Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1973 A hybrid-mode characterization of microstrip transmission lines Thomas Lee McRoberts Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Chemical Engineering Commons Recommended Citation McRoberts, Thomas Lee, "A hybrid-mode characterization of microstrip transmission lines " (1973). Retrospective Theses and Dissertations. 5105. https://lib.dr.iastate.edu/rtd/5105 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This material was produced from a microfilm copy of the original document. 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Xerox University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 74-9138 McROBERTS, Thomas Lee, 1943- A HYBRID-MODE CHARACTERIZATION OF MICROSTRIP TRANSMISSION LINES. Iowa State University, Ph.D., 1973 Engineering, chemical University Microfilms, A XEROX Company, Ann Arbor, Michigan A hybrid"mode characterization of microstrip transmission lines by Thomas Lee McRoberts A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of The Requirements for the Degree of DOCTOR OF PHILOSOPHY Major: Electrical Engineering Approved: Signature was redacted for privacy. In Charge of Major Work Signature was redacted for privacy. For the Major Department Signature was redacted for privacy. Iowa State University Ames, Iowa 1973 il TABLE OF CONTENTS I. INTRODUCTION 1 A. Purpose 1 B. Statement of the Problem 1 C. Method of Solution 4 II. MICROSTRIP FIELDS 5 A. Historical Background 5 B. Normal Mode Expansion 10 Co Current on Microstrip 24 D. Microstrip Parameters 30 E. Series Summation 38 III. CALCULATOR SOLUTION 40 A. Propagation Constant 40 B. Characteristic Impedance 42 IV. NUMERICAL RESULTS AND DISCUSSION 45 Ao Introductory Comments 45 B. Comparison of Models 46 C. Comparison of Model with Other Theories and with Experimental Results 57 D. Effect of Waveguide Size on Effective Dielectric Constant 77 E. Waveguide Currents and Fields on the Dielectric Interface 84 F. Desk Calculator Results 88 G. Higher Order and Evanescent Modes 89 iii V. SUMMARY Am CONCLUSIONS 96 VI. LITERATURE CITED 98 VII. ACKNOWLEDGMENTS 104 VIII. APPENDIX A: FIELD POTENTIAL COEFFICIENTS 105 IX. APPENDIX B: FOURIER COEFFICIENTS FOR ASSUMED MICROSTRIP CURRENT 108 X. APPENDIX C: LIMIT SERIES 112 A. Boundary Condition Series 112 B. Power Series 114 C. Current Series 116 XI. APPENDIX D: POWER AND CURRENT ON MICROSTRIP 117 A. Microstrip Power Calculation 117 B. Longitudinal Current on Microstrip 123 C. Longitudinal Current in the Waveguide Walls 124 XII. APPENDIX E: MITTRA AND ITOH'S TECHNIQUE 127 A. Summary of Results 127 B. Computer Implementation 134 XIII. APPENDIX F: COMPUTER PROGRAM LISTINGS 140 1 I. INTRODUCTION A. Purpose The purpose of this work is to investigate the dynamic electrical properties of microstrip transmission line. A full-wave formulation that accounts for the dispersion characteristics of the propagation constant and characteristic impedance will be developed. This model will account for both propagating and evanescent modes. Therefore, it is amenable to mode-matching techniques used in the solution of microstrip discontinuity problems. The model to be developed uses an assumed current density on the strip conductor. When appropriate approximations are made in the form of this current density, the computation time required to determine the propagation constants and characteristic impedance will be con­ siderably leas than that of similar models. Also, the storage requirements of this simplified model can be reduced sufficiently to allow a solution on a programmable desk calculator. B. Statement of the Problem There are several related parallel conducting strip transmission line configurations of current interest in microwave engineering. These are illustrated in Figure 1. Usually region 1 is filled with a dielectric material and region 2 is free space, but there has been considerable interest in the case where region 1 is a biased ferrite. 2 Figure 1. Parallel strip transmission line. 3 The case where region 1 Is a semi-conducting material has also been Investigated. In addition to this basic configuration, lines with several dielectric layers and with two or more coupled parallel con­ ducting strips have been considered. When both regions are filled with the same material, the system Is called strip line, with the special case s = a/2 called balanced strip line. Mlcrostrlp denotes the configuration where the two regions are filled with different materials. Usually s = d for mlcrostrlp, but the material of region 1 Is occasionally coated over the narrow strip for protection. When a and region 2 Is free space, the configura­ tion is called open mlcrostrlp. The term shielded mlcrostrlp ori­ ginally denoted the case where a Is finite, but in recent years it has also been used to describe the system with finite width upper and lower conductors, connected at their edges by perpendicular conducting surfaces. This configuration has also been called closed mlcrostrlp and "mlcrostrlp in a box". In this work, we will be concerned with the development of a theoretical model to account for the high frequency characteristics of this type of structure. The effects of varying the mlcrostrlp parameters and the enclosing waveguide size will be investigated, and a model for open mlcrostrlp which is easily solved on a programmable desk calculator will be developed. 4 C. Method of Solution In order to find the fields on the microstrip, a source-free normal mode expansion of TE and TM modes in inhomogeneous rectangular waveguide will be made. The current on the strip will be assumed known, and a Fourier series solution for the fields will be obtained. This method of solution is a variation of Denlinger's [16] - [18] techniques for open microstrip. Throughout this work, a time dependence of e^^*^ will be assumed and will be suppressed. Thus, the field quantities which will be used in this analysis will be in phasor form. They can be converted to the real-time field expressions by standard transform equations [27, pp. 13-16]. 5 II. MICROSTRIP FIELDS A. Historical Background Although mlcrostrlp was first described In the early 1950's [%], [25], [39], it was not widely used until the middle I960's because of high radiation and dielectric losses and the inability to maintain the necessary tolerances on physical dimensions. These problems have been largely surmounted, and the use of mlcrostrlp has become increasingly popular for a wide range of applications because of its simplicity and its adaptability to microwave Integrated circuit techniques. Most early analyses of mlcrostrlp involved a quasi-static, or TEN mode, assumption although the presence of the dielectric-air interface precludes the existence of this mode except at zero frequency. This assumption reduces the problem to two-dimensions and its solution has been approached by a variety of methods. Assadourian and Rimai [2] and Wheeler [54], [55] used a conformai mapping technique. Caulton, Hughes, and Sobol [7] used Wheeler's theory to present detailed design data for a wide range of geometries and substrate materials. They also included corrections for finite width conductors. Silvester [ 49] used image theoiry coupled with a Green's function approach to determine the charge distribution on the strip and thus the propagation characteristics of the line. Gunston and Weale [26] 6 present a similar solution. Hill, Reckord, and Winner [31] also used image theory to investigate coupled lines of finite width. The relaxation method was used by Green [24], Stinehelfer [50], and Baler [3]. These solutions assumed the microstrip was enclosed in a conducting box distant from the line. Yamashita [58], Yamashita and Atsuki [59], [60], and Yamashita and Mittra [61] considered a variational method to investigate a variety of microstrip and microstrip-related problems. Byrant and Weiss [5], [6] derive a "dielectric Green's function" to express the fields at the dielectric interface.