Pattern Reconfigurable Printed Antennas and Time Domain Method of Characteristic Modes for Antenna Analysis and Design

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PATTERN RECONFIGURABLE PRINTED ANTENNAS AND TIME DOMAIN METHOD OF CHARACTERISTIC MODES FOR 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

Nuttawit Surittikul, M.S., B.S.

* * * * *

The Ohio State University

2006

Dissertation Committee: Approved by

Prof. Roberto G. Rojas, Ph.D., Adviser Prof. Fernando Teixeira, Ph.D. Adviser Prof. Patrick Roblin, Ph.D. Graduate Program in Electrical and Computer Engineering c Copyright by ° Nuttawit Surittikul

2006 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 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 This dissertation is dedicated to

my parents,

my wife

and

the spirit of my uncle

iv ACKNOWLEDGMENTS

I would like to express my sincere gratitude to my advisor, Professor Roberto G. Ro- jas, for his extreme patience, invaluable discussions, academic training, encouragement, and excellent guidance throughout my Ph.D. course years and also this dissertation. He has always been there whenever I needed his help and there is certainly no way I could have achieved my dream without him. I would also like to acknowledge my dissertation reading committee, Prof. Patrick Roblin and Prof. Fernando

Teixeira, for taking out of their busy schedules to help me along in this doctoral process.

Thanks is also extended to my friends at ESL - Simon Lee, Ibrahim Kursat

Sendur, Siddarth Iyer, Matthew Dexter, Niru Nahar, Jeanne Rockway, Yasutaka

Horiki, Khalid Jamil, Yik-Kiong Hue, Eugene Lee, Kwan-Ho Lee, Seung-Mo Seo, and

Koray Tap. We had a great time and I will surely miss playing soccer with our ESL soccer team.

I would like to also acknowledge all the Thai Students at OSU for their support, love and joy we have shared: Danai Torrungrueng, Jatupum Jenwatanavet, Panuwat

Janpugdee, Pongsak Mahachoklertwattana, Titipong Lertwiriyaprapa, Yuddapoom

Srisukh, Praphun Naenna, and Alongkorn Darawankul. I will surely miss our 3:00 pm coﬀee break. A special thanks also goes to Panuwat Janpugdee, who has always

v looked out for me since the ﬁrst day we met. Thanks for your invaluable suggestions

on life, work, career, and family. For sure, I do have three brothers, not just two!

I also want to acknowledge the support I received from from Dr. Wladimiro

Villarroel and the AGC Automotive Americas R&D Inc. Through your invaluable

suggestion, time, and patience, I’ve been able to complete my dissertation. I truly appreciate having the opportunity to be apart of AAAR.

None of this would have been possible without the love, support and encourage-

ment of my family. Mom and Dad, I did it. I am forever thankful to them for allowing

me to fulﬁll my dream. To my brothers, Chaiyapruk and Wittawat, thanks for all

the love and support. To my uncle, Nid, thanks for your encouragement, support,

and suggestion. I am sure you would be so proud of me if you were here. I love you.

Until we meet again.

Last but not least, my sincere thanks to my wife for her love, support, and under-

standing throughout my graduate school time. Thanks for believing in me, encour- aging me when I was down (many many times). I’m sure we will spend more time together from now on. We have been through a lot. I can’t thank you enough. I love you.

vi VITA

August 22, 1976 ...... Born - Phichit, Thailand

May 1997 ...... B.S., Electrical Engineering, Chula- longkorn University, Bangkok, Thai- land December 2000 ...... M.S., Electrical Engineering, The Ohio State University, Columbus, Ohio July 2000-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 Let- ters.

N. Surittikul and R. G. Rojas, “Time Domain Method of Characteristic Modes • for the Analysis and Design of Antennas”, to be submitted to IEEE Transac- tions on Antennas and Propagation.

vii 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 Qual- • ity 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, 2006.

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, 2005.

N. Surittikul and R. G. Rojas, “Analysis of Reconﬁgurable Printed Anten- • nas using Characteristic Modes: FDTD Approach”, IEEE AP-S International Symposium and USNC/URSI National Radio Science Meetings, Monterey, CA, June 20-25, 2004.

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, 2003.

N. Surittikul and R. G. Rojas, “Reconﬁgurable Circularly Polarized Dual Band • Stacked Microstrip Antenna”, EM Measurements Consortium Meeting, Colum- bus, OH, July 31-August 1, 2003.

K. W. Lee, R. G. Rojas and N. Surittikul, “Surface Wave Control for Reconﬁg- • urable Printed Antenna Applications”, IEEE AP-S International Symposium and USNC/URSI National Radio Science Meetings, San Antonio, TX, June 16-21, 2002 (invited).

viii R. G. Rojas, K. W. Lee, and N. Surittikul, “Reconﬁgurable GPS Antenna”, • National Radio Science Meeting (URSI), Boulder, CO, January 9-12, 2002 (invited).

R. G. Rojas, K. W. Lee, and N. Surittikul, “Reconﬁgurable GPS Antenna”, EM • Measurements Consortium Meeting, Columbus, OH, July 31-August 1, 2001.

Academic Reports

R. G. Rojas and N. Surittikul, “Reconﬁgurable Printed Antenna for GPS • Applications”, The Ohio State University, The ElectroScience Laboratory, De- partment of Electrical and Computer Engineering, Columbus, Ohio, April 2001, Technical Report 739356-1.

R. G. Rojas, K. W. Lee and N. Surittikul, “Reconﬁgurable Printed Antenna • for GPS Applications”, The Ohio State University, The ElectroScience Labo- ratory, Department of Electrical and Computer Engineering, Columbus, Ohio, September 2001, Technical Report 739356-2.

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 2002, Technical Report 741202-1.

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 2003, Technical Report 741202-2.

R. G. Rojas, N. Surittikul and S. Iyer, “Multilayer Reconﬁgurable GPS An- • tennas and Platform Eﬀects”, The Ohio State University, The ElectroScience Laboratory, Department of Electrical and Computer Engineering, Columbus, Ohio, October 2004, Technical Report 746584-1.

ix R. G. Rojas, N. Surittikul and S. Iyer, “Multilayer Reconﬁgurable GPS An- • tennas and Platform Eﬀects”, The Ohio State University, The ElectroScience Laboratory, Department of Electrical and Computer Engineering, Columbus, Ohio, November 2004, Technical Report 745379-1.

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 2004.

N. Surittikul, “Ph.D. Candidacy Examination”, The Ohio State University, • The ElectroScience Laboratory, Department of Electrical and Computer Engi- neering, Columbus, Ohio, May 2004.

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 Engi- neering, Columbus, Ohio, December 2005, Technical Report 746584-2.

FIELDS OF STUDY

Major Field: Electrical Engineering

Studies in: Electromagnetic Prof. Roberto Rojas Prof. Fernando Teixeira Prof. Edward Newman Microwave Circuits: Design and Analysis Prof. Patrick Roblin Mathematics Prof. Ulrich Gerlach

x TABLE OF CONTENTS

Page

Abstract ...... ii

Dedication ...... iv

Acknowledgments ...... v

Vita ...... vii

List of Tables ...... xiv

List of Figures ...... xv

Chapters:

1. Introduction ...... 1

1.1 Background and Motivation ...... 1 1.2 Literature Review ...... 4 1.3 Organization of This Dissertation ...... 13

2. Development of the Single Band Radiation Pattern Reconﬁgurable An- tenna for GPS Application ...... 16

2.1 Introduction ...... 16 2.1.1 Motivation ...... 16 2.1.2 Principle of Operation ...... 17 2.2 Previous Works ...... 19 2.2.1 1st Prototype ...... 20 2.2.2 2nd Prototype ...... 25 2.3 Asymmetry Consideration of the Radiation Pattern on the Azimuth Plane ...... 26

xi 2.3.1 Identiﬁcation of the Cause of an Asymmetry in Radiation Pattern on the Azimuth Plane ...... 28 2.4 Description of New Antenna Geometry ...... 34 2.5 Design Procedure ...... 37 2.5.1 Design of Parasitic Ring ...... 37 2.5.2 Design of the Switching Circuit ...... 42 2.6 Microstrip Feed Network for Circular Polarization ...... 50 2.7 Measured Results and Discussions ...... 52 2.7.1 Impedance Characteristics ...... 52 2.7.2 Radiation Characteristics ...... 54 2.8 A Summary and Conclusions ...... 55

3. Development of the Dual Band Radiation Pattern Reconﬁgurable Antenna for GPS Application ...... 60

3.1 Introduction ...... 60 3.2 Basic Antenna Geometry ...... 61 3.3 Feed Conﬁguration ...... 62 3.3.1 Input Impedance ...... 64 3.3.2 Microstrip Feed Network for Circular Polarization ...... 66 3.4 Design of Parasitic Structures (Strips/Rings) ...... 70 3.4.1 2-D Strip/Ring Parametric Study ...... 70 3.4.2 3-D Strip/Ring Parametric Study ...... 73 3.5 Asymmetry Consideration of the Radiation Pattern on the Azimuth Plane ...... 78 3.6 Description of New Antenna Geometry ...... 80 3.6.1 Basic Geometry ...... 80 3.6.2 Parasitic Structure and Switching Circuitry Design . . . . . 83 3.7 Measured Results and Discussions ...... 86 3.7.1 Impedance Characteristics ...... 88 3.7.2 Radiation Characteristics ...... 90 3.8 Summary and Conclusions ...... 108

4. Development of the Time Domain Method of Characteristic Modes for the Analysis and Design of Antennas ...... 110

4.1 Introduction ...... 110 4.2 Characteristic Modes ...... 112 4.3 Computation of Characteristic Modes ...... 116 4.3.1 Conventional Method ...... 117 4.3.2 Proposed Method ...... 118

xii 5. Numerical Results ...... 132

5.1 Rectangular Cross Section Waveguide ...... 132 5.2 Printed Dipole Antenna ...... 134 5.3 Air Dielectric Patch Antenna ...... 139 5.4 Pattern Reconﬁgurable Antenna ...... 141 5.5 Log-Periodic Antenna ...... 149 5.6 A Summary and Conclusions ...... 154

6. Conclusions ...... 156

6.1 A Summary and Conclusion of This Dissertation ...... 156 6.2 Future Work ...... 157 6.2.1 RF MEMS Switches ...... 157 6.2.2 Antenna Feed Technique ...... 158 6.2.3 Reconﬁgurable Array ...... 158 6.2.4 GPS Antenna with Excellent Axial Ratio ...... 159 6.2.5 Characteristic Modes for Material Bodies ...... 159

Bibliography ...... 161

xiii LIST OF TABLES

Table Page

5.1 Comparison of the resonances of the rectangular waveguide obtained from the analytical solution and the proposed method...... 134

5.2 Comparison of the resonances of the air dielectric patch antenna obtained from the cavity model and the proposed method...... 140

xiv 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...... 6

1.2 Geometry of a frequency reconﬁgurable leaky mode/multifunction printed antenna [22]...... 7

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...... 7

1.4 Geometry of a RF MEMS reconﬁgurable Vee antenna [3]...... 8

1.5 Geometry of a reconﬁgurable single turn square spiral printed antenna capable of both radiation pattern and frequency reconﬁgurability [12]. 9

1.6 Stacked reconﬁgurable array of balanced bowtie antennas: Lower and upper band elements are alternatively activated using MEMS switches [1]. 10

1.7 A patch antenna with switchable slots (PASS) for RHCP/LHCP diversity [49]...... 11

1.8 Geometry of a polarization reconﬁgurable patch antenna with integrated MEMS actuator [40]...... 12

xv 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...... 17

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

2.3 Circular polarized microstrip antenna with diode-loaded metallic ring around the patch (top view)...... 20

2.4 Circularly polarized microstrip antenna with small ground plane and diode-loaded metallic ring around the patch (top view) ...... 22

2.5 Circularly polarized microstrip antenna with small ground plane and diode-loaded metallic ring around the patch (bottom view) . . . . . 22

2.6 Simulated radiation pattern at 1.575 GHz for a circularly polarized antenna with small ground plane ...... 23

2.7 Simulated axial ratio at 1.575 GHz for a circularly polarized antenna with small ground plane ...... 23

2.8 Measured radiation pattern at 1.588 GHz for a circularly polarized antenna with small ground plane ...... 24

2.9 Measured radiation pattern at 1.576 GHz for a circularly polarized antenna with small ground plane ...... 24

2.10 Measured axial ratio at 1.588 GHz for a circularly polarized antenna with small ground plane ...... 25

2.11 Circularly polarized microstrip antenna with small ground plane and diode-loaded metallic ring around the patch (top view)...... 26

2.12 Measured radiation pattern and axial ratio at 1.572 GHz for a circularly polarized antenna with small ground plane...... 27

2.13 Comparison of calculated far-ﬁeld radiation patterns (Eφ) for antenna with the square parasitic ring between the two states of the switch operations (on/oﬀ) at φ = 0◦, 15◦, 30◦, 45◦, 60◦and 90◦...... 29

xvi 2.14 Calculated input impedance and S11 of the patch on an inﬁnite substrate. 30

2.15 Far field radiation pattern of the patch on an infinite dielectric slab with an infinite ground plane...... 30

2.16 Geometry of a patch antenna on a ﬁnite dielectric slab with a square partial ground plane...... 31

2.17 Far-ﬁeld radiation pattern of a patch antenna on a ﬁnite dielectric slab with a square partial ground plane...... 32

2.18 Geometry of a patch antenna on a ﬁnite dielectric slab with a octagonal partial ground plane...... 33

2.19 Far-ﬁeld radiation pattern of a patch antenna on a ﬁnite dielectric slab with an octagonal partial ground plane...... 34

2.20 Comparison of calculated far-ﬁeld radiation patterns (Eφ) of the antenna with the circular parasitic ring at φ=0◦, 15◦, 30◦, 45◦, 60◦ and 90◦ ...... 35

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 ( 0.12λd) which is used for surface wave excitation...... 36

2.22 Surface currents induced on the octagonal parasitic ring without any cuts...... 40

2.23 Geometry of the patch surrounded by (a) full octagonal parasitic ring (switches on) and (b) cut octagonal parasitic ring (switch oﬀ). . . . . 40

2.24 Comparison of calculated (FDTD) directivity patterns (Dφ) between the full and cut ring conﬁgurations for φ=0◦ , 15◦, 30◦, 45◦, 60◦ and 75◦. 41

2.25 Calculated (FDTD) radiation patterns (Eφ) from the reconﬁgurable antenna: (a) Pattern radiated by the patch without the ring (b) Pat- tern radiated by ring by itself (but mounted on the substrate) with switches on and (c) same as (b) but switches are oﬀ...... 43

xvii 2.26 Schematic representation of the switch circuit components inserted in the switching cuts introduced in the parasitic ring...... 44

2.27 ADS schematic for Philips BAP51-02 diode...... 46

2.28 Schematic to determine the ”impedance model” for every switching circuit for forward and reverse bias conditions...... 47

2.29 Calculated (HFSS) gain patterns (Gφ) for on and oﬀ states of switches for φ=0◦ , 15◦, 30◦, 45◦, 60◦ and 90◦...... 49

2.30 Schematic of the two-stage Wilkinson power divider...... 50

2.31 Implemented two-stage Wilkinson power divider. The substrate (RT/Duroid 5870, thickness=1.575 mm) dimensions are 125 mm 65 mm. . . . . 51 × 2.32 Measured frequency response of the two-stage Wilkinson power divider. 52

2.33 Geometry of the implemented reconﬁgurable antenna...... 53

2.34 Comparison of the measured input impedance between the on and oﬀ states of the switches...... 53

2.35 Measured gain patterns (Gφ) for the on and oﬀ states of the switches for φ=0◦,φ=15◦, φ=45◦ and φ=90◦...... 56

2.36 Measured gain patterns (Gθ) for the on and oﬀ states of the switches for φ=0◦, φ=15◦, φ=45◦ and φ=90◦...... 56

2.37 Measured axial ratio for the on and oﬀ states of the switches for φ=0◦, φ=15◦, φ=45◦ and φ=90◦...... 57

2.38 Measured right hand circular polarized gain patterns (GRHCP ) for the on and oﬀ states of the switches for φ=0◦, φ=15◦, φ=45◦ and φ=90◦. 57

2.39 Measured azimuth patterns for the on and oﬀ states of the switches for θ=0◦, θ=30◦ and θ=50◦...... 58

xviii 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, Eθ...... 63

3.2 Cross section of a reconﬁgurable dual band microstrip antenna. . . . 63

3.3 Feed conﬁguration of the dual band antenna...... 66

3.4 Calculated input impedance and S11 response for upper radiating patch. The feed probe is located 4.74 mm from the center of the L1 patch. . 67

3.5 Calculated input impedance and S11 response for lower radiating patch. The feed probe is located 11.06 mm from the center of the L2 patch. 67

3.6 The two-stage Wilkinson power divider for the dualband antenna. The substrate (RT/Duroid 6002)...... 69

3.7 Measured return loss of the two stage Wilkinson feeding circuit at the L1 band...... 70

3.8 Measured return loss of the two stage Wilkinson feeding circuit at the L2 band...... 71

3.9 Cross section of 2-D equivalent problems ...... 72

3.10 Comparison of vertical ﬁeld component obtained from 2-D and 3-D models at L1 band ...... 73

3.11 Comparison of vertical ﬁeld component between two diﬀerent strip width at the L1 band ...... 74

3.12 Comparison of vertical ﬁeld component between two diﬀerent strip width at the L2 band ...... 74

3.13 Geometry of a reconﬁgurable dual band stacked patch antenna for controlling antenna pattern at L2 band only (Scheme A) ...... 75

xix 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) ...... 76

3.15 Example 1 (Scheme A) : Antenna radiation pattern and axial ratio versus angle at L2 band ...... 77

3.16 Example 2 (Scheme B) : Antenna radiation pattern and axial ratio versus angle at L1 band ...... 78

3.17 Example 3 (Scheme B) : Antenna radiation pattern and axial ratio versus angle at L1 band ...... 79

3.18 Example 3 (Scheme B) : Antenna radiation pattern and axial ratio versus angle at L2 band ...... 80

3.19 Calculated radiation pattern of the dual band antenna with a square substrate at 1.575 GHz and 1.227 GHz...... 81

3.20 Calculated radiation pattern of the dual band antenna with an octagonal substrate at 1.575 GHz and 1.227 GHz...... 82

3.21 New proposed geometry of a dual band antenna...... 83

3.22 Geometry of the dual band antenna surrounded by (a) a full octagonal parasitic ring (b) loaded parasitic ring...... 86

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...... 87

3.24 Geometry of the dual band antenna surrounded by a full octagonal parasitic ring loaded with (a) cut strips (b) uncut strips...... 88

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...... 89

xx 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...... 90

3.27 Schematic representation of the switching circuit component loaded on the solid ring...... 91

3.28 Calculated radiation pattern of the dual band antenna with a octagonal substrate at 1.575 GHz...... 92

3.29 Calculated radiation pattern of the dual band antenna with a octagonal substrate at 1.575 GHz...... 93

3.30 Calculated axial ratio of the dual band antenna with a octagonal substrate at 1.575 GHz...... 94

3.31 Calculated radiation pattern of the dual band antenna with a octagonal substrate at 1.227 GHz...... 95

3.32 Calculated radiation pattern of the dual band antenna with a octagonal substrate at 1.227 GHz...... 96

3.33 Calculated axial ratio of the dual band antenna with a octagonal substrate at 1.227 GHz...... 97

3.34 Geometry of the implemented pattern reconﬁgurable dual band antenna: top layer...... 98

3.35 Geometry of the implemented pattern reconﬁgurable dual band antenna: middle layer...... 98

3.36 Geometry of the implemented pattern reconﬁgurable dual band antenna: bottom layer...... 99

3.37 Measured input impedance of the upper radiating patch...... 99

3.38 Measured input impedance of the lower radiating patch...... 100

3.39 Measured Gθ pattern of the dual band antenna at the L1 band. . . . 101

xxi 3.40 Measured Gφ pattern of the dual band antenna at the L1 band. . . . 102

3.41 Measured axial ratio of the dual band antenna at the L1 band. . . . . 103

3.42 Measured Gθ pattern of the dual band antenna at the L2 band. . . . 104

3.43 Measured Gφ pattern of the dual band antenna at the L2 band. . . . 105

3.44 Measured axial ratio of the dual band antenna at the L2 band. . . . . 106

3.45 Measured Gθ pattern of the dual band antenna at the L1 band. Note all the switching components are removed...... 107

3.46 Measured Gφ pattern of the dual band antenna at the L1 band. Note all the switching components are removed...... 108

3.47 Measured axial ratio of the dual band antenna at the L1 band. Note all the switching components are removed...... 109

4.1 Geometry of a rectangular cross section waveguide. The waveguide is of inﬁnite length in the z direction...... 114

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 ...... 118

4.3 A sequence of random numbers of uniform distribution and its corresponding spectral calculation...... 122

4.4 A time signature of a Gaussian pulse with sinusoidal carrier at center frequency of interest and its corresponding spectral calculation. . . . 122

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 ...... 123

4.6 Geometry of a microstrip antenna with air substrate...... 124

4.7 Frequency spectra of the induced current on the radiating patch and the ﬁrst characteristic mode...... 124

xxii 4.8 Proposed algorithm for computing the scattered electric ﬁeld. . . . . 125

4.9 Proposed algorithm for computing the scattered electric ﬁeld. . . . . 126

4.10 A wave reﬂects back and forth between the resonator mirrors, a Fabry- Perot etalon resonator...... 126

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...... 129

5.1 DFT Spectra of the Ez component at six diﬀerent monitoring points inside the guide...... 133

5.2 Geometry of a printed dipole...... 135

5.3 Frequency spectra of the induced current on the printed dipole. . . . 136

5.4 The 1st eigencurrent on the printed dipole antenna and its corresponding eigenﬁeld at 0.820 GHz...... 137

5.5 The 2nd eigencurrent on the printed dipole antenna and its corresponding eigenﬁeld at 1.740 GHz...... 137

5.6 The 3rd eigencurrent on the printed dipole antenna and its corresponding eigenﬁeld at 2.530 GHz...... 138

5.7 The 4th eigencurrent on the printed dipole antenna and its corresponding eigenﬁeld at 3.500 GHz...... 138

5.8 The 5th eigencurrent on the printed dipole antenna and its corresponding eigenﬁeld at 4.440 GHz...... 139

5.9 DFT spectra of the current, Jx and Jy, on the top conducting patch of a microstrip patch mounted with an air substrate...... 141

5.10 The 1st eigencurrent on the radiating patch and its corresponding eigenﬁeld at 0.913 GHz...... 142

5.11 The 2nd eigencurrent on the radiating patch and its corresponding eigenﬁeld at 1.345 GHz...... 142

xxiii 5.12 The 3rd eigencurrent on the radiating patch and its corresponding eigenﬁeld at 1.670 GHz...... 143

5.13 Frequency spectra of the current induced on the octagonal ring. . . . 144

5.14 The 1st eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 0.443 GHz (the 1st degenerated mode). 145

5.15 The 1st eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 0.443 GHz (the 2nd degenerated mode). 145

5.16 The 4th eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 1.412 GHz (the 1st degenerated mode). 146

5.17 The 4th eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 1.412 GHz (the 2nd degenerated mode). 146

5.18 The 5th eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 1.685 GHz (the 1st degenerated mode). 147

5.19 The 5th eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 1.685 GHz (the 2nd degenerated mode). 147

5.20 The 2nd eigencurrent on the ring when the switches are turned oﬀ and its corresponding eigenﬁeld at 1.425 GHz...... 148

5.21 The 3rd eigencurrent on the ring when the switches are turned oﬀ and its corresponding eigenﬁeld at 1.598 GHz...... 148

5.22 Calculated radiation pattern (Eφ) of the single antenna mounted on an octagonal substrate...... 150

5.23 Calculated radiation pattern (Eφ) of the single antenna mounted on an octagonal substrate. The ring dimension has been modiﬁed such that the 3rd mode resonates as close as possible to the frequency of operation (1.575 GHz)...... 150

5.24 Geometry of a log-periodic toothed planar antenna...... 152

5.25 Frequency spectra of the current induced on the log-periodic antenna. 152

xxiv 5.26 The 1st eigencurrent on the log periodic antenna and its corresponding eigenﬁeld at 0.685 GHz...... 153

5.27 The 2nd eigencurrent on the log periodic antenna and its corresponding eigenﬁeld at 1.000 GHz...... 153

5.28 The 3rd eigencurrent on the log periodic antenna and its corresponding eigenﬁeld at 1.275 GHz...... 154

xxv 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 +10◦ 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 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, recon-

ﬁgurable 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 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 anten-

nas, the Theory of Characteristic Modes, ﬁrst introduced by Garbacz [4, 6] and then

reﬁned by Harrington [9, 10], has been 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, λn. The magnitude of the eigenvalue indicates how well that particular mode radiates. Modes with small λ are good radiators, | n| whereas those with large λ are poor radiators. The closer the eigenvalue is to zero, | n| 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 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 or-

der to minimize the antenna’s weight and volume. 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 oper-

ating frequency, polarization or radiation pattern, in real time condition is referred

to as a reconﬁgurable antenna. Reconﬁgurable antennas have the 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 an-

tenna 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

4 the literature. For instance, Weedon, et al. reported a reconﬁgurable multi-band antenna integrated with radio frequency micro electro mechanical systems (RF MEMS)

switches for applications at drastically diﬀerent frequency bands, such as communi-

cations at the L band (1-2 GHz) and synthetic aperture radar (SAR) at the X band

(8-12.5 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 formed by 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, the 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.

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 [20], 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 reduces the number and size of the antennas mounted on

board tremendously, especially in a multi-band communication system where weight

and volume are critical issues.

5 (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.

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 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.

6 Patch Patch Switches

Leaky Wave Antenna Array Parasitic Patch Parasitic

Figure 1.2: Geometry of a frequency reconﬁgurable leaky mode/multifunction printed antenna [22].

Radiating Patch Diode Switches 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.

7 Reconfigurable Vee Antenna

Main Beam Direction Push/Pull Bar

Transmission Lines Actuator Actuator Bias

Figure 1.4: Geometry of a RF MEMS reconﬁgurable Vee antenna [3].

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

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 reconﬁg-

urability, however they can be made both frequency and pattern reconﬁgurable si-

multaneously. Huﬀ et al. [12] has proposed a frequency and pattern reconﬁgurable microstrip antenna using multiple switch connections. Figure 1.5 illustrates a geom-

etry 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 pat-

tern away from the broadside, whilst maintaining a common impedance bandwidth

8 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].

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.

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.

9 Top View

Side View

Lower Band Element Upper Band Element

Upper Band Elements

Lower Band Elements

Feeds connected Ground Plane with MEMS Switches

Figure 1.6: Stacked reconﬁgurable array of balanced bowtie antennas: Lower and upper band elements are alternatively activated using MEMS switches [1].

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, 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 tremen- dous growth of wireless communications and radar systems. A design of a microstrip

10 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].

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) 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, depending upon the operating state of the diode switches. 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. [40].

Nearly Square Patch Antenna

¡ MEMS Actuator

GSG RF Probe Pads

Microstrip Impedance Matching Feed Transformer

Figure 1.8: Geometry of a polarization reconﬁgurable patch antenna with integrated MEMS actuator [40].

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

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 GPS applications. Thus, the motivation, basic principle of operation

12 as well as design examples of our proposed reconﬁgurable printed antenna will be introduced and discussed in more detail in the next chapter.

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 dissertation 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 ex-

plained. 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 pro-

totypes 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.

13 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 at the L1

band. 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 Chap-

ter 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 al-

gorithm is realized in the time domain. Useful information, such as the resonances

14 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, 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 CHAPTER 2

DEVELOPMENT OF THE SINGLE BAND RADIATION PATTERN RECONFIGURABLE ANTENNA FOR GPS APPLICATION

2.1 Introduction

2.1.1 Motivation

The antenna that possesses the ability to modify its radiation properties in real

time is referred to as a reconﬁgurable antenna. The radiation properties could be 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 z

Switch Loaded Ring/Strip

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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.

2.1.2 Principle of Operation

The work described here deals with the design and analysis of a pattern recon-

ﬁgurable 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 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 the

17 level of the sidelobes as well as the backlobes. However, electrically thick microstrip antennas have the advantage of providing a larger operational bandwidth over mi-

crostrip antennas mounted on thin substrates. For the particular application under

consideration, the control of the surface waves is crucial to achieve pattern reconﬁg-

urability. 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 [14,15,17,24,27,30,43]. 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 z O O

Direct Space Wave Direct Space Wave Edge Diffracted Space Wave Modified Edge Diffracted Space Wave

Edge Diffracted Surface Wave Modified Edge Diffracted Surface Wave

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(a) Radiating Patch without Parasitic Ring (b) Radiating Patch with Parasitic Ring

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 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 ( 0.1λ 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=90◦) direction at the truncation of the substrate.

The diffracted surface wave fields interfere, depending on their phase, constructively and destructively with the (Eφ) 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 Conducting Radiating strips 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 (Eφ) 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.

2.2.1 1st 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

20 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 40 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 ( 0.12λ within ≈ the dielectric). The dimensions of the square substrate are 177.8 mm 177.8 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 patterns of the E , E field components as well as axial ratio patterns in the y z plane are φ θ − shown in Figure 2.6 through Figure 2.10. The measured 3-dB beamwidth of the Eφ pattern is 70◦ and 80◦ 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 Eθ 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 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 φ o Simulated Eφ component at freq = 1.575 GHz ( = 90 )

Diodes off 0 Diodes on

−10

−20

−30 Magnitude (dB)

−40 −180 −135 −90 −45 0 45 90 135 180 γ (degree) φ o Simulated Eθ component at freq = 1.575 GHz ( = 90 )

Diodes off 0 Diodes on

−10

−20

−30 Magnitude (dB)

−40 −180 −135 −90 −45 0 45 90 135 180 γ (degree)

Figure 2.6: Simulated radiation pattern at 1.575 GHz for a circularly polarized antenna with small ground plane

Simulated Axial Ratio Plot at freq = 1.575 GHz (φ=90o) 15 Diodes off 14 Diodes on

6 Axial Ratio (dB) 5

0 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 γ (degree)

Figure 2.7: Simulated axial ratio at 1.575 GHz for a circularly polarized antenna with small ground plane

23 φ o Measured Eφ component at freq = 1.588 GHz ( =90 )

Diodes off 0 Diodes on

−10

−20

−30 Magnitude (dB)

−40 −180 −135 −90 −45 0 45 90 135 180 γ (degree) φ o Measured Eθ component at freq = 1.588 GHz ( =90 )

Diodes off 0 Diodes on

−10

−20

−30 Magnitude (dB)

−40 −180 −135 −90 −45 0 45 90 135 180 γ (degree)

Figure 2.8: Measured radiation pattern at 1.588 GHz for a circularly polarized antenna with small ground plane

φ o Measured Eφ component at freq = 1.576 GHz ( =90 )

0 Diodes off Diodes on

−10

−20

Magnitude (dB) −30

−40 −180 −135 −90 −45 0 45 90 135 180 γ (degree) φ o Measured Eθ component at freq = 1.576 GHz ( =90 )

0 Diodes off Diodes on

−10

−20

Magnitude (dB) −30

−40 −180 −135 −90 −45 0 45 90 135 180 γ (degree)

Figure 2.9: Measured radiation pattern at 1.576 GHz for a circularly polarized antenna with small ground plane

24 Measured Axial Ratio Plot at freq = 1.588 GHz (φ=90o) 15 Diodes off 14 Diodes on

6 Axial Ratio (dB) 5

0 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 γ (degree)

Figure 2.10: Measured axial ratio at 1.588 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. As expected, the current ring shape does not produce a symmetric − azimuthal pattern. Other feeding scheme as well as ring shapes will be introduced later in this dissertation to obtain more symmetric azimuthal patterns. The purpose of the first antenna configuration was to demonstrate that reconfigurability can be achieved.

2.2.2 2nd Prototype

Another antenna example for controlling the horizontal ﬁeld component, Eφ, was implemented and tested as seen in Figure 2.11. The substrate has a dielectric constant of 9.2 with a thickness of 0.8 mm. The dimensions of the square substrate are 177.8 mm 177.8 mm. To excite a circularly polarized radiation pattern that is symmetric ×

25 Figure 2.11: Circularly polarized microstrip antenna with small ground plane and diode-loaded metallic ring around the patch (top view).

in the azimuth plane, the antenna is fed by four probes of equal magnitude signals with 90o phase increments. Figure 2.12 shows the measured radiation pattern and axial ratio versus angle of the proposed antenna. By turning the diode switches on and

off, the horizontal field component, i.e. Eφ, is modified by 10 dB in the neighborhood

of the horizon. On the other hand, the vertical ﬁeld component, i.e. Eθ, stays

unchanged, as expected. Nonetheless, the radiation pattern is not quite symmetric

as expected due to the measurement and fabrication errors. It was discoverd that the location of one of the probes was 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=0◦,90◦). As mentioned − − 26 E component (XZ plane) freq=1.572 GHz E component φ θ Axial Ratio 5 5 10

Diodes off 9 Diodes on 0 0

−5 −5 7

6 −10 −10

−15 −15

Magnitude (dB) Magnitude (dB) 4 Axial Ratio (dB)

−20 −20 3

−25 −25 Diodes off Diodes off 1 Diodes on Diodes on

−30 −30 0 −180 −90 0 90 180 −180 −90 0 90 180 −90 −60 −30 0 30 60 90 γ (Degree) γ (Degree) γ (Degree)

Figure 2.12: Measured radiation pattern and axial ratio at 1.572 GHz for a circularly polarized antenna with small ground plane.

above, the radiation patterns on the two planes are nearly identical, and yield a signiﬁcant change in antenna ﬁeld pattern (Eφ) along the horizon. However, the

radiated patterns on any other elevation planes, φ=15◦, 30◦, 45◦ and 60◦, are very

diﬀerent from the patterns on the principal elevation planes, especially when the switches are turned on. In other words, the antenna radiates an asymmetric pattern

in the azimuth plane as depicted in Figure 2.13. Additionally, the ﬁeld magnitudes

when the switches are on are even higher than those when the switches are oﬀ for

φ=15◦, 30◦, 45◦ and 60◦. As a result, the antenna can reconﬁgure its radiation

pattern only on the principal elevation planes. In order to make the radiation pattern

symmetric in the azimuth, the sources that generate the asymmetry in the patterns

must be identiﬁed and eliminated accordingly. The asymmetry in radiation pattern

27 may possibly arise from numerous factors, such as the shapes of the ring, ground plane, radiating patch or even the dielectric slab.

2.3.1 Identiﬁcation of the Cause of an Asymmetry in Radi- ation 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 was first investigated.

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,

1.575 GHz, and the return loss is as low as -30 dB at this frequency.

Figure 2.15 depicts the radiated ﬁeld components, Eφ and Eθ, 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

antenna radiates a symmetric azimuthal pattern. As a result, there is no need to

adjust or modify the geometry of the radiating patch.

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

28 φ o φ o Magnitude of Eφ at =0 Magnitude of Eφ at =90 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −35 | (dB) | (dB) φ φ

|E −40 |E −40 −45 switches on −45 switches on switches off switches off −50 −50 −55 −55 −60 −60 −180−135 −90 −45 0 45 90 135 180 −180−135 −90 −45 0 45 90 135 180

φ o φ o Magnitude of Eφ at =15 Magnitude of Eφ at =30 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −35 | (dB) | (dB) φ φ

|E −40 |E −40 −45 switches on −45 switches on switches off switches off −50 −50 −55 −55 −60 −60 −180−135 −90 −45 0 45 90 135 180 −180−135 −90 −45 0 45 90 135 180

φ o φ o Magnitude of Eφ at =45 Magnitude of Eφ at =60 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −35 | (dB) | (dB) φ φ

|E −40 |E −40 −45 switches on −45 switches on switches off −50 −50 switches off −55 −55 −60 −60 −180−135 −90 −45 0 45 90 135 180 −180−135 −90 −45 0 45 90 135 180 γ (Degree) γ (Degree)

Figure 2.13: Comparison of calculated far-ﬁeld radiation patterns (Eφ) for antenna with the square parasitic ring between the two states of the switch operations (on/oﬀ) at φ = 0◦, 15◦, 30◦, 45◦, 60◦and 90◦.

29 Input impedance of the square patch 60 Real Part 50 Imaginary Part

) 40 Ω 30 20 10

Impedance ( 0 −10 −20 1.4 1.425 1.45 1.475 1.5 1.525 1.55 1.575 1.6 1.625 1.65 1.675 1.7 1.725 1.75 1.775 1.8

Magnitude of the S of the square patch 11 0

−5

−10

−15 | (dB) 1

−201 |S −25

−30

−35 1.4 1.425 1.45 1.475 1.5 1.525 1.55 1.575 1.6 1.625 1.65 1.675 1.7 1.725 1.75 1.775 1.8 Frequency (GHz)

Figure 2.14: Calculated input impedance and S11 of the patch on an inﬁnite substrate.

Eθ (grounded infinite substrate) Eφ (grounded infinite substrate) −10 −10

−15 −15

−20 −20

−25 −25 | (dB) | (dB) θ φ |E |E

−30 −30 φ=0o φ=0o φ=15o φ=15o φ=30o φ=30o φ o φ o −35 =45 −35 =45 φ=60o φ=60o φ=75o φ=75o φ=90o φ=90o −40 −40 −90 −60 −30 0 30 60 90 −90 −60 −30 0 30 60 90 γ (Degree) γ (Degree)

Figure 2.15: Far field radiation pattern of the patch on an infinite dielectric slab with an infinite ground plane.

30 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.

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 2.16.

Figure 2.17 exhibits the radiated electric fields , Eθ and Eφ, 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

31 Eθ (partially grounded finite substrate) Eφ (partially grounded finite substrate) −10 −10

−15 −15

−20 −20 | (dB) | (dB) θ φ |E |E

o φ=0 φ=0o −25 o −25 φ=15 φ=15o o φ=30 φ=30o o φ=45 φ=45o o φ=60 φ=60o o φ=75 φ=75o o φ=90 φ=90o −30 −30 −180−135 −90 −45 0 45 90 135 180 −180−135 −90 −45 0 45 90 135 180 γ (Degree) γ (Degree)

Figure 2.17: Far-ﬁeld radiation pattern of a patch antenna on a ﬁnite dielectric slab with a square partial ground plane.

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, 0◦ and 90◦.

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 follows.

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 in-

spected ﬁrst (Figure 2.18), since we need to ensure that the antenna radiates sym-

metric ﬁeld patterns on the azimuth planes before adding the octagonal parasitic

ring to the antenna. Figure 2.19 shows the radiated ﬁeld components, Eθ and Eφ,

of the antenna described above. Clearly, both components are fairly symmetric for

32 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.

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 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 2.20. Clearly, the Eφ 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, Eθ, remains unchanged between the two states of the switch operation as expected.

33 Eθ (Partially grounded finite substrate) Eφ (Partially grounded finite substrate) 25 25

20 20

15 15 | (dB) | (dB) θ φ |E |E

0o 0o 15o 15o o 30o 10 30 10 45o 45o 60o 60o 75o 75o 90o 90o

5 5 −180−135 −90 −45 0 45 90 135 180 −180−135 −90 −45 0 45 90 135 180 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.

2.4 Description of New Antenna Geometry

As mentioned earlier, the antenna considered here is designed for the L1 GPS

frequency, namely, 1.575 GHz. Although two concepts for controlling both vertical

and horizontal ﬁeld components, i.e. Eθ and Eφ respectively, the work presented in

this chapter considers a scheme to modify the beamwidth of the horizontal ﬁeld com-

ponent, Eφ, while the Eθ component remains unchanged due to the geometry of the

parasitic structure. The basic antenna geometry is shown in Figure 2.21. It consists

of a square radiating patch of size, P = 27.50 mm, mounted on a dielectric substrate

of relative permittivity (dielectric constant) equal to 9.2. The dielectric substrate is

177.80 mm 177.80 mm with thickness of 7.62 mm (0.1213λ ). The radiating patch × d is surrounded by a switch loaded octagonal ring. As mentioned previously, a thick

34 φ o φ o Magnitude of Eφ at =0 Magnitude of Eφ at =90 −5 −5

−10 −10

−15 −15

−20 −20 | (dB) | (dB) φ φ

|E −25 |E −25 Switch On −30 Switch Off −30

−35 −35 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ o φ o Magnitude of Eφ at =15 Magnitude of Eφ at =30 −5 −5

−10 −10

−15 −15

−20 −20 | (dB) | (dB) φ φ

|E −25 |E −25

−30 −30

−35 −35 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ o φ o Magnitude of Eφ at =45 Magnitude of Eφ at =60 −5 −5

−10 −10

−15 −15

−20 −20 | (dB) | (dB) φ φ Switch on |E −25 |E −25

−30 −30 Switch off

−35 −35 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 γ (Degree) γ (Degree)

Figure 2.20: Comparison of calculated far-ﬁeld radiation patterns (Eφ) of the antenna with the circular parasitic ring at φ=0◦, 15◦, 30◦, 45◦, 60◦ and 90◦

35 y

Parasitic Structure Switching Circuit

W Radiating Patch

R2 x D R1 Antenna Cross Section

(a) Top View z

Parasitic Structure Radiating Patch P 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 ( 0.12λd) which is used for surface wave excitation.

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 (Eφ), a thin ring is used so the longitudinal induced currents are dominant while the transverse currents are weak. Furthermore,

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.

36 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 broadside all the way to the horizon. A CP polarized pattern can be generated by exciting two orthogonal current modes with 90◦ 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 90◦.

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 90◦ 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 2.6.

2.5 Design Procedure

This section discusses design considerations of both the parasitic ring structure and the switching circuit.

2.5.1 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 recon-

ﬁgurability in only two principal planes, i.e. x z and y z planes. It is, however, − − 37 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 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

38 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 compo-

nent. 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

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 sur-

rounded 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 2.23.

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 (R2), size of ring (R1), 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 (177.80 mm 177.80 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, R1=

39 Magnitude of surface current (J ), 1.575 GHz s

0.9 40 0.8

60 0.7 y 0.6 80

y X 0.5

100 0.4

0.3

120 0.2

0.1 140

40 60 80 100 120 140 x

Figure 2.22: Surface currents induced on the octagonal parasitic ring without any cuts.

Octagonal ParasiticRing y y Radiating Patch

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).

40 Directivity (Dφ) Directivity (Dφ) 10 10 φ=0o Uncut Ring φ=45o Uncut Ring φ=0o Cut Ring φ=45o Cut Ring o o 5 φ=15 Uncut Ring 5 φ=60 Uncut Ring φ=15o Cut Ring φ=60o Cut Ring φ=30o Uncut Ring φ=75o Uncut Ring o o 0 φ=30 Cut Ring 0 φ=75 Cut Ring

−5 −5

−10 −10 (dB) (dB) φ φ D D

−15 −15

−20 −20

−25 −25

−30 −30 0 45 90 135 180 0 45 90 135 180 θ (degree) θ (degree)

Figure 2.24: Comparison of calculated (FDTD) directivity patterns (Dφ) between the full and cut ring conﬁgurations for φ=0◦ , 15◦, 30◦, 45◦, 60◦ and 75◦.

75.625 mm, D=6.875 mm and R2=23.375 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 com-

ponent (Eφ) for various azimuth planes. As can be seen, there is almost a 7-10 dB

change along the horizon (90◦) in the directivity pattern of Eφ between the on/oﬀ

states of the ring, except for the φ = 75◦ plane cut. Even larger changes can be

observed around θ 110◦ 135◦. Unlike the square ring case, these patterns demon- ≈ − strate that reconﬁgurability is maintained in azimuth. In other words, the radiation

pattern of Eφ along the horizon is always lower when the switches are turned oﬀ

41 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 2.25. 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 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.

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

42 Eφ Patch Eφ Ring (Diodes On) Eφ Ring (Diodes Off) 10 10 10 φ=0o 5 φ=90o 5 5

0 0 0

−5 −5 −5

−10 −10 −10 | (dB) | (dB) | (dB) φ φ φ

|E −15 |E −15 |E −15

−20 −20 −20

−25 −25 −25

−30 −30 −30 0 45 90 135 180 0 45 90 135 180 0 45 90 135 180 θ (Degree) θ (Degree) θ (Degree)

Eφ Patch Eφ Ring (Diodes On) Eφ Ring (Diodes Off) 200 200 200

150 150 150

100 100 100

50 50 50

0 0 0 (Degree) (Degree) (Degree) φ −50 φ −50 φ −50 /E /E /E −100 −100 −100

−150 −150 −150

−200 −200 −200 0 45 90 135 180 0 45 90 135 180 0 45 90 135 180 θ (Degree) θ (Degree) θ (Degree)

Figure 2.25: Calculated (FDTD) radiation patterns (Eφ) 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.

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Figure 2.26: Schematic representation of the switch circuit components inserted in the switching cuts introduced in the parasitic ring.

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 [13]

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-

02, 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

44 the switching ring. Three diodes are included in each switching strip to provide the

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 simula-

tions 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],

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

45 Figure 2.27: ADS schematic for Philips BAP51-02 diode.

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, Zs, (in ohms per square), which is then speciﬁed to the simulator. This can be accomplish using the following equation:

W Z = Z( ) (2.1) s L where W and L are the width and length of the surface, respectively.

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

46 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 = 1.8 + j8.015 Ω and Z = 0.766 j431.226 Ω, respectively. Keeping in mind d d − 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 = 1.878+j8.363 Ω per square and Z = 0.799 j449.97 s s − Ω per square for the forward and reserved bias conditions, respectively.

Figure 2.28: Schematic to determine the ”impedance model” for every switching circuit for forward and reverse bias conditions.

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

47 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 [13].

It was found that the larger the separation, the better the performance. Thus, the two strips are as shown in Figure 2.26. 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=75.625 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 (R2=23.375 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 of just the ring (diodes reverse biased) has been reduced from the ideal case (180◦) when the ring is cut.

48 Calculated Gain Pattern (Gφ) (dB) Calculated Gain Pattern (Gφ) (dB) 10 10 φ=0o Switch On φ=45o Switch On φ=0o Switch Off φ=45o Switch Off φ=15o Switch On φ=60o Switch On o o 5 φ=15 Switch Off 5 φ=60 Switch Off φ=30o Switch On φ=90o Switch On φ=30o Switch Off φ=90o Switch Off

0 0

−5 −5 (dB) (dB) φ φ G G

−10 −10

−15 −15

−20 −20 0 45 90 135 180 0 45 90 135 180 θ (degree) θ (degree)

Figure 2.29: Calculated (HFSS) gain patterns (Gφ) for on and oﬀ states of switches for φ=0◦ , 15◦, 30◦, 45◦, 60◦ and 90◦.

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:

R1=67.50 mm, D =15 mm, W =30 mm in the principal planes and W =31.334 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 2.26. As expected, the performance is not as good as the ideal case shown in Figure 2.24; however, the reconﬁgurability is maintained.

49 Output Signal Port #2 Input Signal Power Power Port #1 Divider Divider

o Output Signal Port #3 90 Phase Shifter

o 90 Phase Power Output Signal Port #4 Shifter Divider

o 90 Phase Output Signal Port #5 Shifter

Figure 2.30: 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 90◦ 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 2.30, 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.

50 (a) Front View (b) Back View

Figure 2.31: Implemented two-stage Wilkinson power divider. The substrate (RT/Duroid 5870, 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. TMM10i, ²r = 9.8) such that it ﬁts on the ground plane of the antenna. The measured magnitudes of S21, S31, S41 and S51 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

0.2 dB at 1.575 GHz. In addition, Figure 2.32(b) shows the measured phase response over the same frequency band. As shown, the relative phase increment at 1.575 GHz

is 0◦, 89.7◦, 185.3◦ and 275.3◦ respectively. Thus, it is shown that a circularly po-

larized pattern can be achieved using this feed network. It is also worth noting that the coupling between these output ports (i.e. S23, S24, etc.) is very insigniﬁcant,

approximately -35 dB.

51 Measured Magnitude of S Vs Frequency i1 Measured Relative Output Phase Vs Frequency −6.5 300 |S | 21 |S | 31 270 |S | phase(S )−phase(S )) 41 21 21 |S | 240 phase(S )−phase(S )) −6.7 51 31 21 phase(S )−phase(S )) 41 21 210 phase(S )−phase(S )) 51 21

180 −6.9 150 | (dB) 1 i 120 |S −7.1

Phase (Degree) 90

−7.3 30

−7.5 −30 1.55 1.555 1.56 1.565 1.57 1.575 1.58 1.585 1.59 1.595 1.6 1.55 1.555 1.56 1.565 1.57 1.575 1.58 1.585 1.59 1.595 1.6 Frequency (GHz) Frequency (GHz) (a) Magnitude (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.

2.7.1 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, 1.575 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.

52 Figure 2.33: Geometry of the implemented reconﬁgurable antenna.

Magnitude of S Vs. Frequency ii 0

−5 | (dB) i i

|S −10 Port 2 Switch On Port 3 Switch On Port 2 Switch Off Port 3 Switch Off −15 1.2 1.3 1.4 1.5 1.6 1.7 1.8 9 Frequency (Hz) x 10 Phase of S Vs. Frequency ii

150

100

0 (Degree) i

i −50

/S −100

−150

1.2 1.3 1.4 1.5 1.6 1.7 1.8 9 Frequency (Hz) x 10

Figure 2.34: Comparison of the measured input impedance between the on and oﬀ states of the switches.

53 2.7.2 Radiation Characteristics

Figure 2.35 shows a comparison of the measured elevation gain pattern for the

horizontal component (Gφ) for the on and off states of the switches at φ◦ = 0◦, 15◦, 45◦ and 90◦. As predicted, the measured gain patterns are very similar to the simulated results shown in Figure 2.29. 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 (Gθ) for the on and off states of the switches at φ◦ = 0◦, 15◦, 45◦ and 90◦. 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◦ = 0◦, 15◦, 45◦ and 90◦. It is noted that when switches

are activated, the antenna represents an excellent axial ratio that is less than 3 dB

for θ between 0◦ and 90◦ in all planes, (φ = 0◦, 15◦, 45◦, 90◦). On the other hand, the

axial ratio of the switches oﬀ cases is below 3 dB for θ between 0◦ and 60◦. 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◦ = 0◦, 15◦, 45◦

and 90◦. 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

54 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 =

0◦, 30◦ and 50◦. 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=50◦. 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 con- sisting 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

55 Measured Gain Pattern (Gφ) (dB) 5

0 (dB) φ φ ° −5 =0 Switch On ° φ=0 Switch Off ° φ=15 Switch On ° Measured G φ=15 Switch Off ° −10 φ=45 Switch On ° φ=45 Switch Off ° φ=90 Switch On ° φ=90 Switch Off −15 0 45 90 135 180 θ (degree)

Figure 2.35: Measured gain patterns (Gφ) for the on and oﬀ states of the switches for φ=0◦,φ=15◦, φ=45◦ and φ=90◦.

Measured Gain Pattern (Gθ) (dB) 5

0 (dB) θ φ ° −5 =0 Switch On ° φ=0 Switch Off ° φ=15 Switch On ° Measured G φ=15 Switch Off ° −10 φ=45 Switch On ° φ=45 Switch Off ° φ=90 Switch On ° φ=90 Switch Off −15 0 45 90 135 180 θ (degree)

Figure 2.36: Measured gain patterns (Gθ) for the on and oﬀ states of the switches for φ=0◦, φ=15◦, φ=45◦ and φ=90◦.

56 Measured Axial Ratio (dB) 10 ° φ=0 Switch On 9 ° φ=0 Switch Off ° 8 φ=15 Switch On ° φ=15 Switch Off 7 ° φ=45 Switch On ° 6 φ=45 Switch Off ° φ=90 Switch On 5 ° φ=90 Switch Off 4

Measured AR (dB) 3

0 0 30 60 90 θ (degree)

Figure 2.37: Measured axial ratio for the on and oﬀ states of the switches for φ=0◦, φ=15◦, φ=45◦ and φ=90◦.

Measured RHCP (dB) 10

° φ=0 Switch On ° φ=0 Switch Off −5 ° φ=15 Switch On ° φ=15 Switch Off ° φ=45 Switch On °

Measured RHCP Patterns (dB) −10 φ=45 Switch Off ° φ=90 Switch On ° φ=90 Switch Off −15 0 45 90 135 180 θ (degree)

Figure 2.38: Measured right hand circular polarized gain patterns (GRHCP ) for the on and oﬀ states of the switches for φ=0◦, φ=15◦, φ=45◦ and φ=90◦.

57 Measured Azimuth Gain Pattern (Gθ) (dB) Measured Azimuth Gain Pattern (Gφ) (dB) 10 10

8 8

6 6

4 4

(dB) 2 (dB) 2 θ φ

0 0 θ ° ° =0 Switch Off θ=0 Switch Off −2 θ ° −2 ° =0 Switch On θ=0 Switch On ° Measured G θ Measured G ° −4 =30 Switch Off −4 θ=30 Switch Off ° θ=30 Switch On θ ° −6 −6 =30 Switch On θ ° ° =50 Switch Off θ=50 Switch Off −8 θ ° −8 ° =50 Switch On θ=50 Switch On −10 −10 0 45 90 135 180 225 270 315 360 0 45 90 135 180 225 270 315 360 φ (degree) φ (degree)

Measured Right Handed Circularly Polarized Azimuth Gain Pattern Measured Axial Ratio (dB) 15 15

° θ=0 Switch Off ° θ=0 Switch On 10 12 ° θ=30 Switch Off ° θ=30 Switch On θ ° 5 9 =50 Switch Off ° θ=50 Switch On

° 0 θ=0 Switch Off 6 ° θ=0 Switch On ° Measured AR (dB) θ=30 Switch Off ° Measured RHCP Gain (dB) −5 θ=30 Switch On 3 ° θ=50 Switch Off ° θ=50 Switch On −10 0 0 45 90 135 180 225 270 315 360 0 45 90 135 180 225 270 315 360 φ (degree) φ (degree)

Figure 2.39: Measured azimuth patterns for the on and oﬀ states of the switches for θ=0◦, θ=30◦ and θ=50◦.

58 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 (0◦ < φ < 360◦) 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 (Eθ). 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.

59 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 applications 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 operates at the two GPS frequencies of L1 (1.575 GHz) and L2 (1.227

GHz) but it is reconﬁgurable only at the L1 band. Unlike the single band antenna, the goal of the dual band antenna is to control the vertical component of the electric

ﬁeld, Eθ. 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

60 provides the reconﬁgurability. The requirement for right hand circularly polarized

radiation patterns from the two antennas places certain demands on the feeding net-

work. The design 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=0◦ and 90◦). It is found that the reconfigurability falls off dramatically as the observation angle moves away from the principal planes. This 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 its characteristics evalued, 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 Fig- ures 3.1 and 3.2. The bottom dielectric layer has a thickness (H3) of 4.9212 mm with a dielectric constant (²3) of 3.27. The middle dielectric layer has a thickness (H2) of

3.2808 mm with a dielectric constant (²2) of 9.2, while the top dielectric layer has the same thickness (H1) and dielectric constant (²1) as the middle layer, namely 3.2808

61 mm and 9.2, respectively. The shape of all substrate layers is initially a square. Un- like 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 50.56 mm × 50.56 mm, while the L1 (1.575 GHz) patch is located on top of the middle layer, and its dimensions are 25.28 mm 25.28 mm. The initial substrate size was chosen to × be 177.8 mm 177.8 mm originally (same as the single band case). The parasitic × rings are positioned in the middle and top layers. It is to be noted that only the top parasitic ring 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 1.575 GHz and 1.227 GHz. Right hand circular polarization is required at both bands. To achieve this polarization, 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

90◦ 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.

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63 3.3.1 Input Impedance

In a typical printed antenna, the input impedance is a function of a feed position

on the patch and 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 location 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 up to 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

64 the entire coaxial cable through the L2 patch, so that the outer conductor shielding

the probe will reduce mutual coupling between two antennas. 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 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, S11, of the L1 and L2 patches, accordingly. It can be observed that the upper patch resonates at 1.578 GHz with the return loss of -20 dB. Similarly, the lower patch resonates approximately at 1.223 GHz with the return loss of -40 dB.

65 (a) Feed coaxial cable of the L1 and L2 patches. (b) Side view

Figure 3.3: Feed conﬁguration of the dual band antenna.

3.3.2 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 90◦ 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.

66 Input Impedance and |S | of the Upper Radiating Patch (L1) 11 100 Resistance Reactance ) Ω 50

0 Impedance (

−50 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Frequency (GHz)

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−10

| (dB) −15 1 1

|s −20

−25

−30 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Frequency (GHz)

Figure 3.4: Calculated input impedance and S11 response for upper radiating patch. The feed probe is located 4.74 mm from the center of the L1 patch.

Input Impedance and |S | of the Lower Radiating Patch (L2) 11 100 Resistance Reactance ) Ω 50

0 Impedance (

−50 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Frequency (GHz)

−10

−20 | (dB) 1 −301 |s

−40

−50 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Frequency (GHz)

Figure 3.5: Calculated input impedance and S11 response for lower radiating patch. The feed probe is located 11.06 mm from the center of the L2 patch.

67 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 the 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 50Ω lines required to feed these cables, and to ensure that the lines do not touch each other, a substrate (RT/Duroid

6002) 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 5870). Also, the thickness of the substrate is 0.51 mm (20 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 100Ω (2 50Ω), 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 0.2 dB at 1.575 GHz. In addition, the

68 (a) Layout (b) Implemented circuit

Figure 3.6: The two-stage Wilkinson power divider for the dualband antenna. The substrate (RT/Duroid 6002).

measured phase response over the same frequency band shows the relative phase increment at 1.575 GHz is 0◦, 90.0◦, 180.3◦ and 265.3◦ 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 0.2 dB at 1.227

GHz. Further, the measured phase response over the same frequency band shows the relative phase increment at 1.227 GHz is 0◦, 93.3◦, 179.1◦ and 277.2◦ 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. S23, S24, etc.) is very low, approximately -35 dB.

69 Measured Magnitude Response of S of Feeding Circuit for the L1 Patch i1 −5.5 S 21 S 31 S −6 41 S 51

−6.5 | (dB) 1 i |S

−7

−7.5 1.55 1.555 1.56 1.565 1.57 1.575 1.58 1.585 1.59 1.595 1.6 9 Frequency (Hz) x 10

Measured Relative Output Phase of Feeding Circuit for the L1 Patch 300 270 240 210 180 150 phase(S −S ) 120 21 41 phase(S −S ) 90 31 41 phase(S −S ) 60 41 41

Relative Phase (Degree) phase(S −S ) 30 51 41 0 −30 1.55 1.555 1.56 1.565 1.57 1.575 1.58 1.585 1.59 1.595 1.6 9 Frequency (Hz) x 10

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)

3.4.1 2-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

70 Measured Magnitude Response of S of Feeding Circuit for the L2 Patch i1 −6 S 21 S −6.2 31 S 41 S 51 −6.4 | (dB) 1 i −6.6 |S

−6.8

−7 1.2 1.205 1.21 1.215 1.22 1.225 1.23 1.235 1.24 1.245 1.25 9 Frequency (Hz) x 10

Measured Relative Output Phase of Feeding Circuit for the L2 Patch 300 270 phase(S −S ) 240 21 41 phase(S −S ) 210 31 41 phase(S −S ) 180 41 41 phase(S −S ) 150 51 41 120 90 60

Relative Phase (Degree) 30 0 −30 1.2 1.205 1.21 1.215 1.22 1.225 1.23 1.235 1.24 1.245 1.25 9 Frequency (Hz) x 10

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

71 y

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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 3.10 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

72 Comparison of |Eθ| 2D VS 3D (L1) Phase Comparison of Eθ 2D VS 3D (L1) 5 50 3D 3D 2D 2D

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−15 Phase of E

−150 −20

−25 −200 −180−135 −90 −45 0 45 90 135 180 −180−135 −90 −45 0 45 90 135 180 γ (Degree) γ (Degree)

Figure 3.10: 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.

3.4.2 3-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,

73 Comparison of magnitude of Eθ for L1 Band −30 w1=0.0257 m w1=0.0567 m −35

−40

−45

−50 | (dB) θ |E −55

−60

−65

−70 −90 −45 0 45 90 135 180 225 270 γ (Degree)

Figure 3.11: Comparison of vertical ﬁeld component between two diﬀerent strip width at the L1 band

Comparison of magnitude of Eθ for L2 Band −25 w1=0.0257 m w1=0.0567 m −30

−35

−40

−45 | (dB) θ |E −50

−55

−60

−65 −90 −45 0 45 90 135 180 225 270 γ (Degree)

Figure 3.12: Comparison of vertical ﬁeld component between two diﬀerent strip width at the L2 band

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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 3.14.

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 30 dB drop

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in the vertical ﬁeld component along the horizon is obtained by increasing the strip width as shown in Figure 3.15. 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 2.05 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

76 φ o Scheme A : Eφ component 1.227 GHz ( =0 ) −10 −20 −30 | (dB)

−40φ w1=0.0158 m |E −50 w1=0.0316 m −60 −180 −150 −120 −90 −60 −30 0 30 60φ o 90 120 150 180 Scheme A : Eθ component 1.227 GHz ( =0 ) −10 −20 −30 | (dB)

−40θ

|E w1=0.0158 m −50 w1=0.0316 m −60 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 Scheme A : Axial Ratio 1.227 GHz (φ=0o) 18 15 12 9 6 w1=0.0158 m w1=0.0316 m 3 Axial Ratio (dB) 0 −90 −60 −30 0 30 60 90 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 0.79 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 10 dB simultaneous drop in the vertical ﬁeld components,

Eθ, 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

77 φ o Scheme B : Eφ component 1.575 GHz ( =0 ) −10 −20 −30 | (dB)

−40φ

|E w1=0.0205 m −50 w1=0.0237 m −60 −180 −150 −120 −90 −60 −30 0 30 60φ o 90 120 150 180 Scheme B : Eθ component 1.575 GHz ( =0 ) −10

−20 | (dB)

−30θ w1=0.0205 m |E w1=0.0237 m −40

−180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 Scheme B : Axial Ratio 1.575 GHz (φ=0o) 18 15 12 9 w1=0.0205 m 6 w1=0.0237 m 3 Axial Ratio (dB) 0 −90 −60 −30 0 30 60 90 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=0◦ and 90◦). 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.

78 φ o Scheme B : Eφ component 1.575 GHz ( =0 ) −10 −20 −30 | (dB)

−40φ

|E w1=0.0079 m −50 w1=0.0237 m −60 −180 −150 −120 −90 −60 −30 0 30 60φ o 90 120 150 180 Scheme B : Eθ component 1.575 GHz ( =0 ) −10

−20 | (dB)

−30θ

|E w1=0.0079 m −40 w1=0.0237 m

−180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 Scheme B : Axial Ratio 1.575 GHz (φ=0o) 18 15 12 9 w1=0.0079 m 6 w1=0.0237 m 3 Axial Ratio (dB) 0 −90 −60 −30 0 30 60 90 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 3.19. Hence the square substrate is not suitable for this application, and replaced by the octagonal substrate. Figure. 3.20 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

79 φ o Scheme B : Eφ component 1.227 GHz ( =0 ) −10 −20 −30 | (dB)

−40φ

|E w1=0.0079 m −50 w1=0.0237 m −60 −180 −150 −120 −90 −60 −30 0 30 60φ o 90 120 150 180 Scheme B : Eθ component 1.227 GHz ( =0 ) −10

−20 | (dB)

−30θ

|E w1=0.0079 m −40 w1=0.0237 m

−180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 Scheme B : Axial Ratio 1.227 GHz (φ=0o) 18 15 12 9 w1=0.0079 m 6 w1=0.0237 m 3 Axial Ratio (dB) 0 −90 −60 −30 0 30 60 90 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 0.3 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

3.6.1 Basic Geometry

The new geometry of the three layer dual band antenna is shown in Figure 3.21.

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

80 |Eφ| of the Dual Band Antenna with Square Substrate at the L1 Frequency |Eθ| of the Dual Band Antenna with Square Substrate at the L1 Frequency 5 5

0 0

−5 −5

−10 ° −10 φ=0 ° | (dB) | (dB) φ θ φ =15

|E −15 ° |E −15 φ=30 ° φ=45 −20 ° −20 φ=60 ° φ=75 −25 ° −25 φ=90

−30 −30 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

|Eφ| of the Dual Band Antenna with Square Substrate at the L2 Frequency |Eθ| of the Dual Band Antenna with Square Substrate at the L2 Frequency 5 5

0 0

−5 −5

−10 −10 | (dB) | (dB) φ θ

|E −15 |E −15

−20 −20

−25 −25

−30 −30 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.19: Calculated radiation pattern of the dual band antenna with a square substrate at 1.575 GHz and 1.227 GHz.

81 |Eφ| of the Dual Band Antenna with Octagonal Substrate at the L1 Frequency |Eθ| of the Dual Band Antenna with Octagonal Substrate at the L1 Frequency 5 5

0 0

−5 −5

° −10 φ=0 −10 φ ° | (dB) =15 | (dB) φ ° θ

|E −15 φ=30 |E −15 ° φ=45 ° −20 φ=60 −20 ° φ=75 ° −25 φ=90 −25

−30 −30 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

|Eφ| of the Dual Band Antenna with Octagonal Substrate at the L2 Frequency |Eθ| of the Dual Band Antenna with Octagonal Substrate at the L2 Frequency 5 5

0 0

−5 −5

−10 −10 | (dB) | (dB) φ θ

|E −15 |E −15

−20 −20

−25 −25

−30 −30 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.20: Calculated radiation pattern of the dual band antenna with an octagonal substrate at 1.575 GHz and 1.227 GHz.

82 Figure 3.21: New proposed geometry of a dual band antenna.

size was chosen to be 177.8 mm 177.8 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, 228.6 mm 228.6 mm is chosen × for this application.

3.6.2 Parasitic Structure and Switching Circuitry Design

The dual band reconﬁgurable antenna is initially aimed to provide pattern re-

conﬁgurability of the vertical electric ﬁeld component, Eθ, 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

83 study, the two states of the parasitic structure are secured, a solid octagonal ring and a switch loaded octagonal ring, i.e. a solid ring with four extra strips as shown in

Figure 3.22. 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 3.23.

The approach to arrive at the two states of the ring is based on designing the ring by itself whose radiation pattern cancels out the pattern radiated by the antenna with no ring along the horizon at 1.575 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 3.22. 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 3.23. 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

84 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 closer to the pattern radiated by the antenna with loaded ring. Further, those small strips will be cut such that thier current distributions, 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 are also presented in Figure 3.25. It is certain that we can obtain the same reconfigurability

( 7-8 dB) along the horizon region as described in Figure 3.23. 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. Fig- ures 3.28, 3.29 and 3.30 illustrate the radiation patterns and axial ratio of the dual band antenna at 1.575 GHz on several elevation planes, φ = 0◦, 15◦, 30◦, 45◦, 60◦ and

90◦. It can be seen from Figure 3.28 that nearly a 6-8 dB drop in Eθ is obtained by activating the switches loaded on the parasitic ring. However, the horizontal field component, Eφ, remains mostly unchanged between the two operational states of the switches, on and off. It is also worth noting that the simulated radiation patterns shown here are not calibrated or normalized to any standard gain horn. 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 0◦ θ 70◦ on most eleva- ≤ ≤ tion planes. Likewise, Figures 3.31, 3.32 and 3.33 illustrate the radiation patterns

85 and axial ratio of the dual band antenna at 1.227 GHz on several elevation planes,

φ = 0◦, 15◦, 30◦, 45◦, 60◦ and 90◦. In this case, both Eθ and Eφ remain almost the

same between the two states of the switches. In addition, the axial ratio remains less

than 3 dB for 0◦ θ 60◦ 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

86 φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =0 (L1 Band). |Eθ| (dB) with Octgonal Substrate at =90 (L1 Band). −15 −15

−20 −20

−25 −25

−30 −30 | (dB) | (dB) θ θ

|E −35 |E −35 Loaded Ring Loaded Ring −40 −40 Solid Ring Solid Ring −45 −45 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =15 (L1 Band). |Eθ| (dB) with Octgonal Substrate at =30 (L1 Band). −15 −15

−20 −20

−25 −25

−30 −30 | (dB) | (dB) θ θ

|E −35 |E −35 Loaded Ring Loaded Ring −40 Solid Ring −40 Solid Ring

−45 −45 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =45 (L1 Band). |Eθ| (dB) with Octgonal Substrate at =60 (L1 Band). −15 −15

−20 −20

−25 −25

−30 −30 | (dB) | (dB) θ θ

|E −35 |E −35 Loaded Ring Loaded Ring −40 Solid Ring −40 Solid Ring

−45 −45 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) 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.

87 (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.

parasitic ring having same dimension as the ring located on the top layer. Recall 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 3.36.

3.7.1 Impedance Characteristics

After glueing each substrate together, the input impedance of each patch is measured. However, it was found later that there is a small shift in the resonances of both radiating patches. The slight drift in the resonant frequencies 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 at- taching each substrate. As a results the patch dimensions must be slightly modiﬁed.

The upper patch dimension is increased from 25.28 mm to 32 mm, while that of the lower patch is changed from 50.56 mm to 52 mm. Figure 3.37 and Figure 3.38 show

88 φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =0 (L1 Band). |Eθ| (dB) with Octgonal Substrate at =90 (L1 Band). −15 −15

−20 −20

−25 −25

−30 −30 | (dB) | (dB) θ θ

|E −35 |E −35 Ring with Uncut Strips Ring with Uncut Strips −40 Ring with Cut Strips −40 Ring with Cut Strips

−45 −45 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =15 (L1 Band). |Eθ| (dB) with Octgonal Substrate at =30 (L1 Band). −15 −15

−20 −20

−25 −25

−30 −30 | (dB) | (dB) θ θ

|E −35 |E −35 Ring with Uncut Strips Ring with Uncut Strips −40 Ring with Cut Strips −40 Ring with Cut Strips

−45 −45 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =45 (L1 Band). |Eθ| (dB) with Octgonal Substrate at =60 (L1 Band). −15 −15

−20 −20

−25 −25

−30 −30 | (dB) | (dB) θ θ

|E −35 |E −35 Ring with Uncut Strips Ring with Uncut Strips −40 Ring with Cut Strips −40 Ring with Cut Strips

−45 −45 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 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.

89 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.

the return loss of the four ports on the upper and lower patches, respectively. It is

clear that both patches demonstrate minimum return losses approximately right at their frequencies of operation, 1.575 GHz and 1.227 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.

3.7.2 Radiation Characteristics

The measured radiation patterns at the L1 and L2 bands are presented in this subsection. Note that the measured radiation patterns shown here are normalized to the same standard gain horn mention in Chapter 2. Figure 3.39 shows a measured gain pattern of the vertical ﬁeld component, Gθ, at 1.575 GHz on four elevation

90 Figure 3.27: Schematic representation of the switching circuit component loaded on the solid ring.

planes; 0◦, 45◦, 90◦ and 135◦. It is obvious that by activating the switches, the recon-

ﬁgurability around the horizon region is obtained in the order of 3-4 dB. Similarly,

Figure 3.40 displays a measured gain pattern of the horizontal ﬁeld component, Gφ, on the same elevation planes; 0◦, 45◦, 90◦ and 135◦. As expected, the Gφ 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 depends strongly on the state of the switch operation as depicted in Figures 3.41.

91 φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =0 (L1 Band). |Eθ| (dB) with Octgonal Substrate at =15 (L1 Band). 30 30 Switch On Switch On 25 Switch Off 25 Switch Off

20 20

15 15 | (dB) | (dB) θ θ

|E 10 |E 10

5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =30 (L1 Band). |Eθ| (dB) with Octgonal Substrate at =45 (L1 Band). 30 30 Switch On Switch On 25 Switch Off 25 Switch Off

20 20

15 15 | (dB) | (dB) θ θ

|E 10 |E 10

5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =60 (L1 Band). |Eθ| (dB) with Octgonal Substrate at =75 (L1 Band). 30 30 Switch On Switch On 25 Switch Off 25 Switch Off

20 20

15 15 | (dB) | (dB) θ θ

|E 10 |E 10

5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.28: Calculated radiation pattern of the dual band antenna with a octagonal substrate at 1.575 GHz.

92 φ ° φ ° |Eφ| (dB) with Octgonal Substrate at =0 (L1 Band). |Eφ| (dB) with Octgonal Substrate at =15 (L1 Band). 30 30 Switch On Switch On 25 Switch Off 25 Switch Off

20 20

15 15 | (dB) | (dB) φ φ

|E 10 |E 10

5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eφ| (dB) with Octgonal Substrate at =30 (L1 Band). |Eφ| (dB) with Octgonal Substrate at =45 (L1 Band). 30 30 Switch On Switch On 25 Switch Off 25 Switch Off

20 20

15 15 | (dB) | (dB) φ φ

|E 10 |E 10

5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eφ| (dB) with Octgonal Substrate at =60 (L1 Band). |Eφ| (dB) with Octgonal Substrate at =75 (L1 Band). 30 30 Switch On Switch On 25 Switch Off 25 Switch Off

20 20

15 15 | (dB) | (dB) φ φ

|E 10 |E 10

5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.29: Calculated radiation pattern of the dual band antenna with a octagonal substrate at 1.575 GHz.

93 ° ° Axial Ratio of the Dual Band Antenna at φ=0 (1.575 GHz) Axial Ratio of the Dual Band Antenna at φ=15 (1.575 GHz) 20 20

15 15 Switch On Switch On Switch Off Switch Off 10 10 |AR| (dB) |AR| (dB) 5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

° ° Axial Ratio of the Dual Band Antenna at φ=30 (1.575 GHz) Axial Ratio of the Dual Band Antenna at φ=45 (1.575 GHz) 20 20

15 15 Switch On Switch On Switch Off Switch Off 10 10 |AR| (dB) |AR| (dB) 5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

° ° Axial Ratio of the Dual Band Antenna at φ=60 (1.575 GHz) Axial Ratio of the Dual Band Antenna at φ=75 (1.575 GHz) 20 20

15 15 Switch On Switch On Switch Off Switch Off 10 10 |AR| (dB) |AR| (dB) 5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.30: Calculated axial ratio of the dual band antenna with a octagonal substrate at 1.575 GHz.

94 φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =0 (L2 Band). |Eθ| (dB) with Octgonal Substrate at =15 (L2 Band). 30 30

25 25

20 20

15 15 | (dB) | (dB) θ θ

|E 10 |E 10 Switch On Switch On Switch Off Switch Off 5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =30 (L2 Band). |Eθ| (dB) with Octgonal Substrate at =45 (L2 Band). 30 30

25 25

20 20

15 15 | (dB) | (dB) θ θ

|E 10 |E 10 Switch On Switch On Switch Off Switch Off 5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eθ| (dB) with Octgonal Substrate at =60 (L2 Band). |Eθ| (dB) with Octgonal Substrate at =75 (L2 Band). 30 30

25 25

20 20

15 15 | (dB) | (dB) θ θ |E |E 10 Switch On 10 Switch On Switch Off Switch Off 5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.31: Calculated radiation pattern of the dual band antenna with a octagonal substrate at 1.227 GHz.

95 φ ° φ ° |Eφ| (dB) with Octgonal Substrate at =0 (L2 Band). |Eφ| (dB) with Octgonal Substrate at =15 (L2 Band). 30 30

25 25

20 20

15 15 | (dB) | (dB) φ φ

|E 10 |E 10 Switch On Switch On Switch Off 5 Switch Off 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eφ| (dB) with Octgonal Substrate at =30 (L2 Band). |Eφ| (dB) with Octgonal Substrate at =45 (L2 Band). 30 30

25 25

20 20

15 15 | (dB) | (dB) φ φ

|E 10 |E 10 Switch On Switch On 5 Switch Off 5 Switch Off

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

φ ° φ ° |Eφ| (dB) with Octgonal Substrate at =60 (L2 Band). |Eφ| (dB) with Octgonal Substrate at =75 (L2 Band). 30 30

25 25

20 20

15 15 | (dB) | (dB) φ φ

|E 10 |E 10 Switch On Switch On Switch Off 5 5 Switch Off

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.32: Calculated radiation pattern of the dual band antenna with a octagonal substrate at 1.227 GHz.

96 ° ° Axial Ratio of the Dual Band Antenna at φ=0 (1.227 GHz) Axial Ratio of the Dual Band Antenna at φ=15 (1.227 GHz) 20 20

15 15 Switch On Switch On Switch Off Switch Off 10 10 |AR| (dB) |AR| (dB) 5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

° ° Axial Ratio of the Dual Band Antenna at φ=30 (1.227 GHz) Axial Ratio of the Dual Band Antenna at φ=45 (1.227 GHz) 20 20

15 15 Switch On Switch On Switch Off Switch Off 10 10 |AR| (dB) |AR| (dB) 5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180

° ° Axial Ratio of the Dual Band Antenna at φ=60 (1.227 GHz) Axial Ratio of the Dual Band Antenna at φ=75 (1.227 GHz) 20 20

15 15 Switch On Switch On Switch Off Switch Off 10 10 |AR| (dB) |AR| (dB) 5 5

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.33: Calculated axial ratio of the dual band antenna with a octagonal substrate at 1.227 GHz.

97 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.

98 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 0

−2

−4 Port 1 Port 2 −6 Port 3 Port 4 | Upper Patch (dB) i i −8 |S

−10 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 9 Frequency (Hz) x 10

180

0 (Degree) i i /S −90

−180 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 9 Frequency (Hz) x 10

Figure 3.37: Measured input impedance of the upper radiating patch.

99 Magnitude and Phase Response of the Return Loss on the Lower Patch 0

−5 Port1

Port 2

Port 3 −10 | Lower Patch (dB) i i Port 4 |S

−15 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 9 Frequency (Hz) x 10

180

0 (Degree) i i /S −90

−180 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 9 Frequency (Hz) x 10

Figure 3.38: Measured input impedance of the lower radiating patch.

100 φ ° φ ° Measured |Gθ| (dB) at =0 (L1 Band) Measured |Gθ| (dB) at =45 (L1 Band) 5 5 Switch On Switch On Switch Off Switch Off

0 0

−5 −5 | (dB) | (dB) θ θ

|G −10 |G −10

−15 −15

−20 −20 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

φ ° φ ° Measured |Gθ| (dB) at =90 (L1 Band) Measured |Gθ| (dB) at =135 (L1 Band) 5 5 Switch On Switch On Switch Off Switch Off

0 0

−5 −5 | (dB) | (dB) θ θ

|G −10 |G −10

−15 −15

−20 −20 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.39: Measured Gθ pattern of the dual band antenna at the L1 band.

101 φ ° φ ° Measured |Gφ| (dB) at =0 (L1 Band) Measured |Gφ| (dB) at =45 (L1 Band) 5 5 Switch On Switch On Switch Off Switch Off

0 0

−5 −5 | (dB) | (dB) φ φ

|G −10 |G −10

−15 −15

−20 −20 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

φ ° φ ° Measured |Gφ| (dB) at =90 (L1 Band) Measured |Gφ| (dB) at =135 (L1 Band) 5 5 Switch On Switch On Switch Off Switch Off

0 0

−5 −5 | (dB) | (dB) φ φ

|G −10 |G −10

−15 −15

−20 −20 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.40: Measured Gφ pattern of the dual band antenna at the L1 band.

Likewise, Figures 3.42 and 3.43 represent the measured Gθ and Gφ at 1.227 GHz

on four elevation planes; 0◦, 45◦, 90◦ 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 3.44.

102 ° ° Measured Axial Ratio (dB) at φ=0 (L1 Band) Measured Axial Ratio (dB) at φ=45 (L1 Band) 20 20

18 Switch On 18 Switch On Switch Off Switch Off 16 16

14 14

12 12

10 10

|AR| (dB) 8 |AR| (dB) 8

6 6

4 4

2 2

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

° ° Measured Axial Ratio (dB) at φ=90 (L1 Band) Measured Axial Ratio (dB) at φ=135 (L1 Band) 20 20 Switch On 18 18 Switch On Switch Off Switch Off 16 16

14 14

12 12

10 10

|AR| (dB) 8 |AR| (dB) 8

6 6

4 4

2 2

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.41: Measured axial ratio of the dual band antenna at the L1 band.

103 φ ° φ ° Measured |Gθ| (dB) at =0 (L2 Band) Measured |Gθ| (dB) at =45 (L2 Band) 5 5 Switch On Switch On Switch Off Switch Off

0 0

−5 −5 | (dB) | (dB) θ θ

|G −10 |G −10

−15 −15

−20 −20 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

φ ° φ ° Measured |Gθ| (dB) at =90 (L2 Band) Measured |Gθ| (dB) at =135 (L2 Band) 5 5 Switch On Switch On Switch Off Switch Off

0 0

−5 −5 | (dB) | (dB) θ θ

|G −10 |G −10

−15 −15

−20 −20 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.42: Measured Gθ pattern of the dual band antenna at the L2 band.

104 φ ° φ ° Measured |Gφ| (dB) at =0 (L2 Band) Measured |Gφ| (dB) at =45 (L2 Band) 5 5 Switch On Switch On Switch Off Switch Off

0 0

−5 −5 | (dB) | (dB) φ φ

|G −10 |G −10

−15 −15

−20 −20 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

φ ° φ ° Measured |Gφ| (dB) at =90 (L2 Band) Measured |Gφ| (dB) at =135 (L2 Band) 5 5 Switch On Switch On Switch Off Switch Off

0 0

−5 −5 | (dB) | (dB) φ φ

|G −10 |G −10

−15 −15

−20 −20 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.43: Measured Gφ pattern of the dual band antenna at the L2 band.

It is shown through the measurement that only a 3-4 dB reconﬁgurability in Gθ

is secured along the end-ﬁre direction. This is clearly a few dB lower from what

simulations predict. Nevertheless, by examining the measured pattern when all the

switch components are removed, we found nearly a 5-6 dB reconﬁgurability in Gθ

between the uncut and cut strip cases (see Figures 3.45- 3.47). The decrease in

reconfigurability, thereby, arises from the switching circuit. Obviously, the design of the switching circuit has to be modified in order to achieve more reconfigurability in the Gθ component along the horizon.

105 ° ° Measured Axial Ratio (dB) at φ=0 (L2 Band) Measured Axial Ratio (dB) at φ=45 (L2 Band) 20 20 Switch On Switch On 18 Switch Off 18 Switch Off

16 16

14 14

12 12

10 10

|AR| (dB) 8 |AR| (dB) 8

6 6

4 4

2 2

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

° ° Measured Axial Ratio (dB) at φ=90 (L2 Band) Measured Axial Ratio (dB) at φ=135 (L2 Band) 20 20 Switch On Switch On 18 Switch Off 18 Switch Off

16 16

14 14

12 12

10 10

|AR| (dB) 8 |AR| (dB) 8

6 6

4 4

2 2

0 0 −180 −135 −90 −45 0 45 90 135 180 −180 −135 −90 −45 0 45 90 135 180 θ (Degree) θ (Degree)

Figure 3.44: Measured axial ratio of the dual band antenna at the L2 band.

106 φ ° Measured Gθ (dB) at =0 (L1 Band) 5 Cut Strips Uncut Strips 0

−5

−10 (dB) θ G

−15

−20

−25 −180 −135 −90 −45 0 45 90 135 180 θ (Degree)

Figure 3.45: Measured Gθ pattern of the dual band antenna at the L1 band. Note all the switching components are removed.

107 φ ° Measured Gφ (dB) at =0 (L1 Band) 5 Cut Strips Uncut Strips 0

−5

−10 (dB) φ G

−15

−20

−25 −180 −135 −90 −45 0 45 90 135 180 θ (Degree)

Figure 3.46: Measured Gφ pattern of the dual band antenna at the L1 band. Note all the switching components are removed.

3.8 Summary and Conclusions

In the work reported here we addressed issues concerning the design and analysis

of a dual band, circularly polarized, reconﬁgurable (at the L1 band) printed antenna

for GPS applications. We proposed a novel reconﬁgurable dual band stacked patch antennas which 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, Eθ, along the region of interest is achieved at the L1 band.

108 ° Measured Axial Ratio (dB) at φ=0 20 Cut Strips Uncut Strips 18

8 Measured |AR| (dB) 6

0 −180 −135 −90 −45 0 45 90 135 180 θ (Degree)

Figure 3.47: Measured axial ratio of the dual band antenna at the L1 band. Note all the switching components are removed.

109 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 is usually done using simple design formulas 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,

The Theory of Characteristic Modes, first introduced by Garbacz [4, 6] and then refined by Harrington [9, 10], has been used for a while 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, λn. The magnitude of the eigenvalue

110 indicates how well that particular mode radiates. Modes with small λ are good | n| radiators, whereas those with large λ are poor radiators. The closer the eigenvalue | n| 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 accuracy of the proposed technique, simulated results are thereby compared to analytical solutions when available. An excellent agreement between the resonances and the current modes obtained from the

FDTD simulations and the theoretical values is achieved for all cases.

111 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 with dimensions

a and b as exhibited in Figure 4.1. It is a hollow metallic tube of inﬁnite length in the 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 (TMz) 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, En, as shown in (4.1)

E = anEn (4.1) Xn

where an is the strength of each modal ﬁeld, En. 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).

2 j ∂ Az Ex = −ωµ² ∂x∂z 2 j ∂ Az Ey = −ωµ² ∂y∂z 2 j ∂ 2 Ez = ( 2 + β )Az (4.2) −ωµ² ∂z 1 ∂Az Hx = −µ ∂y 1 ∂Az Hy = −µ ∂x

112 Hz = 0

where

jβzz Az(x, y, z) = Bmn sin(βxx) sin(βyy)e− (4.3)

2π mπ βx = = m = 1, 2, 3 . . . (4.4) λx a

2π nπ βy = = n = 1, 2, 3 . . . (4.5) λy b

In (4.4) and (4.5), βx and βy represent the mode wave number in x and y directions,

respectively. These permissible values of βx and βy 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), (fc)mn, as described in (4.6).

1 mπ 2 nπ 2 (fc)mn = ( ) + ( ) (4.6) 2π√µ²r a b 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 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

113 Y

a Z

Figure 4.1: Geometry of a rectangular cross section waveguide. The waveguide is of inﬁnite length in the z direction.

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, Jn, as shown in (4.7).

J = αnJn (4.7) Xn

where αn 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, λn. The magnitude of λn determines how well that particular

mode radiates. Modes with small λ are good radiators, whilst those with large λ | n| | 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

s of αn will be demonstrated later in this section. The electric field En radiated by the eigencurrent, Jn will be called the characteristic field or eigenfield. The field is

114 linearly related to the current, and hence can also be described in modal summation as shown in (4.8).

s E = αnEn (4.8) Xn 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 , Es = (1 + jλ )δ (4.9) h m ni n mn where δ is the Kronecker delta ( 1 if m=n, and 0 if m=n ). Keep in mind that mn 6 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 αn 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 is composed of the scattered field, Es(ω), and the known incident field, Ei(ω), as described in (4.10).

(Es(ω) + Ei(ω)) = 0 (4.10) |tan

s The total scattered ﬁeld is a linear superposition of each scattered ﬁeld, En, produced

by each eigencurrent, Jn, as expressed in (4.8), and thus,

( α Es (ω) + Ei(ω)) = 0 (4.11) n n |tan Xn

115 By applying the inner product of Jm to (4.11) and using the orthogonality mentioned in (4.9), αn can consequently be determined as shown in (4.13). Note that the

numerator of (4.13) is called modal excitation coeﬃcient [10].

α J , Es (ω) + J , Ei(ω) = 0 (4.12) nh m n i h m i Xn J , Ei(ω) V i α = h n i = n (4.13) n − J , Es (ω) 1 + jλ h n n i n As a result, the modal expression of the total current on the conducting surface is shown below.

V iJ J = n n (4.14) 1 + jλ Xn n Clearly from (4.14), the strength of each mode mainly depends upon two factors.

i The ﬁrst one is the modal excitation coeﬃcient, Vn, which depends strongly on the

excitation of the structure. The second factor is the eigenvalue, λn. Obviously, the

smaller the λn becomes, the stronger the contribution to the total current is obtained

from that particular current mode. Note that λ ranges from to + as the n −∞ ∞

frequency varies. However λn 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

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

116 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.

4.3.1 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 , relating the induced current to the tangential electric ﬁeld on the con- L ducting 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 (4.10), 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, , operating on the current induced on the conducting L bodies as represented in (4.15). Since this operator is symmetric, its hermitian parts,

and are also real and symmetric operators as shown in (4.16). R X

Es = [ (J)] (4.15) |tan L tan

= = + j (4.16) L|tan Z R X

(J ) = λ J (4.17) X n nR n We shall now consider the generalized eigenvalue equation of the operator, which Z could be expressed in numerous ways. However, by choosing a particular weighted

eigenvalue equation, Harrington [8] simpliﬁed (4.17) as the generalized eigenvalue

117 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, λn, 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][Jn] = λn[R][Jn] (4.18)

Form a matrix equation using MM

Eigencurrents J n and Eigenvalues λn

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

4.3.2 Proposed Method

The new proposed method for computing the characteristic modes will be imple-

mented in the time domain using the FDTD technique. The three dimensional FDTD

118 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 genearl, two schemes of source excitation are employed to initialize FDTD simulations ; (a) source excitation with imposed time dependence and (b) initial conditions with no time dependence. For the 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”’ scheme is time independent. The ﬁelds are initially deﬁned over the computational domain at t=0 and the time dependence emerges through time-stepping. Notice that the initial

ﬁelds are usually obtained by a previous simulation or are dictated by the boundary conditions.

To calculate a spectral response, the structure 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 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 corresponding frequency spectrum, respectively. Note that the spectral components are found by performing a Discrete Fourier Transform (DFT) of

119 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 time stepping

FDTD algorithm. However, as time marches on, we record the time varying wave-

forms, 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 mini-

mize the error of predicting the resonances, several FDTD runs are performed with

diﬀerent seed numbers for random number generations. In addition, various obser-

vation or monitoring points are required to ensure that all the resonant modes are captured. In other 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. However we found the modes to be somewhat

contaminated with other modes. The scheme we are currently using is based on

the source excitation technique. In this scheme, the 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 at each resonant frequency. These

narrow band signals are intentionally chosen to compute time-averaged quantities

120 and ﬁelds at one particular frequency. Figure 4.4(a) shows a time signature of a

Gaussian pulse with a sinusoidal carrier at the frequency of interest. Furthermore,

Figure 4.4(b) depicts DFT spectrum of the corresponding signal. As shown, the

excitation is conﬁned 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 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 scat-

s tered field, En, is in fact the field radiated by each current mode, Jn. Computation of the scattered field is initiated by replacing the structure with the calculated current mode, Jn. In order to obtain its impulse response, Jn 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 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, Jn, and

s the scattered ﬁeld, En, over the surface of the conducting bodies.

121 A sequence of random numbers of uniform distribution 2 1000

900

1.5 800

700 1

600

0.5 500

400 Random Number

0 300 Spectrum of Random Number 200 −0.5

100

−1 0 100 200 300 400 500 600 700 800 900 1000 0 1 2 3 4 5 6 7 8 9 10 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.

1 1.5

0.8

0.6

0.4 1

0.2

0 Excitation −0.2

0.5 −0.4 Spectrum of Excitation Signal

−0.6

−0.8

−1 0 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 10 −8 Time (s) x 10 Frequency (GHz)

(a) A Gaussian pulse with a sinusoidal carrier at the center (b) and its corresponding frequency spectrum. frequency of interest

Figure 4.4: A time signature of a Gaussian pulse with sinusoidal carrier at center frequency of interest and its corresponding spectral calculation.

122 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

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, Ei is recorded and DFT-ed over the surface where the structure was once located. Once Ei is known, the modal excitation coefficient can be computed using (4.13). Computation of the scattered and incident fields is summarized in

Figure 4.8 and Figure 4.9, respectively.

123 z

L =15.6 cm Radiating Patch z

W =10.4 cm y h = 3.17 mm

ε D2=16.64 cm Ground Plane r =1 Radiating Patch ε r =1 y D1 =16.64 cm x Ground Plane (a) A microstrip antenna with air substrate (b) Side View

Figure 4.6: Geometry of a microstrip antenna with air substrate.

0.03 th Location 1 5 Location 2 0.025 rd nd 3 Location 3 2 Location 4 0.02 Location 5 6th

(f)| 0.015 x th th th |J 4 7th 8 9 0.01

0.005 0.9 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 40 Frequency (GHz) 0.8

60 y 0.7 0.03 th 5 0.6 1st 6th 0.025 rd 80 x 3 y 0.5 0.02 100 0.4

(f)| 0.015 y 4th |J 0.3 8th 0.01 120 0.2 0.005 0.1 0 140 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Frequency (GHz) 40 60 80 100 120 140 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.

124 Replace structure with computed current mode, J n .

Excite each J n with Gaussain pluse.

Far Field Near Field

s Use equivalence theorem and Save and DFT the scattered field, E n , near field to far field transformation. over the surface of structure.

s Compute eigenvalue < J n , E n >=1+j λn

Figure 4.8: Proposed algorithm for computing the scattered electric ﬁeld.

Computation of the Quality Factor

Methods for extracting relevant information, such as quality factors and band-

widths, are proposed here. Quality factor, Qn, is often used to characterize electrical

resonance circuits and microwave resonators. The parameter is deﬁned as

2π(stored energy) Q = (4.19) n energy loss per cycle

In this work, the quality factor could be computed with 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, Qn, is inversely proportional to the antenna bandwidth, BW . The quality factor is thereby expressed as Q 1/BW , where BW is the bandwidth of each current mode readily n ' captured from the current spectrum. Based on a simple resonator model, it can be shown that the bandwidth of each current mode is associated with the losses of the resonator. Low loss resonators have sharp peaks centered at each resonant frequency,

125 Computation of the incident field is realized in the absence of the structure.

Excite the source.

i Save and DFT the incident field, E , over the surface where the structure was located.

i i Compute V n = < J n , E >

Figure 4.9: Proposed algorithm for computing the scattered electric ﬁeld.

resulting in small bandwidths and thus high quality factors. On the other hand, lossy

resonators have wider resonant peaks, and clearly larger bandwidths with smaller

quality factors.

Figure 4.10: A wave reﬂects back and forth between the resonator mirrors, a Fabry- Perot etalon resonator.

126 To better understand this concept, let us examine the modes of an optical res-

onator constructed of two parallel, highly reﬂective, ﬂat mirrors separated by a distance d as shown in Figure 4.10. 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 wave that reproduces itself after a single round trip.

Let us now consider a monochromatic plane wave of complex amplitude Uo (Fig-

ure 4.10) 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 U1. Similarly, another round trip results in a wave amplitude U2, 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 [38],

U = U0 + U1 + U2 + U3 + . . . (4.20)

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

127 reﬂections and by absorption in the medium. Consequently, U1 = hU0, where h =

jϕ re− . Likewise, the phasor U2 is related to U1 by the same complex factor h, as are all consecutive phasors. The total wave, U, is readily expressed as

U = U0 + U1 + U2 + U3 + . . .

2 3 = U0 + hU0 + h U0 + h U0 + . . . (4.21) 2 3 = U0(1 + h + h + h + . . .)

= U0/(1 h) − The intensity of the total wave, U, in the resonator is deﬁned as

I = U 2 | | 2 jϕ 2 = U0 / 1 re− | | | − | 2 2 = I0/[(1 r cos(ϕ)) + (r sin(ϕ)) ] (4.22) − 2 = I0/(1 + r 2r cos(ϕ)) − 2 2 = I0/[(1 r) + 4r sin (ϕ/2)] − and thus

I I = max , (4.23) 1 + (2F/π)2 sin2(ϕ/2)

2 2 1/2 where I = U0 /(1 r) and F = πr /(1 r). max | | − − 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 4.11.

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,

128 Field Intensity of a Fabry−Perot Resonator, r=0.95 and d=0.5 meter 1

0.8

0.6

0.4 Field Intensity (I) 0.2

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 9 Frequency (Hz) x 10

Field Intensity of a Fabry−Perot Resonator, r=0.75 and d=0.5 meter 1

0.8

0.6

0.4 Field Intensity (I) 0.2

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 9 Frequency (Hz) x 10

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.

129 I I = max , (4.24) 1 + (2F/π)2 sin2(2dπν/c) where c is the speed of light.

The second method for computing the antenna quality factor is found by post-

processing the eigencurrent. The quality factor, Qn, could be alternatively determined

by observing the rate of the stored energy loss, and is deﬁned as Qn = ωn/τn, where

ωn are the resonances of the structure and τn is the characteristic mode lifetime found

from the exponential decay of the envelope of the ﬁeld radiated by the nth current

mode, provided only a single resonance exists at ωn. Note this assumption is based

on the optical resonator found in [38]. Calculation of the spectral resonances, ωn, 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,

ωn, of the structure are assumed to occur at the spectral peaks.

To compute τn, we ﬁrst need to determine the characteristic modes of the struc-

ture. 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.

130 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

mode is used as a initial boundary value for the next FDTD run, and the ﬁeld radi-

ated by this particular current mode is also recorded. Note that τn is computed from

the inverse of the exponential decay of the envelope of the ﬁeld radiated by the nth

th current mode. As a result, Qn of each n 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 Qn.

131 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 purpose, 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. Fur-

thermore, 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 accuaracy of our proposed technique, we ﬁrst apply the method

to a simple structure such as the rectangular cross section waveguide described the

section 4.2. The ﬁrst step is to determine the resonances or cut oﬀ frequencies of the

structure. For the waveguide under consideration, the lateral dimensions are a=100

132 mm, and b=50 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 Ez could be found using the same procedure described earlier. Figure 5.1 illustrates the DFT spectra of the Ez component at the six distinct monitoring points inside the guide. It can be seen that only a particular set of the spectral Ez 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 component inside the waveguide z 400 Location 1 Location 2 Location 3 350 Location 4 Location 5 Location 6 300

250

(f) | 200 z | E

150

100

0 0 1 2 3 4 5 6 7 8 9 10 Frequency (GHz)

Figure 5.1: DFT Spectra of the Ez component at six diﬀerent monitoring points inside the guide.

133 Table 5.1: Comparison of the resonances of the rectangular waveguide obtained from the analytical solution and the proposed method.

Resonant Modes T M11 T M21 T M31 T M12 T M22 Analytical Solution (GHz) 3.351 4.239 5.404 6.180 6.703 Proposed Method (GHz) 3.364 4.253 5.418 6.194 6.711

Resonant Modes T M32 T M51 T M42 T M13 T M23 Analytical Solution (GHz) 7.494 8.072 8.479 9.117 9.480 Proposed Method (GHz) 7.504 8.086 8.491 9.121 9.493

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 dimensions of the printed dipole are 16.5 mm and 6.5 mm in length and width, respectively. The DFT spectra of the

134 a = 7.5 mm

50 Ω b = 16.5 mm

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., fres(n) ∼= n∆f, where ∆f is the ﬁrst resonance of the dipole, 0.82 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.

135 0.03 Location 1 Location 2 Location 3 Location 4 0.025 Location 5

4th 6th 1st 0.02

(f)| 0.015 2 y |J

0.01 5th 3rd

0.005

0 0 1 2 3 4 5 6 7 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 spatial variation 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 spatial variation

136 20 Eigen Field: 1st Mode (0.820 GHz) 0.9 0 25

0.8 −5 30 0.7 −10 35 0.6 −15

y 40 0.5 −20 (dB)

0.4 θ

45 E −25 0.3 50 −30 0.2

55 0.1 −35

60 70 80 90 100 −40 x −180 −90 0 90 180 γ (Degree) (a) The 1st mode (b) and its corresponding eigenﬁeld.

Figure 5.4: The 1st eigencurrent on the printed dipole antenna and its corresponding eigenﬁeld at 0.820 GHz.

20 Eigen Field: 2nd Mode (1.740 GHz) 0.9 25 0

0.8 −5 30 0.7 −10 35 0.6 −15

y 40 0.5 −20 (dB)

0.4 θ 45 E −25 0.3 50 −30 0.2

55 0.1 −35

60 70 80 90 100 −40 x −180 −90 0 90 180 γ (Degree) (a) The 2ndmode (b) and its corresponding eigenﬁeld.

Figure 5.5: The 2nd eigencurrent on the printed dipole antenna and its corresponding eigenﬁeld at 1.740 GHz.

137 20 Eigen Field: 3rd Mode (2.530 GHz) 0.9 25 0

0.8 −5 30 0.7 −10 35 0.6 −15

y 40 0.5 −20 (dB)

0.4 θ 45 E −25 0.3 50

0.2 −30

55 0.1 −35

60 70 80 90 100 −40 x −180 −90 0 90 180 γ (Degree) (a) The 3rd mode (b) and its corresponding eigenﬁeld.

Figure 5.6: The 3rd eigencurrent on the printed dipole antenna and its corresponding eigenﬁeld at 2.530 GHz.

20 Eigen Field: 4th Mode (3.500 GHz) 0.9 0 25

0.8 −5 30 0.7 −10 35 0.6 −15

y 40 0.5 −20 (dB)

0.4 θ

45 E −25 0.3 50 −30 0.2

55 0.1 −35

60 70 80 90 100 −40 x −180 −90 0 90 180 γ (Degree) (a) The 4th mode (b) and its corresponding eigenﬁeld.

Figure 5.7: The 4th eigencurrent on the printed dipole antenna and its corresponding eigenﬁeld at 3.500 GHz.

138 20 Eigen Field: 5th Mode (4.440 GHz) 0.9 0 25

0.8 −5 30 0.7 −10 35 0.6 −15

y 40 0.5 −20 (dB)

0.4 θ

45 E −25 0.3 50 −30 0.2

55 0.1 −35

60 70 80 90 100 −40 x −180 −90 0 90 180 γ (Degree) (a) The 5th mode (b) and its corresponding eigenﬁeld.

Figure 5.8: The 5th eigencurrent on the printed dipole antenna and its corresponding eigenﬁeld at 4.440 GHz.

of the excitation 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 ultra wideband antennas involves 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 (²r) of 1.0, is our next example. The antenna geometry was shown in

Figure 4.6. In this case, the radiating patch dimensions are 104 mm in width and 156

mm in length. The square ground plane is 166.4 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.

139 As in the previous example, the DFT current spectra on the radiating patch is captured in a similar fashion. As observed in 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

1 mπ 2 nπ 2 model, fres(mn) = 2 ( ) + ( ) where W and L are the width and length ∼ π√µo²o W L p of the radiating patch orderly, and m,n=0,1,2,. . . , we obtain an excellent agreement

between the results acquired from both methods (as shown in Table 5.2). Moreover,

Figure 5.10 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

Figure 5.12.

Table 5.2: Comparison of the resonances of the air dielectric patch antenna obtained from the cavity model and the proposed method.

Resonant Modes (0,1) (1,0) (1,1) (0,2) (1,2) Cavity Model (GHz) 0.962 1.442 1.733 1.923 2.404 Proposed Method (GHz) 0.913 1.345 1.648 1.865 2.323

Resonant Modes (2,0)/(0,3) (2,1) (1,3) (2,2) (2,3) Cavity Model (GHz) 2.885 3.041 3.225 3.467 4.080 Proposed Method (GHz) 2.738 2.993 3.112 3.354 3.928

140 0.03 th Location 1 5 Location 2 0.025 rd nd 3 Location 3 2 Location 4 0.02 Location 5 6th

(f)| 0.015 x th th th |J 4 7th 8 9 0.01

0.005

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Frequency (GHz)

0.03 5th 1st 6th 0.025 3rd 0.02

(f)| 0.015 y 4th |J 8th 0.01

0.005

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Frequency (GHz)

Figure 5.9: DFT spectra of the current, Jx and Jy, 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, turning 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 for the two operational

141 φ=90o

0 0.9 40 −10 0.8 −20 Eφ 60 y 0.7 −30 Eθ 0.6 −40 −180 −90 0 90 180 80 x γ y 0.5 (Degree) φ=0o 100 0.4 0 0.3 −10 120 0.2 −20 Eφ 0.1 −30 140 Eθ −40 40 60 80 100 120 140 −180 −90 0 90 180 x γ (Degree) (a) The 1st eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.10: The 1st eigencurrent on the radiating patch and its corresponding eigen- ﬁeld at 0.913 GHz.

φ=90o

0 0.9 40 −10 0.8 −20 Eφ 60 0.7 −30 Eθ y 0.6 −40 −180 −90 0 90 180 80 γ y 0.5 (Degree) x φ=0o 100 0.4 0 0.3 −10 120 0.2 −20 Eφ 0.1 140 −30 Eθ −40 40 60 80 100 120 140 −180 −90 0 90 180 x γ (Degree) (a) The 2nd eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.11: The 2nd eigencurrent on the radiating patch and its corresponding eigen- ﬁeld at 1.345 GHz.

142 φ=90o

0 0.9 40 −10 0.8 −20 Eφ 60 0.7 −30 Eθ 0.6 −40 −180 −90 0 90 180 80 γ y 0.5 (Degree) φ=0o 100 0.4 x 0 0.3 −10 120 0.2 −20 Eφ 0.1 −30 140 Eθ −40 40 60 80 100 120 140 −180 −90 0 90 180 γ (Degree) (a) The 3rd eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.12: The 3rd eigencurrent on the radiating patch and its corresponding eigen- ﬁeld at 1.670 GHz.

states 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 can be seen, numerous current modes are induced ( every 0.4 GHz) in a fashion similar to the ≈ resonances attained by a loop antenna. At the L1 band, the radiation pattern when the switches are on is mostly contributed from the patterns radiated by the 4th and

5th 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 to see that the ring exhibits fewer resonant modes around the operating frequency. However, the

3rd resonant mode, 1.598 GHz, resonates right around the operating frequency, 1.575

GHz. As a result, the ﬁelds radiated by the ring are generated mostly by the 3rd

143 1 1 Location 1 Location 1 0.9 Location 2 0.9 Location 2 Location 3 Location 3 0.8 Location 4 0.8 Location 4 Location 5 Location 5 0.7 th 0.7 4 6th 0.6 Switch "On" 0.6 Switch "Off" 0.5 0.5 3rd |J (f)| |J (f)| 15th 0.4 1st 0.4 th 2nd th 14 nd 0.3 12 0.3 2 rd th th 3 5 th th 13 th th 7 8 th th th st 4 5 9 10 11 1 th th th th 0.2 0.2 6 7 8 9

0.1 0.1

0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 Frequency (GHz) Frequency (GHz) (a) Switches are turned on (full ring). (b) Switches are turned oﬀ (cut ring).

Figure 5.13: Frequency spectra of the current induced on the octagonal ring.

current mode. The assumption can be validated by comparing the total radiation

pattern at 1.575 GHz, to the pattern radiated by the 3rd current mode.

Figure 5.14 to Figure 5.19 depict the 1st, 4th and 5th modes along with their

corresponding eigenpatterns. Clearly, the horizontal ﬁeld component (Eφ) radiated

by the full ring (see Figure 2.25) is almost identical to the eigenﬁelds radiated from

the 4th and 5th modes, but very distinct from that of the 1st mode. Consequently, the

ﬁeld radiated from the full ring at the L1 band arises primarily from the 4th and 5th

modes.

Similarly, Figure 5.20 and 5.21 describe the 2nd and 3rd characteristic modes to-

gether with their eigenpatterns. It is also clear that the horizontal ﬁeld component

nd (Eφ) radiated by the cut ring is very similar to the eigenpatterns radiated by the 2

and 3rd modes. In other words, the ﬁeld radiated from the cut ring at the L1 band is

mostly due to the ﬁelds contributed by the 2nd and 3rd modes.

144 φ=90o

−10 0.9 20 E −20 φ 0.8 Eθ 40 −30 0.7 −40 60 −180 −90 0 90 180 0.6 γ (Degree) 80 0.5 φ=0o 100 0.4 0

120 0.3 −10 y 140 0.2 −20

0.1 −30 160 x −40 20 40 60 80 100 120 140 160 −180 −90 0 90 180 γ (Degree) (a) The 1st eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.14: The 1st eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 0.443 GHz (the 1st degenerated mode).

φ=90o

0.9 20 −10

0.8 −20 40 Eφ 0.7 −30 Eθ 60 −40 0.6 −180 −90 0 90 180 80 γ (Degree) 0.5 φ=0o 100 0.4 0 120 0.3 −10 y 0.2 140 −20

0.1 −30 160 x −40 20 40 60 80 100 120 140 160 −180 −90 0 90 180 γ (Degree) (a) The 1st eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.15: The 1st eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 0.443 GHz (the 2nd degenerated mode).

145 φ=90o

0 0.9 20 −10 0.8 40 −20 Eφ 0.7 −30 Eθ 60 0.6 −40 −180 −90 0 90 180 80 γ 0.5 (Degree) φ=0o 100 0.4 0 120 0.3 y −10 0.2 140 −20

0.1 −30 160 x −40 20 40 60 80 100 120 140 160 −180 −90 0 90 180 γ (Degree) (a) The 4th eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.16: The 4th eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 1.412 GHz (the 1st degenerated mode).

φ=90o

0 0.9 20 −10 0.8 40 −20 Eφ 0.7 −30 E 60 θ 0.6 −40 −180 −90 0 90 180 80 γ 0.5 (Degree) φ=0o 100 0.4 0 120 0.3 y −10 0.2 140 −20

0.1 −30 160 x −40 20 40 60 80 100 120 140 160 −180 −90 0 90 180 γ (Degree) (a) The 4th eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.17: The 4th eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 1.412 GHz (the 2nd degenerated mode).

146 φ=90o

0 0.9 20 −10

0.8 −20 40 Eφ 0.7 −30 Eθ 60 0.6 −40 −180 −90 0 90 180 80 γ 0.5 (Degree) φ=0o 100 0.4 0 120 0.3 y −10 0.2 140 −20

0.1 −30 160 x −40 20 40 60 80 100 120 140 160 −180 −90 0 90 180 γ (Degree) (a) The 5th eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.18: The 5th eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 1.685 GHz (the 1st degenerated mode).

φ=90o

0.9 −10 20 −20 0.8 Eφ 40 −30 E 0.7 θ 60 −40 0.6 −180 −90 0 90 180 γ 80 (Degree) 0.5 φ=0o 100 0.4 0 120 0.3 −10 y 140 0.2 −20

0.1 −30 160 x −40 20 40 60 80 100 120 140 160 −180 −90 0 90 180 γ (Degree) (a) The 5th eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.19: The 5th eigencurrent on the ring when the switches are turned on and its corresponding eigenﬁeld at 1.685 GHz (the 2nd degenerated mode).

147 φ=90o

−10 0.9 20 −20 0.8 Eφ 40 −30 E 0.7 θ 60 −40 −180 −90 0 90 180 0.6 γ (Degree) 80 0.5 φ=0o 100 0.4 0 120 y 0.3 −10

140 0.2 −20

0.1 −30 160 x −40 20 40 60 80 100 120 140 160 −180 −90 0 90 180 γ (Degree) (a) The 2nd eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.20: The 2nd eigencurrent on the ring when the switches are turned oﬀ and its corresponding eigenﬁeld at 1.425 GHz.

φ=90o

−10 0.9 20 −20 0.8 Eφ 40 −30 0.7 Eθ 60 −40 −180 −90 0 90 180 0.6 γ (Degree) 80 0.5 φ=0o 100 0.4 0

120 0.3 −10 y 140 0.2 −20

0.1 −30 160 x −40 20 40 60 80 100 120 140 160 −180 −90 0 90 180 γ (Degree) (a) The 3rd eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.21: The 3rd eigencurrent on the ring when the switches are turned oﬀ and its corresponding eigenﬁeld at 1.598 GHz.

148 For the antenna under consideration, it is clear that the information drawn from

the proposed method could be very useful in 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 3rd mode of the cut ring case resonates at 1.598 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

rd from the 3 current mode. Figure 5.22 shows the horizontal ﬁeld component, Eφ, of the cut and solid ring cases for φ=0◦ and φ=90◦. It is clear that nearly a 5 dB drop in the Eφ component is obtained along the horizon direction. However, after adjusting

the dimension of the cut ring such that its 3rd current mode resonates exactly at the

L1 band, a 7-8 dB change in the Eφ component is secured along the horizon direction as described in Figure 5.23.

5.5 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 mi-

crostrip antennas. To achieve large bandwidths, the so called frequency independent antennas should be used. Although not strictly a frequency independent antenna,

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, narrow-beam antenna having structural geometry such that

149 |Eφ| of a Single Band Antenna with Octagonal Substrate (1.575 GHz) −10

−15

−20

−25 | (dB) φ |E

° −30 Uncut Ring φ=0 ° Uncut Ring φ=90 ° Cut Ring φ=0 −35 ° Cut Ring φ=90

−40 −180 −135 −90 −45 0 45 90 135 180 θ (Degree)

Figure 5.22: Calculated radiation pattern (Eφ) of the single antenna mounted on an octagonal substrate.

|Eφ| of a Single Band Antenna with Octagonal Substrate (1.575 GHz) −10

−15

−20

−25 | (dB) φ |E

° −30 Uncut Ring φ=0 ° Uncut Ring φ=90 ° Cut Ring φ=0 −35 ° Cut Ring φ=90

−40 −180 −135 −90 −45 0 45 90 135 180 θ (Degree)

Figure 5.23: Calculated radiation pattern (Eφ) of the single antenna mounted on an octagonal substrate. The ring dimension has been modiﬁed such that the 3rd mode resonates as close as possible to the frequency of operation (1.575 GHz).

150 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 usually considered to be frequency independent antennas.

The length and spacing of the elements of the log-periodic antenna increase logarith- mically 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 5.24. 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 periodic fashion. The ﬁrst three eigen

current as well as their corresponding eigenpatterns are expressed in Figure 5.26, 5.27

and 5.28. The pattern for each of the modes looks almost identical in the vertical

ﬁeld component (Eθ), 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. The 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.

151 120

100

20 x

20 40 60 80 100 120

Figure 5.24: Geometry of a log-periodic toothed planar antenna.

0.1 rd 2nd 3 Location 1 0.08 st Location 2 1 Location 3 0.06 4th th Location 4 5 th (f)| 6 Location 5 x 0.04 |J th 7 8th 0.02

0 0 0.5 1 1.5 2 2.5 3 3.5 4 Frequency (GHz)

0.1 3rd 0.08 2nd th 0.06 4 th

(f)| st 5 y 1 0.04 th |J 6 th 7 th 0.02 8

0 0 0.5 1 1.5 2 2.5 3 3.5 4 Frequency (GHz)

Figure 5.25: Frequency spectra of the current induced on the log-periodic antenna.

152 ° φ=90 5

0.9 0 20 0.8 −5 0.7 40 −10 0.6

60 0.5 −15 |E (dB)| 0.4 −20 80 0.3 z −25

100 0.2 Eθ

−30 Eφ x 0.1 120 −35 20 40 60 80 100 120 −180 −90 0 90 180 γ (Degree) (a) The 1st eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.26: The 1st eigencurrent on the log periodic antenna and its corresponding eigenﬁeld at 0.685 GHz.

° φ=90 5

0.9 0 20 0.8 −5

0.7 40 −10 0.6 −15 60 0.5 |E (dB)| 0.4 −20 80 0.3 z −25 0.2 100 Eθ −30 E x 0.1 φ 120 −35 20 40 60 80 100 120 −180 −90 0 90 180 γ (Degree) (a) The 2nd eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.27: The 2nd eigencurrent on the log periodic antenna and its corresponding eigenﬁeld at 1.000 GHz.

153 ° φ=90 5

0.9 0 20 0.8 −5 0.7 40 −10 0.6

60 0.5 −15 |E (dB)| 0.4 −20 80 0.3 z −25 100 0.2 Eθ −30 x 0.1 Eφ 120 −35 20 40 60 80 100 120 −180 −90 0 90 180 γ (Degree) (a) The 3rd eigencurrent (b) and its corresponding eigenﬁeld.

Figure 5.28: The 3rd eigencurrent on the log periodic antenna and its corresponding eigenﬁeld at 1.275 GHz.

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

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

154 antennas, such as resonances, current distributions, and their corresponding radiation patterns. In principle, a desired antenna pattern can be achieved by exciting the proper current modes/modes.

155 CHAPTER 6

CONCLUSIONS

6.1 A Summary and Conclusion of This Dissertation

The work considered here discusses the development of a novel pattern reconﬁg-

urable printed antenna element for Global Positioning System (GPS) applications.

This antenna element consists of a microstrip patch, fed by four probes, and sur-

rounded 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

156 antenna along the horizon. This dissertation also shows that microstrip antennas can be fabricated with a thick substrate without the usual surface wave problem.

This dissertation also summarizes the development of the theory of characteristic modes using a time domain Maxwell equations solver. This method 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 posi-

tioning system (GPS) and a log-periodic antenna which is a wideband structure. To

access the accuracy 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.

6.2 Future Work

6.2.1 RF MEMS Switches

The antennas considered in this work use electronic switching implemented with

PIN diodes. Radio frequency microelectromechanical systems (RF MEMS) switches

are miniature devices that use a mechanical movement to achieve either a short circuit

or an open circuit in a transmission line. They can provide an alternative to these

solid state switches, as they exhibit certain advantages, namely, smaller size, low

157 intermodulation products, high isolation and low insertion loss, over the PIN diodes considered in this work. Using a method similar to that used to model the diodes,

RF MEMS devices can be incorporated into the design of the reconﬁgurable antennas discussed here. An optimization scheme similar to that carried out using the PIN diode switches can be implemented to achieve optimum performance.

While the advantages of RF MEMS devices over the solid state device have been discussed above, they possess certain drawbacks when opposed to solid state devices, such as slow switching speed, low power handling, actuation voltage, reliability and packaging. Despite the disadvantage mentioned above, RF MEMS devices possess certain characteristics that make them an attractive candidate for future work.

6.2.2 Antenna Feed Technique

For the application under the consideration, the antenna is required to radiate a right hand circular polarization. For this intention, four feed points per patch are required. This feed conﬁguration, especially for the dual band antenna, is however not so straightforward, since there is a need to pass the feed cables through the L2 patch (see Chapter 3). It is therefore desirable to design a new feeding technique that simpliﬁes the whole feed mechanism. This is challenging area where our antenna could be improved.

6.2.3 Reconﬁgurable Array

For our proposed scheme, a reconfigurable antenna consists of a radiating element surrounded by a switch-loaded parasitic ring. The reconfigurability is obtained through the use of two different ring configurations. Nevertheless, it is possible to have an array whose pattern can be reconfigured through the use of a parasitic ring

158 surrounding the entire array. The parasitic ring can add another degree of freedom to the design of the array. This research topic is deﬁnitely a very promising area left

to be explored.

6.2.4 GPS Antenna with Excellent Axial Ratio

It was discovered during our study that the microstrip antenna surrounded by a parasitic ring exhibits an excellent axial ratio. In fact, a good axial ratio ( 3 dB) ≤ is secured for 0◦ θ 100◦. This is usually very diﬃcult to achieve. A circularly ≤ ≤ polarized microstrip antenna normally yields a good axial ratio for 0◦ θ 50◦. ≤ ≤ Nevertheless the axial ratio becomes worse particularly when the elevation angle (θ) approaches the end-ﬁre direction. This problem could be resolved by adding the parasitic ring to the patch antenna.

Around the horizon region, the patch antenna element mounted on a finite substrate normally radiates a Eθ component stronger than a Eφ component. On the contrary, the parasitic solid ring by itself radiates the Eφ component stronger than the Eθ component. By combining these field components, both vertical and horizontal field components have more or less the same strength along the horizon. This could result in a very good axial ratio, providing a proper relative phase between the two field components is achieved.

6.2.5 Characteristic Modes for Material Bodies

In this dissertation, an alternative technique for computing the characteristic modes was proposed. The new method obviously employs the FDTD algorithm.

Demonstration on the new proposed method was mostly applied only the conducing

159 bodies. It is however interesting to apply our proposed method to other material bodies, such as dielectric and magnetic bodies. The basic difference is that the current in material bodies is a volume distribution, while for perfectly conducting bodies it is a surface distribution. The characteristic modes of material bodies have most of the properties of those for perfectly conducting bodies, and should find similar uses. For electrical small and intermediate size bodies, only a few modes suffice to characterize the radiation properties of the body. Because of their orthogonality, they should find use in problems involving synthesis and optimization of antennas and scatterers. Be- cause they characterize the body independent of the excitation, these modes provide a better understanding of the basic mechanism of radiation and scattering by material bodies.

160 BIBLIOGRAPHY

[1] J. T. Bernhard, R. Wang., R. Clark, and P. Mayes. Stacked reconﬁgurable antenna elements for space-based radar applications. 2001 IEEE AP-S Interna- tional Symposium, 1:158–161, 2001.

[2] M. Cabedo-Fabres, E. Antonio-Daviu, M. Ferrando-Bataller, and A. Valero- Nogueira. On the use of characteristic modes to describe patch antenna performance. IEEE APS International Symposium and URSI Radio Science Meeting, Columbus, OH, June 2003.

[3] J.-C. Chiao, Y. Fu, I. M. Chio, M. DeLisio, and L.-Y. Lin. Mems reconﬁgurable vee antenna. Microwave Symposium Digest, 1999 IEEE MTT-S International, 4:1515–1518, 1999.

[4] R. J. Garbacz. A generalized expansion for radiated and scattered ﬁelds. Ph.D. Dissertation, Ohio State University, Columbus, OH, 1968.

[5] R. J. Garbacz and D. M. Pozar. Antenna shape synthesis using characteristic modes. IEEE Trans. Antennas Propagat., 30:340–350, May 1982.

[6] R. J. Garbacz and R. H. Turpin. A generalized expansion for radiated and scattered ﬁelds. IEEE Trans. Antennas Propagat., 19:348–358, May 1971.

[7] Ramesh Garg, Prakash Bhartia, Inder Bahl, and Apisak Ittipiboon. Microstrip Antenna Design Handbook. Artech House, 2001.

[8] R. F. Harrington. Time-Harmonic Electromagnetic Fields. New York: McGraw- Hill, 1961.

[9] R. F. Harrington and J. R. Mautz. Computation of characteristic modes for conducting bodies. IEEE Trans. Antennas Propagat., 19(5):629–639, Sept. 1971.

[10] R. F. Harrington and J. R. Mautz. Theory of characteristic modes for conducting bodies. IEEE Trans. Antennas Propagat., 19(5):622–628, Sept. 1971.

[11] R. F. Harrington and J. R. Mautz. Control of radar scattering by reactive loading. IEEE Trans. Antennas Propagat., 20(4):446–454, Jul. 1972.

161 [12] G. H. Huﬀ, J. Feng, and J. T. Bernhard. A novel radiation pattern and frequency reconﬁgurable single turn square spiral microstrip antenna. IEEE Microwave and Wireless Components Letter, 13(2):57–59, Febuary 2003.

[13] S. Iyer. Design of Switching Circuits for Reconﬁgurable Antennas. Master’s thesis, The Ohio State University, Dept. Electrical and Computer Eng., 2004.

[14] K. W. Lee and R. G. Rojas. Study of novel adaptive printed antenna element using surface waves. Dig. Int. Symp. Antennas Propagat. Soc., 4:2796–2799, July 1999.

[15] K. W. Lee and R. G. Rojas. Novel scheme for design of adaptive printed antenna elements. 2000 IEEE AP-S International Symposium and URSI Radio Science Meeting, Salt Lake City, Utah, July 16-21 2000.

[16] K. W. Lee and R. G. Rojas. Reconﬁgurable GPS Antenna. Technical Report 737675-2, The Ohio State University ElectroScience Lab., August 2000.

[17] K. W. Lee, N. Surittikul, and R. G. Rojas. Surface wave control for reconﬁgurable printed antenna applications. 2002 IEEE AP-S International Symposium and USNC/URSI National Radio Science Meeting, San Antonio, TX, June 16-21 2002.

[18] D. Liu, R. J. Garbacz, and D. M. Pozar. Antenna synthesis and optimization using generalized characteristic modes. IEEE Trans. Antennas Propagat., 38(6):862–868, Jun. 1990.

[19] J. R. Mautz and R. F. Harrington. Modal analysis of loaded n-port scatterers. IEEE Trans. Antennas Propagat., 20(4):446–454, Jul. 1972.

[20] W. Menzel. A new travelling wave antenna in microstrip. Arch. Elek. Uherfra- gung, 33:137–140, 1979.

[21] A. A. Oliner and K. S. Lee. Microstrip leaky wave strip antennas. 1986 IEEE AP-S International Symposium, pages 443–446, 1986.

[22] Y. Qian, B. C. C. Chang, M. F. Chang, and T. Itoh. Reconﬁgurable leaky- mode/multifunction patch antenna structure. Electron. Lett., 35:104–105, 1999.

[23] R. G. Rojas and K. W. Lee. Control of Surface Waves in Planar Printed Anten- nas. Technical Report 735571-1, The Ohio State University ElectroScience Lab., August 1998.

[24] R. G. Rojas and K. W. Lee. Control of surface waves in planar printed antennas. IEEE APS International Symposium and URSI Radio Science Meeting, Atlanta, Georgia, (invited paper), June 1998.

162 [25] R. G. Rojas and K. W. Lee. Analysis and design of Novel Adaptive Printed Antennas for GPS Appplications. Technical Report 737675-1, The Ohio State University ElectroScience Lab., December 1999.

[26] R. G. Rojas and K. W. Lee. Study of Novel Adaptive Printed Antenna Element for GPS Appplications. Technical Report 735571-2, The Ohio State University ElectroScience Lab., March 1999.

[27] R. G. Rojas and K. W. Lee. Surface wave control using non-periodic parasitic strips in printed antennas. IEE Proceedings - Microwaves, Antennas and Prop- agation, 148(1):25–28, Febuary 2001.

[28] R.G. Rojas, K. W. Lee, and N. Surittikul. Reconﬁgurable gps antenna. EM Measurements Consortium Meeting, Columbus, OH, July 31 - August 1 2001.

[29] R.G. Rojas, K. W. Lee, and N. Surittikul. Reconﬁgurable Printed Antenna for GPS Applications. Technical Report 739356-1, The Ohio State University ElectroScience Lab., September 2001.

[30] R.G. Rojas, K. W. Lee, and N. Surittikul. Reconﬁgurable gps antenna. National Radio Science Meeting (URSI), Boulder, CO, January 9-12 2002.

[31] R.G. Rojas and N. Surittikul. Reconﬁgurable Printed Antenna for GPS Appli- cations. Technical Report 739356-1, The Ohio State University ElectroScience Lab., April 2001.

[32] R.G. Rojas and N. Surittikul. Reconﬁgurable Dual Band Stacked Microstrip Antenna for GPS Applications. Technical Report 741202-2, The Ohio State University ElectroScience Lab., August 2003.

[33] R.G. Rojas and N. Surittikul. Reconﬁgurable dual band stacked microstrip antenna for gps applications. EM Measurements Consortium Meeting, Columbus, OH, July 31 - August 1 2003.

[34] R.G. Rojas, N. Surittikul, and S. Iyer. Mulilayer Reconﬁgurable GPS Antenna and Platform Eﬀects. Technical Report 746584-1, The Ohio State University ElectroScience Lab., October 2004.

[35] R.G. Rojas, N. Surittikul, and S. Iyer. Mulilayer Reconﬁgurable GPS Antenna and Platform Eﬀects. Technical Report 745379-1, The Ohio State University ElectroScience Lab., November 2004.

[36] R.G. Rojas, N. Surittikul, and K.W. Lee. Reconﬁgurable Printed Antenna for GPS Applications. Technical Report 741202-1, The Ohio State University Elec- troScience Lab., August 2002.

163 [37] V. H. Rumsey. Frequency Independent Antennas. Wiley, 1966.

[38] B. E. A. Saleh and M. C. Teich. Fundamentals of Photonics. Wiley, 1991.

[39] K. Sickels. Private communication. AFRL, WPAFB.

[40] R. N. Simons, D. Chun, and L. P. B. Katehi. Polarization reconﬁgurable patch antenna using microelectromechanical systems (mems) actuators. 2002 IEEE AP-S International Symposium, 2:6–9, 2002.

[41] W. L. Stutzman and G. A. Thiele. Antenna Theory and Design. Wiley, 1998.

[42] N. Surittikul and R. G. Rojas. Analysis of reconﬁgurable antenna using method of characteristic modes: Fdtd approach. 2004 IEEE AP-S International Symposium and USNC/URSI National Radio Science Meeting, Monterey, CA, June 20-25 2004.

[43] N. Surittikul, R. G. Rojas, and K.W. Lee. Reconﬁgurable circularly polarized dual band stacked microstrip antenna. 2003 IEEE AP-S International Sympo- sium and USNC/URSI National Radio Science Meeting, Columbus, OH, June 22-27 2003.

[44] R. B. Waterhouse. Microstrip Patch Antennas: A Designer’s Guide. Kluwer Academic Pubblishers, 2003.

[45] Philips Semiconductors Website. Philips rf manual: product and design manual for rf small signal discretes.

[46] Philips Semiconductors Website. www.semiconductors.phillips.com.

[47] W. H. Weedon, W. J. Payne, and G. M. Rebeiz. Mems-switched reconﬁgurable antennas. 2001 IEEE AP-S International Symposium, 3:654–657, July 8-13 2001.

[48] K. L. Wong. Compact and Broadband Microstrip Antennas. John Wiley and Sons, 2002.

[49] F. Yang and Y. Rahmat-Samii. A reconﬁgurable patch antenna using switchable slots for circular polarization diversity. IEEE Microwave and Wireless Compo- nents Letter, 12(3):96–98, March 2002.

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