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 5 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 5 .... 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
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
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 TE on Linear-Phase
Filters .................................................... 199
10.1 Introduction .......................................... 199
10.2 TEon 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
11.3.1 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
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
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