AN ABSTRACT OF THE THESIS OF MohammedAshrafSultan for the degree of Doctor of Philosophy in Electrical and Computer Engineering presen- ted on Alril 28, 1986 Title: THE RADIATION CHARACTERISTICS OF OPEN-AND CLOSED- RING MICROSTRIP ANTENNAS Redacted for privacy Abstract approved: Dr. Vijai°K. Tripath1- The purpose of this study is toinvestigate the radiation characteristics of open- andclosed-ring micro- strip structures for applications asmicrowave antenna elements. The expressions for the radiationfields of these structures are obtained from the aperturefields of the ideal cavity model associatedwith the microstrip structure.The expressions for theradiation fields are then used to calculate the radiationcharacteristics of these microstrip structures. The radiation fields of theideal gap structure(gap angle 0) are derived in Chapter 3. For this case the aperture fields can be expressedeither in terms of the spherical Bessel functions (odd-modes) orin terms of the Bessel functions of integer order(even-modes) which is shown to result in a convergentseries or closed form expressions respectively for theradiation fields. study of the radiation patterns for thevarious modes of the ideal gap open-ring structuresreveals that the first radial TM12 mode can potentially be an efficient useful mode for applications of this structure as aradiating element. The radiation fields of the general annularand cir- cular sectors are numerically examinedin the following chapter in terms of the various physical parametersof these structures. The derived expressions forthe radia- tion fields are used to study the radiation patterns, radiation:peak in the broadside direction andthe beam- width of these structures for various sectorangles, widths and the modes of excitation. This includes the special cases of quarter, half, three-quartersand ideal gap open-ring structures. It is shown that theradiation properties of these structures are comparablewith other microstrip antennas and should result inthe applications of such sectors as useful radiating elements. An important part of this workis the study of closed-ring microstrip structures whichis presented in Chapter 5. It is shown that all of theuseful properties of such structures for various modes ofexcitation can be derived from the radiation fields. The expressions for the antenna characteristics such as totalradiated power, directivity, bandwidth and input impedance arederived from the expressions for the radiation fields. These parameters are then evaluated for theuseful TM12 and TM11 modes for typical structures. The results should be help- ful in the design of such structures forapplications as radiating elements. Copyright by Mohammed Ashraf Sultan April 28, 1986 All Rights Reserved THE RADIATION CHARACTERISTICS OF OPEN- AND CLOSED-RING MICROSTRIP ANTENNAS by Mohammed Ashraf Sultan A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Completed April 28, 1986 Commencement June 1986 APPROVED: Redacted for privacy Professor of Electrical and ComputerEngineering in Charge of Major Redacted for privacy Head of the Electrical airld ComputerEngineering Department Redacted for privacy Dean of Gradu School 1 J Date thesis is presented April 28, 1986 Typed by Admin. HQ for Mohammed Ashraf Sultan DEDICATION For everyonewho is looking for loveand peace. For everyonewho wants to knowhow fair god is. For my mother for her love, patience anddetermination to help me walk through this life with a smile. For my father for his financial support of mymother's goal. ACKNOWLEDGEMENTS Thank God for the health and energy I foundduring this course of study, assuring him that I'll go towards achieving the second dream regardless of lack of health or problems I may forsee. Thanks is extended to include all of the department faculty members, staff and students for their cooperation and encouragement during this course of study, especially Dr. Tripathi for his patience. Thanks to Dr. Oberhettinger for his cooperation via mail. Thanks to Admin. HQ, especially Ms. Celeste Correia for diligence in typing this thesis. TABLE OF CONTENTS 1. ORIENTATION OF THE STUDY 1 1.1 Microstrip Antennas 3 1.2 Statement of the Problem 6 2. REVIEW OF RELATED LITERATURE 7 2.1 The Radiation Characteristics 7 2.2 Analysis of Microstrip Antenna 10 2.3 Principle of Field Equivalence 15 2.4 The Radiation Fields 18 2.5 Classification and Discussion of Other Analy- 21 sis Methods 2.5.1 Magnetic (or Electric) Wall Methods 22 2.5.2 Patch Current DistributionMethods 25 2.5.3 Spectral Domain Methods 27 2.6 Comparison of Cavity Model withOther Analy- 28 sis Methods 2.7 Concluding Remarks 31 32 3. ANALYSIS OF THE OPEN-RING MICROSTRIP ANTENNA 3.1 Antenna Analysis 33 3.2 Formulation of the Integral Equation 38 3.3 Method of Solution for Radiation Fields 40 3.4 Results and Discussion 45 3.5 Concluding Remark6 50 51 4. THE RADIATION BEHAVIOR OF AN ANNULAR SECTOR MICRO- STRIP ANTENNA 4.1 Review of Resonant Frequencies and Field Dis- 52 tribution 4.2 Derivation of Radiation Fields 56 4.2.1 Radiation Fields from the Curved Aper- 58 tures 4.2.2 Radiation Fields from the Linear Aper- 61 tures 4.3 The Gap Effects and the Radiation Peak 62 4.4 Results and Discussion 65 4.4.1 Quarter and Three-Quarters Ring Anten- 67 nas 4.4.2 Half-Ring Antenna 71 4.4.3 Ideal Gap Open-Ring Antenna 76 4.4.4 General Annular Sector Antenna 80 4.5 Concluding Remarks 88 5. THE RADIATION CHARACTERISTICS OF A CLOSED-RING 89 MICROSTRIP ANTENNA 5.1 Review of the Radiation Fields 90 5.2 Formulation of the Problems, Method of Solu- 91 tions and Results 5.2.1 Total Energy Stored 93 5.2.2 Radiated Power, Losses and Q-Factor 94 5.2.3 Resonance and Input Impedance 106 5.2.4 Radiation Resistance 113 5.2.5 Bandwidth 116 5.2.6 Efficiency, Directivity and Gain 119 5.3 Typical Example 123 5.4 Concluding Remarks 124 6. SUMMARY AND CONCLUSIONS 125 BIBLIOGRAPHY 127 APPENDICES Appendix A - Vector Transformations 133 Appendix B - Power Radiated from a Closed-Ring 138 Microstrip Antenna LIST OF FIGURES 1.1 General configuration of a microstrip antenna 3 1.2 Some of the investigated microstrip antenna con- figurations 2.1 A microstrip-fed rectangular patch 11 (a) Probe or coax feed (b) Line feed 2.2 The cavity model of microstrip patch antenna 11 2.3 The choice of selecting a closed surface 17 2.4 Block diagram for computing radiated fields from 18 known M sources 2.5 Example to calculate the phase delay between any 19 point in the source and the observation point 2.6 The concept of segmentation anddesegmentation 23 techniques 2.7 Wire-grid model of microstrip patch antenna 26 3.1 The open-ring microstrip antenna and the top 33 view of the magnetic wall model 3.2 Field analysis for axial and radial modes of an 37 ideal gap open-ring antenna (a) Normalized Ezversus p (b) Normalized E versus (c) Field distribution 3.3 Radiationpatterns of an ideal gap open-ring 48 antenna for axial TM11, TM21 and TM31 modes (excluding gap fields) 3.4 Radiation patterns of an ideal gap open-ring 49 antenna for radial modes (excluding gapfields) (a) TM12 mode (b) TM22 mode 4.1 Normalized resonant frequency versus sector 53 angle for TM11 and TM12 modes for a typical case 4.2 Normalized Ez of annular sector for various sec- 54 for angles (a) as a function of p (b) as a function of 4 4.3 Equivalent magnetic current sources of an annu- 56 lar sector antenna 4.4 Radiation patterns for a quarter-ring antenna 68 (a) for TM11 mode with differentwidths (b) for TM11 and TM21 modes (c) for TM12 mode 4.5 Radiationpatterns for a three-quarters-ring 69 antenna (a) for TM11 mode with different widths (b) for TM11 and TM21 modes (c) for TM12 mode 4.6 Radiation pattern of a half-ring antenna excited 72 in TM11 mode 4.7 Radiationpatterns for thehalf-ring antenna 73 excited in TMil mode (a) for different widths (b) for the limiting case as 'a' becomes small 4.8 Radiation patterns for the half-ring antenna for 75 TM11, TM21 and TM31modes (a) E-plane (b) H-plane 4.9 Radiation patterns for thehalf-ringantenna 75 excited in TM12 mode 4.10 Gap effect on the radiation patterns of an ideal 77 gap open-ring antenna excited in TM11mode 4.11 Radiationpatterns for the ideal gap open-ring 78 antenna excited in TM11mode (a) for different widths (b) for the limiting case as 'a' becomes small 4.12 Radiationpatterns for the ideal gapopen-ring 79 antenna for TM11, TM21 and TM31 modes 4.13 Gap effect of the radiation patterns of an ideal 79 gap open-ring antenna excited in TM12mode 4.14 Radiation patterns for annular sector antenna 81 excited in TM11 mode for different sectorangle 4.15 Radiationpatterns for annular sector antenna 83 excited in TMil mode (a) a=45° (67 a=85° (c) a=135° (d) a=170° (e) a=210° (f) a=225° (g) a=315° (h) a=355° 4.16 Radiationpatterns for annular sector antenna 87 excited in TM12 mode (a) a=60° (b) a=120° 5.1 The closed-ring microstrip antenna and its equi- 90 valent cavity model 5.2 Radiated power vs h for different widths and Er 102 for a closed-ring antenna excited in TM11 mode 5.3 Radiated power vs frequency for different widths 103 and h for a closed-ring antenna excited in TM11 mode 5.4 Q-factors vs h for different widths of a closed- 107 ring antenna excited in Tn.]. mode 5.5 Q-factors vs h for different Er for a closed- 107 ring antenna excited in TM11 mode 5.6 Resonant input impedance vs h for different 109 widths and er for a closed-ring antenna excited in TM11 mode, outer-edge fed point 5.7 Input impedance vs frequency for different h for 111 a closed-ring