RF and Microwave Coupled-Line Circuits Second Edition

R. K. Mongia I. J. Bahl P. Bhartia J. Hong

(5 A R T E C H H O U S E BOSTON|LONDON a r t e c h h o u s e . c o m

Contents

Foreword to the First Edition Xv

Preface to the Second Edition xvii

Preface to the First Edition Xxi

CHAPTER 1

Introduction i

1.1 Coupled Structures 1 1.1.1 Types of Coupled Structures 3 1.1.2 Coupling Mechanism 4

1.2 Components Based on Coupled Structures 6 1.2.1 Directional Couplers 6 1.2.2 Filters 8

1.3 Applications 11 1.4 Scope of the Book 13

References 13

CHAPTER 2

Microwave Network Theory 1 7

2.1 Actual and Equivalent Voltages and Currents 17 2.1.1 Normalized Voltages and Currents 18 2.1.2 Unnormalized Voltages and Currents 21 2.1.3 Reflection Coefficient, VSWR, and Input Impedance 22 2.1.4 Quantities Required to Describe the State of a Transmission

Line 24 2.2 Impedance and Admittance Matrix Representation of a Network 26

2.2.1 Impedance Matrix 26 2.2.2 Admittance Matrix 27 2.2.3 Properties of Impedance and Admittance Parameters of a

Passive Network 27 2.3 Scattering Matrix 28

2.3.1 Unitary Property 30 2.3.2 Transformation with Change in Position of Terminal Planes 31

VII

VIII Contents

2.3.3 Reciprocal Networks 32 2.3.4 Relationship Between Normalized and Unnormalized Matrices 32

2.4 Special Properties of Two-, Three-, and Four-Port Passive, Lossless Networks 32 2.4.1 Two-Port Networks 33 2.4.2 Three-Port Reciprocal Networks 34 2.4.3 Three-Port Nonreciprocal Networks 35 2.4.4 Four-Port Reciprocal Networks 36

2.5 Special Representation of Two-Port Networks 38 2.5.1 ABCD Parameters 38 2.5.2 Reflection and Transmission Coefficients in Terms of ABCD

Parameters 40 2.5.3 Equivalent T and Yl Networks of Two-Port Circuits 41

2.6 Conversion Relations 43 2.7 Scattering Matrix of Interconnected Networks 45

2.7.1 Scattering Parameters of Reduced Networks 47 2.7.2 Reduction of a Three-Port Network into a Two-Port Network 48 2.7.3 Reduction of a Two-Port Network into a One-Port Network 49 2.7.4 Reduction of a Four-Port Network into a Two-Port Network 50 References 51

CHAPTER 3

Characteristics of Planar Transmission Lines 53

3.1 General Characteristics of TEM and Quasi-TEM Modes 53 3.1.1 TEM Modes 57 3.1.2 Quasi-TEM Modes 58 3.1.3 Skin Depth and Surface Impedance of Imperfect Conductors 59 3.1.4 Conductor Loss of TEM and Quasi-TEM Modes 60

3.2 Representation of Capacitances of Coupled Lines 61 3.2.1 Even- and Odd-Mode Capacitances of Symmetrical Coupled

Lines 62 3.2.2 Parallel-Plate and Fringing Capacitances of Single and Coupled

Planar Transmission Lines 66 3.3 Characteristics of Single and Coupled Striplines 68

3.3.1 Single Stripline 69 3.3.2 Edge-Coupled Striplines 73

3.4 Characteristics of Single and Coupled Microstrip Lines 74 3.4.1 Single Microstrip 75 3.4.2 Coupled Microstrip Lines 81

3.5 Single and Coupled Coplanar Waveguides 83 3.5.1 Coplanar Waveguide 84 3.5.2 Coplanar Waveguide with Upper Shielding 86 3.5.3 Conductor-Backed Coplanar Waveguide with Upper Shielding 87 3.5.4 Coupled Coplanar Waveguides 88

3.6 Suspended and Inverted Microstrip Lines 88

Contents IX

3.7 Broadside-Coupled Lines 93 3.7.1 Broadside-Coupled Striplines 94 3.7.2 Broadside-Coupled Suspended Microstrip Lines 95 3.7.3 Broadside-Coupled Offset Striplines 96

3.8 Slot-Coupled Microstrip Lines 99 References 102

CHAPTER 4

Analysis of Uniformly Coupled Lines 105

4.1 Even- and Odd-Mode Analysis of Symmetrical Networks 106 4.1.1 Even-Mode Excitation 108 4.1.2 Odd-Mode Excitation 109

4.2 Directional Couplers Using Uniform Coupled Lines 111 4.2.1 Forward-Wave (or Codirectional) Directional Couplers 114 4.2.2 Backward-Wave Directional Couplers 116

4.3 Uniformly Coupled Asymmetrical Lines 120 4.3.1 Parameters of Asymmetrical Coupled Lines 121 4.3.2 Distributed Equivalent Circuit of Coupled Lines 126 4.3.3 Relation Between Normal Mode (c and TT) and Distributed

Line Parameters 130 4.3.4 Approximate Distributed Line or Normal-Mode Parameters of

Asymmetrical Coupled Lines 132 4.4 Directional Couplers Using Asymmetrical Coupled Lines 133

4.4.1 Forward-Wave Directional Couplers 133 4.4.2 Backward-Wave Directional Couplers 136

4.5 Design of Multilayer Couplers 138 4.5.1 Determination of Capacitance and Inductance Parameters

Using Sonnet Lite 139 4.5.2 Coupler Design 140 References 147

CHAPTER 5

Broadband Forward-Wave Directional Couplers 149

5.1 Forward-Wave Directional Couplers 150 5.1.1 3-dB Coupler Using Symmetrical Microstrip Lines 151 5.1.2 Design and Performance of 3-dB Asymmetrical Couplers 153 5.1.3 Ultra-Broadband Forward-Wave Directional Couplers 155

5.2 Coupled-Mode Theory 156 5.2.1 Nature of Coupling Coefficient K\2 and Ki\ 158 5.2.2 Waves on Lines 1 and 2 in the Presence of Coupling 158 5.2.3 Coupled-Mode Theory and Even- and Odd-Mode Analysis 160 5.2.4 Coupling Between Asymmetrical Lines 161

5.3 Coupled-Mode Theory for Weakly Coupled Resonators 163 References 165

X Contents

CHAPTER 6 Parallel-Coupled TEM Directional Couplers 167

6.1 Coupler Parameters 167 6.2 Single-Section Directional Coupler 169

6.2.1 Frequency Response 169 6.2.2 Design 171 6.2.3 Compact Couplers 176 6.2.4 Equivalent Circuit of a Quarter-Wave Coupler 176

6.3 Multisection Directional Couplers 177 6.3.1 Theory and Synthesis 177 6.3.2 Limitations of Multisection Couplers 184

6.4 Techniques to Improve Directivity of Microstrip Couplers 186 6.4.1 Lumped Compensation 186 6.4.2 Use of Dielectric Overlays 189 6.4.3 Use of Wiggly Lines 189 6.4.4 Other Techniques 192 References 194

CHAPTER 7

Nonuniform Broadband TEM Directional Couplers 197

7.1 Symmetrical Couplers 197 7.1.1 Coupling in Terms of Even-Mode Characteristic Impedance 199 7.1.2 Synthesis 201 7.1.3 Technique for Determining Weighting Functions 206 7.1.4 Electrical and Physical Length of a Coupler 209 7.1.5 Design Procedure 210

7.2 Asymmetrical Couplers 214 References 217

CHAPTER 8

Tight Couplers 219

8.1 Introduction 219 8.2 Branch-Line Couplers 220

8.2.1 Modified Branch-Line Coupler 223 8.2.2 Reduced-Size Branch-Line Coupler 225 8.2.3 Lumped-Element Branch-Line Coupler 230 8.2.4 Broadband Branch-Line Coupler 233

8.3 Rat-Race Coupler 233 8.3.1 Modified Rat-Race Coupler 237 8.3.2 Reduced-Size Rat-Race Coupler 239 8.3.3 Lumped-Element Rat-Race Coupler 240

8.4 Multiconductor Directional Couplers 242 8.4.1 Theory of Interdigital Couplers 243 8.4.2 Design of Interdigital Couplers 245

8.5 Tandem Couplers 252

Contents XI

8.6 Multilayer Tight Couplers 255 8.6.1 Broadside Couplers 255 8.6.2 Re-Entrant Mode Couplers 258

8.7 Compact Couplers 261 8.7.1 Lumped-Element Couplers 262 8.7.2 Spiral Directional Couplers 262 8.7.3 Meander Line Directional Coupler 263

8.8 Other Tight Couplers 264 References 265

CHAPTER 9

Coupled-Line Filter Fundamentals 269

9.1 Introduction 269 9.1.1 Types of Filters 270 9.1.2 Applications 270

9.2 Theory and Design of Filters 271 9.2.1 Maximally Fiat or Butterworth Prototype 272 9.2.2 Chebyshev Response 272 9.2.3 Other Response-Type Filters 275 9.2.4 LC Filter Transformation 275 9.2.5 Filter Analysis and CAD Methods 279 9.2.6 Some Practical Considerations 280

9.3 Parallel-Coupled Line Filters 283 9.3.1 Design Example 285

9.4 Interdigital Filters 287 9.4.1 Design Examples 287

9.5 Combline Filters 290 9.5.1 Design Example 291

9.6 The Hairpin-Line Filter 295 9.6.1 Design Example 297

9.7 Parallel-Coupled Bandstop Filter 300 9.7.1 Design Example 301 References 304

CHAPTER 10

Advanced Coupled-Line Filters 307

10.1 Introduction 307 10.2 Coupled-Line Filters with Enhanced Stopband Performance 307

10.2.1 Design Using Unevenly-Coupled Stages 307 10.2.2 Design Using Periodically Nonuniform Coupled Lines 314 10.2.3 Design Using Meandered Parallel-Coupled Lines 320 10.2.4 Design Using Defected Ground Structures 324

10.3 Coupled-Line Filters Exhibiting Advanced Filtering Characteristics 327 10.3.1 Filters with Cross-Coupled Resonators 327 10.3.2 Filters with Source-Load Coupling 335 10.3.3 Filters with Asymmetrie Port Excitations 347

Contents

10.4 Interdigital Filters Using Stepped Impedance Resonators 352 10.4.1 Narrowband Design 354 10.4.2 Wideband Design 356

10.5 Dual-Band Filters 359 References 367

CHAPTER 11

Filters Using Advanced Materials and Technologies 371

11.1 Introduction 371 11.2 Superconductor Coupled-Line Filters 371

11.2.1 Cascaded Quadruplet and Triplet Filters 371 11.2.2 High-Order Selective Filters with Group-Delay Equalization 377

11.3 Micromachined Filters 385 11.3.1 Miniature Interdigital Filters on Silicon 387 11.3.2 Overlay Coupled CPW Filters 390

11.4 Filters Using Advanced Dielectric Materials 391 11.4.1 Low-Temperature Cofired Ceramic Filters 392 11.4.2 Liquid Crystal Polymer Filters 396

11.5 Filters for Ultra-Wideband (UWB) Technology 400 11.5.1 Optimum Stub Line Filters 401 11.5.2 Multimode Coupled-Line Filters 406 11.5.3 Microstrip-Coplanar Waveguide Coupled-Line Filters 410 11.5.4 UWB Filters with Notch Band 421

11.6 Metamaterial Filters 428 References 438

CHAPTER 12

Coupled-Line Circuit Components 443

12.1 DC Blocks 443 12.1.1 Analysis 443 12.1.2 Broadband DC Block 446 12.1.3 Biasing Circuits 446 12.1.4 Millimeter-Wave DC Block 449 12.1.5 High-Voltage DC Block 451

12.2 Coupled-Line Transformers 452 12.2.1 Open-Circuit Coupled-Line Transformers 452 12.2.2 Transmission Line Transformers 456

12.3 Interdigital Capacitor 461 12.3.1 Approximate Analysis 462 12.3.2 Full-Wave Analysis 464

12.4 Spiral Inductors 465 12.5 Spiral Transformers 472 12.6 Other Coupled-Line Components 475

References 476

CHAPTER 13

Baluns 481

13.1 Introduction 481 13.2 Microstrip-to-Balanced Stripline Balun 482 13.3 Analysis of a Coupled-Line Balun 486 13.4 Planar Transmission Line Baluns 490

13.4.1 Analysis 493 13.4.2 Examples 496

13.5 Marchand Balun 498 13.5.1 Coaxial Marchand Balun 501 13.5.2 Synthesis of Marchand Balun 505 13.5.3 Examples of Marchand Baluns 509

13.6 Other Baluns 518 13.6.1 Coplanar Waveguide Baluns 518 13.6.2 Triformer Balun 518 13.6.3 Planar-Transformer Balun 519 References 524

About the Authors 529

Index 531