Advanced Design Techniques and Realizations of Microwave and RF Filters

Foreword xiii

Preface xv

PART I MICROWAVE FILTER FUNDAMENTALS 1

1 Scattering Parameters and ABCD Matrices 3

1.1 Introduction 3

1.2 Scattering Matrix of a Two-Port System 4

1.2.1 Definitions 4

1.2.2 Computing the S Parameters 6

1.2.3 S-Parameter Properties 10

1.3 ABCD Matrix of a Two-Port System 10

1.3.1 ABCD Matrix of Basic Elements 11

1.3.2 Cascade and Multiplication Property 12

1.3.3 Input Impedence of a Loaded Two-Port 14

1.3.4 Impedance and Admittance Inverters 14

1.3.5 ABCD-Parameter Properties 17

1.4 Conversion from Formulation S to ABCD and ABCD to S 18

1.5 Bisection Theorem for Symmetrical Networks 18

1.6 Conclusions 21

References 21

2 Approximations and Synthesis 23

2.1 Introduction 23

2.2 Ideal Low-Pass Filtering Characteristics 24

2.3 Functions Approximating the Ideal Low-Pass Magnitude Response 25

2.3.1 Butterworth Function 25

2.3.2 Chebyshev Function 26

2.3.3 Elliptic Function 27

2.3.4 Generalized Chebyshev (Pseudoelliptic) Function 29

2.4 Functions Approximating the Ideal Low-Pass Phase Response 30

2.4.1 Bessel Function 30

2.4.2 Rhodes Equidistant Linear-Phase Function 31

2.5 Low-Pass Lumped Ladder Prototypes 32

2.5.1 General Synthesis Technique 32

2.5.2 Normalized Low-Pass Ladders 36

2.6 Impedance and Frequency Scaling 39

2.6.1 Impedance Scaling 39

2.6.2 Frequency Scaling 40

2.7 LC Filter Example 41

2.8 Impedance and Admittance Inverter Ladders 41

2.8.1 Low-Pass Prototypes 41

2.8.2 Scaling Flexibility 42

2.8.3 Bandpass Ladders 44

2.8.4 Filter Examples 45

2.9 Conclusions 46

References 46

3 Waveguides and Transmission Lines 49

3.1 Introduction 49

3.2 Rectangular Waveguides and Cavities 49

3.2.1 Rectangular Waveguides 49

3.2.2 Rectangular Cavities 52

3.3 Circular Waveguides and Cavities 53

3.3.1 Circular Waveguides 53

3.3.2 Cylindrical Cavities 55

3.4 Evanescent Modes 56

3.5 Planar Transmission Lines 57

3.6 Distributed Circuits 60

3.7 Conclusions 63

References 64

4 Categorization of Microwave Filters 67

4.1 Introduction 67

4.2 Minimum-Phase Microwave Filters 68

4.2.1 General Design Steps 68

4.2.2 Minimum-Phase Filter Examples 70

4.3 Non-Minimum-Phase Symmetrical Response Microwave Filters 70

4.3.1 General Design Steps 71

4.3.2 Non-Minimum-Phase Symmetrical Response Filter Examples 73

4.3.3 Microwave Linear-Phase Filters 73

4.4 Non-Minimum-Phase Asymmetrical Response Microwave Filters 74

4.4.1 General Design Steps 74

4.4.2 Non-Minimum-Phase Asymmetrical Response Filter Examples 77

4.4.3 Multimode Microwave Filters by Optimization 79

4.5 Conclusions 79

References 80

PART II MINIMUM-PHASE FILTERS 83

5 Capacitive-Gap Filters for Millimeter Waves 85

5.1 Introduction 85

5.2 Capacitive-Gap Filters 86

5.2.1 Capacitive-Gap Filter Structure 86

5.2.2 Design Procedures 87

5.2.3 Step-by-Step Design Example 91

5.2.4 Filter Realizations 93

5.3 Extension to Millimeter Waves 95

5.3.1 Millimeter-Wave Technology 95

5.3.2 Fifth-Order Chebyshev Capacitive-Gap Filter at 35 GHz 96

5.4 Electromagnetic Characterization of SSS 99

5.5 Conclusions 102

References 102

6 Evanescent-Mode Waveguide Filters with Dielectric Inserts 105

6.1 Introduction 105

6.2 Evanescent-Mode Waveguide Filters 106

6.2.1 Scattering and ABCD Descriptions of the Structure 108

6.2.2 Equivalent Circuit of the Structure 110

6.2.3 Filter Design Procedure 115

6.2.4 Design Examples and Realizations 117

6.3 Folded Evanescent-Mode Waveguide Filters 121

6.3.1 Scattering and ABCD Descriptions of the Additional Elements 123

6.3.2 Filter Design Procedure 125

6.3.3 Design Examples and Realizations 125

6.4 Conclusions 127

References 128

7 Interdigital Filters 131

7.1 Introduction 131

7.2 Interdigital Filters 131

7.3 Design Method 135

7.3.1 Prototype Circuit 135

7.3.2 Equivalent Circuit 137

7.3.3 Input and Output 140

7.3.4 Case of Narrowband Filters 141

7.3.5 Frequency Transformation 141

7.3.6 Physical Parameters of the Interdigital Filter 142

7.4 Design Examples 145

7.4.1 Wideband Example 145

7.4.2 Narrowband Example 147

7.5 Realizations and Measured Performance 148

7.6 Conclusions 150

References 151

8 Combline Filters Implemented in SSS 153

8.1 Introduction 153

8.2 Combline Filters 153

8.3 Design Method 156

8.3.1 Prototype Circuit 156

8.3.2 Equivalent Circuit 157

8.3.3 Input and Output 159

8.3.4 Feasibility 162

8.3.5 Physical Parameters of the Combline Structure 162

8.4 Design Example 165

8.5 Realizations and Measured Performance 168

8.6 Conclusions 169

References 170

PART III NON-MINIMUM-PHASE SYMMETRICAL RESPONSE FILTERS 171

9 Generalized Interdigital Filters with Conditions on Amplitude and Phase 173

9.1 Introduction 173

9.2 Generalized Interdigital Filter 174

9.3 Simultaneous Amplitude and Phase Functions 175

9.3.1 Minimum-Phase Functions with Linear Phase 175

9.3.2 Non-Minimum-Phase Functions with Simultaneous Conditions on the Amplitude and Phase 177

9.3.3 Synthesis of Non-Minimum-Phase Functions with Simultaneous Conditions on the Amplitude and
Phase 180

9.4 Design Method 182

9.4.1 Even-Mode Equivalent Circuit 182

9.4.2 Frequency Transformation 186

9.4.3 Physical Parameters of the Interdigital Structure 187

9.5 Design Example 191

9.6 Realizations and Measured Performance 194

9.7 Conclusions 195

References 197

10 Temperature-Stable Narrowband Monomode TE011 Linear-Phase Filters 199

10.1 Introduction 199

10.2 TE011 Filters 200

10.3 Low-Pass Prototype 200

10.3.1 Amplitude 200

10.3.2 Delay 201

10.3.3 Synthesis of the Low-Pass Prototype 202

10.4 Design Method 204

10.4.1 Matching the Coupling 204

10.4.2 Selecting the Cavities 207

10.4.3 Defining the Coupling 208

10.5 Design Example 210

10.6 Realizations and Measured Performance 213

10.6.1 Amplitude and Phase Performance 213

10.6.2 Temperature Performance 214

10.7 Conclusions 215

References 217

PART IV NON-MINIMUM-PHASE ASYMMETRICAL RESPONSE FILTERS 219

11 Asymmetrical Capacitive-Gap Coupled Line Filters 221

11.1 Introduction 221

11.2 Capacitive-Gap Coupled Line Filters 222

11.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 222

11.3.1 In-Line Network 225

11.3.2 Analysis of the In-Line Network 226

11.3.3 Synthesis of the In-Line Network 229

11.3.4 Frequency Transformation 232

11.4 Design Method 233

11.5 Design Example 238

11.6 Realization of the CGCL Filter 243

11.7 Conclusions 244

References 245

12 Asymmetrical Dual-Mode TE102/TE301 Thick Iris Rectangular In-Line Waveguide Filters with Transmission Zeros 247

12.1 Introduction 247

12.2 TE102/TE301 Filters 248

12.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 248

12.3.1 Fundamental Element 249

12.3.2 Analysis of the In-Line Network 250

12.3.3 Synthesis by Simple Extraction Techniques 252

12.3.4 Frequency Transformation 254

12.4 Design Method 256

12.4.1 Equivalent Circuit of Monomode and Bimode Cavities 256

12.4.2 Optimization Approach 256

12.5 Design Example 262

12.6 Realizations and Measured Performance 266

12.6.1 Third-Order Filter with One Transmission Zero 266

12.6.2 Fourth-Order Filter with Two Transmission Zeros 268

12.7 Conclusions 269

References 270

13 Asymmetrical Cylindrical Dual-Mode Waveguide Filters with Transmission Zeros 273

13.1 Introduction 273

13.2 Dual-Mode Cylindrical Waveguide Filters 274

13.3 Synthesis of Low-Pass Asymmetrical Generalized Chebyshev Filters 275

13.3.1 Synthesis From a Cross-Coupled Prototype 275

13.3.2 Extracting the Elements from the Chain Matrix 277

13.3.3 Coupling Graph and Frequency Transformation 281

13.4 Design Method 284

13.4.1 Rotation Matrix 284

13.4.2 Cruciform Iris 286

13.4.3 Physical Parameters of the Irises 290

13.5 Realizations and Measured Performance 292

13.5.1 Fourth-Order Filter with One Transmission Zero on the Left 292

13.5.2 Fourth-Order Filter with Two Ransmission Zeros on the Right 293

13.5.3 Sixth-Order Filter with One Transmission Zero on the Right 295

13.6 Conclusions 296

References 296

14 Asymmetrical Multimode Rectangular Building Block Filters Using Genetic Optimization 299

14.1 Introduction 299

14.2 Multimode Rectangular Waveguide Filters 300

14.3 Optimization-Based Design 302

14.3.1 Genetic Algorithm 302

14.3.2 Example 308

14.4 Realizations 313

14.4.1 Fourth-Order Filter with Two Transmission Zeros 313

14.4.2 Seventh-Order Filter with Four Transmission Zeros 314

14.4.3 Extension to a Tenth-Order Filter with Six Transmission Zeros 318

14.5 Conclusions 320

References 320

Appendix 1: Lossless Systems 323

Appendix 2: Redundant Elements 325

Appendix 3: Modal Analysis of Waveguide Step Discontinuities 328

Appendix 4: Trisections with Unity Inverters on the Inside or on the Outside 338

Appendix 5: Reference Fields and Scattering Matrices for Multimodal Rectangular Waveguide Filters 340

Index 353