【分享】Lumped Elements for RF and Microwave Circuits

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Lumped Elements for RF and Microwave Circuits

Inder Bahl

Artech House
Boston · London

Contents
Preface xvii
Acknowledgments xix
1 Introduction 1
1.1 History of Lumped Elements 1
1.2 Why Use Lumped Elements for RF and
Microwave Circuits? 2
1.3 L, C, R Circuit Elements 4
1.4 Basic Design of Lumped Elements 6
1.4.1 Capacitor 7
1.4.2 Inductor 8
1.4.3 Resistor 8
1.5 Lumped-Element Modeling 9
1.6 Fabrication 11
1.7 Applications 12
References 13
2 Inductors 17
2.1 Introduction 17
vii
viii Lumped Elements for RF and Microwave Circuits
2.2 Basic Definitions 18
2.2.1 Inductance 18
2.2.2 Magnetic Energy 18
2.2.3 Mutual Inductance 20
2.2.4 Effective Inductance 20
2.2.5 Impedance 21
2.2.6 Time Constant 21
2.2.7 Quality Factor 22
2.2.8 Self-Resonant Frequency 23
2.2.9 Maximum Current Rating 23
2.2.10 Maximum Power Rating 23
2.2.11 Other Parameters 23
2.3 Inductor Configurations 24
2.4 Inductor Models 25
2.4.1 Analytical Models 25
2.4.2 Coupled-Line Approach 28
2.4.3 Mutual Inductance Approach 34
2.4.4 Numerical Approach 36
2.4.5 Measurement-Based Model 38
2.5 Coupling Between Inductors 45
2.5.1 Low-Resistivity Substrates 45
2.5.2 High-Resistivity Substrates 46
2.6 Electrical Representations 50
2.6.1 Series and Parallel Representations 50
2.6.2 Network Representations 51
References 52
3 Printed Inductors 57
3.1 Inductors on Si Substrate 58
3.1.1 Conductor Loss 60
3.1.2 Substrate Loss 63
3.1.3 Layout Considerations 64
3.1.4 Inductor Model 65
3.1.5 Q-Enhancement Techniques 69
3.1.6 Stacked-Coil Inductor 80
3.1.7 Temperature Dependence 84
Contents ix
3.2 Inductors on GaAs Substrate 86
3.2.1 Inductor Models 87
3.2.2 Figure of Merit 88
3.2.3 Comprehensive Inductor Data 88
3.2.4 Q-Enhancement Techniques 104
3.2.5 Compact Inductors 112
3.2.6 High Current Handling Capability Inductors 116
3.3 Printed Circuit Board Inductors 118
3.4 Hybrid Integrated Circuit Inductors 121
3.4.1 Thin-Film Inductors 121
3.4.2 Thick-Film Inductors 124
3.4.3 LTCC Inductors 126
3.5 Ferromagnetic Inductors 127
References 129
4 Wire Inductors 137
4.1 Wire-Wound Inductors 137
4.1.1 Analytical Expressions 137
4.1.2 Compact High-Frequency Inductors 144
4.2 Bond Wire Inductor 146
4.2.1 Single and Multiple Wires 147
4.2.2 Wire Near a Corner 150
4.2.3 Wire on a Substrate Backed by a Ground Plane 151
4.2.4 Wire Above a Substrate Backed by a Ground
Plane 153
4.2.5 Curved Wire Connecting Substrates 154
4.2.6 Twisted Wire 155
4.2.7 Maximum Current Handling of Wires 155
4.3 Wire Models 156
4.3.1 Numerical Methods for Bond Wires 156
4.3.2 Measurement-Based Model for Air Core
Inductors 156
4.3.3 Measurement-Based Model for Bond Wires 158
4.4 Magnetic Materials 160
References 161
x Lumped Elements for RF and Microwave Circuits
5 Capacitors 163
5.1 Introduction 163
5.2 Capacitor Parameters 165
5.2.1 Capacitor Value 165
5.2.2 Effective Capacitance 166
5.2.3 Tolerances 166
5.2.4 Temperature Coefficient 166
5.2.5 Quality Factor 167
5.2.6 Equivalent Series Resistance 167
5.2.7 Series and Parallel Resonances 167
5.2.8 Dissipation Factor or Loss Tangent 170
5.2.9 Time Constant 170
5.2.10 Rated Voltage 170
5.2.11 Rated Current 170
5.3 Chip Capacitor Types 171
5.3.1 Multilayer Dielectric Capacitor 171
5.3.2 Multiplate Capacitor 172
5.4 Discrete Parallel Plate Capacitor Analysis 173
5.4.1 Vertically Mounted Series Capacitor 173
5.4.2 Flat-Mounted Series Capacitor 176
5.4.3 Flat-Mounted Shunt Capacitor 177
5.4.4 Measurement-Based Model 178
5.5 Voltage and Current Ratings 181
5.5.1 Maximum Voltage Rating 181
5.5.2 Maximum RF Current Rating 181
5.5.3 Maximum Power Dissipation 182
5.6 Capacitor Electrical Representation 185
5.6.1 Series and Shunt Connections 185
5.6.2 Network Representations 187
References 188
6 Monolithic Capacitors 191
6.1 MIM Capacitor Models 192
6.1.1 Simple Lumped Equivalent Circuit 193
Contents xi
6.1.2 Coupled Microstrip-Based Distributed Model 194
6.1.3 Single Microstrip-Based Distributed Model 198
6.1.4 EC Model for MIM Capacitor on Si 202
6.1.5 EM Simulations 204
6.2 High-Density Capacitors 206
6.2.1 Multilayer Capacitors 208
6.2.2 Ultra-Thin-Film Capacitors 211
6.2.3 High-K Capacitors 212
6.2.4 Fractal Capacitors 212
6.2.5 Ferroelectric Capacitors 214
6.3 Capacitor Shapes 216
6.3.1 Rectangular Capacitors 217
6.3.2 Circular Capacitors 218
6.3.3 Octagonal Capacitors 218
6.4 Design Considerations 220
6.4.1 Q-Enhancement Techniques 220
6.4.2 Tunable Capacitor 223
6.4.3 Maximum Power Handling 223
References 227
7 Interdigital Capacitors 229
7.1 Interdigital Capacitor Models 230
7.1.1 Approximate Analysis 230
7.1.2 J -Inverter Network Equivalent Representation 235
7.1.3 Full-Wave Analysis 236
7.1.4 Measurement-Based Model 238
7.2 Design Considerations 239
7.2.1 Compact Size 239
7.2.2 Multilayer Capacitor 241
7.2.3 Q-Enhancement Techniques 244
7.2.4 Voltage Tunable Capacitor 247
7.2.5 High-Voltage Operation 249
7.3 Interdigital Structure as a Photodetector 249
References 251
xii Lumped Elements for RF and Microwave Circuits
8 Resistors 253
8.1 Introduction 253
8.2 Basic Definitions 255
8.2.1 Power Rating 255
8.2.2 Temperature Coefficient 256
8.2.3 Resistor Tolerances 256
8.2.4 Maximum Working Voltage 256
8.2.5 Maximum Frequency of Operation 257
8.2.6 Stability 257
8.2.7 Noise 257
8.2.8 Maximum Current Rating 257
8.3 Resistor Types 257
8.3.1 Chip Resistors 258
8.3.2 MCM Resistors 258
8.3.3 Monolithic Resistors 258
8.4 High-Power Resistors 265
8.5 Resistor Models 267
8.5.1 EC Model 268
8.5.2 Distributed Model 269
8.5.3 Meander Line Resistor 270
8.6 Resistor Representations 272
8.6.1 Network Representations 272
8.6.2 Electrical Representations 272
8.7 Effective Conductivity 274
8.8 Thermistors 276
References 276
9 Via Holes 279
9.1 Types of Via Holes 279
9.1.1 Via Hole Connection 279
9.1.2 Via Hole Ground 281
9.2 Via Hole Models 282
9.2.1 Analytical Expression 283
Contents xiii
9.2.2 Quasistatic Method 284
9.2.3 Parallel Plate Waveguide Model 286
9.2.4 Method of Moments 287
9.2.5 Measurement-Based Model 289
9.3 Via Fence 290
9.3.1 Coupling Between Via Holes 293
9.3.2 Radiation from Via Ground Plug 293
9.4 Plated Heat Sink Via 294
9.5 Via Hole Layout 294
References 296
10 Airbridges and Dielectric Crossovers 299
10.1 Airbridge and Crossover 299
10.2 Analysis Techniques 301
10.2.1 Quasistatic Method 301
10.2.2 Full-Wave Analysis 306
10.3 Models 308
10.3.1 Analytical Model 308
10.3.2 Measurement-Based Model 310
References 315
11 Transformers and Baluns 317
11.1 Basic Theory 318
11.1.1 Parameters Definition 318
11.1.2 Analysis of Transformers 319
11.1.3 Ideal Transformers 322
11.1.4 Equivalent Circuit Representation 323
11.1.5 Equivalent Circuit of a Practical Transformer 325
11.1.6 Wideband Impedance Matching Transformers 326
11.1.7 Types of Transformers 329
11.2 Wire-Wrapped Transformers 329
11.2.1 Tapped Coil Transformers 329
11.2.2 Bond Wire Transformer 332
11.3 Transmission-Line Transformers 332
xiv Lumped Elements for RF and Microwave Circuits
11.4 Ferrite Transformers 336
11.5 Parallel Conductor Winding Transformers on Si
Substrate 339
11.6 Spiral Transformers on GaAs Substrate 341
11.6.1 Triformer Balun 344
11.6.2 Planar-Transformer Balun 345
References 349
12 Lumped-Element Circuits 353
12.1 Passive Circuits 353
12.1.1 Filters 353
12.1.2 Hybrids and Couplers 356
12.1.3 Power Dividers/Combiners 370
12.1.4 Matching Networks 372
12.1.5 Lumped-Element Biasing Circuit 377
12.2 Control Circuits 380
12.2.1 Switches 381
12.2.2 Phase Shifters 387
12.2.3 Digital Attenuator 390
References 392
13 Fabrication Technologies 395
13.1 Introduction 395
13.1.1 Materials 396
13.1.2 Mask Layouts 401
13.1.3 Mask Fabrication 401
13.2 Printed Circuit Boards 402
13.2.1 PCB Fabrication 404
13.2.2 PCB Inductors 405
13.3 Microwave Printed Circuits 405
13.3.1 MPC Fabrication 407
13.3.2 MPC Applications 408
13.4 Hybrid Integrated Circuits 410
13.4.1 Thin-Film MICs 410
Contents xv
13.4.2 Thick-Film Technology 412
13.4.3 Cofired Ceramic and Glass-Ceramic Technology 414
13.5 GaAs MICs 416
13.5.1 MMIC Fabrication 418
13.5.2 MMIC Example 421
13.6 CMOS Fabrication 421
13.7 Micromachining Fabrication 424
References 425
14 Microstrip Overview 429
14.1 Design Equations 429
14.1.1 Characteristic Impedance and Effective Dielectric
Constant 429
14.1.2 Effect of Strip Thickness 431
14.2 Design Considerations 432
14.2.1 Effect of Dispersion 433
14.2.2 Microstrip Losses 433
14.2.3 Quality Factor Q 435
14.2.4 Enclosure Effect 438
14.2.5 Frequency Range of Operation 443
14.2.6 Power-Handling Capability 444
14.3 Coupled Microstrip Lines 456
14.3.1 Even-Mode Capacitance 457
14.3.2 Odd-Mode Capacitance 458
14.3.3 Characteristic Impedances 459
14.3.4 Effective Dielectric Constants 459
14.4 Microstrip Discontinuities 460
14.5 Compensated Microstrip Discontinuities 461
14.5.1 Step-in-Width 461
14.5.2 Chamfered Bend 462
14.5.3 T-Junction 463
References 465
xvi Lumped Elements for RF and Microwave Circuits
Appendix 469
About the Author 471
Index 473

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