and frequency reconfigurability [12] Stacked reconfigurable array of balanced bowtie antennas: Lower and upper band elements are alternatively activated using MEMS switches [1] A patch antenna with switchable slots (PASS) for RHCP/LHCP diversity [49] Geometry of a polarization reconfigurable patch antenna with integrated MEMS actuator [4] xii

13 2.1 Scenario of a radiation pattern reconfigurable antenna in the presence of intentional/unintentional interferences. These jamming signals are assumed to be incident along the horizon direction Principle of operation for the radiation pattern reconfigurable antenna. The scheme is based on the modification of the propagation constant of surfaces waves Circular polarized microstrip antenna with diode-loaded metallic ring around the patch (top view) Circularly polarized microstrip antenna with small ground plane and diode-loaded metallic ring around the patch (top view) Circularly polarized microstrip antenna with small ground plane and diode-loaded metallic ring around the patch (bottom view) Simulated radiation pattern at GHz for a circularly polarized antenna with small ground plane Simulated axial ratio at GHz for a circularly polarized antenna with small ground plane Measured radiation pattern at GHz for a circularly polarized antenna with small ground plane Measured radiation pattern at GHz for a circularly polarized antenna with small ground plane Measured axial ratio at GHz for a circularly polarized antenna with small ground plane Circularly polarized microstrip antenna with small ground plane and diode-loaded metallic ring around the patch (top view) Measured radiation pattern and axial ratio at GHz for a circularly polarized antenna with small ground plane Comparison of calculated far-field radiation patterns (E φ ) for antenna with the square parasitic ring between the two states of the switch operations (on/off) at φ =, 15, 3, 45, 6 and xiii

14 2.14 Calculated input impedance and S 11 of the patch on an infinite substrate Far field radiation pattern of the patch on an infinite dielectric slab with an infinite ground plane Geometry of a patch antenna on a finite dielectric slab with a square partial ground plane Far-field radiation pattern of a patch antenna on a finite dielectric slab with a square partial ground plane Geometry of a patch antenna on a finite dielectric slab with a octagonal partial ground plane Far-field radiation pattern of a patch antenna on a finite dielectric slab with an octagonal partial ground plane Comparison of calculated far-field radiation patterns (E φ ) of the antenna with the circular parasitic ring at φ=, 15, 3, 45, 6 and Geometry of proposed reconfigurable antenna. A square patch is surrounded by the switch-loaded octagonal metallic ring. The radiating element is mounted on the thick substrate (.12λ d ) which is used for surface wave excitation Surface currents induced on the octagonal parasitic ring without any cuts Geometry of the patch surrounded by (a) full octagonal parasitic ring (switches on) and (b) cut octagonal parasitic ring (switch off) Comparison of calculated (FDTD) directivity patterns (D φ ) between the full and cut ring configurations for φ=, 15, 3, 45, 6 and Calculated (FDTD) radiation patterns (E φ ) from the reconfigurable antenna: (a) Pattern radiated by the patch without the ring (b) Pattern radiated by ring by itself (but mounted on the substrate) with switches on and (c) same as (b) but switches are off xiv

15 2.26 Schematic representation of the switch circuit components inserted in the switching cuts introduced in the parasitic ring ADS schematic for Philips BAP51-2 diode Schematic to determine the impedance model for every switching circuit for forward and reverse bias conditions Calculated (HFSS) gain patterns (G φ ) for on and off states of switches for φ=, 15, 3, 45, 6 and Schematic of the two-stage Wilkinson power divider Implemented two-stage Wilkinson power divider. The substrate (RT/Duroid 587, thickness=1.575 mm) dimensions are 125 mm 65 mm Measured frequency response of the two-stage Wilkinson power divider Geometry of the implemented reconfigurable antenna Comparison of the measured input impedance between the on and off states of the switches Measured gain patterns (G φ ) for the on and off states of the switches for φ=,φ=15, φ=45 and φ= Measured gain patterns (G θ ) for the on and off states of the switches for φ=, φ=15, φ=45 and φ= Measured axial ratio for the on and off states of the switches for φ=, φ=15, φ=45 and φ= Measured right hand circular polarized gain patterns (G RHCP ) for the on and off states of the switches for φ=, φ=15, φ=45 and φ= Measured azimuth patterns for the on and off states of the switches for θ=, θ=3 and θ= xv

16 3.1 Geometry of a pattern reconfigurable dual band microstrip antenna. The antenna is to operate at the two GPS frequencies (L1 (1.575 GHz) and L2 (1.227 GHz) bands). It is worth noting that the goal of the proposed dual band antenna is to control the vertical component of the electric field, E θ Cross section of a reconfigurable dual band microstrip antenna Feed configuration of the dual band antenna Calculated input impedance and S 11 response for upper radiating patch. The feed probe is located 4.74 mm from the center of the L1 patch Calculated input impedance and S 11 response for lower radiating patch. The feed probe is located 11.6 mm from the center of the L2 patch The two-stage Wilkinson power divider for the dualband antenna. The substrate (RT/Duroid 62) Measured return loss of the two stage Wilkinson feeding circuit at the L1 band Measured return loss of the two stage Wilkinson feeding circuit at the L2 band Cross section of 2-D equivalent problems Comparison of vertical field component obtained from 2-D and 3-D models at L1 band Comparison of vertical field component between two different strip width at the L1 band Comparison of vertical field component between two different strip width at the L2 band Geometry of a reconfigurable dual band stacked patch antenna for controlling antenna pattern at L2 band only (Scheme A) xvi

17 3.14 Geometry of a reconfigurable dual band stacked patch antenna for controlling antenna pattern at L1 band only as well as at L1 and L2 bands simultaneously (Scheme B) Example 1 (Scheme A) : Antenna radiation pattern and axial ratio versus angle at L2 band Example 2 (Scheme B) : Antenna radiation pattern and axial ratio versus angle at L1 band Example 3 (Scheme B) : Antenna radiation pattern and axial ratio versus angle at L1 band Example 3 (Scheme B) : Antenna radiation pattern and axial ratio versus angle at L2 band Calculated radiation pattern of the dual band antenna with a square substrate at GHz and GHz Calculated radiation pattern of the dual band antenna with an octagonal substrate at GHz and GHz New proposed geometry of a dual band antenna Geometry of the dual band antenna surrounded by (a) a full octagonal parasitic ring (b) loaded parasitic ring Calculated radiation pattern of the dual band antenna with a octagonal substrate. The antenna is surrounded by a (a) full octagonal parasitic ring (b) loaded parasitic ring Geometry of the dual band antenna surrounded by a full octagonal parasitic ring loaded with (a) cut strips (b) uncut strips Calculated radiation pattern of the dual band antenna with a octagonal substrate. The antenna is surrounded by a full octagonal parasitic ring (a) with cut strips (b) with uncut strips xvii

18 3.26 Geometry of the proposed dual band antenna. The antenna is surrounded by the switch-loaded octagonal parasitic ring. The radiating elements are mounted on the thick substrate which is used for surface wave excitation Schematic representation of the switching circuit component loaded on the solid ring Calculated radiation pattern of the dual band antenna with a octagonal substrate at GHz Calculated radiation pattern of the dual band antenna with a octagonal substrate at GHz Calculated axial ratio of the dual band antenna with a octagonal substrate at GHz Calculated radiation pattern of the dual band antenna with a octagonal substrate at GHz Calculated radiation pattern of the dual band antenna with a octagonal substrate at GHz Calculated axial ratio of the dual band antenna with a octagonal substrate at GHz Geometry of the implemented pattern reconfigurable dual band antenna: top layer Geometry of the implemented pattern reconfigurable dual band antenna: middle layer Geometry of the implemented pattern reconfigurable dual band antenna: bottom layer Measured input impedance of the upper radiating patch Measured input impedance of the lower radiating patch Measured G θ pattern of the dual band antenna at the L1 band xviii

19 3.4 Measured G φ pattern of the dual band antenna at the L1 band Measured axial ratio of the dual band antenna at the L1 band Measured G θ pattern of the dual band antenna at the L2 band Measured G φ pattern of the dual band antenna at the L2 band Measured axial ratio of the dual band antenna at the L2 band Measured G θ pattern of the dual band antenna at the L1 band. Note all the switching components are removed Measured G φ pattern of the dual band antenna at the L1 band. Note all the switching components are removed Measured axial ratio of the dual band antenna at the L1 band. Note all the switching components are removed Geometry of a rectangular cross section waveguide. The waveguide is of infinite length in the z direction The conventional algorithm for calculating the characteristic modes. This approach is performed in the frequency domain using the method of moment (MoM) technique A sequence of random numbers of uniform distribution and its corresponding spectral calculation A time signature of a Gaussian pulse with sinusoidal carrier at center frequency of interest and its corresponding spectral calculation Proposed algorithm for calculating the characteristic modes. This novel method is performed in the time domain using the finite difference time domain (FDTD) technique Geometry of a microstrip antenna with air substrate Frequency spectra of the induced current on the radiating patch and the first characteristic mode xix

20 4.8 Proposed algorithm for computing the scattered electric field Proposed algorithm for computing the scattered electric field A wave reflects back and forth between the resonator mirrors, a Fabry- Perot etalon resonator Field intensity of a Fabry-Perot resonator as a function of frequency, ν. It is clear that resonator with small loss (large r) shows sharp spectral peaks DFT Spectra of the E z component at six different monitoring points inside the guide Geometry of a printed dipole Frequency spectra of the induced current on the printed dipole The 1 st eigencurrent on the printed dipole antenna and its corresponding eigenfield at.82 GHz The 2 nd eigencurrent on the printed dipole antenna and its corresponding eigenfield at 1.74 GHz The 3 rd eigencurrent on the printed dipole antenna and its corresponding eigenfield at 2.53 GHz The 4 th eigencurrent on the printed dipole antenna and its corresponding eigenfield at 3.5 GHz The 5 th eigencurrent on the printed dipole antenna and its corresponding eigenfield at 4.44 GHz DFT spectra of the current, J x and J y, on the top conducting patch of a microstrip patch mounted with an air substrate The 1 st eigencurrent on the radiating patch and its corresponding eigenfield at.913 GHz The 2 nd eigencurrent on the radiating patch and its corresponding eigenfield at GHz xx

21 5.12 The 3 rd eigencurrent on the radiating patch and its corresponding eigenfield at 1.67 GHz Frequency spectra of the current induced on the octagonal ring The 1 st eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at.443 GHz (the 1 st degenerated mode) The 1 st eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at.443 GHz (the 2 nd degenerated mode) The 4 th eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at GHz (the 1 st degenerated mode) The 4 th eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at GHz (the 2 nd degenerated mode) The 5 th eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at GHz (the 1 st degenerated mode) The 5 th eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at GHz (the 2 nd degenerated mode) The 2 nd eigencurrent on the ring when the switches are turned off and its corresponding eigenfield at GHz The 3 rd eigencurrent on the ring when the switches are turned off and its corresponding eigenfield at GHz Calculated radiation pattern (E φ ) of the single antenna mounted on an octagonal substrate Calculated radiation pattern (E φ ) of the single antenna mounted on an octagonal substrate. The ring dimension has been modified such that the 3 rd mode resonates as close as possible to the frequency of operation (1.575 GHz) Geometry of a log-periodic toothed planar antenna Frequency spectra of the current induced on the log-periodic antenna. 151 xxi

22 5.26 The 1 st eigencurrent on the log periodic antenna and its corresponding eigenfield at.685 GHz The 2 nd eigencurrent on the log periodic antenna and its corresponding eigenfield at 1. GHz The 3 rd eigencurrent on the log periodic antenna and its corresponding eigenfield at GHz xxii

23 CHAPTER 1 INTRODUCTION 1.1 Background and Motivation Reconfigurable antennas are receiving a lot of attention for application in diverse areas like communications, surveillance etc., due to their ability to modify their radiation characteristics in real time. These characteristics can be the radiation pattern, frequency of operation, polarization or even a combination of these features in real time. Low cost antennas that can alter their radiation patterns during real time operating conditions are required in response to intentional/unintentional interferences. In particular, the application under consideration is a global positioning system (GPS) antenna element mounted on top of the aircraft, which receives GPS signals from satellites overhead. The antenna is a microstrip patch antenna, which radiates a broad field pattern. The broadside direction is the direction from which the desired GPS signals from the satellites arrive. The application also assumes the presence of interfering signals, in the form of jamming signals, which arrive at the antenna from directions approximately +1 to -15 from the end-fire direction [39]. This is a common scenario for antennas on airborne platforms. The antenna is, therefore, designed to be able to reconfigure its radiation pattern during real time operation 1

24 such that it maintains its broad pattern in the absence of interferences, and is capable of narrowing its pattern beamwidth, when the interfering signals arrive at the antenna, to suppress these undesired signals as much as possible. In addition, reconfigurable antennas can be a cheaper alternative to traditional adaptive arrays or they can be incorporated into adaptive arrays to improve their performance by providing additional degrees of freedom. The first purpose of this dissertation is thereby to develop and implement novel concepts for reconfigurable antennas. In other words, the antennas that reconfigure their radiation patterns in real time are being investigated. This is being accomplished by means of analysis, design, computer simulations and implementation of prototypes. Physically-based 2 dimensional (2-D) and 3 dimensional (3-D) models are developed to understand the behavior of this class of antennas. Numerical techniques such as the method of moments (MoM), the finite difference time domain (FDTD) and the finite element method (FEM) are used to obtain numerical results of the radiation patterns, input impedances, polarization properties, etc. Once the optimal designs are obtained, they are implemented and measured to access the feasibility of the proposed concepts. The other objective of this dissertation is to develop an alternative tool to assist the design and analysis of antennas. Most antenna design and analysis are usually done using simple design formula or purely numerical techniques, such as finite difference time domain (FDTD), method of moment (MoM), finite element method (FEM), etc. Although these methods are very accurate, unfortunately, they don t offer as much physical insight to the behavior of the antennas such as resonances of their 2

25 natural modes, current distributions of these modes, and their corresponding radiation patterns. Owing to its advantage of giving clear physical insight to the behavior of antennas, Theory of Characteristic Modes, first introduced by Garbacz [4, 6] and then refined by Harrington [9, 1], has been long used in many applications such as analysis of radiation and scattering [2, 19], antenna shape synthesis [5, 18] and radiation pattern synthesis [11]. Characteristic modes are defined as a set of real current on the surface of a conducting body that depend only on its geometry, but are independent of any specific source or excitation. Associated with each characteristic mode is a real characteristic value or eigenvalue, λ n. The magnitude of the eigenvalue indicates how well that particular mode radiates. Modes with small λ n are good radiators, whereas those with large λ n are poor radiators. The closer the eigenvalue is to zero, and accordingly to resonance, the more significant is its contribution to the total radiation pattern. Relevant information about antennas resonant behavior can also be secured by examining characteristic modes variation with frequency. To the best of our knowledge, the conventional approach for computing the characteristic modes has been realized thus far only in the frequency domain. The calculation of the resonances is, nevertheless, considerably time consuming, as we need to sweep the frequency and observe the eigenvalue for each particular mode. In this dissertation, we develop an alternative method for computing the characteristic modes employing the finite difference time domain (FDTD) technique. The proposed technique provides a major advantage over the conventional one in that wide-band spectrum calculations are possible from only one FDTD run. As a result, the antenna resonances could be captured from just a single FDTD run. The 3

26 information secured from the new proposed method, such as resonances, current distributions, their corresponding radiation patterns, and quality factor, is very useful for the analysis and design of antennas. Proposed algorithm as well as some design examples are carried out in more detail later in this dissertation. 1.2 Literature Review Modern communication and radar systems require the antenna systems with multiple functions and multi-band coverage. As most antennas are mounted on ships, aircrafts or other vehicles, it is very desirable to develop a single radiating element with capabilities of performing different functions and/or multi-band operating in order to minimize antennas weight and space occupation. The idea of reconfigurability has been around for awhile. A brief overview on the reconfigurable techniques is thereby discussed in this section. An antenna that possesses the ability to modify its characteristics, such as operating frequency, polarization or radiation pattern, in real time condition is referred to as a reconfigurable antenna. Reconfigurable antennas have a promising potential to add substantial degrees of freedom and functionality to mobile communications and phase array systems. Many reconfigurable antennas can be readily found in the literature. Nonetheless, most reconfigurable antennas concentrate on changing their operating frequencies while maintaining their radiation characteristics [12]. This type of antenna is referred to as a frequency reconfigurable antenna. Modern communication systems demand transmitters and/or receivers with multi-band operation, as a result, numerous techniques for achieving frequency reconfigurability have been proposed in the literature. For instance, Weedon, et al. reported a reconfigurable multi-band 4

27 antenna integrated with the radio frequency micro electro mechanical systems (RF MEMS) switches for applications at drastically different frequency bands, such as communications at the L band (1-2 GHz) and synthetic aperture radar (SAR) at the X band ( GHz) [47]. In this case, the reconfigurable patch module (RPM) consists of a 3 3 array of square patches connected together by the RF MEMS switches as depicted in Figure 1.1. Ideally, the RF MEMS switch has two operational states, on and off. The on state represents a short circuit, while the off state exhibits an open circuit. On one hand, when all switches are in the off state, the total radiation pattern is contributed from the pattern radiated by each small patch (Figure 1.1(a)), as a result, the antenna resonates at a higher frequency band. On the other hand, when all switches are turned on, the antenna effective area is clearly larger, an entire area of a 3 3 patch array. The antenna accordingly resonates at a lower frequency band (Figure 1.1(b)). Furthermore, it is found that the total radiation patterns are nearly identical between the two states of the switch operation. (a) OPEN Configuration (b) CLOSED Configuration Figure 1.1: Top views of a 3 3 patch antenna array fabricated on a substrate [47]. The rectangular patches are connected by the RF MEMS switches. The antenna operating frequency could be modified by activating the RF MEMS switches. (a) antenna geometry when switches are turned off (b) antenna geometry when switches are turned on. 5

28 Patch Patch Switches Leaky Wave Antenna Array Parasitic Patch Parasitic Figure 1.2: Geometry of a frequency reconfigurable leaky mode/multifunction printed antenna [22]. Another example of the frequency reconfigurable antenna is described by Qian et al. [22]. It consists of a linear array of microstrip-based leaky-mode antennas as shown in Figure 1.2. The work on the microstrip-based leaky-mode antennas has been originally done by Menzel [2], and further investigated by Oliner et al. [21]. By activating the switches connected on the radiating patches, the resonant frequency can be modified. Clearly, the operating frequency is controlled by the state of the switch operation. This technique tremendously reduces the number and size of the antennas mounted on board, especially in a multi-band communication system where weight and volume are critical issues. Controlling the beam direction and/or varying the beam shape while maintaining the operating frequency and bandwidth could also enhance the system performance. For example, in the presence of intentional or unintentional co-channel interference, it is necessary for the antenna to generate a null or minimize its radiation pattern 6

29 Diode Switches Radiating Patch Parasitic Ring Ground Plane Figure 1.3: Geometry of a radiation pattern reconfigurable patch antenna surrounded by a switch-loaded parasitic structure [23]. This reconfigurable scheme is based on the modification of the characteristics of the surface waves, and thus the radiation pattern, through the use the switch loaded parasitic structure. The surface waves are modified simply by activating the switches. in responding to the arrival of the undesired signals. The reconfigurability could be secured by activating the switches loaded on the antenna element, as a result, either the electrical or mechanical antenna characteristics are modified, thus changing their radiation patterns in real time condition. This type of antenna is referred to as a radiation pattern reconfigurable antenna. Rojas and Lee demonstrated that by activating the diode switches loaded on the parasitic structure (Figure 1.3), the characteristic of the induced surface waves could be modified, and thus changing its radiation pattern in real time [14 17,23 36,42,43]. It is shown that the application under consideration exhibits the use of the diode switches to modify the electrical property of the antenna. Unlike the previous example, the switches could also be employed to alter the mechanical property of the antenna. Chiao et al. [3] described a pattern reconfigurable Vee antenna using the RF MEMS switches as the actuators. Their proposed antenna consists of a movable planar Vee antenna connected to the actuators as represented 7

30 Reconfigurable Vee Antenna Main Beam Direction Push/Pull Bar Actuator Actuator Bias Transmission Lines Figure 1.4: Geometry of a RF MEMS reconfigurable Vee antenna [3]. in Figure 1.4. The direction of the Vee antenna, and hence the antenna main beam direction, is controlled by the operating state of the actuators. The beam steering and shaping capacities can be achieved by running different states of the actuators. In general, most antennas are capable of either frequency or pattern reconfigurability, however they can be made both frequency and pattern reconfigurable simultaneously. Huff et al. [12] has proposed a frequency and pattern reconfigurable microstrip antenna using multiple switch connections. Figure 1.5 illustrates a geometry of a switch loaded antenna which resonates at 3.7 GHz with a linear polarized pattern. One set of the switch connections redirects its main beam radiation pattern away from the broadside, whilst maintaining a common impedance bandwidth with the baseline configuration. The second set of the switch connections, however, shifts the operating frequency from 3.7 GHz to 6 GHz, while preserving a broadside radiation pattern. 8

31 Radiating Element Ground Plane Probe Feeding "Off State" "On State" 1st Switch Set : Via Hole connected through MEMS Switch "Off State" "On State" 2nd Switch Set : MEMS Switch Figure 1.5: Geometry of a reconfigurable single turn square spiral printed antenna capable of both radiation pattern and frequency reconfigurability [12]. Another example of the frequency and pattern reconfigurable antenna can also be found in the work of Bernhard et al. [1]. The stacked balanced bowtie antenna structure is shown in Figure 1.6. Clearly, The lower bowtie antennas locate on the substrate, while the upper ones is on the top of the superstrate. Note that the lower bowtie antennas are electrically larger than the upper ones in size. Consequently, they resonates at a lower frequency band. Note that each antenna feed point is connected to the source via the RF MEMS switch, and only one antenna arrays radiate at a time. The operating frequency is thus determined by the states of the RF MEMS switches. In other words, if the lower band is chosen, the RF MEMS switches connected to the lower bowtie antennas will be activated, and vice versa. It is also worth noticing that when the lower bowtie antennas are radiating, the upper bowtie antennas are virtually the floating parasitic elements for the lower ones, 9

32 Top View Side View Lower Band Element Upper Band Element Upper Band Elements Lower Band Elements Feeds connected with MEMS Switches Ground Plane Figure 1.6: Stacked reconfigurable array of balanced bowtie antennas: Lower and upper band elements are alternatively activated using MEMS switches [1]. and thus slightly broadening the impedance bandwidth. On the other hand, an operation of the upper bowtie antennas require that the lower antennas must be grounded via the RF MEMS switches. In this case, the lower bowtie antennas are simply an equivalent ground plane for the upper ones. Antennas with polarization diversity are gaining popularity due to the tremendous increment of the wireless communications and radar systems. A design of a microstrip antenna with switchable slots (PASS) was introduced to accomplish a circular polarization diversity by Yang et al. [49]. Two orthogonal slots are introduced into the radiating patch and two pin diodes are used to switch the slots on and off (Figure 1.7). By activating the switches on and off, the antenna radiates with either right hand circular polarization (RHCP) or left hand circular polarization (LHCP) 1

33 Radiating Patch Diode Switch Probe Feeding Ground Plane Substrate (a) LHCP Patch Antenna (b) RHCP Patch Antenna Figure 1.7: A patch antenna with switchable slots (PASS) for RHCP/LHCP diversity [49]. by sharing the same feeding probe. The feeding probe is located on the diagonal line of the patch. Note that the antenna radiates either RHCP or LHCP at a time, depended upon the operating state of the diodes switch. Therefore, there is no coupling induced between the two polarizations. An antenna that can alternate its radiation pattern between circular and linear polarization at a fixed operating frequency has been proposed by Simons et al. [4]. Figure 1.8 shows the geometry of the proposed antenna. The antenna consists of a nearly square microstrip antenna (to excite a circular polarized radiation pattern), integrated with an RF MEMS actuator for switching the polarization. When the RF MEMS actuator is in the off state, the perturbation of the modes is negligible and thus the patch radiates a circularly polarized pattern. Nevertheless, when the 11

34 Nearly Square Patch Antenna MEMS Actuator GSG RF Probe Pads Microstrip Feed Impedance Matching Transformer Figure 1.8: Geometry of a polarization reconfigurable patch antenna with integrated MEMS actuator [4]. RF MEMS actuator is turned on, the phase relation between the two current modes on the patch is disturbed, as a result, causing the patch to radiate a dual linearly polarized pattern. The reconfigurable antennas demonstrated in this section are only a few examples found in the literature. Generally speaking, reconfigurable antennas could be designed to fit the goal of each application. As mentioned earlier, the goal of this research is to develop and implement concepts for a single and dual band pattern reconfigurable antennas for the GPS application. Thus, the motivation, basic principle of operation as well as design examples of our proposed reconfigurable printed antenna will be introduced and discussed in more detail in the next chapter. 12

35 1.3 Organization of This Dissertation The remaining portion of this dissertation consists of five chapters, involving design and implementation of single and dual band reconfigurable antennas for GPS application, and development of the time domain method of the characteristic modes for the analysis and design of antennas, followed by a concluding chapter. The report is organized as follows. Chapter 2 introduces the motivation, principles of operation as well as some design issues and implementation of the single band GPS antenna. The geometrical details of the antenna and the design procedure for the parasitic structure and the switching circuitry that surround the patch are explained. It should be kept in mind that the horizontal component of the electric field is under control in this antenna. The measured results obtained from the antenna are discussed. These experimental results show a good agreement to the trends predicted by the simulated results. Nevertheless, analysis of the initail single band antenna prototypes reveal an asymmetry of the azimuthal pattern as the observation angle (φ) moves away from the principal planes. It is observed that the reconfigurability falls off dramatically as the observation angle moves away from the principal planes. The reasons for the asymmetry are investigated, and modifications to the antenna geometry are made accordingly. Once the modifications are made, the parasitic structure as well as the switching circuitry are redesigned to provide the desired reconfigurability. The new design is afterward fabricated and tested. Measured results obtained with this antenna are discussed at the end. Chapter 3 explains the concept and geometry of the dual band antenna, which is to operate at both GPS frequencies of L1 (1.575 GHz) and L2 (1.227 GHz) bands, along with the design of the ring configurations that provide the reconfigurability. 13

36 It is worth noting that control of the vertical component of the electric field is the main goal of the dual band antenna. The requirement for right circularly polarized radiation patterns from the two antennas places certain demands on the feed network, which are included and discussed in this chapter. Nevertheless the first few designs of the dual band antenna also exhibit the asymmetry of the pattern as the observation angle moves away from the principal planes. It is observed that the reconfigurability falls off dramatically as the observation angle moves away from the principal planes. This is mostly due to the geometry of the dielectric substrates and the parasitic structures. Once the modifications are made accordingly, the parasitic structure and the switching circuitry are designed to achieve the desired reconfigurability. The new design is afterward implemented and evaluated. Measured results obtained with this antenna are discussed at the end of the chapter. An alternative method to compute the characteristic modes is presented in Chapter 4. Concepts and background on the characteristic modes are first introduced. For the sake of simplicity, a rectangular waveguide is given as the first example to illustrate the concept of characteristic modes. Normally, the conventional method for computing the characteristic modes is realized in the frequency domain technique. An alternative technique for the calculation of the characteristic modes is proposed in the chapter, and later explained in detail. It is noted that the new proposed algorithm mis realized in the time domain. Useful information, such as the resonances of the natural modes, their current distributions, their corresponding radiation patterns, as well as quality factor and bandwidth, can be readily extracted from the new proposed technique. In Chapter 5, the use of the method of characteristic modes on the analysis and design of antennas, such as printed dipoles, microstrip antenna, 14

37 log-periodic antenna etc., is demonstrated and discussed. Finally, a brief summary to this dissertation, and a summary of the work done, are given in Chapter 6. This chapter also includes some directions for future research. 15

38 CHAPTER 2 DEVELOPMENT OF THE SINGLE BAND RADIATION PATTERN RECONFIGURABLE ANTENNA FOR GPS APPLICATION 2.1 Introduction Motivation The antenna that possesses the ability to modify its radiation properties in real time is referred to as a reconfigurable antenna. The term radiation properties could be referred to as its radiation pattern, operating frequency, polarization, or even a combination of these qualities. The focus of this work is on pattern reconfigurable antennas. Low cost antennas that can adjust their radiation patterns in real time are required in the presence of intentional/unintentional interferences, which are assumed to be incident along the horizon. Hence in the presence of jamming signals, the reconfigurable microstrip antenna is required to adjust its antenna beamwidth to suppress these unwanted signals as much as possible, as shown in Figure 2.1. The work described here deals with the design and analysis of radiation pattern reconfigurable concepts where the passive microstrip antenna elements are integrated with switches. Although the switches can be either RF MEMS, photonics or electronic, only the diode switches are currently being used in our proposed design. 16

39 z Switch Loaded Ring/Strip x Jamming / Undesired Signal "Radiation Pattern" Recofigurable Antenna Figure 2.1: Scenario of a radiation pattern reconfigurable antenna in the presence of intentional/unintentional interferences. These jamming signals are assumed to be incident along the horizon direction Principle of Operation The work described here deals with the design and analysis of a pattern reconfigurable antenna concept where a passive microstrip antenna element is surrounded with a parasitic ring loaded with switches. It is well known that the radiation pattern from the microstrip antenna originates mostly from three contributions as shown in Figure 2.2(a). One of the contributions comes from the surface wave that is diffracted at the edges so it radiates away from the surface. In general, the use of electrically thick substrates where strong surface waves can be excited is avoided when printed antennas are designed. These surface waves are considered as a loss mechanism because they travel along the substrate and radiate to free space at the truncation/edge of the substrate, usually distorting the main beam radiation pattern and increasing 17

40 the level of the sidelobes as well as the backlobes. However, electrically thick microstrip antennas have the advantage of providing a larger operational bandwidth over microstrip antennas mounted on thin substrates. For the particular application under consideration, the control of the surface waves is crucial to achieve pattern reconfigurability. Our proposed reconfigurable scheme is based on the modification of the EM propagation characteristics of the surface waves, and thus the radiation pattern, through the use of a metallic switch-loaded parasitic structure, such that the radiated surface waves contribute to the main beam pattern (see Figure 2.2(b)) in a controlled fashion [14, 15, 17, 24, 27, 3, 43]. The switches provide two different ring configurations and pattern reconfigurability is controlled by the two states of the switches (on/off). Although the switches can be either RF MEMS, electronic or photonic-controlled, only diode switches are discussed here. z O z O Direct Space Wave Edge Diffracted Space Wave Edge Diffracted Surface Wave Direct Space Wave Modified Edge Diffracted Space Wave Modified Edge Diffracted Surface Wave x (a) Radiating Patch without Parasitic Ring (b) Radiating Patch with Parasitic Ring x Figure 2.2: Principle of operation for the radiation pattern reconfigurable antenna. The scheme is based on the modification of the propagation constant of surfaces waves. 18

41 2.2 Previous Works The proposed reconfigurable antenna consists of a circularly polarized patch element and a parasitic metallic ring loaded with switches and mounted on an electrically thick substrate (.1λ within the dielectric) as depicted in Figure 2.3. Note that the ground plane is smaller than the parasitic ring. Thus, there is no a metallic ground plane structure underneath the ring. As mentioned in the previous section, in a conventional microstrip antenna, the total radiated field consists of the direct space field from the patch, edge-diffracted space wave fields and edge-diffracted surface wave fields. In most conventional microstrip antennas, the substrate is thin to minimize the strength of the surfaces waves. On the other hand, for microstrip antennas mounted on electrically thick substrates, the edge-diffracted surface wave field can be strong and have a magnitude larger than the diffracted space wave field. For the proposed antenna to work properly, it is required that a strong surface wave field be excited. As mentioned above, this is accomplished here by using a thick substrate. In our antenna structure, the tangential surface wave components (TE modes) are stronger than the normal field (z-directed) component in the region between the edges of the ground plane and the edges of the substrate while the normal surface wave field component dominates in the region above the ground plane. These surface waves will diffract mainly in the end-fire (θ=9 ) direction at the truncation of the substrate. The diffracted surface wave fields interfere, depending on their phase, constructively and destructively with the (E φ ) components of the fields radiated by the patch. To achieve pattern reconfigurability, a parasitic metallic ring is added along the top surface of the substrate. The phase of the surface wave incident on the edge of the substrate changes due to the addition of the ring while its amplitude does not change 19

42 Conducting strips Radiating patch Switch Switch Partially grounded dielectric substrate Figure 2.3: Circular polarized microstrip antenna with diode-loaded metallic ring around the patch (top view). significantly. In other words, the ring itself radiates a field but it is not as strong as the edge diffracted surface field. Since the phase of the edge diffracted surface field changes, the total radiated field is modified in the end-fire direction. For the control of the radiated (E φ ) field component, the spacing between the parasitic ring and the patch element has the most significant effect while the width of the ring has only a secondary effect on the overall radiation pattern. Note that the locations of the switches, the switch structure and its biasing structure can have a significant impact on the radiation pattern if they are not designed properly st Prototype To access the validity of the proposed scheme, a reconfigurable circularly polarized microstrip antenna was built and the antenna characteristics were measured. A finite difference time domain (FDTD) computer code was employed to obtain the initial 2

43 design. The microstrip antenna element was designed to operate at the L1 (1.575 GHz) GPS band and provides a right-hand circularly polarized (RHCP) radiation pattern at broadside. The patch has a size of 4 mm 25 mm and is probe-fed along the diagonal of the patch as depicts in Figures 2.4 and 2.5. The substrate has a relative dielectric constant of 9.2 and a thickness of 7.6 mm (.12λ within the dielectric). The dimensions of the square substrate are mm mm. The ground plane of the patch has a size of 98 mm 63 mm. The switches-loaded metallic ring has a width of 7.6 mm. The inner edge of the ring is located at 48 mm and 49 mm from the edges of the patch along the x- and y- directions, respectively. Currently, the switches are implemented with pin-diodes. However, it is possible to replace the diode-switches with MEMS switches. Simulated and measured of the E φ, E θ as well as axial ratio patterns at the y z plane are shown in from Figure 2.6 to Figure 2.1. The measured 3-dB beamwidth of the E φ pattern is 7 and 8 when the diodes are off and on, correspondingly. Note the amplitude difference of approximately 8 db in the end-fire direction between the two operating switch states. On the other hand, the experimental E θ pattern remains relatively unchanged during the switching. Moreover, the antenna is able to maintain a good axial ratio at broadside. Finally, the measured reflection coefficient (S11) is 7 db at L1. The mismatch is due to the large inductance of the probe for the thick substrate. It can be improved with a matching network. The concept of using a parasitic metallic ring loaded with switches to adaptively change the radiation pattern in real time is demonstrated. A reconfigurable antenna was fabricated and tested to prove the concept. The antenna is able to provide approximate 6 db pattern difference in the end-fire direction between the on and 21

44 Figure 2.4: Circularly polarized microstrip antenna with small ground plane and diode-loaded metallic ring around the patch (top view) Figure 2.5: Circularly polarized microstrip antenna with small ground plane and diode-loaded metallic ring around the patch (bottom view) 22

45 Simulated E φ component at freq = GHz (φ = 9 o ) Magnitude (db) Diodes off Diodes on γ (degree) Simulated E θ component at freq = GHz (φ = 9 o ) Magnitude (db) Diodes off Diodes on γ (degree) Figure 2.6: Simulated radiation pattern at GHz for a circularly polarized antenna with small ground plane Simulated Axial Ratio Plot at freq = GHz (φ=9 o ) Diodes off Diodes on Axial Ratio (db) γ (degree) Figure 2.7: Simulated axial ratio at GHz for a circularly polarized antenna with small ground plane 23

46 Measured E φ component at freq = GHz (φ=9 o ) Magnitude (db) Diodes off Diodes on γ (degree) Measured E component at freq = GHz (φ=9 o ) θ Magnitude (db) Diodes off Diodes on γ (degree) Figure 2.8: Measured radiation pattern at GHz for a circularly polarized antenna with small ground plane Measured E φ component at freq = GHz (φ=9 o ) Diodes off Diodes on Magnitude (db) γ (degree) Measured E θ component at freq = GHz (φ=9 o ) Diodes off Diodes on Magnitude (db) γ (degree) Figure 2.9: Measured radiation pattern at GHz for a circularly polarized antenna with small ground plane 24

47 15 14 Measured Axial Ratio Plot at freq = GHz (φ=9 o ) Diodes off Diodes on Axial Ratio (db) γ (degree) Figure 2.1: Measured axial ratio at GHz for a circularly polarized antenna with small ground plane off states of the switches in the principle y z plane. A similar result is obtained in the x z plane. Currently, various types of feeding schemes and ring shapes are being studied to obtain a more symmetric azimuthal pattern. As expected, the current ring shape does not produce a symmetric azimuthal pattern nd Prototype Another antenna example for controlling the horizontal field component, E φ, was implemented and tested as seen in Figure The substrate has a dielectric constant of 9.2 with a thickness of.8 mm. The dimensions of the square substrate are mm mm. To excite a circularly polarized radiation pattern, the antenna is fed by four probes of equal magnitude signals with 9 o phase increments. Figure 2.12 shows the measured radiation pattern and axial ratio versus angle of the proposed 25

48 Figure 2.11: Circularly polarized microstrip antenna with small ground plane and diode-loaded metallic ring around the patch (top view). antenna. By turning the diode switches on and off, the horizontal field component, i.e. E φ, is modified by 1 db in the neighborhood of the horizon. On the other hand, the vertical field component, i.e. E θ, stays unchanged, as expected. Nonetheless, the radiation pattern is not quite symmetric due to the measurement and fabrication errors. As mentioned earlier, the antenna is fed by four probes. However, the location of one of the probes is off by 1 mm, thus yielding an asymmetry in the radiation pattern. 2.3 Asymmetry Consideration of the Radiation Pattern on the Azimuth Plane Thus far, the design of the reconfigurable antenna has been concentrating only on the principal elevation planes (x z, y z planes or φ=,9 ). As mentioned above, the radiation patterns on the two planes are nearly identical, and yield a significant change in antenna field pattern (E φ ) along the horizon. However, the 26

49 E φ component (XZ plane) freq=1.572 GHz 5 5 E θ component 1 Axial Ratio 9 Diodes off Diodes on Magnitude (db) 1 15 Magnitude (db) 1 15 Axial Ratio (db) Diodes off Diodes on 25 Diodes off Diodes on γ (Degree) γ (Degree) γ (Degree) Figure 2.12: Measured radiation pattern and axial ratio at GHz for a circularly polarized antenna with small ground plane. radiated patterns on any other elevation planes, φ=15, 3, 45 and 6, are very different from the patterns on the principal elevation planes, especially when the switches are activated on. In other words, the antenna radiates an asymmetric pattern on the azimuth as depicted in Figure Additionally, the field magnitudes of the switches on case are even higher than those of the switches off case for φ=15, 3, 45 and 6. As a result, antenna can reconfigure its radiation pattern only on the principal elevation planes. In order to make the radiation pattern symmetric on the azimuth, the sources that generate the asymmetry in the patterns must be identified and eliminated accordingly. The asymmetry in radiation pattern may possibly arise from numerous factors, such as the shapes of the ring, ground plane, radiating patch or even dielectric slab. 27

50 E φ E φ E φ Magnitude of E φ at φ= o switches on switches off Magnitude of E φ at φ=15 o switches on switches off Magnitude of E φ at φ=45 o switches on switches off γ (Degree) E φ E φ E φ Magnitude of E φ at φ=9 o switches on switches off Magnitude of E φ at φ=3 o switches on switches off Magnitude of E φ at φ=6 o switches on switches off γ (Degree) Figure 2.13: Comparison of calculated far-field radiation patterns (E φ ) for antenna with the square parasitic ring between the two states of the switch operations (on/off) at φ =, 15, 3, 45, 6 and 9. 28

51 Impedance (Ω) Input impedance of the square patch Real Part Imaginary Part Magnitude of the S 11 of the square patch S Frequency (GHz) Figure 2.14: Calculated input impedance and S 11 of the patch on an infinite substrate Identification of the Cause of an Asymmetry in Radiation Pattern on the Azimuth Plane Patch Antenna on Infinite Substrate Since the radiating patch is of a square shape, its radiation may be asymmetric on the azimuth plane. Therefore, we must ensure that the pattern obtained from the antenna by itself is symmetric on any azimuth plane. To achieve this, the radiating patch on an infinite dielectric slab with an infinite ground plane is being investigated first. Figure 2.14 illustrates the input impedance and insertion loss of the antenna described above. Clearly from the figure, the antenna resonates almost at the desired frequency, GHz, and the return loss is as low as -3 db at this frequency. Figure 2.15 depicts the radiated field components, E φ and E θ, of the antenna on the infinite substrate for various elevation planes. Evidently, both components are symmetric for all elevation planes. We can, therefore, conclude that the square patch 29

52 E θ (grounded infinite substrate) E φ (grounded infinite substrate) E θ 25 E φ φ= o φ=15 o φ=3 o φ=45 o φ=6 o φ=75 o φ=9 o γ (Degree) 3 35 φ= o φ=15 o φ=3 o φ=45 o φ=6 o φ=75 o φ=9 o γ (Degree) Figure 2.15: Far field radiation pattern of the patch on an infinite dielectric slab with an infinite ground plane. antenna radiates a symmetric pattern on the azimuth. As a result, there is no need to adjust or modify the geometry of the radiating patch due to the reason explained above. Patch Antenna on Finite Substrate In this experiment, we need to study the effect of the truncation of the dielectric slab on the antenna radiation pattern. Thus, the same patch antenna from the previous subsection is located on the dielectric slab of finite dimension. Note that the dielectric slab is partially grounded. Since the scheme to control the horizontal field component requires the ground plane to be smaller than the dielectric slab dimension. Furthermore the ground plane also has a square shape as illustrated in Figure

53 Radiating Patch Patially Grounded dielectric Substrate Figure 2.16: Geometry of a patch antenna on a finite dielectric slab with a square partial ground plane. Figure 2.17 exhibits the radiated electric fields, E θ and E φ, of the antenna on the finite substrate for several elevation planes. As illustrated, both field components are nearly identical for all elevation planes. Hence, we now can conclude that the antenna on the finite substrate also radiates symmetric patterns for all elevation planes. As a result, there is also no need to modify the shape of the dielectric slab for the reason described above. It is now clear that the only source that mostly generates the asymmetry in the radiation pattern on the azimuth plane must be the parasitic structure. Because the shape of the parasitic structure is symmetric only on the principal elevation planes resulting in symmetric patterns only on those corresponding planes. Conversely, the parasitic structure is asymmetry on any other elevation planes; as a result, the symmetry on the radiation pattern falls off drastically once the observation angle, φ, moves away from the principal planes, and 9. 31

54 E θ (partially grounded finite substrate) E φ (partially grounded finite substrate) E θ 2 E φ 2 φ= o 25 φ=15 o φ=3 o φ=45 o φ=6 o φ=75 o φ=9 o γ (Degree) φ= o 25 φ=15 o φ=3 o φ=45 o φ=6 o φ=75 o φ=9 o γ (Degree) Figure 2.17: Far-field radiation pattern of a patch antenna on a finite dielectric slab with a square partial ground plane. The new parasitic structure that produces symmetric patterns on the azimuth is proposed here. The square parasitic ring is replaced by an octagonal parasitic ring. The square ground plane is also substituted by an octagonal ground plane. Parametric studies on the new proposed design are presented and carried out as followed. The patch antenna on the finite dielectric slab with the octagonal partial ground plane is investigated in this subsection. The antenna with no parasitic ring is inspected first (Figure 2.18), since we need to ensure that the antenna radiates symmetric field patterns on the azimuth planes before adding the octagonal parasitic ring to the antenna. Figure 2.19 shows the radiated field components, E θ and E φ, of the antenna described above. Clearly, both components are fairly symmetric for all elevation planes. The maximum deviation in the magnitude of both components is less than 1.5 db. The octagonal parasitic structure is afterward included to the 32

55 Radiating Patch Patially Grounded dielectric Substrate Figure 2.18: Geometry of a patch antenna on a finite dielectric slab with a octagonal partial ground plane. antenna. The switches integrated with the parasitic structure are assumed to have two operational states, on and off, as same as the switches of the square parasitic ring. A parametric study on the ring dimension as well as the location of the switches is carried out. The best design, so far, obtained from this parametric study is presented in Figure 2.2. Clearly, the E φ patterns are fairly symmetric on the azimuth plane, and nearly a 7-8 db drop in the horizontal component is obtained along the horizon between the two states of the switch operation. Moreover, although not shown here, the vertical field component, E θ, remains unchanged between the two states of the switch operation as expected. 2.4 Description of New Antenna Geometry As mentioned earlier, the antenna considered here is designed for the L1 GPS frequency, namely, GHz. Although two concepts for controlling both vertical and 33

56 E θ (Partially grounded finite substrate) E φ (Partially grounded finite substrate) E θ 15 E φ 15 1 o 15 o 3 o 45 o 6 o 75 o 9 o 1 o 15 o 3 o 45 o 6 o 75 o 9 o γ (Degree) γ (Degree) Figure 2.19: Far-field radiation pattern of a patch antenna on a finite dielectric slab with an octagonal partial ground plane. horizontal field components, i.e. E θ and E φ respectively, the work presented in this dissertation considers a scheme to modify the beamwidth of the horizontal field component, E φ, while the E θ component remains unchanged due to the geometry of the parasitic structure. The basic antenna geometry is shown in Figure It consists of a square radiating patch of size, P = 27.5 mm, mounted on a dielectric substrate of relative permittivity (dielectric constant) equal to 9.2. The dielectric substrate is mm mm with thickness of 7.62 mm (.1213λ d ). The radiating patch is surrounded by a switch loaded octagonal ring. As mentioned previously, a thick substrate was specifically chosen in order to excite surface waves. Control of the surface waves is implemented using a switch loaded octagonal ring. For purposes of controlling the horizontal field component (E φ ), a thin ring is used so the longitudinal induced currents are dominant while the transverse currents are weak. Furthermore, 34

57 Magnitude of E φ at φ= o Magnitude of E φ at φ=9 o E φ Switch On Switch Off E φ Magnitude of E φ at φ=15 o Magnitude of E φ at φ=3 o E φ E φ Magnitude of E φ at φ=45 o Magnitude of E φ at φ=6 o E φ E φ Switch on 3 3 Switch off γ (Degree) γ (Degree) Figure 2.2: Comparison of calculated far-field radiation patterns (E φ ) of the antenna with the circular parasitic ring at φ=, 15, 3, 45, 6 and 9 35

58 y Parasitic Structure Switching Circuit W Radiating Patch Antenna Cross Section D R2 R1 x (a) Top View z Radiating Patch P Parasitic Structure T x R2 Ground Plane Partially Grounded Dielectric Substrate (b) Antenna Cross Section Figure 2.21: Geometry of proposed reconfigurable antenna. A square patch is surrounded by the switch-loaded octagonal metallic ring. The radiating element is mounted on the thick substrate (.12λ d ) which is used for surface wave excitation. the ground plane of the antenna is smaller than the substrate and ring and it is also octagonal in shape to maintain a symmetric pattern in azimuth. Although a GPS antenna is designed to receive signals directly from satellites overhead, there is the potential for multipath interference because the antenna can also pick up signals that bounce back from the ground or from objects located nearby the antenna. Hence, GPS antennas are designed to receive circularly polarized (CP) waves to minimize the multipath problem. However, it is difficult to maintain CP from 36

59 broadside all the way to the horizon. A CP polarized pattern can be generated by exciting two orthogonal current modes with 9 phase difference. Various techniques for CP excitation can be found in the literature [7, 44, 48]. Probe feeding is one of many alternatives used to produce a CP pattern. For a square patch, circular polarization can be obtained by using two probes fed with a phase separation of 9. For the antenna considered here, two additional probes are added to improve the symmetry of the radiation pattern. The four probes are required to have a 9 phase progression. This is achieved with a two-stage Wilkinson power divider. The design of the power divider is discussed in greater detail in section Design Procedure This section discusses design considerations of both the parasitic ring structure and the switching circuit Design of Parasitic Ring The design of the parasitic structure begins with the determination of the parasitic ring geometry. Previously, the antenna element was fabricated on a square substrate with a square ground plane surrounded by the parasitic ring also square in shape. That initial design focussed in introducing a concept for obtaining maximum reconfigurability in only two principal planes, i.e. x z and y z planes. It is, however, found that the design yields an asymmetric pattern in azimuth owing to the geometry of the parasitic ring. As a result, the reconfigurability deteriorates as the observation angle moves away from the principal planes. Along with the parasitic ring contribution, the shape of the ground plane is also a factor in the asymmetry of the radiation pattern. Hence the shape of both parasitic 37

60 structure as well as ground plane is to be modified to simultaneously attain a symmetric pattern in azimuth and maximum reconfigurability. An obvious choice may appear to be a circular parasitic ring. However, it can be shown [27] that for a given size ring, the sides of the rings should be straight and not curved to obtain maximum change in beamwidth. Thus, the circular ring does not provide much reconfigurability. After a parametric study on the parasitic ring and ground plane, it was found that an octagonal ring and ground plane, as depicted in Figure 2.21, is a good compromise between reconfigurability and symmetric in azimuth. It was also found that a ground plane of the same dimensions or larger than the ring did not allow control of the horizontal component by the parasitic ring, and thus no reconfigurability would be possible. For this reason, the ground plane was made of smaller size than the ring and substrate. It turns out that the size of the ground plane adjusts the phase of the radiated surface wave and thus allowing the subtraction of the radiated surface waves from the fields radiated by the patch along the horizon. To obtain reconfigurability, it is necessary to modify the propagation characteristics of the induced surface waves. This can be achieved by introducing a reconfigurable ring to the radiating patch. A reconfigurable ring structure can be obtained by introducing some cuts in the ring to incorporate switches. The location of the cuts in the ring and their respective lengths were first determined by examining the surface current induced on the ring without any cuts. It was found through computer simulations that the cuts must be introduced in regions where the surface currents are maximum and thus achieve change in the beamwidth of the horizontal field component. Figure 2.22 depicts the surface currents induced on the ring without any cuts. As depicted, the magnitude of the surface currents are relatively high in the diagonal 38

61 sections of the ring. As a result, 4 cuts were first introduced in the diagonal sections of the ring. However, it was found that the pattern radiated from the antenna surrounded by ring with 4 cuts is asymmetric and the reconfigurability was obtained for only a few elevation plane cuts. To obtain a symmetric pattern, additional 4 cuts were introduced between the original 4 cuts, resulting in a total of 8 equally spaced cuts in the ring. This configuration radiates a fairly symmetric pattern along any azimuth plane. The two configurations of the ring that provide control of the horizontal field component along the horizon are as shown in Figure The initial optimization was carried out with very simple models for the switches. For the on state, the model shown in Figure 2.23(a) was used, while Figure 2.23(b) was used for the off state. More accurate models for the switches will be introduced in the next section. As can be observed in Figure 2.21, there are four variables that can be varied, namely, size of ground plane (R 2 ), size of ring (R 1 ), width of ring (D) and length of the cuts in the ring where the switches are to be placed (W ). Note that the size of the substrate is fixed (177.8 mm mm) and clearly the ring has to be smaller than the substrate. Using the simple models for the switches mentioned above, the following dimensions were obtained for the parasitic ring and ground plane: W = 22 mm, R 1 = mm, D=6.875 mm and R 2 = mm. A FDTD-based computer code, developed by the authors, was used for this purpose. Since no losses (material, ohmic, impedance mismatch) are included in this model, directivity patterns can be easily obtained. Figure 2.24 illustrates the directivity pattern of the horizontal field component (E φ ) for various azimuth planes. As can be seen, there is almost a 7-1 db change along the horizon (9 ) in the directivity pattern of E φ between the on/off 39

62 Magnitude of surface current (J s ), GHz y.7.6 y 8 X x Figure 2.22: Surface currents induced on the octagonal parasitic ring without any cuts. Octagonal ParasiticRing y Radiating Patch y x x Partially Grounded Dielectric Substrate (a) Switches On (b) Switches Off Figure 2.23: Geometry of the patch surrounded by (a) full octagonal parasitic ring (switches on) and (b) cut octagonal parasitic ring (switch off). 4

63 Directivity (D φ ) Directivity (D φ ) 1 5 φ= o Uncut Ring φ= o Cut Ring φ=15 o Uncut Ring φ=15 o Cut Ring φ=3 o Uncut Ring φ=3 o Cut Ring 1 5 φ=45 o Uncut Ring φ=45 o Cut Ring φ=6 o Uncut Ring φ=6 o Cut Ring φ=75 o Uncut Ring φ=75 o Cut Ring 5 5 D φ (db) 1 D φ (db) θ (degree) θ (degree) Figure 2.24: Comparison of calculated (FDTD) directivity patterns (D φ ) between the full and cut ring configurations for φ=, 15, 3, 45, 6 and 75. states of the ring, except for the φ = 75 plane cut. Even larger changes can be observed around θ Unlike the square ring case, these patterns demonstrate that reconfigurability is maintained in azimuth. In other words, the radiation pattern of E φ along the horizon is always lower when the switches are turned off To better understand the behavior of this reconfigurable antenna, the total radiation pattern can be decomposed into the patterns radiated by the radiating patch without the ring and the pattern radiated by the parasitic ring by itself (but mounted on the substrate) as depicted in Figure The plots (from left to right) represent the magnitude and phase of the pattern radiated by the patch with no ring, the ring by itself when the switches are turned on and the ring by itself when the switches are 41

64 E φ Patch E φ Ring (Diodes On) E φ Ring (Diodes Off) 1 5 φ= o φ=9 o E φ E φ E φ θ (Degree) θ (Degree) θ (Degree) E φ Patch E φ Ring (Diodes On) E φ Ring (Diodes Off) /E φ (Degree) 5 5 /E φ (Degree) 5 5 /E φ (Degree) θ (Degree) θ (Degree) θ (Degree) Figure 2.25: Calculated (FDTD) radiation patterns (E φ ) from the reconfigurable antenna: (a) Pattern radiated by the patch without the ring (b) Pattern radiated by ring by itself (but mounted on the substrate) with switches on and (c) same as (b) but switches are off. turned off, respectively. The idea of our reconfigurable scheme is to make sure that the pattern radiated from one of the two ring configurations (on/off states) cancels out the pattern radiated along the horizon by the patch with no ring. Although the magnitude of both patterns radiated by the ring are almost 3 db lower than the pattern radiated by the patch without ring, the phase of the pattern radiated by the ring with the switches off is out of phase with that of the patch by itself. That explains why the radiation pattern or gain pattern is always lower along the horizon when the switches are turned off. The ring (cut/uncut) and ground plane dimensions attained in this section will be used as the starting point when the switching circuit is considered next. 42

65 2.5.2 Design of the Switching Circuit The reconfigurable antenna described thus far in this dissertation achieves pattern reconfigurability due to two different configurations of the parasitic ring, namely, full and cut ring. It is the job of the switching circuit to bridge these two configurations effectively, keeping in mind that the reconfigurability that can be achieved is highly dependent on the design of the switching circuit. Switching can be implemented by either electronic means using PIN diodes, transistors etc., or by electromechanical means using RF MEMS switches. This dissertation only considers electronic switching using PIN diodes. However, the modelling scheme developed here can be extended to switches using transistors or RF MEMS as well. This section addresses the modelling of the various components that constitute the switching circuit, and optimization of the various parameters available in the design to achieve good reconfigurability. The simulations are done using Ansoft HFSS. Switch Circuit Components and Modelling Figure 2.26 shows the details of the components used in the switching circuit and inserted into the switching cuts introduced in the ring. There are two switching strips, and each switching strip has three switching PIN diodes and two DC block capacitors. The PIN diodes used for this application are Philips PIN diodes, BAP51-2, and they are biased through the use of two bias resistors to set the bias current, while RF chokes are used to prevent the flow of RF current into the DC supply. Two switching strips per switching cut have been inserted to provide more paths for the RF current and to account for the variation in the current along the width of the switching ring. Three diodes are included in each switching strip to provide the 43

66 B BA A I IJ J F F L L W D Diodes DC Blocking Cap Parasitic Ring Bias Resistor E E C C D D E E % % % % % & & & & &!!!!!!! " " " " " " C C D D % % % % % & & & & &!!!!!!! " " " " " " 8 8 % % % % % & & & & &!!!!!!! " " " " " " 8 8 K K G G H H K K ' ' ' ' ' ( ( ( ( ( # # # # # # # $ $ $ $ $ $ : : / / / / / / / / / / G G H H ' ' ' ' ' ( ( ( ( ( # # # # # # # $ $ $ $ $ $ : : ' ' ' ' ' ( ( ( ( ( # # # # # # # $ $ $ $ $ $ : : Conductive Strip ; ; ; ; ; ; < < < < < < ; ; ; ; ; ; < < < < < < ; ; ; ; ; ; < < < < < < ; ; ; ; ; ; < < < < < < ; ; ; ; ; ; < < < < < < ; ; ; ; ; ; < < < < < < ; ; ; ; ; ; < < < < < < ) ) ) ) * * * + + +,,, ) ) ) ) * * * + + +,,, ) ) ) ) * * * + + +,,, ) ) ) ) = = = = * * * > > > + @ ) ) ) ) = = = = * * * > > > + @ ) ) ) ) = = = = * * * > > > + @ ) ) ) ) = = = = * * * > > > + @ ) ) ) ) = = = = * * * > > > + @ RF Choke ) ) ) ) = = = = * * * > > > + @ ) ) ) ) * * * + + +,,, ) ) ) ) * * * + + +,,, ) ) ) ) * * * + + +,,, ) ) ) ) * * * + + +,,, Figure 2.26: Schematic representation of the switch circuit components inserted in the switching cuts introduced in the parasitic ring. maximum isolation possible when the diodes are off. It has been observed through simulations and measurements that one diode per switching strip does not duplicate the desired behavior. In fact, when the diode is on, it can be shown through simulations that the pattern obtained from the antenna is similar to the case when the ring is cut, while when the diode is reverse biased, the pattern of the antenna is similar to the case when the ring is full. The desired behavior is when the diode is forward biased, the antenna should produce a pattern which is identical to the case when the ring is full, and when the diode is reverse biased, it should duplicate the behavior of the cut ring. Three diodes inserted in each switching strip are seen to provide that behavior, and hence are selected for the application. Modelling of the resistors, capacitors and RF chokes in HFSS is done through the use of lumped RLC values, where the value of the component represented by a particular geometry is specified, and the simulator extracts the impedance value at the particular frequency of interest. An equivalent circuit model for the PIN diodes is sought in order to represent them in HFSS. This dissertation considers a linear model for the PIN diodes detailed in an application note on the Philips website [46], 44

67 %$ &'! #"" "7: ; < = < > >.9?A7B ;3 < C < () * +,-. /* 1 2 3* -12 Figure 2.27: ADS schematic for Philips BAP51-2 diode. which is valid from 6 MHz to 6 GHz. Figure 2.27 shows the model used, and the description of the various elements in the model is given in the application note [45]. This model contains diodes to separately emulate the DC and RF characteristics of the PIN diode, and it also accounts for the parasitics in the PIN diode package. While it is not possible to use lumped values for all components in the model, it is possible to obtain the impedance of the overall model at a specific frequency of interest and specific bias condition. This can then be used in the impedance boundary condition provided in HFSS to model the diodes. To implement the impedance boundary conditions, it is first necessary to relate the impedance of a known surface, Z, (in ohms) to the surface impedance, Z s, (in ohms per square), which is then specified to the simulator. This can be accomplish using the following equation: Z s = Z( W L ) (2.1) where W and L are the width and length of the surface, respectively. 45

68 To model the diodes using the impedance boundary condition mentioned above, the impedance of a diode is required. The impedance of a diode is a function of the bias applied to it; hence it is required to simulate these bias conditions to obtain the diode impedance. As mentioned, there are two rows of diodes in each switching cut, and each row contains three diodes. This set of six diodes is biased using a DC voltage of 3 V. The setup employed to obtain the impedance of each diode in the schematic editor of Agilent ADS is shown in Figure 2.28, where each diode is replaced by its equivalent circuit for the simulation. Using the results of the simulation on the sets of diodes, the impedances of each diode, for forward and reverse bias condition (at L1) are Z d = j8.15 Ω and Z d =.766 j Ω, respectively. Keeping in mind that the dimensions of the diodes are 1.15 mm 1.2 mm and using (2.1), the surface impedance of each diode is Z s = j8.363 Ω per square and Z s =.799 j Ω per square for the forward and reserved bias conditions, respectively !",-. #$ + #$ %&' (*) / 1'32/ Figure 2.28: Schematic to determine the impedance model for every switching circuit for forward and reverse bias conditions. 46

69 The models for all the switch circuit components have thus been obtained and the design of the switch circuit for antenna reconfigurability can be done. Note that this procedure can be applied to switch circuit components like RF transistors or RF MEMS, if an equivalent circuit model can be obtained for these components. Optimization of Parasitic Structure It has been mentioned in the previous section that there are two switching strips inserted in each switching cut, with three switching PIN diodes per switching strip. Simulations were performed to optimize the separation between the two strips. It was found that the larger the separation, the better the performance. Thus, the two strips are as shown in Figure Other factors that are to be considered in the design are the width of the ring D, and the length of the switching cuts W introduced in the ring. The initial dimensions for the optimization to be carried out in this section are the dimensions obtained in the previous section, namely, the width of the parasitic structure is D=6.875 mm, the size of the ring is R1= mm, while the length of the switching cut introduced in the ring is W =22 mm. Note that the size of the ground plane remains the same (R 2 = mm). When the switch circuitry is inserted in the gaps and using the models developed for the various switch circuit components, the following pattern behavior is obtained when the diodes are forward and reverse biased. It is observed that the reconfigurability drops considerably from the ideal case considered in the previous section i.e. when the ring is full and when it is cut. A study of the pattern radiated by the parasitic structure, reveals that the loss in reconfigurability is due to diodes when reverse biased. The phase difference created between the patterns of the horizontal component of just the patch and that 47

70 Calculated Gain Pattern (G φ ) (db) Calculated Gain Pattern (G φ ) (db) 1 5 φ= o Switch On φ= o Switch Off φ=15 o Switch On φ=15 o Switch Off φ=3 o Switch On φ=3 o Switch Off 1 5 φ=45 o Switch On φ=45 o Switch Off φ=6 o Switch On φ=6 o Switch Off φ=9 o Switch On φ=9 o Switch Off G φ (db) 5 G φ (db) θ (degree) θ (degree) Figure 2.29: Calculated (HFSS) gain patterns (G φ ) for on and off states of switches for φ=, 15, 3, 45, 6 and 9. of just the ring (diodes reverse biased) has been reduced from the ideal case (18 ) when the ring is cut. Therefore, a systematic optimization is necessary to maintain the patterns of the patch (by itself) and the reverse biased ring (by itself) out of phase. After a lengthly and tedious optimization study, the selected dimensions of the ring are: R 1 =67.5 mm, D =15 mm, W =3 mm in the principal planes and W = mm in the diagonal planes. Figure 2.29 shows calculated radiated patterns for the final design of the reconfigurable antenna. The model includes all the components of the switching circuit depicted in Figure As expected, the performance is not as good as the ideal case shown in Figure 2.24; however, the reconfigurability is maintained. 48

71 Input Signal Power Power Output Signal Port #2 Port #1 Divider Divider o 9 Phase Shifter Output Signal Port #3 o 9 Phase Shifter Power Divider Output Signal Port #4 o 9 Phase Shifter Output Signal Port #5 Figure 2.3: Schematic of the two-stage Wilkinson power divider. 2.6 Microstrip Feed Network for Circular Polarization For the application under consideration, the Wilkinson power divider is selected and implemented using microstrip technology. It was already mentioned that four feeding probes are employed to generate a right handed circularly polarized (RHCP) and a symmetric pattern in azimuth. The four probes are to be fed with equal magnitude signals and with a 9 sequential phase increment between successive feed locations. To generate a RHCP field pattern, the phase increment between successive feed points mentioned should be counterclockwise when the antenna is viewed from the top. As shown in Figure 2.3, the two outputs from the first Wilkinson power divider are of equal magnitude (3 db lower than the input signal) and equal phase. The two outputs from the first power divider are further fed as inputs to two additional power dividers in the second stage. Each second-stage power divider provides two outputs, yielding a total of four outputs. Each output being 6 db (ideally) lower than the input. The four feed outputs thus have the same magnitude. The requirement on phase must also be satisfied by this two stage-power divider. This is done by adding transmission lines of proper length and width. 49

72 (a) Front View (b) Back View Figure 2.31: Implemented two-stage Wilkinson power divider. The substrate (RT/Duroid 587, thickness=1.575 mm) dimensions are 125 mm 65 mm. Figure 2.31 illustrates the front and back of the implemented power divider designed to operate at L1 band. The feeding circuit output ports are connected to the antenna input ports through four short coaxial cables. This was done to test the impedance of each port of the antenna. The feeding circuit could be redesigned using a substrate with higher dielectric constant (e.g. TMM1i, ɛ r = 9.8) such that it fits on the ground plane of the antenna. The measured magnitudes of S 21, S 31, S 41 and S 51 across the band of interest are depicted in Figure 2.32(a). Clearly, they remain fairly constant across the entire band with the maximum deviation (between the ports) of.2 db at GHz. In addition, Figure 2.32(b) shows the measured phase response over the same frequency band. As shown, the relative phase increment at GHz is, 89.7, and respectively. Thus, it is shown that a circularly polarized pattern can be achieved using this feed network. It is also worth noting that the coupling between these output ports (i.e. S 23, S 24, etc.) is very insignificant, approximately -35 db. 5

73 Measured Magnitude of S i1 Vs Frequency S 21 S 31 S 41 S Measured Relative Output Phase Vs Frequency phase(s 21 ) phase(s 21 )) phase(s 31 ) phase(s 21 )) phase(s 41 ) phase(s 21 )) phase(s 51 ) phase(s 21 )) S i Phase (Degree) Frequency (GHz) (a) Magnitude Frequency (GHz) (b) Phase Figure 2.32: Measured frequency response of the two-stage Wilkinson power divider. 2.7 Measured Results and Discussions Figure 2.33 shows a picture of the front view of the reconfigurable antenna, including the parasitic ring and switching circuitry Impedance Characteristics Figure 2.34 illustrates the measured antenna return loss for the two operating states of the switches (on and off cases). Since the measured results of the four probes/ports are almost identical, only the measured results of port 2 and port 3 are represented here. It is clear from the figure that the antenna resonates around the frequency of operation, GHz. In addition, the return loss is just slightly modified when activating the diode switches. This implies that the antenna impedance is weakly dependent on the state of the switch, (on/off). That is the desired property for this reconfigurable antenna. 51

74 Figure 2.33: Geometry of the implemented reconfigurable antenna. Magnitude of S ii Vs. Frequency S ii 5 1 Port 2 Switch On Port 3 Switch On Port 2 Switch Off Port 3 Switch Off Frequency (Hz) x 1 9 Phase of S ii Vs. Frequency /S ii (Degree) Frequency (Hz) x 1 9 Figure 2.34: Comparison of the measured input impedance between the on and off states of the switches. 52

75 2.7.2 Radiation Characteristics Figure 2.35 shows a comparison of the measured elevation gain pattern for the horizontal component (G φ ) for the on and off states of the switches at φ =, 15, 45 and 9. As predicted, the measured gain patterns are very similar to the simulated results shown in Figure It can be seen that the measured gain patterns are fairly symmetric on azimuth. Moreover, the measured gain patterns when the switches are off are consistently lower than those of the switch on case at every elevation plane. The small oscillations of the gain patterns probably arise from the fields scattered by the coaxial cables connecting the antenna and the feeding circuit during the measurement process. Similarly, Figure 2.36 depicts the measured elevation gain pattern of the vertical field component (G θ ) for the on and off states of the switches at φ =, 15, 45 and 9. As expected, the measured gains remain practically unchanged along the horizon for the two operating states of the switches, except for θ 135. Furthermore, Figure 2.37 illustrates the measured axial ratio for the on and off states of the switches at φ =, 15, 45 and 9. It is noted that when switches are activated, the antenna represents an excellent axial ratio that is less than 3 db for θ between and 9 in all planes, (φ =, 15, 45, 9 ). On the other hand, the axial ratio of the switches off cases is below 3 db for θ between and 6. It is clear that the axial ratio is strongly dependent on the operating states of the switches. Figure 2.38 shows a comparison of the measured right handed circular polarized (RHCP) gain pattern for the on and off states of the switches at φ =, 15, 45 and 9. As illustrated, the measured RHCP gain patterns are fairly symmetric on azimuth. Moreover, the measured RHCP gain patterns when the switches are off are consistently lower than those of the switch on case especially in the directions along 53

76 the horizon. As a result, it can be seen from the figure that the antenna can be used not only to minimize those jamming signals, but also to reduce the multi-path signals. To demonstrate the symmetry of the azimuth radiation pattern, Figure 2.39 depicts the measured azimuth patterns for the on and off states of the switches for θ =, 3 and 5. It can be seen that the antenna radiates fairly symmetric patterns for both switches on and off cases. The maximum deviation is less than 2 db when θ=5. Although not included in this dissertation, it is shown through computer simulations that the symmetry on the azimuth could be drastically improved by replacing the square substrate by an octagonal substrate. It is also worth noting that the gain of the antenna under test is readily computed by comparing the magnitude of the measured radiation pattern of the antenna to that of a standard gain horn (AEL H1734). The gain of the antenna under test is obtained by summing the gain of the standard gain horn at the frequency of interest to the difference in magnitude of the measured radiation patterns of the antenna under test and the reference horn. 2.8 A Summary and Conclusions This chapter demonstrates a novel pattern reconfigurable antenna concept consisting of a microstrip patch surrounded by a octagonal parasitic ring mounted on a partially grounded substrate. In this case, the horizontal field component is under control. The reconfigurable scheme is based on the control of surface waves by means of a switch-loaded metallic parasitic ring. The propagating characteristics of the surface wave are controlled by the on/off states of the switches. A design scheme of the parasitic ring as well as the switching circuits are presented in this chapter. It is shown 54

77 5 Measured Gain Pattern (G φ ) (db) Measured G φ (db) 5 φ= Switch On φ= Switch Off φ=15 Switch On φ=15 Switch Off 1 φ=45 Switch On φ=45 Switch Off φ=9 Switch On φ=9 Switch Off θ (degree) Figure 2.35: Measured gain patterns (G φ ) for the on and off states of the switches for φ=,φ=15, φ=45 and φ=9. 5 Measured Gain Pattern (G θ ) (db) Measured G θ (db) 5 φ= Switch On φ= Switch Off φ=15 Switch On φ=15 Switch Off 1 φ=45 Switch On φ=45 Switch Off φ=9 Switch On φ=9 Switch Off θ (degree) Figure 2.36: Measured gain patterns (G θ ) for the on and off states of the switches for φ=, φ=15, φ=45 and φ=9. 55

78 Measured AR (db) Measured Axial Ratio (db) φ= Switch On φ= Switch Off φ=15 Switch On φ=15 Switch Off φ=45 Switch On φ=45 Switch Off φ=9 Switch On φ=9 Switch Off θ (degree) Figure 2.37: Measured axial ratio for the on and off states of the switches for φ=, φ=15, φ=45 and φ=9. 1 Measured RHCP (db) Measured RHCP Patterns (db) 5 φ= Switch On φ= Switch Off 5 φ=15 Switch On φ=15 Switch Off φ=45 Switch On 1 φ=45 Switch Off φ=9 Switch On φ=9 Switch Off θ (degree) Figure 2.38: Measured right hand circular polarized gain patterns (G RHCP ) for the on and off states of the switches for φ=, φ=15, φ=45 and φ=9. 56

79 1 8 6 Measured Azimuth Gain Pattern (G θ ) (db) Measured Azimuth Gain Pattern (G φ ) (db) Measured G θ (db) θ= Switch Off θ= Switch On θ=3 Switch Off θ=3 Switch On θ=5 Switch Off θ=5 Switch On φ (degree) Measured G φ (db) θ= Switch Off θ= Switch On θ=3 Switch Off θ=3 Switch On θ=5 Switch Off θ=5 Switch On φ (degree) Measured Right Handed Circularly Polarized Azimuth Gain Pattern Measured Axial Ratio (db) Measured RHCP Gain (db) 1 5 θ= Switch Off θ= Switch On θ=3 Switch Off 5 θ=3 Switch On θ=5 Switch Off θ=5 Switch On φ (degree) Measured AR (db) θ= Switch Off θ= Switch On θ=3 Switch Off θ=3 Switch On θ=5 Switch Off θ=5 Switch On φ (degree) Figure 2.39: Measured azimuth patterns for the on and off states of the switches for θ=, θ=3 and θ=5. 57

80 that the parasitic structure along with the switching circuits play a crucial role in the pattern reconfigurability that can be achieved by the antenna. Although the pattern is fairly symmetric in azimuth, the azimuthal radiation pattern ( < φ < 36 ) can be made almost constant by using an octagonal substrate. Even though the antenna shown here is designed for GPS applications, this novel concept is also applicable to other applications. For example, it is possible to design the antenna for linear polarization (LP) or to design the parasitic ring for the control of the vertical field component (E θ ). The latter can be achieved by using a thicker parasitic ring. It is also worth noting that GPS antennas are designed to receive signals from satellites overhead. Nonetheless, our reconfigurable scheme is applicable to transmitting antennas as well. Although the switches used in the parasitic ring are PIN diode switches, radio frequency microelectromechanical systems (RF MEMS) switches can provide an alternative to these solid state switches and will be considered in future work. Finally, since GPS signal contain two discrete frequency bands, L1 (1.575 GHz) and L2 (1.227 GHz), dual band GPS antennas, reconfigurable at both GPS frequencies simultaneously would be desirable. This work is currently being carried out and presented in the next chapter. 58

81 CHAPTER 3 DEVELOPMENT OF THE DUAL BAND RADIATION PATTERN RECONFIGURABLE ANTENNA FOR GPS APPLICATION 3.1 Introduction In the previous chapter, design of the pattern reconfigurable single band antenna for GPS application at the L1 frequency was considered. Design of a dual band antenna geometry and its switching circuitry are the focus of this chapter. The dual band antenna is a reconfigurable antenna operating at the two GPS frequencies of L1 (1.575 GHz) and L2 (1.227 GHz) bands. Unlike the single band antenna, the goal of the dual band antenna is to control the vertical component of the electric field, E θ. For this purpose, a parasitic structure together with the switching circuit is incorporated and designed to achieve the pattern reconfigurability. The design of the parasitic structure (strips/rings) is initially done by using a 2-D (MoM) model. An optimized 2-D design is then used as an initial guess for the 3-D (FDTD) design. Results based on 2-D and 3-D models are presented. Keep in mind that the region of interest is still the angular region around the horizon similar to the single band case. The chapter begins with a brief discussion on the geometry of the dual band antenna, along with the design of the parasitic rings and switching circuitry that 59

82 provides the reconfigurability. The requirement for right hand circularly polarized radiation patterns from the two antennas places certain demands on the feeding network. Design consideration of the feeding network is discussed in greater detail in the chapter. Similar to the single band case, the first few designs of the dual band antenna exhibit the asymmetry of the radiation pattern as the observation angle (φ) moves away from the principal planes (φ= and 9 ). It is found that the reconfigurability falls off dramatically as the observation angle moves away from the principal planes is primarily due to the geometry of the dielectric substrates and the parasitic structures. To provide an azimuthally symmetric pattern, an octagonal substrate is used, again following on the considerations for the single band case. Once the modifications are made accordingly, the parasitic structure and the switching circuitry are redesigned to achieve the desired reconfigurability. The new antenna design is afterward implemented and evaluated its characteristics, such as input impedance and radiation pattern. Measured results are compared to simulated ones and discussed at the end of this chapter. 3.2 Basic Antenna Geometry A novel multi-layer design for a reconfigurable dual band (L1/L2) microstrip antenna for GPS applications is proposed in this section. The three-layer stacked patch antenna consists of two radiating patches in the bottom two layers as shown in Figures 3.1 and 3.2. The bottom dielectric layer has a thickness (H3) of mm with a dielectric constant (ɛ 3 ) of The middle dielectric layer has a thickness (H2) of mm with a dielectric constant (ɛ 2 ) of 9.2, while the top dielectric layer has the same thickness (H1) and dielectric constant (ɛ 1 ) as the middle layer, namely

83 mm and 9.2, respectively. The shape of all substrate layers is a square initially. Unlike the single band antenna, the dual band antenna has a complete or full ground plane. The radiating patch for the L2 (1.227 GHz) frequency is located on the top of the bottommost dielectric layer. The dimensions of this patch are 5.56 mm 5.56 mm. While, the L1 (1.575 GHz) patch is located on top of the middle layer, and its dimensions are mm mm. The initial substrate size was chosen to be mm mm originally (same as the single band case). The parasitic structure are positioned in the middle and top layers. It is to be noted that only the top parasitic structure is loaded with the diode switches. 3.3 Feed Configuration The dual band reconfigurable antenna is required to operate at the two GPS frequencies of GHz and GHz. Right hand circular polarization is required at both bands. For this intention, four feed points per patch are required. Indeed, circularly polarized waves can be achieved by exciting the patch using only two feed points with proper excitation. However, it is shown through computer simulation that four feed points provide a more symmetric pattern on any azimuth than the two feed points does. As employed in the single band antenna, the feed points of each band are required to be fed with equal amplitude signals, and a progressive 9 counterclockwise phase shift between successive feed points is required. The Wilkinson power divider is employed for this task, and two stage Wilkinson power dividers are designed for each frequency to provide the four feed outputs with the proper phase relationship between the outputs. 61

84 $ 1 1 -, 2 &% + z Layer1 ε1 Lower Parasitic Ring Layer2 ε2! " #" # / (../ ' '(.. ' ' * *) ) Switch Loaded Parasitic Ring Upper Radiationg Patch, L1 Lower Radiating Patch, L2 Layer3 ε3 x Ground Plane D D y Figure 3.1: Geometry of a pattern reconfigurable dual band microstrip antenna. The antenna is to operate at the two GPS frequencies (L1 (1.575 GHz) and L2 (1.227 GHz) bands). It is worth noting that the goal of the proposed dual band antenna is to control the vertical component of the electric field, E θ. Switch Loaded Ring Upper Radiating Patch Parasitic Ring Lower Radiating Patch Layer 1 ε 1 H1 Layer 2 ε 2 H2 Layer 3 ε 3 Ground Plane D H3 Figure 3.2: Cross section of a reconfigurable dual band microstrip antenna. 62

85 3.3.1 Input Impedance In typical printed antenna, the input impedance is a function of a feed position on the patch, other than the frequency of operation. At the resonance, the impedance of the patch is nearly resistive. The optimum location of the feed points on each patch is initially found by considering just a single feed point per patch for the sake of simplicity. The feed position is moved along one axis of the patch till the desired minimum return loss is obtained at resonance. Note that the other feed points are located symmetrically about the center of the patch. Mutual coupling between the feed points also affects the input impedance, and the effect of mutual coupling is studied by using the four feed probes. A fine tuning of the patch dimensions together with a slight adjustment of the feed point locations yields the desired position for the feeding point. This is done for both the L1 and L2 patches simultaneously. In order to excite the lower or L2 radiating patch, a coaxial cable can simply run from under the ground plane, and the inner probe can therefore run directly from the ground plane upto the desired locations on the L2 patch. Nevertheless, the procedure is not quite straightforward for the L1 or upper patch. The issue here is that a similar way of feeding the L1 patch would require a coaxial cable to run from under the ground plane, and then the center probe to run from the ground plane upto the L1 patch. The L2 patch is located between the ground plane and the L1 patch, hence it would require the probe to pass through an opening in the L2 patch. This would cause coupling of the energy from the L1 feed probe to the L2 patch, and could be responsible for exciting unwanted modes on the L2 patch. Hence it is desired to pass the feed probes for the L1 patch through a point on the L2 patch where the coupling would be minimum. Moreover, it is also desired to pass not only the probes, but the 63

86 entire coaxial cable through the L2 patch, so that the outer conductor shielding the probe will reduce the energy coupled. The point where the dominant mode of the L2 patch experiences a null is the center. For this purpose, the L1 feed cables are to be passed through the center of the L2 patch. The opening in the L2 patch at the center has to be large enough to allow four feed cables to pass through without the outer conductor making contact with the L2 patch. This is necessary since the outer conductor is already connected to the ground plane, and any contact between the outer conductor and the L2 patch will short the L2 patch to the ground plane also. Hence the scheme devised is to pass the feed cables through the opening in the L2 patch and pass the feed cables through the L1 patch with the outer conductor making contact with the L1 patch. This will short the L1 patch to the ground plane. Furthermore, the feed cables pass through the top layer of the antenna, and are then bent downwards. On their downward path, they again make contact with the L1 patch, and finally the probes pass through the middle layer of the antenna, and finally terminate on the L2 patch. The centers of the probes that terminate on the L2 patch, and those of the feed cables that eventually terminate on the L1 patch, are at the feed point locations for the L1 patch. The implementation of the feed probes for the two patches is shown in Figure 3.3. It is worth noting that only two feed cables for the L2 patch are shown for clarity in Figure 3.3 (b). Figures 3.4 and 3.5 depict the calculated input impedance and magnitude of the return loss, S 11, of the L1 and L2 patches, accordingly. It can be observed that the upper patch resonates at GHz with the return loss of -2 db. Similarly, the lower patch resonates approximately at GHz with the return loss of -4 db. 64

87 (a) Feed coaxial cable of the L1 and L2 patches. (b) Side view Figure 3.3: Feed configuration of the dual band antenna Microstrip Feed Network for Circular Polarization To generate a circular poralized radiation pattern, the feed network must provide four equal magnitude outputs with a progressive 9 phase rotation between successive feeding points as described earlier in the previous chapter. The two outputs from the first Wilkinson power divider are of equal magnitude and equal phase. In order to realize four outputs, the two outputs from the first stage power divider are subsequently fed as inputs to two more power dividers in the second stage. Each second stage power divider provides two corresponding outputs, giving a total of four outputs from the final two stage power divider configuration, each output being 6 db lower than the input. The four feed outputs thereby show the same magnitude. The requirement on phase is also to be met by this two stage power divider. Any arbitrary phase can be realized by adding a length of transmission line, with the appropriate length and width. Similarly, the schematic for the two stage Wilkinson power divider can be found from the previous chapter. 65

88 1 Input Impedance and S 11 of the Upper Radiating Patch (L1) Resistance Reactance Impedance (Ω) Frequency (GHz) s Frequency (GHz) Figure 3.4: Calculated input impedance and S 11 response for upper radiating patch. The feed probe is located 4.74 mm from the center of the L1 patch. 1 Input Impedance and S 11 of the Lower Radiating Patch (L2) Resistance Reactance Impedance (Ω) Frequency (GHz) 1 s Frequency (GHz) Figure 3.5: Calculated input impedance and S 11 response for lower radiating patch. The feed probe is located 11.6 mm from the center of the L2 patch. 66

89 For the sake of simplicity, it is advisable to locate all the power dividers on a single dielectric substrate, and further, to attach the ground plane of feeding circuit to the antenna ground plane. This will eliminate the need to run additional cables from the power divider outputs to the coaxial cables feeding the antenna, which in turn will reduce losses in the feed signal. This requires the six power dividers (three each per frequency band) to be on a single substrate the same size as that of the antenna. Also, the feed cables for the L1 patch pass through an opening in the L2 patch, and they are very close to each other. In order to realize the 5Ω lines required to feed these cables, and to ensure that the lines do not touch each other, a substrate (RT/Duroid 62) with a dielectric constant of 2.94 is chosen. This dielectric constant is higher than the one used for the feed network substrate of the single layer antenna, which is 2.2 (RT/Duroid 587). Also, the thickness of the substrate is.51 mm (2 mil), which allows for lines of less width to be used. The feeding circuit designed on the substrate mentioned above is illustrated in the Figure 3.6(a) [13]. The two stage power dividers used to feed the two patches are seen in the figure. The design of the power dividers is done based on the theory of the Wilkinson power divider, and on the procedure mentioned earlier. The narrow lines required to reach the feed locations for the L1 patch are also seen. The lumped components required for this design are chip resistors of value 1Ω (2 5Ω), obtained from the theory of the power dividers. The measured magnitudes of relative phases across the frequencies of interest, L1 and L2, are depicted in Figures 3.7 and 3.8, orderly. Clearly from Figure 3.7, the magnitudes remain fairly constant across the entire band of interest with the maximum deviation (between the ports) of.2 db at GHz. In addition, the 67

90 (a) Layout (b) Implemented circuit Figure 3.6: The two-stage Wilkinson power divider for the dualband antenna. The substrate (RT/Duroid 62). measured phase response over the same frequency band shows the relative phase increment at GHz is, 9., 18.3 and respectively. Likewise, the magnitudes of the return loss at the L2 band stay nearly constant over the entire band of interest with the maximum deviation (between the ports) of.2 db at GHz. Further, the measured phase response over the same frequency band shows the relative phase increment at GHz is, 93.3, and respectively. Thus, it is shown that a circularly polarized pattern at both L1 and L2 bands can be readily achieved using this feed network. It is also worth noting that the coupling between these output ports (i.e. S 23, S 24, etc.) is very low, approximately -35 db. 68

91 5.5 Measured Magnitude Response of S i1 of Feeding Circuit for the L1 Patch S 21 S 31 6 S 41 S 51 S i Frequency (Hz) x 1 9 Relative Phase (Degree) Measured Relative Output Phase of Feeding Circuit for the L1 Patch phase(s 21 S 41 ) 9 phase(s S ) phase(s 41 S 41 ) 3 phase(s 51 S 41 ) Frequency (Hz) x 1 9 Figure 3.7: Measured return loss of the two stage Wilkinson feeding circuit at the L1 band. 3.4 Design of Parasitic Structures (Strips/Rings) D Strip/Ring Parametric Study The design of the parasitic strips/rings is actually an optimization process, which can be done with 3-D models of the antenna and the parasitic structures. However, an optimization process with 3-D models can be very time consuming depending on how large the antenna geometry is. Therefore, taking advantage of the symmetry of 69

92 6 Measured Magnitude Response of S i1 of Feeding Circuit for the L2 Patch S 21 S i S 31 S 41 S Frequency (Hz) x 1 9 Relative Phase (Degree) Measured Relative Output Phase of Feeding Circuit for the L2 Patch phase(s 21 S 41 ) 21 phase(s 31 S 41 ) 18 phase(s 41 S 41 ) 15 phase(s S ) Frequency (Hz) x 1 9 Figure 3.8: Measured return loss of the two stage Wilkinson feeding circuit at the L2 band. the antenna, we start with 2-D models which are more efficient. Once an optimized geometry is obtained, it is used as an initial guess for our 3-D design. Figure 3.9 depicts the cross section of the 3-D model, which can be used as a initial 2-D model. The radiating patches are replaced by two magnetic line sources. In other words, at the L1 band, the upper radiating patch is replaced by two magnetic line sources while the lower patch remains simply a metal strip. Similarly, the lower patch is replaced by two magnetic line sources to simulate the radiation pattern at L2 band while the upper patch remains a metal strip. The distance between the line sources 7

93 y x Cross Section of Original 3D Problem Magnetic Line Sources y Magnetic Line Sources y x x Equivalent 2D Problem (L1) Equivalent 2D Problem (L2) Figure 3.9: Cross section of 2-D equivalent problems for each antenna has to be adjusted in order to secure the same radiation pattern as the 3-D model. Note that the parasitic structures are excluded when determining the distance between the line sources. Verification of 2-D Antenna Model The separation between the line sources can be adjusted to get an accurate 2-D model. Figure 3.1 depicts a comparison of a vertical field component obtained from the 2-D and 3-D models at L1 band. It is clear from the figure that the 2-D result matches the 3-D results very well in both magnitude and phase. The separation between line sources for the L2 antenna can be found by using the same method. Optimization of 2-D Strips Once the separations between magnetic line sources are determined, the next step is to focus on the strip design. In this work, design of the 2-D strip could be realized using optimization or parametric study. The reconfigurability is obtained 71

94 Comparison of E θ 2D VS 3D (L1) 5 3D 2D Phase Comparison of E θ 2D VS 3D (L1) 5 3D 2D E θ Phase of E θ (Degree) γ (Degree) γ (Degree) Figure 3.1: Comparison of vertical field component obtained from 2-D and 3-D models at L1 band again through the use of two different states of strip configurations, similar to the single band antenna case. For instance, Figures 3.11 and 3.12 illustrate the radiation pattern versus angle of two different strip widths at both L1 and L2 bands. The blue line represents the radiation pattern of a 25.7 mm strip width. By increasing the strip width to be 56.7 mm, the radiation pattern switches to the red line. It is clear that there is approximately 8 db difference in the vertical field pattern strength along the horizon at L1 and L2 simultaneously D Strip/Ring Parametric Study After an optimal 2-D design is secured, it can be used as an initial guess for the 3-D model. The cross sectional information in Figure 3.9 can be used to obtain the initial dimensions of two different configurations in the 3-D study. The first configuration, 72

95 Comparison of magnitude of E θ for L1 Band 3 35 w1=.257 m w1=.567 m 4 E θ γ (Degree) Figure 3.11: Comparison of vertical field component between two different strip width at the L1 band Comparison of magnitude of E θ for L2 Band 25 3 w1=.257 m w1=.567 m 35 E θ γ (Degree) Figure 3.12: Comparison of vertical field component between two different strip width at the L2 band 73

96 z Switch Loaded Parasitic Strip Layer1 ε !!" 9 9: # # $ $ ; ;< % % & & = = > > ' '( )*+, -. / Upper Radiationg Patch, L1 Lower Parasitic Strip Layer2 ε2 Lower Radiating Patch, L2 Layer3 ε3 x Ground Plane D D y Figure 3.13: Geometry of a reconfigurable dual band stacked patch antenna for controlling antenna pattern at L2 band only (Scheme A) depicted in Figure 3.13, is for controlling the antenna pattern at the L2 band only. Note that the parasitic elements consist of four strips. The second scheme is an antenna for controlling the antenna pattern at the L1 band only, and also at L1 and L2 bands simultaneously. The antenna configuration for the second scheme is almost the same as the first scheme except for the parasitic elements. In this case, the upper and lower parasitic conductors are rings as depicted in Figure Control of Radiation Pattern at L2 Band Only Figure 3.15 depicts the antenna radiation patterns and axial ratio versus angle for scheme A at the L2 band. The blue line represents the radiation pattern and axial ratio of 1.58 cm strip width. By increasing the strip width to 3.16 cm, the radiation pattern switches to the red dashed line. It is to be noted that nearly a 3 db drop 74

97 $ / 1 1 -, 2 ( * *) &% + ) z Layer1 ε1 Lower Parasitic Ring Layer2 ε2! " #" #../ ' '(.. ' ' Switch Loaded Parasitic Ring Upper Radiationg Patch, L1 Lower Radiating Patch, L2 Layer3 ε3 x Ground Plane D D y Figure 3.14: Geometry of a reconfigurable dual band stacked patch antenna for controlling antenna pattern at L1 band only as well as at L1 and L2 bands simultaneously (Scheme B) in the vertical field component along the horizon is obtained by increasing the strip width as shown in Figure Although not shown here, the radiation patterns remains fairly unchanged for both vertical and horizontal field components at the L1 band. Control of Radiation Pattern at L1 Band Only Figure 3.16 depicts the antenna radiation patterns and axial ratio versus angle for scheme B at the L1 band. Similarly, the blue solid line represents the radiation patterns and axial ratio for a ring of 2.5 cm in width. By increasing the ring width to 2.37 cm, the radiation pattern switches to the red dashed line. Note that nearly a 15 db drop in the vertical field component along the horizon is also achieved when 75

98 E φ E θ Scheme A : E φ component GHz (φ= o ) w1=.158 m w1=.316 m Scheme A : E θ component GHz (φ= o ) w1=.158 m w1=.316 m Scheme A : Axial Ratio GHz (φ= o ) 18 Axial Ratio (db) w1=.158 m w1=.316 m γ (Degree) Figure 3.15: Example 1 (Scheme A) : Antenna radiation pattern and axial ratio versus angle at L2 band the ring width is increased. Although not shown here, the pattern at the L2 band remains the same when the ring strip width is increased. Control of Radiation Pattern at L1 and L2 Bands Simultaneously Figures 3.17 and 3.18 show the antenna radiation patterns and axial ratios versus angle for scheme B at the L1 and L2 bands, respectively. The blue solid line represents the radiation pattern and axial ratio of a ring of.79 cm in width. By widening the ring to 2.37 cm, the radiation pattern switches to the red dashed line. It can be observed that nearly a 1 db simultaneous drop in the vertical field components, E θ, is achieved along the horizon region at the L1 and L2 bands. The new proposed scheme demonstrates a larger change in beamwidth, thus yielding a larger drop in the 76

99 E φ Scheme B : E φ component GHz (φ= o ) w1=.25 m w1=.237 m Scheme B : E θ component GHz (φ= o ) E θ w1=.25 m w1=.237 m Axial Ratio (db) Scheme B : Axial Ratio GHz (φ= o ) w1=.25 m w1=.237 m γ (Degree) Figure 3.16: Example 2 (Scheme B) : Antenna radiation pattern and axial ratio versus angle at L1 band vertical field component along the horizon when compared to the schemes presented in Chapter 2. The reason behind the larger drop in the field strength is that the new proposed antenna design has more degrees of freedom, as more varieties of the dielectric profile and the geometry of the two parasitic structures can be carried out. 3.5 Asymmetry Consideration of the Radiation Pattern on the Azimuth Plane The design of the dual band antenna was by far concentrated only on the principal planes (φ= and 9 ). Unfortunately, the antenna exhibit an asymmetry of the radiation pattern on the azimuth. It is observed that the reconfigurability falls off dramatically as the observation angle (φ) moves away from the principal planes. 77

100 E φ E θ Axial Ratio (db) Scheme B : E φ component GHz (φ= o ) 4 5 w1=.79 m w1=.237 m Scheme B : E θ component GHz (φ= o ) w1=.79 m w1=.237 m Scheme B : Axial Ratio GHz (φ= o ) w1=.79 m w1=.237 m γ (Degree) Figure 3.17: Example 3 (Scheme B) : Antenna radiation pattern and axial ratio versus angle at L1 band The investigation on the asymmetry of the pattern is done in the same fashion as the single band antenna case. In the case of the single band antenna considered in Chapter 2, the pattern radiated from just the patch by itself on the square substrate is found to be fairly symmetric on any azimuthal plane, hence the shape of only the parasitic structure and the ground plane is modified to provide the desired symmetry. However in the dual band multilayer antenna, it is found that the patterns of just the radiating patches by themselves for the two frequencies on the square substrates are asymmetric as depicted in Figure Hence the square substrate is not suitable for this application, and replaced by the octagonal substrate. Figure. 3.2 describes the radiation patterns of the dual band antenna with mounted on the octagonal dielectric substrate. It is clear that the antenna radiates a fairly symmetric pattern. Along the 78

101 E φ Scheme B : E φ component GHz (φ= o ) w1=.79 m w1=.237 m Scheme B : E θ component GHz (φ= o ) E θ w1=.79 m w1=.237 m Axial Ratio (db) Scheme B : Axial Ratio GHz (φ= o ) w1=.79 m w1=.237 m γ (Degree) Figure 3.18: Example 3 (Scheme B) : Antenna radiation pattern and axial ratio versus angle at L2 band horizon direction, the maximum field variations of.3 db and 1.5 db are secured at the L1 and L2 bands, respectively. For this purpose, the octagonal substrate is a suitable candidate for our proposed dual band antenna. 3.6 Description of New Antenna Geometry Basic Geometry The new geometry of the three layer dual band antenna is shown in Figure The dielectric substrate profile as well as the radiating patch dimensions remain unchanged from the initial designs. However, the shape of all substrate layers is octagonal, in order to provide an azimuthally symmetric pattern. The antenna has a complete ground plane, unlike that of the single band antenna. The initial substrate 79

102 E φ of the Dual Band Antenna with Square Substrate at the L1 Frequency 5 E θ of the Dual Band Antenna with Square Substrate at the L1 Frequency E φ φ= φ=15 φ=3 φ=45 φ=6 φ=75 φ=9 E θ θ (Degree) θ (Degree) E φ of the Dual Band Antenna with Square Substrate at the L2 Frequency E θ of the Dual Band Antenna with Square Substrate at the L2 Frequency E φ 1 15 E θ θ (Degree) θ (Degree) Figure 3.19: Calculated radiation pattern of the dual band antenna with a square substrate at GHz and GHz. 8

103 E φ of the Dual Band Antenna with Octagonal Substrate at the L1 Frequency 5 E θ of the Dual Band Antenna with Octagonal Substrate at the L1 Frequency E φ φ= φ=15 φ=3 φ=45 φ=6 φ=75 φ=9 E θ θ (Degree) θ (Degree) E φ of the Dual Band Antenna with Octagonal Substrate at the L2 Frequency E θ of the Dual Band Antenna with Octagonal Substrate at the L2 Frequency E φ 1 15 E θ θ (Degree) θ (Degree) Figure 3.2: Calculated radiation pattern of the dual band antenna with an octagonal substrate at GHz and GHz. 81

104 Figure 3.21: New proposed geometry of a dual band antenna. size was chosen to be mm mm initially, but this size is inadequate to locate the switching ring far enough away so that it does not affect the pattern of the L1 and L2 patches and still be sufficiently wide to influence the pattern of the L1 patch. Hence a substrate with larger dimensions, mm mm is chosen for this application Parasitic Structure and Switching Circuitry Design The dual band reconfigurable antenna is initially aimed to provide pattern reconfigurability of the vertical electric field component, E θ, at the L1 band. The reconfigurability is obtained again through the use of two different states of the parasitic structure, similar to the single band antenna. After an intensive parametric 82

105 study, the two states of the parasitic structure are secured, a solid octagonal ring and a loaded octagonal ring, i.e. a solid ring with four extra strips as shown in Figure In addition to the ring located on the top layer, another parasitic solid ring is inserted on the middle layer. Note that the dimension of the lower parasitic ring is identical to that of the top solid ring, and no switch is loaded on the lower ring. Nonetheless, this lower ring has a bearing on the reconfigurability obtained, as it provides a stronger induced surface current on the top ring. The new proposed design can provide nearly 7-8 db drop in the vertical electric field component along the horizon as seen in Figure The approach to arriving at the two states of the ring is based on designing the ring by itself whose radiation pattern cancelling out the pattern radiated by the antenna with no ring along the horizon at GHz. After securing the solid ring, it is subsequently loaded with four extra strips to alter the phase of the diffracted surface wave, and thus the radiation pattern at the L1 band. As a result, the pattern radiated by the loaded ring by itself will not cancel out the pattern radiated by the antenna with no ring along the horizon region anymore. It is to be noted that an extensive parametric study on the strip dimension was conducted, in order to obtain the desired reconfigurability. The next task is to integrate to switching circuitry to the initial parasitic ring designs described in Figure The switch-loaded ring must try to imitate the same current distribution as shown in the solid and loaded ring cases, while maintaining the same reconfigurability described in Figure It is however clear that there is no conducting strip on the rings for inserting the diode switches. Hence, the ring geometry is remodified to resolve this issue. By inspecting the surface current 83

106 distribution induced on the solid and loaded rings, we can redesign the parasitic structures. The loaded ring can be emulated by adding some vertical and horizontal strips to the solid ring until the antenna pattern is similar or getting close to the pattern radiated by the antenna with loaded ring. Further, those small strips will be cut such that its current distribution, and thus the radiation pattern, at the L1 band are similar to those of the solid ring case. As a result, Figure 3.24 shows the modified ring configurations. Their corresponding radiation patterns is also presented in Figure It is certain that we can obtain the same reconfigurability ( 7-8 db) along the horizon region as described in It is also worth noting that the cut positions on both vertical and horizontal strips are the potential locations of the diode switches. Finally, design of the switching circuitry was conducted in a similar fashion as described in the single band antenna case. The final design of the dual band antenna and the parasitic structure are illustrated in Figures 3.26 and 3.27, respectively. Figures 3.28, 3.29 and 3.3 illustrate the radiation patterns and axial ratio of the dual band antenna at GHz on several elevation planes, φ =, 15, 3, 45, 6 and 9. It can be seen from Figure 3.28 that nearly a 6-8 db drop in E θ is obtained by activating the switches loaded on the parasitic ring. However, the horizontal field component, E φ, remains mostly unchanged between the two operational states of the switches, on and off. The dual band antenna also reveals an excellent axial ratio especially when all switches are turned off. The axial ratio remains less than 3 db for θ 7 on most elevation planes. Likewise, Figures 3.31, 3.32 and 3.33 illustrate the radiation patterns and axial ratio of the dual band antenna at GHz on several elevation planes, φ =, 15, 3, 45, 6 and 9. In this case, both E θ 84

107 and E φ remain almost the same between the two states of the switches. In addition, the axial ratio remains less than 3 db for θ 6 on most elevation planes. (a) Antenna with solid ring (b) Antenna with loaded ring Figure 3.22: Geometry of the dual band antenna surrounded by (a) a full octagonal parasitic ring (b) loaded parasitic ring. 3.7 Measured Results and Discussions This section llustrates the geometry of the implemented pattern reconfigurable dual band antenna, as well as its corresponding measured radiation patterns at both the L1 and L2 bands. Figure 3.34 through Figure 3.36 depict the top, middle, and bottom substrates of the implemented dual band antenna, respectively. It can be seen that only the switch-loaded parasitic ring is located on the top layer. Whereas the middle substrate contains both the radiating patch for the L1 band and another parasitic ring having same dimension as the ring located on the top layer. Remind 85

108 15 2 E θ with Octgonal Substrate at φ= (L1 Band) E θ with Octgonal Substrate at φ=9 (L1 Band). E θ Loaded Ring Solid Ring E θ Loaded Ring Solid Ring E θ with Octgonal Substrate at φ=15 (L1 Band) E θ with Octgonal Substrate at φ=3 (L1 Band). E θ Loaded Ring Solid Ring E θ Loaded Ring Solid Ring E θ with Octgonal Substrate at φ=45 (L1 Band) E θ with Octgonal Substrate at φ=6 (L1 Band). E θ Loaded Ring Solid Ring θ (Degree) E θ Loaded Ring Solid Ring θ (Degree) Figure 3.23: Calculated radiation pattern of the dual band antenna with a octagonal substrate. The antenna is surrounded by a (a) full octagonal parasitic ring (b) loaded parasitic ring. 86

109 (a) Antenna with cut strips (b) Antenna with uncut strips Figure 3.24: Geometry of the dual band antenna surrounded by a full octagonal parasitic ring loaded with (a) cut strips (b) uncut strips. that no switch is loaded on the lower ring. In addition, only the radiating patch for the L2 band is located on the bottom substrate as described in Figure Impedance Characteristics After glueing each substrate together, the input impedance of each patch is measured. However, it is later found out that there is a small shift in the resonances of both radiating patches. The drift in resonances may arise from either the air gap at the interface of each layer, created during the glueing process, or the change in effective dielectric constant of the substrate due to the expoxy used for attaching each substrate. As a results, the patch dimensions must be slightly modified. The upper patch dimension is increased from mm to 32 mm, while that of the lower patch is changed from 5.56 mm to 52 mm. Figure 3.37 and Figure 3.38 show the return loss of the four ports on the upper and lower patches, respectively. It is 87

110 E θ with Octgonal Substrate at φ= (L1 Band). E θ with Octgonal Substrate at φ=9 (L1 Band) E θ Ring with Uncut Strips Ring with Cut Strips E θ Ring with Uncut Strips Ring with Cut Strips E θ with Octgonal Substrate at φ=15 (L1 Band). E θ with Octgonal Substrate at φ=3 (L1 Band) E θ Ring with Uncut Strips Ring with Cut Strips E θ Ring with Uncut Strips Ring with Cut Strips E θ with Octgonal Substrate at φ=45 (L1 Band). E θ with Octgonal Substrate at φ=6 (L1 Band) E θ Ring with Uncut Strips Ring with Cut Strips E θ Ring with Uncut Strips Ring with Cut Strips θ (Degree) θ (Degree) Figure 3.25: Calculated radiation pattern of the dual band antenna with a octagonal substrate. The antenna is surrounded by a full octagonal parasitic ring (a) with cut strips (b) with uncut strips. 88

111 Figure 3.26: Geometry of the proposed dual band antenna. The antenna is surrounded by the switch-loaded octagonal parasitic ring. The radiating elements are mounted on the thick substrate which is used for surface wave excitation. clear that both patches demonstrate minimum return losses approximately right at their frequencies of operation, GHz and GHz. Also not shown here, it is demonstrated through computer simulations and measurement that by activating the switches loaded on the parasitic ring, the resonance of the L1 and L2 patches are slightly modified by only a few MHz Radiation Characteristics The measured radiation patterns at the L1 and L2 bands are presented in this subsection. Figure 3.39 shows a measured gain pattern of the vertical field component, G θ, at GHz on four elevation planes;, 45, 9 and 135. It is obvious that by activating the switches, the reconfigurability around the horizon region is obtained in the order of 3-4 db. Similarly, Figure 3.4 displays a measured gain pattern of the 89

112 Figure 3.27: Schematic representation of the switching circuit component loaded on the solid ring. horizontal field component, G φ, on the same elevation planes;, 45, 9 and 135. As expected, the G φ remains mostly unchanged between the two operational states of the switch. In addition, the measured axial ratio matches the simulations fairly well and indicates that it strongly depends on the state of the switch operation as depicted in Figures

113 E θ with Octgonal Substrate at φ= (L1 Band). E θ with Octgonal Substrate at φ=15 (L1 Band) Switch On Switch Off 3 25 Switch On Switch Off E θ E θ E θ with Octgonal Substrate at φ=3 (L1 Band). E θ with Octgonal Substrate at φ=45 (L1 Band) Switch On Switch Off 3 25 Switch On Switch Off E θ E θ E θ with Octgonal Substrate at φ=6 (L1 Band). E θ with Octgonal Substrate at φ=75 (L1 Band) Switch On Switch Off 3 25 Switch On Switch Off E θ E θ θ (Degree) θ (Degree) Figure 3.28: Calculated radiation pattern of the dual band antenna with a octagonal substrate at GHz. 91

114 E φ with Octgonal Substrate at φ= (L1 Band). E φ with Octgonal Substrate at φ=15 (L1 Band) Switch On Switch Off 3 25 Switch On Switch Off E φ E φ E φ with Octgonal Substrate at φ=3 (L1 Band). E φ with Octgonal Substrate at φ=45 (L1 Band) Switch On Switch Off 3 25 Switch On Switch Off E φ E φ E φ with Octgonal Substrate at φ=6 (L1 Band). E φ with Octgonal Substrate at φ=75 (L1 Band) Switch On Switch Off 3 25 Switch On Switch Off E φ E φ θ (Degree) θ (Degree) Figure 3.29: Calculated radiation pattern of the dual band antenna with a octagonal substrate at GHz. 92

115 2 Axial Ratio of the Dual Band Antenna at φ= (1.575 GHz) 2 Axial Ratio of the Dual Band Antenna at φ=15 (1.575 GHz) AR 15 1 Switch On Switch Off AR 15 1 Switch On Switch Off Axial Ratio of the Dual Band Antenna at φ=3 (1.575 GHz) 2 Axial Ratio of the Dual Band Antenna at φ=45 (1.575 GHz) AR 15 1 Switch On Switch Off AR 15 1 Switch On Switch Off Axial Ratio of the Dual Band Antenna at φ=6 (1.575 GHz) 2 Axial Ratio of the Dual Band Antenna at φ=75 (1.575 GHz) AR 15 1 Switch On Switch Off AR 15 1 Switch On Switch Off θ (Degree) θ (Degree) Figure 3.3: Calculated axial ratio of the dual band antenna with a octagonal substrate at GHz. 93

116 E θ with Octgonal Substrate at φ= (L2 Band). E θ with Octgonal Substrate at φ=15 (L2 Band) E θ Switch On Switch Off E θ Switch On Switch Off E θ with Octgonal Substrate at φ=3 (L2 Band). E θ with Octgonal Substrate at φ=45 (L2 Band) E θ Switch On Switch Off E θ Switch On Switch Off E θ with Octgonal Substrate at φ=6 (L2 Band). E θ with Octgonal Substrate at φ=75 (L2 Band) E θ Switch On Switch Off E θ Switch On Switch Off θ (Degree) θ (Degree) Figure 3.31: Calculated radiation pattern of the dual band antenna with a octagonal substrate at GHz. 94

117 E φ with Octgonal Substrate at φ= (L2 Band). E φ with Octgonal Substrate at φ=15 (L2 Band) E φ Switch On Switch Off E φ Switch On Switch Off E φ with Octgonal Substrate at φ=3 (L2 Band). E φ with Octgonal Substrate at φ=45 (L2 Band) E φ Switch On Switch Off E φ Switch On Switch Off E φ with Octgonal Substrate at φ=6 (L2 Band). E φ with Octgonal Substrate at φ=75 (L2 Band) E φ Switch On Switch Off E φ Switch On Switch Off θ (Degree) θ (Degree) Figure 3.32: Calculated radiation pattern of the dual band antenna with a octagonal substrate at GHz. 95

118 2 Axial Ratio of the Dual Band Antenna at φ= (1.227 GHz) 2 Axial Ratio of the Dual Band Antenna at φ=15 (1.227 GHz) AR 15 1 Switch On Switch Off AR 15 1 Switch On Switch Off Axial Ratio of the Dual Band Antenna at φ=3 (1.227 GHz) 2 Axial Ratio of the Dual Band Antenna at φ=45 (1.227 GHz) AR 15 1 Switch On Switch Off AR 15 1 Switch On Switch Off Axial Ratio of the Dual Band Antenna at φ=6 (1.227 GHz) 2 Axial Ratio of the Dual Band Antenna at φ=75 (1.227 GHz) AR 15 1 Switch On Switch Off AR 15 1 Switch On Switch Off θ (Degree) θ (Degree) Figure 3.33: Calculated axial ratio of the dual band antenna with a octagonal substrate at GHz. 96

119 Figure 3.34: Geometry of the implemented pattern reconfigurable dual band antenna: top layer. Figure 3.35: Geometry of the implemented pattern reconfigurable dual band antenna: middle layer. 97

120 Figure 3.36: Geometry of the implemented pattern reconfigurable dual band antenna: bottom layer. Magnitude and Phase Response of the Return Loss on the Upper Patch S ii Upper Patch (db) Port 1 Port 2 Port 3 Port Frequency (Hz) x /S ii (Degree) Frequency (Hz) x 1 9 Figure 3.37: Measured input impedance of the upper radiating patch. 98

121 Magnitude and Phase Response of the Return Loss on the Lower Patch S ii Lower Patch (db) 5 1 Port1 Port 2 Port 3 Port Frequency (Hz) x /S ii (Degree) Frequency (Hz) x 1 9 Figure 3.38: Measured input impedance of the lower radiating patch. 99

122 Measured G θ at φ= (L1 Band) Measured G θ at φ=45 (L1 Band) 5 Switch On Switch Off 5 Switch On Switch Off G θ 5 1 G θ θ (Degree) θ (Degree) Measured G θ at φ=9 (L1 Band) Measured G θ at φ=135 (L1 Band) 5 Switch On Switch Off 5 Switch On Switch Off G θ 5 1 G θ θ (Degree) θ (Degree) Figure 3.39: Measured G θ pattern of the dual band antenna at the L1 band. 1

123 Measured G φ at φ= (L1 Band) Measured G φ at φ=45 (L1 Band) 5 Switch On Switch Off 5 Switch On Switch Off G φ 5 1 G φ θ (Degree) θ (Degree) Measured G φ at φ=9 (L1 Band) Measured G φ at φ=135 (L1 Band) 5 Switch On Switch Off 5 Switch On Switch Off G φ 5 1 G φ θ (Degree) θ (Degree) Figure 3.4: Measured G φ pattern of the dual band antenna at the L1 band. Likewise, Figures 3.42 and 3.43 represent the measured G θ and G φ at GHz on four elevation planes;, 45, 9 and 135. As anticipated, both antenna gain patterns remain nearly identical between the two states of the switch operation, on and off. Measured axial ratio is also depicted in Figure

124 2 Measured Axial Ratio (db) at φ= (L1 Band) 2 Measured Axial Ratio (db) at φ=45 (L1 Band) Switch On Switch Off Switch On Switch Off AR AR θ (Degree) θ (Degree) Measured Axial Ratio (db) at φ=9 (L1 Band) Switch On Switch Off Measured Axial Ratio (db) at φ=135 (L1 Band) Switch On Switch Off AR AR θ (Degree) θ (Degree) Figure 3.41: Measured axial ratio of the dual band antenna at the L1 band. 12

125 Measured G θ at φ= (L2 Band) Measured G θ at φ=45 (L2 Band) 5 Switch On Switch Off 5 Switch On Switch Off G θ 5 1 G θ θ (Degree) θ (Degree) Measured G θ at φ=9 (L2 Band) Measured G θ at φ=135 (L2 Band) 5 Switch On Switch Off 5 Switch On Switch Off G θ 5 1 G θ θ (Degree) θ (Degree) Figure 3.42: Measured G θ pattern of the dual band antenna at the L2 band. 13

126 Measured G φ at φ= (L2 Band) Measured G φ at φ=45 (L2 Band) 5 Switch On Switch Off 5 Switch On Switch Off G φ 5 1 G φ θ (Degree) θ (Degree) Measured G φ at φ=9 (L2 Band) Measured G φ at φ=135 (L2 Band) 5 Switch On Switch Off 5 Switch On Switch Off G φ 5 1 G φ θ (Degree) θ (Degree) Figure 3.43: Measured G φ pattern of the dual band antenna at the L2 band. It is shown through the measurement that only a 3-4 db reconfigurability in G θ is secured along the end-fire direction. This is clearly a few db lower from what simulation predicts. Nevertheless, by examining at the measured pattern when all the switch components are removed, we found nearly a 5-6 db reconfigurability in G θ between the uncut and cut strip cases (see Figures ). The decrease in reconfigurability, thereby, arises from the switching circuit. Design of the switching circuit is certainly required to be modified in order to achieve more reconfigurability in the G θ component along the horizon. 14

127 2 18 Measured Axial Ratio (db) at φ= (L2 Band) Switch On Switch Off 2 18 Measured Axial Ratio (db) at φ=45 (L2 Band) Switch On Switch Off AR AR θ (Degree) θ (Degree) 2 18 Measured Axial Ratio (db) at φ=9 (L2 Band) Switch On Switch Off 2 18 Measured Axial Ratio (db) at φ=135 (L2 Band) Switch On Switch Off AR AR θ (Degree) θ (Degree) Figure 3.44: Measured axial ratio of the dual band antenna at the L2 band. 15

128 5 Measured G θ (db) at φ= (L1 Band) Cut Strips Uncut Strips 5 G θ (db) θ (Degree) Figure 3.45: Measured G θ pattern of the dual band antenna at the L1 band. Note all the switching components are removed. 16

129 5 Measured G φ (db) at φ= (L1 Band) Cut Strips Uncut Strips 5 G φ (db) θ (Degree) Figure 3.46: Measured G φ pattern of the dual band antenna at the L1 band. Note all the switching components are removed. 3.8 A Summary and Conclusions In the work reported here we addressed issues concerning the design and analysis of a dual band, circularly polarized, reconfigurable printed antenna for the GPS application. We proposed novel reconfigurable dual band stacked patch antennas for GPS application. They consist of a three layer stacked microstrip patches with two radiating patches in the bottom two layers. The upper radiating patch is designed for L1 band, while the lower one is designed to operate at L2 band. Two parasitic rings are located in the middle and top layers. It is demonstrated through both simulation and measurement that approximately a 3-5 db drop in the vertical electric field component, E θ, along the region of interest is achieved. 17

130 2 18 Measured Axial Ratio (db) at φ= Cut Strips Uncut Strips Measured AR θ (Degree) Figure 3.47: Measured axial ratio of the dual band antenna at the L1 band. Note all the switching components are removed. 18

131 CHAPTER 4 DEVELOPMENT OF THE TIME DOMAIN METHOD OF CHARACTERISTIC MODES FOR THE ANALYSIS AND DESIGN OF ANTENNAS 4.1 Introduction Most antenna design and analysis are usually done using simple design formula or purely numerical techniques, such as finite difference time domain (FDTD), method of moment (MoM), finite element method (FEM), etc. Although these methods are very accurate, unfortunately, they don t offer as much physical insight to the behavior of the antennas such as resonances, current distributions, and their corresponding radiation patterns. Owing to its advantage of giving clear physical insight to the behavior of antennas, Theory of Characteristic Modes, first introduced by Garbacz [4, 6] and then refined by Harrington [9, 1], has been long used in many applications such as analysis of radiation and scattering [2, 19], antenna shape synthesis [5, 18] and radiation pattern synthesis [11]. Characteristic modes are defined as a set of real current on the surface of a conducting body that depend only on its geometry, but are independent of any specific source or excitation. Associated with each characteristic mode is a real characteristic value or eigenvalue, λ n. The magnitude of the eigenvalue indicates 19

132 how well that particular mode radiates. Modes with small λ n are good radiators, whereas those with large λ n are poor radiators. The closer the eigenvalue is to zero, and accordingly to resonance, the more significant is its contribution to the total radiation pattern. Relevant information about antennas resonant behavior can also be secured by examining characteristic modes variation with frequency. The conventional approach for computing the characteristic modes has been realized thus far only in the frequency domain. The calculation of the resonances is, nevertheless, considerably time consuming, as we need to sweep the frequency and observe the eigenvalue for each particular mode. In this dissertation we develop an alternative method for computing the characteristic modes employing the finite difference time domain (FDTD) technique. The proposed technique provides a major advantage over the conventional one in that wide-band spectrum calculations are possible from only one FDTD run, as a result, the antenna resonances could be captured from just a single FDTD run. The work described here is divided into two chapters covering several aspects including a brief overview on the characteristic modes, the new proposed method for computing the characteristic modes, as well as some numerical results. Background on the characteristic modes is given in Section 4.2. The alternative method for calculating the characteristic modes is proposed in Section 4.3. In Chapter 5, we compute the resonances as well as the characteristic currents and patterns using the proposed method for various antenna types. To assess the validation of the proposed technique, simulated results are thereby compared to the analytical solutions. An excellent agreement between the resonances and the current modes obtained from the FDTD simulations 11

133 and the theoretical values is achieved for all cases. A conclusion is finally carried out at the end of this dissertation. 4.2 Characteristic Modes To appreciate the idea of the characteristic modes, we shall simply discuss a fundamental example such as a rectangular cross section waveguide of lateral dimension of a and b as exhibited in Figure 4.1. It is a hollow metallic tube of infinite length in z direction. The fields existing within this waveguide are characterized by the zero tangential components of E on the four conducting walls. Without loss of generality, it is assumed that only the transverse magnetic (TM z ) modes exist inside the waveguide in this example. The total field inside the waveguide could be expressed as an infinite summation of each modal field, E n, as shown in (4.1) E = n a n E n (4.1) where a n is the strength of each modal field, E n. Since the waveguide is bound in the x and y directions, each mode must represent a standing wave in both directions. The field configurations (modes) that can exist inside the guide depend on the boundary conditions imposed by the geometry of such structure, and hence can be expressed as (4.2) and (4.3). E x = j 2 A z ωµɛ x z E y = j 2 A z ωµɛ y z E z = j ωµɛ ( 2 + β 2 )A z 2 z (4.2) 111

134 H x = 1 A z µ y H y = 1 A z µ x H z = where A z (x, y, z) = B mn sin(β x x) sin(β y y)e jβzz (4.3) β x = 2π = mπ λ x a m = 1, 2, 3... (4.4) β y = 2π λ y = nπ b n = 1, 2, 3... (4.5) In (4.4) and (4.5), β x and β y represent the mode wave number in x and y directions, respectively. These permissible values of β x and β y are referred to as the eigenvalues or characteristic values of the structure. It is worth noting that each modal field has a distinct cut off frequency (or resonance), (f c ) mn, as described in (4.6). (f c ) mn = 1 2π ( mπ µɛ a )2 + ( nπ b )2 (4.6) The set of these infinite modal field configurations is referred to as the natural modes or the characteristic modes of the structure. Although, the example mentioned earlier is an interior or cavity problem, the theory of characteristic mode is applicable to any exterior or antenna problem as well. As briefly described in Section 4.1, characteristic modes are defined as a set of the real currents induced on the surface of the conducting bodies. These current 112

135 Y b X Z a Figure 4.1: Geometry of a rectangular cross section waveguide. The waveguide is of infinite length in the z direction. modes only depend upon the geometry of the bodies, and are independent of any specific source or excitation of the systems. Furthermore, these modes form a closed and orthogonal set (for lossless case) that can be used to expand the total current. Hence the total current, J, on the conducting surfaces can be expressed as a modal summation of each characteristic mode, J n, as shown in (4.7). J = n α n J n (4.7) where α n are the modal strengths that needed to be determined. These unknown coefficients are related and controlled by some real numbers, namely the characteristic values or eigenvalues, λ n. The magnitude of λ n determines how well that particular mode radiates. Modes with small λ n are good radiators, whilst those with large λ n are poor radiators. The closer the eigenvalue is to zero, and accordingly to resonance, the more significant is its contribution to the total radiation pattern. Computation of α n will be demonstrated later in this section. The electric field E s n radiated by 113

136 the eigencurrent, J n will be called the characteristic field or eigenfield. The field is linearly related to the current, and hence can also be described in modal summation as shown in (4.8). E = n α n E s n (4.8) Note that the scattered fields also form an orthogonal set in the Hilbert space of all square-integrable vector function over the sphere at infinity. The orthogonality relationship between the current and scattered field over the conducting surface is given in (4.9). J m, E s n = (1 + jλ n )δ mn (4.9) where δ mn is the Kronecker delta ( 1 if m=n, and if m n ). Keep in mind that the inner product shown in (4.9) is based on the assumption that each current mode radiated a unit power scattered field. The computation of the α n derives from the boundary condition on the conducting surfaces, that is the tangential component of the total electric field vanishes on the conducting surfaces. The total field in fact composes of the scattered field, E s (ω), and the known incident field, E i (ω), as described in (4.1). (E s (ω) + E i (ω)) tan = (4.1) The total scattered field is a linear superposition of each scattered field, E s n, produced by each eigencurrent, J n, as expressed in (4.8), and thus, 114

137 ( n α n E s n(ω) + E i (ω)) tan = (4.11) By applying the inner product of J m to (4.11) and using the orthogonality mentioned in (4.9), α n can consequently be determined as shown in (4.13). Note that the numerator of (4.13) is called modal excitation coefficient [1]. α n J m, E s n(ω) + J m, E i (ω) = (4.12) n α n = J n, E i (ω) J n, E s n(ω) = V n i (4.13) 1 + jλ n As a result, the modal expression of the total current on the conducting surface is shown below. J = n V i nj n 1 + jλ n (4.14) Clearly from (4.14), the strength of each mode mainly depends upon two factors. The first one is the modal excitation coefficient, V i n, which depends strongly on the excitation of the structure. The second factor is the eigenvalue, λ n. Obviously, the smaller the λ n becomes, the stronger the contribution to the total current is obtained from that particular current mode. Note that λ n ranges from to + as frequency varies. However λ n approaches zero as the frequency gets close to the resonance of that particular mode. 4.3 Computation of Characteristic Modes A novel technique for computing the characteristic modes is proposed here. To the best of our knowledge the calculation of the characteristic modes has been performed 115

138 thus far only in the frequency domain. A conventional method, proposed by [8], is first briefly reviewed. An alternative technique for computing the characteristic modes will be performed in the time domain using the finite difference time domain (FDTD) method. The procedure as well as its advantages over the conventional method are explained in more detail in the section Conventional Method The computation of the characteristic modes for the conducting bodies has been realized only in the frequency domain by diagonalizing the operator, free space Green s function L, relating the induced current to the tangential electric field on the conducting bodies. Calculation of the characteristic modes initiates from the boundary condition on the conducting surfaces, that is the tangential component of the total electrical field must be zero. As described in (4.1), the total field consists of the known incident field and the scattered field. The scattered field is computed from the free space Green s function, L, operating on the current induced on the conducting bodies as represented in (4.15). Since this operator is symmetric, its hermitian parts, R and X are also real and symmetric operators as shown in (4.16). E s tan = [L(J)] tan (4.15) L tan = Z = R + jx (4.16) X (J n ) = λ n RJ n (4.17) 116

139 We shall now consider the generalized eigenvalue equation of the Z operator, which could be expressed in numerous ways. However, by choosing a particular weighted eigenvalue equation, Harrington [8] simplified (4.17) as the generalized eigenvalue equation for the conducting bodies due to the fact that the scattered fields also form an orthogonal set over the sphere at infinity. This generalized eigenvalue equation is subsequently converted into a matrix equation using the method of moment (MoM) technique as illustrated in (4.18). The eigencurrents as well as the eigenvalues of the structures are computed by diagonalizing the proposed matrix equation. The resonant frequency of each current mode can be found by examining its eigenvalue variation with frequency. Since we know that an eigenvalue, λ n, approaches zero at when the frequency gets close to the resonance of that corresponding mode. The traditional method is summarized in Figure 4.2. [X][J n ] = λ n [R][J n ] (4.18) Form a matrix equation using MM Eigencurrents J n and Eigenvalues λ n Sweep frequency for resonances Figure 4.2: The conventional algorithm for calculating the characteristic modes. This approach is performed in the frequency domain using the method of moment (MoM) technique 117

140 4.3.2 Proposed Method The new proposed method for computing the characteristic modes will be implemented in the time domain using the FDTD technique. The three dimensional FDTD method is a general and straight forward implementation of Maxwell s equations and provides a rigorous solution to a variety of electromagnetic wave problems. The major advantage of the proposed method is that the wide-band spectral calculations are possible from just a single FDTD run. Computation of the Resonances and Characteristic Modes In typical, two types of source excitation are employed in FDTD simulations ; (a) source excitation with imposed time dependence and (b) initial conditions with no time dependence. For source excitation technique, the source amplitude is determined at every time step according to a specified function, normally a sinusoidal with pulse envelope or a CW signal. The most common spatial source types are point current sources (such as dipoles) or input waves (such as plane waves, Gaussian beams and waveguide mode). Whereas, the initial condition excitation is time independent. The fields is initially defined over the computational domain at t= and let time dependence emerges through time-stepping. Notice that the initial fields are usually obtained by previous simulation or approximation method. To calculate a spectral response, structures should be therefore exposed to a very wide-band excitation. To do so, the initial conditions on the electric fields in the entire computational domain are generated with random numbers of a uniform distribution. This is equivalent to exciting the structure with a very wide-band signal. Figure 4.3(a) and Figure 4.3(b) show a sequence of random numbers of uniform distribution and its 118

141 corresponding frequency spectrum, respectively. Note that the spectral components are found by performing a the Discrete Fourier Transform (DFT) of these random numbers. It is clear from Figure 4.3(b) that a wide-band excitation is secured using the method mentioned above. After initializing the domain, the fields are then updated using a normal time stepping FDTD algorithm. However, as time marches on, we record the time varying waveforms, either the surface currents on the conducting bodies or the fields inside the structure and simultaneously perform the DFT of these time varying signals to obtain their frequency responses. The resonances of the structure are assumed to occur at the spectral peaks. Keep in mind that it is not guaranteed that all the resonances of the structure will be captured from just a single FDTD run, thus in order to minimize the error of predicting the resonances, several FDTD runs are performed with different seed numbers for random number generations. In addition, various observation or monitoring points are required to ensure that all the resonant modes are captured. In order words it is possible that the time domain waveform is sampled at a null of that particular mode, resulting in a weak DFT spectrum. It is worth noting that by combining these DFT spectra obtained from several monitoring point, cleaner spectrum peaks can be obtained. Once the resonances are determined, the characteristic modes can be captured in two ways. They can be directly obtained from the original FDTD run initiated with the random initial condition. contaminated with other modes. However we found the modes to be somewhat The scheme we are currently using is based on the source excitation technique. For this intention, at each resonant frequency, the 119

142 structure is illuminated with a narrow band signal such as sinusoidal with pulse envelope, i.e. a Gaussian pulse with a sinusoidal carrier at center frequency of interest. These narrow band signal are intentionally chosen to compute time-averaged quantities and fields at one particular frequency. Figure 4.4(a) shows a time signature of a Gaussian pulse with sinusoidal carrier at center frequency of interest. Furthermore, Figure 4.4(b) depicts DFT spectrum of the corresponding signal. As shown, the excitation is contained mostly to the frequency of interest. It is worth noting that we need to illuminate the structure with a narrow band signal in every polarization just to ensure that the characteristic mode is completely and correctly captured. The new proposed technique for computing the resonances and the characteristic modes is summarized in Figure 4.5. To demonstrate the use of the proposed method, let us apply the method to a simple structure such a microstrip antenna with air substrate as depicted in Figure 4.6. The resonances of the antenna as well as the first characteristic mode are calculated using the method mentioned above as displayed in Figure 4.7(a) and Figure 4.7(b), respectively. The computed resonant frequencies are then compared to an analytical solutions, and an excellent agreement is established. Computation of the Scattered and Incident field The procedure for computing the scattered electric field is given here. The scattered field, E s n, is in fact the field radiated by each current mode, J n. Computation of the scattered field initiates from replacing a structure with calculated current mode, J n. In order to obtain its impulse response, J n is thereby excited with a Gaussian pulse, a wide band spectral signal. The scattered field on the conducting body can be captured using the same DFT technique mentioned in the preceding subsection. Further, the eigenfield or the far field scattered field is computed using the equivalence 12

143 2 A sequence of random numbers of uniform distribution 1 9 Random Number Spectrum of Random Number Index (n) Frequency (GHz) (a) A sequence of random numbers of uniform distribution. (b) and its corresponding frequency spectrum. Figure 4.3: A sequence of random numbers of uniform distribution and its corresponding spectral calculation Excitation Spectrum of Excitation Signal Time (s) x Frequency (GHz) (a) A Gaussian pulse with a sinusoidal carrier at the center frequency of interest (b) and its corresponding frequency spectrum. Figure 4.4: A time signature of a Gaussian pulse with sinusoidal carrier at center frequency of interest and its corresponding spectral calculation. 121

144 Initialize volumetric E field with random numbers of uniform distribution (wide band excitation). Determine the resonant frequencies Update H and E fields using FDTD Save and DFT the current/fields inside structure to capture the resonances. Peaks on DFT spectra are the resonances of the structure. Capture the current mode At each resonant frequency, illuminate the structure with narrow band excitation (sinusoidal signal). Save and DFT J n at each resonance. Figure 4.5: Proposed algorithm for calculating the characteristic modes. This novel method is performed in the time domain using the finite difference time domain (FDTD) technique theorem along with a near field to far field transformation. The eigenvalue of each mode could be computed by the inner product of the current, J n, and the scattered field, E s n, over the surface of the conducting bodies. Likewise, the incident field can be computed in a similar fashion. Note that the incident field is realized in the absence of the structure. Consequently, the structure is removed from the computational domain. The same excitation source, used for the scattered field computation, is again turned on in the absence of the structure. The time varying field, E i is recorded and DFT-ed over the surface where the structure was once located. Once E i is known, the modal excitation coefficient can be computed 122

145 z L =15.6 cm Radiating Patch z W =1.4 cm h = 3.17 mm y Ground Plane ε r =1 D2=16.64 cm Radiating Patch x D1 =16.64 cm (a) A microstrip antenna with air substrate Ground Plane (b) Side View ε r =1 y Figure 4.6: Geometry of a microstrip antenna with air substrate. J x (f) nd 3 rd 4 th 5 th 6 th th 8th 7 9 th Location 1 Location 2 Location 3 Location 4 Location Frequency (GHz) J y (f) st 3 rd 4 th 5 th 6 th Frequency (GHz) 8 th y y x x (a) Frequency Spectra of the induced current on the radiating patch. (b) The first current mode on the radiating patch. Figure 4.7: Frequency spectra of the induced current on the radiating patch and the first characteristic mode. 123

146 using (4.13). Computation of the scattered and incident fields is summarized in Figure 4.8 and Figure 4.9, respectively. Replace structure with computed current mode,. J n Excite each J n with Gaussain pluse. Far Field Near Field Use equivalence theorem and near field to far field transformation. over the surface of structure. E s n Save and DFT the scattered field,, J n E s n Compute eigenvalue <, >=1+j λ n Figure 4.8: Proposed algorithm for computing the scattered electric field. Computation of the incident field is realized in the absence of the structure. Excite the source. E i Save and DFT the incident field,, over the surface where the structure was located. V i n J n E i Compute = <, > Figure 4.9: Proposed algorithm for computing the scattered electric field. 124

147 Computation of the Quality Factor Methods for extracting relevant information, such as quality factors and bandwidths, are proposed here. Quality factor, Q n, is often used to characterize electrical resonance circuits and microwave resonators. The parameter is defined as Q n = 2π(stored energy) energy loss per cycle (4.19) In this work, the quality factor could be computed in two distinct approaches. The first algorithm for computing the antenna quality factor could be directly found from the bandwidth of each characteristic mode. In general, the quality factor, Q n, is inversely proportional to the antenna bandwidth, BW. The quality factor is thereby expressed as Q n 1/BW, where BW is the bandwidth of each current mode readily captured from the current spectrum. Based on the optical resonator model, it can be shown that bandwidth of each current mode associates with loss of the resonator. Lossless Resonator has sharp peaks centered at each resonant frequency, resulting in small bandwidths and thus high quality factors. On the other hand, lossy resonator provides wider resonant peaks, and clearly larger bandwidths with smaller quality factors. To better understand this concept, let us examine the modes of a resonator constructed of two parallel, highly reflective, flat mirrors separated by a distance d as shown in Figure 4.1. This simple one dimensional resonator is known as a Fabry- Perot etalon. We shall first consider an ideal resonator whose mirrors are lossless. The resonator modes can be determined by following a wave as it travels back and forth between the two mirrors. A resonant mode is a self reproducing wave, i.e., a 125

148 Figure 4.1: A wave reflects back and forth between the resonator mirrors, a Fabry- Perot etalon resonator. wave that reproduces itself after a single round trip. The phase shift imparted by the two mirror reflections is or 2π, i.e., π at each mirror. Let us now consider a monochromatic plane wave of complex amplitude U o (Figure 4.1) travelling to the right along the axis of the resonator. The wave is later reflected from mirror 2 and propagates back to mirror 1 where it is again reflected. Its amplitude thereby becomes U 1. Similarly, another round trip results in a wave amplitude U 2, and so on and so forth. In addition, their magnitudes are identical because there is no loss associated with the reflection and propagation. The total wave, U, inside the resonator is therefore represented by the infinite sum of phasors of equal magnitude, U = U + U 1 + U 2 + U (4.2) 126

149 It is worth noting that the phase difference of two consecutive phasors imparted by a single round trip of propagation must be ϕ = k2d = 2nπ; n = 1, 2, 3,..., in order to have a build-up of finite power in the resonator. This strict condition on the frequencies of the waves that are permitted to exist inside a resonator is relaxed when the resonator is lossy. In the presence of loss, the phasors are no longer of equal magnitude. The magnitude ratio of two consecutive phasors is the round trip amplitude attenuation factor r introduced by the two mirror reflections and by absorption in the medium. Consequently, U 1 = hu, where h = re jϕ. Likewise, the phasor U 2 is related to U 1 by the same complex factor h, as are all consecutive phasors. The total wave, U, is readily expressed as U = U + U 1 + U 2 + U = U + hu + h 2 U + h 3 U +... = U (1 + h + h 2 + h ) (4.21) = U /(1 h) The intensity of the total wave, U, in the resonator is defined as I = U 2 = U 2 / 1 re jϕ 2 = I /[(1 r cos(ϕ)) 2 + (r sin(ϕ)) 2 ] (4.22) = I /(1 + r 2 2r cos(ϕ)) = I /[(1 r) 2 + 4r sin 2 (ϕ/2)] and thus 127

150 1 Field Intensity of a Fabry Perot Resonator, r=.95 and d=.5 meter.8 Field Intensity (I) Frequency (Hz) x Field Intensity of a Fabry Perot Resonator, r=.75 and d=.5 meter.8 Field Intensity (I) Frequency (Hz) x 1 9 Figure 4.11: Field intensity of a Fabry-Perot resonator as a function of frequency, ν. It is clear that resonator with small loss (large r) shows sharp spectral peaks. I = where I max = U 2 /(1 r) 2 and F = πr 1/2 /(1 r). I max 1 + (2F/π) 2 sin 2 (ϕ/2), (4.23) F is a parameter inversely proportional to the loss associated with the resonator and known as the finesse of the resonator. Small loss results in a large F, and therefore sharp resonant peaks, and vice versa as clearly depicted in Figure Furthermore, Equation 4.23 could be further simplified to obtain the the total field intensity as a function of frequency, ν, as shown in the following equation, I = I max 1 + (2F/π) 2 sin 2 (2dπν/c), (4.24) 128

151 where c is the speed of light. The second method for computing the antenna quality factor is found by postprocessing the eigencurrent. The quality factor, Q n, could be alternatively determined by observing the rate of the stored energy loss, and is defined as Q n = ω n /τ n, where ω n are the resonances of the structure and τ n is the characteristic mode lifetime found from the exponential decay of the envelope of the field radiated by the n th current mode, provided only a single resonance is excited. Note this assumption is based on the optical resonator found in [38]. Calculation of the spectral resonances, ω n, can be done using the same technique proposed earlier. The structure is first exposed to a very wide-band excitation to determine its resonances. To do so, the initial conditions on the electric fields in the entire computational domain are generated with random numbers having a uniform distribution. This is equivalent to exciting the structure with a very wide-band signal. After initializing the domain, the fields are then updated using the well known leapfrog FDTD algorithm. However, at every time step, we record the time waveforms of the surface (conducting surfaces) or volumetric (material bodies) currents of the structure and simultaneously perform the DFT of these time dependent signals to obtain their frequency responses. The resonances, ω n, of the structure are assumed to occur at the spectral peaks. To compute τ n, we first need to determine the characteristic modes of the structure. At each resonant frequency, the structure is illuminated with a narrow band signal such as sinusoidal signals with pulse envelope. These narrow band signals are intentionally chosen to compute fields and/or currents at one particular frequency. The characteristic modes are captured by DFT-ing a time signature of the current on the body of the structure. After securing the characteristic modes, each current 129

152 mode is used as a initial boundary value for the next FDTD run, and the field radiated by this particular current mode is also recorded. Note that τ n is computed from the inverse of the exponential decay of the envelope of the field radiated by the n th current mode. As a result, Q n of each n th current mode can be computed using the formula provided earlier. It is also worth noting that the bandwidth of the mode is inversely proportional to Q n. 13

153 CHAPTER 5 NUMERICAL RESULTS This Chapter primarily focuses on the numerical results, such as resonances, current modes, and their corresponding radiation patterns, obtained using the method presented in the previous chapter. Furthermore, the application of the proposed method to the analysis and design of several structures is also demonstrated and discussed. For this intention, the rectangular cross section waveguide is given as the first example. The resonant frequencies are calculated using the proposed technique and compared to the theoretical solutions. Computation of the resonances and the characteristic modes of several resonant antennas, such as a printed dipole antenna, a microstrip antenna and a reconfigurable antenna, is carried out in this section. Furthermore, a broadband antenna, such as a log periodic antenna, is investigated and discussed at the end of this chapter. 5.1 Rectangular Cross Section Waveguide To assess the validation of our proposed technique, we first apply the method to a simple structure such as the rectangular cross section waveguide described in the section 4.2. Our first intention is to determine the resonances or cut off frequencies of the structure. For the waveguide under consideration, the lateral dimensions are 131

154 a=1 mm, and b=5 mm in length and width, respectively. Without loss of generality, it is assumed that only the T M z modes are excited inside the guide. The DFT spectra of the E z could be found using the same procedure described earlier. Figure 5.1 illustrates the DFT spectra of the E z component at the six distinct monitoring points inside the guide. It can be seen that only a particular set of the spectral E z field component exists inside the waveguide. These frequency components are indeed the resonances of the waveguide. By comparing the simulated resonances to the analytical solutions (Table 5.1), we discover an excellent agreement between the resonances produced by both methods DFT Spectra of the E z component inside the waveguide Location 1 Location 2 Location 3 Location 4 Location 5 Location 6 25 E z (f) Frequency (GHz) Figure 5.1: DFT Spectra of the E z inside the guide. component at six different monitoring points 132

155 Table 5.1: Comparison of the resonances of the rectangular waveguide obtained from the analytical solution and the proposed method. Resonant Modes T M 11 T M 21 T M 31 T M 12 T M 22 Analytical Solution (GHz) Proposed Method (GHz) Resonant Modes T M 32 T M 51 T M 42 T M 13 T M 23 Analytical Solution (GHz) Proposed Method (GHz) Keep in mind that, in this simulation, we are not interested in computing the strength of each resonance. In fact we are focusing on determining the location of the resonant frequencies. It is also worth noting that the strength of each resonance depends not only on the locations of the monitoring points but also on the excitation of the system. Furthermore, sufficient monitoring points are required to ensure that all the resonances are captured. Since the field distribution varies from mode to mode. It is possible that some of the monitoring points might be on the null of that particular mode resulting in a weak DFT spectrum. 5.2 Printed Dipole Antenna The dipole has been chosen for the sake of illustration because it is probably the most familiar type of antenna. It consists of two colinear thin wires each about a quarter of a wavelength long. The gap between them forms the terminal region as depicted in Figure 5.2. In this example, the physical dimension of the printed dipole is 16.5 mm and 6.5 mm in length and width, respectively. The DFT spectra of the 133

156 a = 7.5 mm 5 Ω b = 16.5 mm y x Figure 5.2: Geometry of a printed dipole. current induced on the printed dipole is captured and shown in Figure 5.3. It can be seen that only a discrete set of resonances is captured. Furthermore, the calculated resonances match very well with the analytical ones, i.e., f res (n) = n f, where f is the first resonance of the dipole,.82 GHz in this case, and n = 1, 2, 3,... This formulation is based on the assumption that the dipole is very thin compared to the wavelength. Computation of the resonances is not quite straight forward due to the geometry of the printed dipole. However, our method exhibits an advantage over the conventional way in that it can predict the resonances of the printed dipole more precisely when the dipole is no longer thin compared to the wavelength as shown in this problem. Figure 5.4 to Figure 5.8 portray the first five eigencurrents along with their corresponding eigenpatterns. It can be seen from these figures that the dipole is quite a narrow band antenna, as the eigenfields vary significantly as the frequency changes. 134

157 .3.25 Location 1 Location 2 Location 3 Location 4 Location st 4 th 6 th J y (f).15 2 nd.1 3 rd 5 th Frequency (GHz) Figure 5.3: Frequency spectra of the induced current on the printed dipole. It is clear that the method of characteristic modes can also be used to improve the antenna performance. For instance, it can be applied to synthesize the antenna feeding mechanism such that the printed dipole antenna radiates an ultra wide band pattern. Recall that the contribution from the particular current mode to the total radiation pattern is a function of the incident field or the excitation (see Eqn. 4.13). Wide band excitation could be achieved as long as the proper excitation is employed. In other words, in order to strongly excite any particular mode, the spectral of the incident field should be identical or at least as similar as possible to that of the current mode. To secure the wide band radiation pattern, the spectral of the excitation 135

158 y y x Eigen Field: 1 st Mode (.82 GHz) E θ (db) (a) The 1 st mode γ (Degree) (b) and its corresponding eigenfield. Figure 5.4: The 1 st eigencurrent on the printed dipole antenna and its corresponding eigenfield at.82 GHz Eigen Field: 2 nd Mode (1.74 GHz) E θ (db) x (a) The 2 nd mode γ (Degree) (b) and its corresponding eigenfield. Figure 5.5: The 2 nd eigencurrent on the printed dipole antenna and its corresponding eigenfield at 1.74 GHz. 136

159 y y x Eigen Field: 3 rd Mode (2.53 GHz) E θ (db) (a) The 3 rd mode γ (Degree) (b) and its corresponding eigenfield. Figure 5.6: The 3 rd eigencurrent on the printed dipole antenna and its corresponding eigenfield at 2.53 GHz Eigen Field: 4 th Mode (3.5 GHz) E θ (db) x (a) The 4 th mode γ (Degree) (b) and its corresponding eigenfield. Figure 5.7: The 4 th eigencurrent on the printed dipole antenna and its corresponding eigenfield at 3.5 GHz. 137

160 y x Eigen Field: 5 th Mode (4.44 GHz) E θ (db) (a) The 5 th mode γ (Degree) (b) and its corresponding eigenfield. Figure 5.8: The 5 th eigencurrent on the printed dipole antenna and its corresponding eigenfield at 4.44 GHz. should thereby be somewhat a combination of each current mode. On the other hand, it is very difficult to obtain a good input impedance over a wide frequency range. Design of the ultra wideband antennas is obviously a trade off between the radiation performance and the impedance characteristic. 5.3 Air Dielectric Patch Antenna A microstrip antenna mounted on an air substrate, the substrate with the relative permittivity (ɛ r ) of 1., is our next example. The antenna geometry is earlier shown in Figure 4.6. In this case, the radiating patch dimensions are 14 mm in width and 156 mm in length. The square ground plane is mm in size and located 31.7 mm below the radiating patch. Note that the antenna is excited using two feed probes as depicted in Figure 4.6(b). Unlike the classical cavity model, our proposed method is capable of more precisely predicting the resonances of the patch antenna even when the feed probes are present. 138

161 Similar to the previous example, the DFT current spectra on the radiating patch is captured in a similar fashion. Clearly from Figure 5.9, there exist only some spectral components of the surface current induced on the radiating patch. By comparing the resonances obtained from the proposed method to those computed by the cavity model, f res (mn) = 1 2π µ oɛ ( mπ o W )2 + ( nπ L )2 where W and L are the width and length of the radiating patch orderly, and m,n=,1,2,..., we obtain an excellent agreement between the results acquired from both methods (as shown in Table 5.2). Moreover, Figure 5.1 to Figure 5.12 illustrate the first three eigencurrents on the radiating patch as well as their corresponding eigenfields. As expected, the first dominant current mode only flows in the longer direction, y direction, as a result, resonating at a lower frequency, whereas, the second current mode flows in the shorter direction, x direction, thus resonating at a higher frequency band. On the other hand, the third eigencurrent flows simultaneously in both x and it y directions as revealed in the Figure Table 5.2: Comparison of the resonances of the air dielectric patch antenna obtained from the cavity model and the proposed method. Resonant Modes (,1) (1,) (1,1) (,2) (1,2) Cavity Model (GHz) Proposed Method (GHz) Resonant Modes (2,)/(,3) (2,1) (1,3) (2,2) (2,3) Cavity Model (GHz) Proposed Method (GHz)

162 J x (f) nd 3 rd 4 th 5 th 6 th th 8th 7 9 th Location 1 Location 2 Location 3 Location 4 Location Frequency (GHz) st 3 rd 5 th 6 th J y (f) th 8 th Frequency (GHz) Figure 5.9: DFT spectra of the current, J x and J y, on the top conducting patch of a microstrip patch mounted with an air substrate. 5.4 Pattern Reconfigurable Antenna An alternative approach for the analysis and design of the pattern reconfigurable antenna is the focus of this section. For this purpose, we shall first consider the surface current induced on the parasitic ring. Note that a simple switching scheme is being used in this section. In other words, activating the switches on represents the solid ring, while turning off the switches shows the cut ring. Figure 5.13 shows the comparison between the DFT current spectra on the ring of the two operational states 14

163 φ=9 o 4 6 y E φ E θ y x γ (Degree) φ= o E φ E θ x γ (Degree) (a) The 1 st eigencurrent (b) and its corresponding eigenfield. Figure 5.1: The 1 st eigencurrent on the radiating patch and its corresponding eigenfield at.913 GHz. φ=9 o y y x E φ 3 E θ γ (Degree) φ= o E φ E θ x γ (Degree) (a) The 2 nd eigencurrent (b) and its corresponding eigenfield. Figure 5.11: The 2 nd eigencurrent on the radiating patch and its corresponding eigenfield at GHz. 141

164 φ=9 o E φ E θ y x γ (Degree) φ= o E φ E θ γ (Degree) (a) The 3 rd eigencurrent (b) and its corresponding eigenfield. Figure 5.12: The 3 rd eigencurrent on the radiating patch and its corresponding eigenfield at 1.67 GHz. of the switch, on and off. Figure 5.13(a) represents the DFT current spectra on the ring when the switches are activated on (full/solid ring). As seen, numerous current modes are induced in a multiple fashion ( every.4 GHz), similar to the resonances attained by a loop antenna. At the L1 band, the radiation pattern of the switches on case is mostly contributed from the patterns radiated from the 4 th and 5 th current modes. Because they resonate very close to the operating frequency, the L1 band, and accordingly yield the smallest eigenvalue among the induced current modes. On the other hand, Figure 5.13(b) shows the DFT current spectra on the ring when all switches are turned off (cut ring). It is straightforward that the ring exhibits fewer resonant modes around the operating frequency. However, the 3 rd resonant mode, GHz, resonates right around the operating frequency, GHz. As a result, the radiation pattern obtained from the ring is contributed substantially from the 3 rd 142

165 J (f) st 2 nd 3 rd 4 th 5 th 6 th Location 1 Location 2 Location 3 Location 4 Location 5 Switch "On" 15 th 12 th th 14 7 th 8 th 9 th 1 th 11 th 13 th J (f) nd 2 1 st 3 rd 4 th 5 th 6 th 7 th 8 th 9 th Location 1 Location 2 Location 3 Location 4 Location 5 Switch "Off" Frequency (GHz) (a) Switches are turned on (full ring) Frequency (GHz) (b) Switches are turned off (cut ring). Figure 5.13: Frequency spectra of the current induced on the octagonal ring. current mode in this case. The assumption can be validated by comparing the total radiation pattern at GHz, to the pattern radiated by the 3 rd current mode. Figure 5.14 to Figure 5.19 depict the 1 st, 4 th and 5 th modes along with their corresponding eigenpatterns. Clearly, the horizontal field component (E φ ) radiated by the full ring (see Figure 2.25) is almost identical to the eigenfields radiated from the 4 th and 5 th modes, but very distinct from that of the 1 st mode. Consequently, the field radiated from the full ring at the L1 band is arisen primarily from the 4 th and 5 th modes. Similarly, Figure 5.2 and 5.21 describe the 2 nd and 3 rd characteristic modes together with their eigenpatterns. It is also clear that the horizontal field component (E φ ) radiated by the cut ring is very similar to the eigenpatterns radiated from the 2 nd and 3 rd modes. In other words, the field radiated from the cut ring at the L1 band is mostly contributed from the 2 nd and 3 rd modes. 143

166 φ=9 o γ (Degree) φ= o E φ E θ y x γ (Degree) (a) The 1 st eigencurrent (b) and its corresponding eigenfield. Figure 5.14: The 1 st eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at.443 GHz (the 1 st degenerated mode). φ=9 o y E φ 3 E θ γ (Degree) φ= o 16 x γ (Degree) (a) The 1 st eigencurrent (b) and its corresponding eigenfield. Figure 5.15: The 1 st eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at.443 GHz (the 2 nd degenerated mode). 144

167 φ=9 o γ (Degree) φ= o E φ E θ y x γ (Degree) (a) The 4 th eigencurrent (b) and its corresponding eigenfield. Figure 5.16: The 4 th eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at GHz (the 1 st degenerated mode). φ=9 o y E φ 3 E θ γ (Degree) φ= o 16 x γ (Degree) (a) The 4 th eigencurrent (b) and its corresponding eigenfield. Figure 5.17: The 4 th eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at GHz (the 2 nd degenerated mode). 145

168 φ=9 o y E φ 3 E θ γ (Degree) φ= o 16 x γ (Degree) (a) The 5 th eigencurrent (b) and its corresponding eigenfield. Figure 5.18: The 5 th eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at GHz (the 1 st degenerated mode). φ=9 o y γ (Degree) φ= o E φ E θ 16 x γ (Degree) (a) The 5 th eigencurrent (b) and its corresponding eigenfield. Figure 5.19: The 5 th eigencurrent on the ring when the switches are turned on and its corresponding eigenfield at GHz (the 2 nd degenerated mode). 146

169 φ=9 o E φ 3 E θ γ (Degree) φ= o 12 y x γ (Degree) (a) The 2 nd eigencurrent (b) and its corresponding eigenfield. Figure 5.2: The 2 nd eigencurrent on the ring when the switches are turned off and its corresponding eigenfield at GHz. φ=9 o E φ E θ γ (Degree) φ= o y x γ (Degree) (a) The 3 rd eigencurrent (b) and its corresponding eigenfield. Figure 5.21: The 3 rd eigencurrent on the ring when the switches are turned off and its corresponding eigenfield at GHz. 147

170 For the antenna under consideration, it is clear that the information drawn from the proposed method could be very useful to the analysis of the reconfigurable antenna, as it provides more physical insight to the current behavior on the ring. Nonetheless, this information could be further used for the design antenna cycle, such as during the finetuning process. For example, the 3 rd mode of the cut ring case resonates at GHz as illustrated in the previous example. However, the dimension of the cut ring could be readjusted such that the induced current on the cut ring resonates exactly at the L1 band. As a result, a stronger contribution is achieved from the 3 rd current mode. Figure 5.22 shows the horizontal field component, E φ, of the cut and solid ring cases for φ= and φ=9. It is clear that nearly a 5 db drop in the E φ component is obtained along the horizon direction. However, after adjusting the dimension of the cut ring such that its 3 rd current mode resonates exactly at the L1 band, a 7-8 db change in the E φ component is secured along the horizon direction as described in Figure Log-Periodic Antenna One of the major drawbacks of many antennas is that they have a relatively small bandwidth. The is particularly true for the resonant antennas, such as dipole and microstrip antennas. One design named the log periodic antenna is able to provide directivity and gain while being able to operate over a wide bandwidth. The log-periodic antenna is an broadband, multi-element, unidirectional, narrowbeam antenna having structural geometry such that its impedance and radiation characteristics repeat periodically as the logarithm of frequency. In practical, the variations over frequency band of operation are minor, and log-periodic antennas are 148

171 E φ of a Single Band Antenna with Octagonal Substrate (1.575 GHz) E φ Uncut Ring φ= Uncut Ring φ=9 Cut Ring φ= Cut Ring φ= θ (Degree) Figure 5.22: Calculated radiation pattern (E φ ) of the single antenna mounted on an octagonal substrate. E φ of a Single Band Antenna with Octagonal Substrate (1.575 GHz) E φ Uncut Ring φ= Uncut Ring φ=9 Cut Ring φ= Cut Ring φ= θ (Degree) Figure 5.23: Calculated radiation pattern (E φ ) of the single antenna mounted on an octagonal substrate. The ring dimension has been modified such that the 3 rd mode resonates as close as possible to the frequency of operation (1.575 GHz). 149

172 usually considered to be frequency independent antennas. The length and spacing of the elements of the log-periodic antenna increase logarithmically from one end to the other. The log periodic antenna can exist in a number of forms. One of the first log-periodic antennas was the log-periodic toothed planar antenna shown in Fig It is basically similar to the bow-tie antenna except for the teeth. The teeth act to disturb the currents that would flow if the antenna were of bow-tie type. Work on log-periodic antenna was extensively carried out and could be readily found in the literature [37, 41]. Figure 5.25 shows a DFT current spectra induced on the log-periodic antenna. It is clear that the antenna resonates in a logarithm periodical fashion. The first three eigen current as well as their corresponding eigenpatterns are expressed in Figure 5.26, 5.27 and 5.28, orderly. The pattern looks almost identical in the vertical field component (E θ ), which is basically one of the characteristics of the frequency independent antenna. Design of the log-periodic antenna is usually done using a simple formulation or approximation. Although the method approximates reasonably accurate resonances, it is sometimes unable to determine the exact antenna resonances due to the complicated antenna geometry, i.e. antenna of arbitrary shape. Method of characteristic modes can play a crucial role in terms of precisely finetuning the antenna resonances. For example, we can capture the current spectra on the antenna and modify the antenna geometry if necessary to attain the desired resonances. 5.6 A Summary and Conclusions An alternative technique to compute the characteristic modes is proposed in this dissertation. The proposed method is performed in the time domain using the FDTD 15

173 z 2 x Figure 5.24: Geometry of a log-periodic toothed planar antenna. J x (f) nd rd 3 1 st 4 th 5 th 6 th Location 1 Location 2 Location 3 Location 4 Location 5 7 th 8 th Frequency (GHz) J y (f) st rd 3 2 nd 4 th 5 th.2 6 th 7 th 8 th Frequency (GHz) Figure 5.25: Frequency spectra of the current induced on the log-periodic antenna. 151

174 5 φ= E (db) z x γ (Degree) E θ E φ (a) The 1 st eigencurrent (b) and its corresponding eigenfield. Figure 5.26: The 1 st eigencurrent on the log periodic antenna and its corresponding eigenfield at.685 GHz. 5 φ= E (db) z x γ (Degree) E θ E φ (a) The 2 nd eigencurrent (b) and its corresponding eigenfield. Figure 5.27: The 2 nd eigencurrent on the log periodic antenna and its corresponding eigenfield at 1. GHz. 152

175 5 φ= z x E (db) γ (Degree) E θ E φ (a) The 3 rd eigencurrent (b) and its corresponding eigenfield. Figure 5.28: The 3 rd eigencurrent on the log periodic antenna and its corresponding eigenfield at GHz. technique. The major advantage is that the resonances of the structure could be captured in just a single FDTD run. Once the resonances are determined, the eigencurrents as well as their corresponding eigenfields could also be computed. Crucial information, such as quality factor and bandwidth, could be further extracted from our proposed method. It was shown that the proposed method can precisely predict the resonances of the structures by comparing the simulated results to the analytical solutions. An excellent agreement was established from the two approaches. It is clear that the proposed method could be useful for antenna design and analysis, especially during the finetuning process, as it provides more physical insight to the behavior of antennas, such as resonances, current distributions, and their corresponding radiation patterns. Desired antenna pattern can be achieved by exciting the proper current modes/modes. 153