Practical Microstrip Design and Applications

Practical Microstrip Design and Applications Günter Kompa ARTECH H O US E BOSTON|LONDON artechhouse.com . Contents Preface xiii Chapter 1 Introduction...

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Practical Microstrip Design and Applications Günter Kompa

ARTECH H O US E BOSTON|LONDON artechhouse.com

Contents Preface

xiii

Chapter 1

Introduction 1.1 Systematics of Microwave Integrated Circuits 1.2 Circuit Design Methods 1.2.1 Empirical Design 1.2.2 Modern Computer Aided Design References

1 5 7 7 9 13

Chapter 2

Overview of Strip Transmission Lines 2.1 Microstrip Line 2.2 Shielded Microstrip Line 2.3 Triplate 2.4 Suspended Stripline 2.5 Sandwich Line 2.6 Slot Line 2.7 Coplanar Line 2.8 Coupled Microstrip Line 2.9 Antipodal Slot Line 2.10 Finline References

15 19 25 26 26 27 28 30 34 36 38 40

Chapter 3

Methods of Microstrip Analysis 3.1 Conformal Transformation Method After Wheeler 3.1.1 Air-Filled Microstrip Line 3.1.2 Mapping of the Microstrip Conductor Boundaries into a Parallel Plate Structure 3.1.3 Dielectric-Filled Microstrip Line 3.1.4 Effect of Strip Thickness 3.1.5 Microstrip Inductance per Unit Length 3.2 Theory After Schneider 3.2.1 Single-Dielectric Microstrip Line 3.2.2 Effective Dielectric Constant 3.2.3 Analysis and Synthesis Equations After Wheeler 3.3 Impedance Design Formulas After Hammerstad 3.4 Füll-Wave Analysis 3.4.1 Modes of Inhomogeneous Parallel Plate Structure

43 47 48

vn

50 57 69 72 75 75 85 86 87 91 91

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Practical Microstrip Design and Applications 3.4.2 3.4.3

Surface Waves on Dielectric Plate Shielded Microstrip Transmission Line Laterally Open 3.5 Comparison of Discussed Analysis Methods References

96 107 119 119

Chapter 4

Dispersion on Microstrip Line 4.1 Frequency-Dependent Effective Dielectric Constant 4.2 Frequency-Dependent Characteristic Impedance 4.3 Measurement of Dispersion 4.3.1 Sliding Load Method 4.3.2 Resonance Method 4.3.3 Dispersion Measurements of Higher-Order Modes References

123 125 132 138 142 147 160 167

Chapter 5

Planar Waveguide Model 5.1 Definition of Dynamic Waveguide Model References

169 174 184

Chapter 6

Microstrip Discontinuities, Junctions, and Associated Circuit Elements 6.1 OpenEnd 6.1.1 Open End Capacitance and Excess Length 6.1.2 Radiation Resistance 6.2 Step 6.2.1 Quasi-Static Equivalent Circuit 6.2.2 Full-Wave Analysis Using the Planar Waveguide Model 6.2.3 Cascaded Step Discontinuities 6.2.4 Quarter-Wavelength Transformer 6.2.5 Stepped Microstrip Transformer 6.3 T-junction 6.3.1 Quasi-Static Equivalent Circuit 6.3.2 Dynamic Equivalent Circuit 6.3.3 Compensated T-Junction 6.3.4 Special Structures 6.4 Stub 6.5 Bend 6.5.1 Right-Angled Bend 6.5.2 Compensated Bend 6.5.3 Curved Microstrip Bend 6.6 Quasi-Lumped Elements 6.6.1 Series Inductance 6.6.2 Shunt Capacitance 6.7 Circular Disk Resonator

187 189 191 194 208 208 215 228 230 234 236 237 237 241 242 243 249 249 251 254 256 256 261 265

Contents

ix

6.7.1 Radial Transmission Line 6.7.2 Circular Disk Capacitor 6.7.3 Magnetic Wall Model After Watkins 6.7.4 Magnetic Wall Model After Wolff 6.8 Radial Line Stub 6.8.1 Model After Vinding 6.8.2 Model After Giannini 6.8.3 Model After Atwater 6.8.4 Biasing Network 6.9 Series Gap 6.10 Cross Junction References

265 270 272 275 280 282 284 286 288 291 293 296

Chapter 7

Microstrip Loss 7.1 Conductor Loss 7.1.1 Skin Effect 7.1.2 Incremental Inductance Rule 7.2 Dielectric Loss 7.3 Conductor Roughness 7.4 Total Loss References

301 303 305 315 324 327 327 328

Chapter 8

Applications 8.1 Microstrip Filter Design 8.1.1 Basics in Filter Design 8.1.2 Filter Response Types 8.1.3 Design Examples 8.1.4 Frequency Transformations 8.2 Impedance Matching Networks 8.3 Coupled-Line Directional Coupler 8.3.1 Impedance Matrix of Coupled Lines 8.3.2 Scattering Matrix of Coupled Lines 8.3.3 TEM Directional Coupler 8.3.4 Quasi-TEM Directional Coupler 8.3.5 Design Example References

331 331 333 338 347 355 357 362 363 367 370 372 372 374

Chapter 9

Technology 9.1 Substrate 9.1.1 Rigid Substrates 9.1.2 Soft Substrates 9.1.3 Substrate Height 9.2 Chip Devices 9.2.1 Resistor 9.2.2 Capacitor

377 377 378 380 382 383 384 385

Practical Microstrip Design and Applications

X

9.3

Circuit Fabrication 9.3.1 Hybrid Microwave Circuits 9.3.2 Monolithic Microwave Integrated Circuits 9.3.3 Quasi-Monolithic Microwave Integrated Circuits References

386 386 387 388 392

Appendix A Method of Conformal Transformation A. 1 Theory of Functions of a Complex Variable A.l.l Application to Electrostatic Problems A.2 The Schwarz-Christoffel Mapping Theorem A.2.1 Schwarz-Christoffel Theorem References

397 397 404 409 410 416

Appendix B Smith Chart B. 1 Constraction of the Smith Chart B.l.l Analysis of Im(z) = const. B.1.2 Analysis of Re(z) = const. B.1.3 Analysis of | z | = const. B.1.4 Analysis of


417 418 418 419 420 421

433 434

Appendix C Pulse Shaping with Coupled Microstrip and Slot Line References

435 438

Appendix D Modes in Waveguiding Structures D.l Maxwell Equations D. 1.1 Boundary Conditions D. 1.2 Particular Boundary Conditions D.2 Modified Maxwell Equations for Solving Waveguiding Boundary Problems D.2.1 Wave Equation for the Longitudinal Field Components

439 439 442 445

423 426 427 428 429

446 449

Contents D.2.2 Electric and Magnetic Vector Potentials Longitudinal Section Modes D.3.1 Vector Potential in x Direction D.3.2 Vector Potential in y Direction D.4 Classification of Field Modes in Waveguiding Structures D.4.1 TEMMode D.4.2 E Modes D.4.3 H Modes References D.3

Appendix E Definition of Insertion Loss Reference

XI

456 461 462 462 463 464 465 465 468 469 470

Appendix F Table of Quasi-Static Line Parameters After Hammerstad

471

Appendix G Circuit Therory G. 1 Circuit Parameters Interrelating Voltage and Current G.2 S Matrix Concept References Appendix H Orthogonal Series Expansion Method Reference

477 477 480 484 485 490

Appendix I Impedance Matrix of Step Discontinuity References

491 495

Appendix J Coupled Microstrip Lines J. 1 Quasi-Static Coupled Line Parameters J.2 Dispersive Coupled Line Parameters References

497 497 505 511

About the Author

513

Index

515