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1. Introduction 1
2. Network Analysis 7
2.1 Network Variables 7
2.2 Scattering Parameters 8
2.3 Short-Circuit Admittance Parameters 11
2.4 Open-Circuit Impedance Parameters 11
2.5 ABCD Parameters 12
2.6 Transmission Line Networks 12
2.7 Network Connections 14
2.8 Network Parameter Conversions 17
2.9 Symmetrical Network Analysis 18
2.10 Multi-Port Networks 21
2.11 Equivalent and Dual Networks 24
2.12 Multi-Mode Networks 26
References 28
3. Basic Concepts and Theories of Filters 29
3.1 Transfer Functions 29
3.1.1 General Definitions 29
3.1.2 The Poles and Zeros on the Complex Plane 30
3.1.3 Butterworth (Maximally Flat) Response 31
3.1.4 Chebyshev Response 32
3.1.5 Elliptic Function Response 34
3.1.6 Gaussian (Maximally Flat Group-Delay) Response 36
3.1.7 All-Pass Response 37
3.2 Lowpass Prototype Filters and Elements 38
3.2.1 Butterworth Lowpass Prototype Filters 41
3.2.2 Chebyshev Lowpass Prototype Filters 41
3.2.3 Elliptic Function Lowpass Prototype Filters 44
3.2.4 Gaussian Lowpass Prototype Filters 46
3.2.5 All-Pass Lowpass Prototype Filters 47
3.3 Frequency and Element Transformations 48
3.3.1 Lowpass Transformation 49
3.3.2 Highpass Transformation 51
3.3.3 Bandpass Transformation 51
3.3.4 Bandstop Transformation 53
3.4 Immittance Inverters 54
3.4.1 Definition of Immittance, Impedance and Admittance Inverters 54
3.4.2 Filters with Immittance Inverters 56
3.4.3 Practical Realization of Immittance Inverters 60
3.5 Richards’Transformation and Kuroda Identities 61
3.5.1 Richards’Transformation 61
3.5.2 Kuroda Identities 66
3.5.3 Coupled-Line Equivalent Circuits 66
3.6 Dissipation and Unloaded Quality Factor 69
3.6.1 Unloaded Quality Factors of Lossy Reactive Elements 70
3.6.2 Dissipation Effects on Lowpass and Highpass Filters 71
3.6.3 Dissipation Effects on Bandpass and Bandstop Filters 73
References 75
4. Transmission Lines and Components 77
4.1 Microstrip Lines 77
4.1.1 Microstrip Structure 77
4.1.2 Waves in Microstrip 77
4.1.3 Quasi-TEM Approximation 78
4.1.4 Effective Dielectric Constant and Characteristic Impedance 78
4.1.5 Guided Wavelength, Propagation Constant, Phase
4.1.5 Velocity, and Electrical Length 80
4.1.6 Synthesis of W/h 80
4.1.7 Effect of Strip Thickness 81
4.1.8 Dispersion in Microstrip 82
4.1.9 Microstrip Losses 83
4.1.10 Effect of Enclosure 84
4.1.11 Surface Waves and Higher-Order Modes 84
4.2 Coupled Lines 84
4.2.1 Even- and Odd-Mode Capacitances 85
4.2.2 Even- and Odd-Mode Characteristic Impedances and Effective
4.1.5 Dielectric Constants 87
4.2.3 More Accurate Design Equations 87
vi CONTENTS
4.3 Discontinuities and Components 89
4.3.1 Microstrip Discontinuities 89
4.3.2 Microstrip Components 93
4.3.3 Loss Considerations for Microstrip Resonators 102
4.4 Other Types of Microstrip Lines 104
References 106
5. Lowpass and Bandpass Filters 109
5.1 Lowpass Filters 109
5.1.1 Stepped-Impedance L-C Ladder Type Lowpass Filters 109
5.1.2 L-C Ladder Type of Lowpass Filters using Open-Circuited Stubs 112
5.1.3 Semilumped Lowpass Filters Having Finite-Frequency
5.1.3 Attenuation Poles 116
5.2 Bandpass Filters 121
5.2.1 End-Coupled, Half-Wavelength Resonator Filters 121
5.2.2 Parallel-Coupled, Half-Wavelength Resonator Filters 127
5.2.3 Hairpin-Line Bandpass Filters 129
5.2.4 Interdigital Bandpass Filters 133
5.2.5 Combline Filters 142
5.2.6 Pseudocombline Filters 148
5.2.7 Stub Bandpass Filters 151
References 158
6. Highpass and Bandstop Filters 161
6.1 Highpass Filters 161
6.1.1 Quasilumped Highpass Filters 161
6.1.2 Optimum Distributed Highpass Filters 165
6.2 Bandstop Filters 168
6.2.1 Narrow-Band Bandstop Filters 168
6.2.2 Bandstop Filters with Open-Circuited Stubs 176
6.2.3 Optimum Bandstop Filters 182
6.2.4 Bandstop Filters for RF Chokes 188
References 190
7. Advanced Materials and Technologies 191
7.1 Superconducting Filters 191
7.1.1 Superconducting Materials 191
7.1.2 Complex Conductivity of Superconductors 192
7.1.3 Penetration Depth of Superconductors 193
7.1.4 Surface Impedance of Superconductors 194
7.1.5 Nonlinearity of Superconductors 197
7.1.6 Substrates for Superconductors 199
7.1.7 HTS Microstrip Filters 200
7.1.8 High-Power HTS Filters 201
7.2 Ferroelectric Tunable Filters 204
CONTENTS vii
7.2.1 Ferroelectric Materials 205
7.2.2 Dielectric Properties 206
7.2.3 Tunable Microstrip Filters 208
7.3 Micromachined Filters 211
7.3.1 MEMS and Micromachining 211
7.3.2 Micromachined Microstrip Filters 211
7.4 MMIC Filters 215
7.4.1 MMIC Technology 215
7.4.2 MMIC Microstrip Filters 216
7.5 Active Filters 217
7.5.1 Active Filter Methodologies 217
7.5.2 Active Microstrip Filters 219
7.6 Photonic Bandgap (PBG) Filters 221
7.6.1 PBG Structures 221
7.6.2 PBG Microstrip Filters 222
7.7 Low-Temperature Cofired Ceramic (LTCC) Filters 224
7.7.1 LTCC Technology 224
7.7.2 Miniaturized LTCC Filters 225
References 227
8. Coupled Resonator Circuits 235
8.1 General Coupling Matrix for Coupled-Resonator Filters 236
8.1.1 Loop Equation Formulation 236
8.1.2 Node Equation Formulation 240
8.1.3 General Coupling Matrix 243
8.2 General Theory of Couplings 244
8.2.1 Synchronously Tuned Coupled-Resonator Circuits 245
8.2.2 Asynchronously Tuned Coupled-Resonator Circuits 251
8.3 General Formulation for Extracting Coupling Coefficient k 257
8.4 Formulation for Extracting External Quality Factor Qe 258
8.4.1 Singly Loaded Resonator 259
8.4.2 Doubly Loaded Resonator 262
8.5 Numerical Examples 264
8.5.1 Extracting k (Synchronous Tuning) 265
8.5.2 Extracting k (Asynchronous Tuning) 267
8.5.3 Extracting Qe 270
References 271
9. CAD for Low-Cost and High-Volume Production 273
9.1 Computer-Aided Design Tools 274
9.2 Computer-Aided Analysis 274
9.2.1 Circuit Analysis 274
9.2.2 Electromagnetic Simulation 279
9.2.3 Artificial Neural Network Modeling 283
viii CONTENTS
9.3 Optimization 285
9.3.1 Basic Concepts 285
9.3.2 Objective Functions for Filter Optimization 286
9.3.3 One-Dimensional Optimization 288
9.3.4 Gradient Methods for Optimization 288
9.3.5 Direct Search Optimization 291
9.3.6 Optimization Strategies Involving EM Simulations 295
9.4 Filter Synthesis by Optimization 299
9.4.1 General Description 299
9.4.2 Synthesis of a Quasielliptic Function Filter by Optimization 299
9.4.3 Synthesis of an Asynchronously Tuned Filter by Optimization 300
9.4.4 Synthesis of a UMTS Filter by Optimization 302
9.5 CAD Examples 306
References 312
10. Advanced RF/Microwave Filters 315
10.1 Selective Filters with a Single Pair of Transmission Zeros 315
10.1.1 Filter Characteristics 315
10.1.2 Filter Synthesis 317
10.1.3 Filter Analysis 320
10.1.4 Microstrip Filter Realization 321
10.2 Cascaded Quadruplet (CQ) Filters 325
10.2.1 Microstrip CQ Filters 326
10.2.2 Design Example 326
10.3 Trisection and Cascaded Trisection (CT) Filters 328
10.3.1 Characteristics of CT Filters 328
10.3.2 Trisection Filters 331
10.3.3 Microstrip Trisection Filters 335
10.3.4 Microstrip CT Filters 340
10.4 Advanced Filters with Transmission Line Inserted Inverters 341
10.4.1 Characteristics of Transmission Line Inserted Inverters 341
10.4.2 Filtering Characteristics with Transmission Line Inserted Inverters 344
10.4.3 General Transmission Line Filter 348
10.5 Linear Phase Filters 350
10.5.1 Prototype of Linear Phase Filter 350
10.5.2 Microstrip Linear Phase Bandpass Filters 355
10.6 Extract Pole Filters 359
10.6.1 Extracted Pole Synthesis Procedure 360
10.6.2 Synthesis Example 366
10.6.3 Microstrip Extracted Pole Bandpass Filters 368
10.7 Canonical Filters 371
10.7.1 General Coupling Structure 371
10.7.2 Elliptic Function/Selective Linear Phase Canonical Filters 373
References 375
CONTENTS ix
11. Compact Filters and Filter Miniaturization 379
11.1 Ladder Line Filters 379
11.1.1 Ladder Microstrip Line 379
11.1.2 Ladder Microstrip Line Resonators and Filters 381
11.2 Pseudointerdigital Line Filters 383
11.2.1 Filtering Structure 383
11.2.2 Pseudointerdigital Resonators and Filters 385
11.3 Miniature Open-Loop and Hairpin Resonator Filters 389
11.4 Slow-Wave Resonator Filters 392
11.4.1 Capacitively Loaded Transmission Line Resonator 392
11.4.2 End-Coupled Slow-Wave Resonator Filters 396
11.4.3 Slow-Wave, Open-Loop Resonator Filters 396
11.5 Miniature Dual-Mode Resonator Filters 404
11.5.1 Microstrip Dual-Mode Resonators 404
11.5.2 Miniaturized Dual-Mode Resonator Filters 408
11.6 Multilayer Filters 410
11.6.1 Wider-Band Multilayer Filters 411
11.6.2 Narrow-Band Multilayer Filters 412
11.7 Lumped-Element Filters 420
11.8 Miniaturized Filters Using High Dielectric Constant Substrates 426
References 428
12. Case Study for Mobile Communications Applications 433
12.1 HTS Subsystems and RF Modules for Mobile Base Stations 433
12.2 HTS Microstrip Duplexers 436
12.2.1 Duplexer Principle 438
` 12.2.2 Duplexer Design 439
12.2.3 Duplexer Fabrication and Test 444
12.3 Preselect HTS Microstrip Bandpass Filters 446
12.3.1 Design Considerations 446
12.3.2 Design of the Preselect Filter 448
12.3.3 Sensitivity Analysis 448
12.3.4 Evaluation of Quality Factor 450
12.3.5 Filter Fabrication and Test 454
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