Microstrip Lines and Slotlines

Second Edition

K.C. Gupta Ramesh Garg

Inder Bahl Prakash Bhartia

Artech House Boston • London

Contents

Preface to the Second Edition xi

Preface to the First Edition xv

Chapter 1 Microstrip Lines I: Quasi-Static Analyses, Dispersion Models, and Measurements 1

1.1 Introduction 1 1.1.1 Planar Transmission Structures 1 1.1.2 Microstrip Field Configuration 2 1.1.3 Methods of Microstrip Analysis 5

1.2 Quasi-Static Analyses of a Microstrip 6 1.2.1 Modified Conformal Transformation Method 6 1.2.2 Finite Difference Method 12 1.2.3 Integral Equation Method 14 1.2.4 Variational Method in the Fourier Transform

Domain 15 1.2.5 Segmentation and Boundary Element Method

(SBEM) 18 1.3 Microstrip Dispersion Models 23

1.3.1 Coupled ТЕМ Mode and TM Mode Model 24 1.3.2 An Empirical Relation 24 1.3.3 Dielectric-Loaded Ridged Waveguide Model 25 1.3.4 Empirical Formulae for Broad Frequency Range 27 1.3.5 Planar Waveguide Model 29 1.3.6 Some Comments 32

1.4 Microstrip Transitions 33 1.4.1 Coaxial-to-Microstrip Transition 34 1.4.2 Waveguide-to-Microstrip Transition 37

vi I MICROSTRIP LINES AND SLOTLINES

1.5 Microstrip Measurements 43 1.5.1 Substrate Dielectric Constant 45 1.5.2 Characteristic Impedance 49 1.5.3 Phase Velocity or Effective Dielectric Constant 50 1.5.4 Attenuation Constant 54

References 56

Chapter 2 Microstrip Lines II: Fullwave Analyses, Design Considerations, and Applications 61

2.1 Methods of Fullwave Analysis 61 2.2 Analysis of an Open Microstrip 63

2.2.1 Integral Equation Method in the Space Domain 64 2.2.2 Galerkin's Method in the Spectral Domain 66 2.2.3 Discussion of Results 68

2.3 Analysis of an Enclosed Microstrip 71 2.3.1 Integral Equation Methods 71 2.3.2 Finite Difference Method 76 2.3.3 Discussion of Results 79

2.4 Design Considerations 83 2.4.1 Microstrip Losses 83 2.4.2 Power Handling Capability 87 2.4.3 Effect of Tolerances 95 2.4.4 Effect of Dielectric Anisotropy 98 2.4.5 Design Equations 102 2.4.6 Frequency Range of Operation 111

2.5 Other Types of Microstrip Lines 115 2.5.1 Suspended and Inverted Microstrip Lines 115 2.5.2 Multilayered Dielectric Microstrip 117 2.5.3 Thin Film Microstrip (TFM) 118 2.5.4 Valley Microstrip Lines 122

2.6 Microstrip Applications 122 2.6.1 Lumped Elements 126 2.6.2 Passive Components 135 2.6.3 Active Components 138 2.6.4 Packages and Assemblies 143 2.6.5 Superconducting Microstrip Circuits 145

References 152

Chapter 3 Microstrip Discontinuities I: Quasi-Static Analysis and Characterization 159

3.1 Introduction 159 3.2 Discontinuity Capacitance Evaluation 161

3.2.1 Matrix Inversion Method 161 3.2.2 Variational Method 167

Contents I vii

3.3 3.4

3.5

3.2.3

3.2.4

Galerkin's Mediod in the Fourier Transform Domain Use of Line Sources With Charge Reversal

Discontinuity Inductance Evaluation Characterization of Various Discontinuities 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.4.6 3.4.7

Open Ends Gaps in a Microstrip Steps in Width Bends T-junctions Cross Junctions Notch

Compensated Microstrip Discontinuities 3.5.1 3.5.2 3.5.3

Step in Width Bends T-junction

Chapter 4 Microstrip Discontinuities II: Fullwave Analysis and Measurements 213

4.1 Planar Waveguide Analysis 213 4.1.1 Discontinuity Characterization 213 4.1.2 Compensation of Discontinuity Reactances 234 4.1.3 Radiation and Parasitic Coupling 234

4.2 Fullwave Analysis of Discontinuities 245 4.2.1 Galerkin's Method in die Spectral Domain 246 4.2.2 Integral Equation Solution in the Space Domain 249 4.2.3 Time Domain Methods for Microstrip

Discontinuity Characterization 250 4.3 Discontinuity Measurements 255

4.3.1 Linear Resonator Method 256 4.3.2 Ring Resonator Method 260 4.3.3 Scattering Parameters Measurement Method 263

References 266

Chapter 5 Slotlines 269 5.1 Introduction 269 5.2 Slotline Analysis 271

5.2.1 Approximate Analysis 271 5.2.2 Transverse Resonance Method 274 5.2.3 Galerkin's Method in the Spectral Domain 277

5.3 Design Considerations 282 5.3.1 Closed-Form Expressions 282 5.3.2 Effect of Metal Thickness 286

viii I MICROSTRIP LINES AND SLOTLINES

5.3.3 Effect of Tolerances 287 5.3.4 Losses in Sloüine 287

5.4 Slotline Discontinuities 292 5.4.1 Short End 292 5.4.2 O p e n End 294

5.5 Other Slotline Configurations 295 5.5.1 Coupled Microstrip-Slotline 295 5.5.2 Conductor-Backed Slotline 297 5.5.3 Conductor-Backed Slotline with a Superstrate 300

5.6 Slotline Transitions 302 5.6.1 Coaxial-to-Slotline Transition 302 5.6.2 Microstrip-to-Slotline Crossjunct ion Transition 305

5.7 Slotline Applications 313 5.7.1 Circuits Using T-junctions 313 5.7.2 Circuits Using Wideband 180° Phase Shift 324 5.7.3 H y b r i d / d e Ronde ' s Branchline Couplers 327 5.7.4 Othe r Types of Slotline Circuits 334

References 334 Appendix 5.A: Susceptance Calculation for the Transverse

Resonance Method 337 Appendix 5.B: Sensitivity Expressions for Sloüine Impedance

and Wavelength 338

Chapter 6 Finlines 341 6.1 Int roduct ion 341 6.2 Analysis of Finlines 344

6.2.1 Transverse Resonance Method 344 6.2.2 Galerkin's Method in the Spectral Domain 346

6.3 Design Considerations 349 6.3.1 Closed-Form Solutions 349 6.3.2 LSE-Mode Dispersion Model 356 6.3.3 Synthesis Equations 358 6.3.4 Conductor Loss in Finlines 360

6.4 Transitions 360 6.4.1 Finline-to-Waveguide Taper Transitions 360 6.4.2 Finline-to-Microstrip Taper Transitions 364

References 369 Appendix 6.A: Susceptance Expression for the Unilateral Finline 371

Chapter 7 Coplanar Lines: Coplanar Waveguide and Coplanar Strips 375 7.1 Introduct ion 375 7.2 Analysis 379

7.2.1 Quasi-Static CPW Analysis Based on the Conformal Mapping Method 379

Contents I ix

7.2.2 Quasi-Static Analysis of Coplanar Strips (CPS) 400 7.2.3 Fullwave Analysis 405

7.3 Design Considerations 411 7.3.1 Design Equations 411 7.3.2 Dispersion 412 7.3.3 Effect of Metallization Thickness 414

7.4 Losses 415 7.4.1 Dielectric Loss 415 7.4.2 Conductor Loss 417 7.4.3 Radiation and Surface Wave Losses 422

7.5 Effect of Tolerances 426 7.6 Comparison With Microstrip Line and Slotline 430 7.7 Transitions 432

7.7.1 Coax-to-CPW Transitions 433 7.7.2 Microstrip-to-CPW Transitions 434 7.7.3 Slotline-to-CPW Transitions 436 7.7.4 CPW-to-CPS Transition 439 7.7.5 CPS-to-Slotline Transitions 440

7.8 Discontinuities in Coplanar Waveguide 441 7.9 Coplanar Line Circuits 443

7.9.1 Circuits With Series and Shunt Reactances in CPW 443

7.9.2 Circuits Using Slotline-CPW Junctions 446 References 451

Chapter 8 Coupled Microstrip Lines 457 8.1 Introduction 457 8.2 General Analysis of Coupled Lines 458

8.2.1 Methods of Analysis 458 8.2.2 Coupled Mode Approach 460 8.2.3 Even- and Odd-Mode Approach 464

8.3 Characteristics of Coupled Microstrip Lines 467 8.3.1 Quasi-Static Analysis 467 8.3.2 Fullwave Analysis 475 8.3.3 Dispersion Models 483

8.4 Measurements on Coupled Microstrip Lines 487 8.4.1 Impedance Measurements 487 8.4.2 Phase Constant Measurements 488

8.5 Design Considerations for Coupled Microstrip Lines 490 8.5.1 Design Equations 490 8.5.2 Losses 498 8.5.3 Effect of Fabrication Tolerances 502

x I MICROSTRIP LINES AND SLOTLINES

8.5.4 Coupled Microstrip Lines With Dielectric Overlays 504

8.5.5 Effect of Dielectric Anisotropy 507 8.6 Coupled Multiconductor Microstrip Lines 508 8.7 Discontinuities in Coupled Microstrip Lines 512

8.7.1 Network Model 513 8.7.2 Open-End Discontinuity 516

References 517

About the Authors 521

Index 525