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FEM Analysis of Quasi-Planar Transmission Lines FEM Analysis of Quasi-Planar Transmission Lines A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment of the Requirements For the Degree of Master of Science In the department of Electrical Engineering University of Saskatchewan Saskatoon 3/1 By Yue Yan November, 99 © Copyright Yue Yan, 1999, All right reserved ABSTRACT The high frequency wireless communication and high-speed electronics industries are demanding increasingly more sophisticated microwave integrated circuits. Today, conventional microwave integrated circuits have used single substrate planar microstrip line or suspended and inverted microstrip lines. Present day microwave integrated circuits, however, cannot rely solely on conventional microstrip line or its derivatives. During the past five years new quasi-planar microstrip lines, known as microshields, have been proposed. Electrical properties of such lines have not been adequately studied either experimentally or theoretically. There is a strong need for such studies. This thesis aims to fill this gap for some newly emerged quasi-planar lines, using the finite element method. By implementing the incremental inductance rule, the finite element method is used for transmission line loss calculation. It is then used in estimating the effects of metal penetration in microshield transmission lines used in modern day microwave circuits. This research will help advance the art of microwav6 integrated circuit technology. ii ACKNOWLEDGMENTS The author would like to express his gratitude and appreciation to Dr. Protap Pramanick for his guidance throughout the course of this work and also for hisl assistance in the co-authoring, preparation and submission of the various papers and l publications referenced in this work. The author would also like to express his gratitude and appreciation to Professor Dave Dodds for his alternate supervising my thesis defense and guidance in the thesis correction. Without his kind help and patient advice, the thesis would not have been completed. iii DEDICATION This thesis is dedicated to the author's dear wife Zhang Lihua, dear daughter Yan Xiaorong and all the author's family members. Without the financial, spiritual and moral support of the author's family members, the thesis would not have been finished. The author would like to take this opportunity to express appreciation to his family members. iv LIST OF SYMBOLS AND ABBREVIATIONS 1.0 Greek and non-Latin Symbols a Attenuation constant 13 Phase constant Propagation constant E Dielectric constant CO Permittivity of free space Er Dielectric constant or relative permittivity Eeff Effective dielectric constant Eeffe Effective dielectric constant of even mode Eeffo Effective dielectric constant of odd mode Eeffee Effective dielectric constant of even-even mode Eeffeo Effective dielectric constant of even-odd mode Eeffoe Effective dielectric constant of odd-even mode Eeffoo Effective dielectric constant of odd-odd mode Exx Dielectric constant in x direction E„ Dielectric constant in y direction SS Skin depth Sr Conductor resistivity with respect to copper Sz The length of circuit segment 8/ The current element in the circuit segment 8 V The voltage element in the circuit segment Conductivity of the metal (I) Electric potential Wave length Magnetic permeability Magnetic permeability in free space Radian frequency Del operator .0 Latin Symbols and Abbreviations Velocity of light in free space Capacitance per unit length Transmission line capacitance per unit length in air only Ca' Air filled transmission line capacitance altered by the skin depth (per unit length) Capacitance in even-even mode Leo Capacitance in even-odd mode woe Capacitance in odd-even mode oo Capacitance in odd-odd mode a Air filled ee capacitance in even-even mode a Air filled capacitance in even eo -odd mode a Air filled Coe capacitance in odd-even mode a Air filled capacitance in odd-odd mode 00 Electric field Frequency Conductance/unit length Magnetic field Electric current Imaginary number Current density distribution Inductance/unit length vi L' Inductance/(unit length) produced by the magnetic field within the conductor R Resistance/unit length RS Surface resistance/unit length th Strip thickness V Voltage vph Phase velocity w Width X Reactance XS Imaginary part of surface imedance/unit length Z Impedance Zo Characteristic impedance Ze Characteristic impedance of even mode Z, Characteristic impedance of odd mode Zee Characteristic impedance of even-even mode Zeo Characteristic impedance of even-odd mode Z oe Characteristic impedance of odd-even mode Z00 Characteristic impedance of odd-odd mode vii TABLE OF CONTENTS ERMISSION TO USE BSTRACT ii CKNOWLEDGEMENTS iii ►EDICATION iv IST OF SYMBOLES AND ABBREVIATIONS ABLE OF CONTENTS viii IST OF TABLES x IST OF FIGURES xi hapter 1. Introduction 1 1.1 Background 1 1.2 Objectives 10 1.3 Organization of the Thesis 11 1.4 Chapter Conclusion 12 hapter 2. Survey of Numerical Techniques Used in Quasi-Planar Microwave Transmission Line Analysis 13 2.1. Useful Parameters of a Quasi-planar Transmission Line 13 2.1.1. The Equivalent Network of a Two-conductor Transmission Line 13 2.1.2. Conductor Loss Coefficient 18 2.1.3. The Effect of Substrate Anisotropy [2.7] 22 2.1.4. Strip Coupling 24 2.2. Basic Numerical Methods 28 2.2.1. The Variational Method in the Spectral Domain 30 2.2.2. Transverse Transmission Line Method in Space Domain 34 viii 2.2.3. The Finite Difference Method 38 2.2.4. The Finite Element Method 44 2.3 Chapter Conclusion 54 Chapter 3. Verification of the Approach and the Computer Codes Used in This Thesis 55 3.1. Analysis of Shielded Microstrip Line with Finite Metallization Thickness 56 3.2. Analysis of Coplanar Coupled Microstrips 58 3.3. Analysis of V-shaped Microshield Line 62 3.4. Loss Calculation of Coaxial Line and the Validity of Proposed Generalization (Equation (2.27)) of Perlow's Equation (Equation (2.26)) 63 3.5 Chapter Conclusion 66 Chapter 4. Study of Metal Penetration Depth in Quasi-Planar Microstrip Lines 67 4.1 Analysis of Effect of Metal Penetration Depth in Shielded Single and Edge Coupled Microstrip Lines 68 4.2 Analysis of Effect of Metal Penetration Depth in Broadside Coupled Shielded Microstrip Lines 74 4.3 Chapter Conclusion 81 Chapter 5. Analysis of Newly Emerged Quasi-planar Microwave Transmission Lines 83 5.1 Study of V- and W-shaped Single and Coupled Microshield Lines 84 5.2 Study of V- and W-shaped Broadside-edge Coupled Microshield Lines 94 5.3 Chapter Conclusion 101 Chapter 6. Thesis Conclusions and Scope for Further Research 103 List of References 108 ix LIST OF TABLES Table 3.1 Calculated characteristic impedances of single shielded microstrip line. 57 x LIST OF FIGURES Figure 1.1. The basic two-conductor transmission line 1 Figure 1.2. Various two-conductor transmission lines 2 Figure 1.3. Conventional microstrip line 3 Figure 1.4. (a) Suspended microstrip, (b) inverted microstrip 4 Figure 1.5 (a) V-shaped microshield line 6 Figure 1.5 (b) V-shaped coupled microshield line 7 Figure 1.5 (c) W-shaped coupled microshield line 7 Figure 1.5 (d) V-shaped broadside-edge coupled microshield line 7 Figure 1.5 (e) W-shaped broadside-edge coupled microshield line 8 Figure 1.5 (f) U-shaped microshield line 8 Figure 1.6 V-shaped coupled microshield line as a four-port network. 9 Figure 1.7 Broadside coupled microshield line as a four-port network 10 structure. Figure 2.1. Equivalent circuit for a two-conductor segment 14 Figure 2.2(a) Reduction of physical dimension by the skin depth 8, in a stripline configuration 20 Figure 2.2(b) Reduction of physical dimension by the skin depth iss. in a 21 microstrip configuration Figure 2.3. Two layered stripline with anisotropic substrates principal axes arbitrarily rotated with respect to x-y coordinate axes 23 Figure 2.4. The cross-section of electromagnetically coupled edge-coupled and 26 broadside coupled strip transmission lines Figure 2.5. The cross-section of electromagnetically coupled broadside-edge- 27 coupled strip transmission lines xi Figure 2.6. The geometric configuration for determining the Green's function in a rectangular region 31 Figure 2.7. The general configurations for suspended microstrip transmission 31 line Figure 2.8. (a) The representative structures for the analysis of microstrip-like transmission lines. (b) and (c) The representative structures for the analysis of microstrip-like transmission lines ( I ) electric wall and 35 ) magnetic wall Figure 2.9. The equivalent transmission line model 37 Figure 2.10. Two-dimensional potential problem 39 Figure 2.11. Finite-difference mesh 39 Figure 2.12. Two-dimensional mesh 40 Figure 2.13. Neumann boundary condition 41 Figure 2.14. Typical finite elements: (a) One dimensional, 44 (b) Two-dimensional, (c) Three-dimensional 45 Figure 2.15. The solution region and its finite element discretization 46 Figure 2.16. Typical triangular element 47 Figure 3.1. Single shielded microstrip line with iso/anisotropic substrates 57 Figure 3.2. Coupled microstrip line 59 Figure 3.3. (a) Odd-mode effective dielectric constant 60 Figure 3.3. (b) Odd-mode characteristic impedance 60 Figure 3.3. (c) Even-mode effective dielectric constant 61 Figure 3.3. (d) Even-mode characteristic impedance 61 Figure 3.4. V-shaped microshield line 62 Figure 3.5. The characteristic impedances of the V-shaped microshield line calculated using the Finite Element Method and the. Conformal 63 Mapping Method Figure 3.6. Conductor losses of a coaxial line calculated using FEM and SFA 65 Figure 3.7. Total losses of shielded microstrip line 66 Figure 4.1. Single shielded microstrip line with iso/anisotropic substrates 69 Figure 4.2. Characteristic impedance as functions of metal penetrating depth t2 70 xii Figure 4.3.
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