electronic filter simulation and design

8/9/2019 electronic filter simulation and design

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ELECTRONIC

FILTER

SIMULATION

DESIGN

Giovanni Bianchi

Roberto Sorrentino

New York hicago San Francisco Lisbon London Madrid M exico ity

Milan New Delhi San Juan Seoul Singapore Sydney Toronto


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Contents

Preface xiii

Acknowledgments xvi

1 Basic Concep ts 1

1.0 Introduction 1

1.1 Basic Definitions 1

1.2 M athematical Background 4

1.2.1 Fourier Transform 4

1.2.2 Laplace Transform 5

1.3 Filter Respon ses 6

1.3.1 Frequency Respo nse 6

1.3.2 Transfer Fun ction 7

1.3.3 Pulse Resp onse 8

1.3.4 Step Response 11

1.4 A pprox imations of the Ideal Low -Pass Characteristic 13

1.4.1 Bu tterworth Approximation 17

1.4.2 Chebysheff Approximation 20

1.4.3 Cauer Approximation 26

1.4.4 Bessel Approx imation 31

1.4.5 Som e Rem arks on the Polynomial Filters 38

1.5 Time Response 39

1.5.1 Step Response i 39

1.5.2 Pulse Response 42

1.6 Representation of 2-Port Linear Networks 43

1.6.1 Impedance M atrix 43

1.6.2 Adm ittance M atrix 45


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1.6.3 ABC D Matrix 46

1.6.4 Scattering Matrix 48

1.6.5 Image Param eters 49

1.7 Related Files 50

References 51

2 Lumped Passive Filters 5 3

2.0 Introduction 53

2.1 Lum ped Passive 2-Port Networks 53

2.2 Impedance and Frequency Normalization of a

Low -Pass Filter 55

2.3 Image Parameters for Low -Pass Filters 57

2.3.1 Constant-A; Low-Pass Filters 59

2.3.2 Procedure for the Dual Filter Derivation 63

2.3.3 m-Derived Low -Pass Filters 66

2.3.4 Procedure for the m-D erived Filter Design 67

2.4 Polynom ial Low -Pass Filters 71

2.4.1 Singly Terminated Polynom ial Low -Pass Filters 71

2.4.2 Doubly Terminated Polynomial Low-Pass F il te rs .. . 84

2.4.3 Some Rem arks on Passive Polynomial Low -Pass

Filters 97

2.4.4 Closed-Form Synthesis Form ulae for LC

Low -Pass Filters 99

2.5 Polynom ial High-Pass, Band-Pass, and Notch Filters 103

2.5.1 High-Pass Filters 105

2.5.2 Band-Pass Filters 109

2.5.3 Notch Filters (or Band-Stop Filters) 120

2.6 Com plementary Filters 122

2.7 Lim itations on Lum ped Passive Filters 125

2.7.1 Dissipation Loss 125

2.7.2 Parasitic Elem ents 129


References 133


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3 Active RC Filters 135

3.0 Introduction 135

3.1 Operational Am plifiers 135

3.1.1 Basic Configurations 136

3.1.2 AC Response 138

3.1.3 Stability 139

3.1.4 Noise in Operational Am plifiers 141

3.1.5 Opam p Dynamic Range 143

3.2 Active Filters Simulating Passive LC Ladder Networks .. 145

3.2.1 Simulation of Shunt Inductors 146

3.2.2 Frequency-Dependent Negative Resistors 148

3.3 Low -Pass Filters Realization with Bi-Quad Cells 152

3.3.1 Factorization of Low -Pass Transfer Function 152

3.3.2 Active Bi-Quad Cells , 156

3.3.3 Active Low -Pass Filter Examples 172

3.4 Active High-Pass Filters 176

3.5 Band-Pass Active Filters 180

3.5.1 Real-Pole Band-Pass Mapping 180

3.5.2 Com plex Pole and Imaginary Zeroes Band-Pass

Mapping 183

3.5.3 Band-Pass Transfer Function Factorization 184

3.5.4 An Example of an Active Band-Pass Filter 188

3.6 Active Notch Filters 191

3.6.1 Notch Response Factorization 192

3.6.2 An Example of an Active Notch Filter 193

3.7 All-Pass Filters 196

3.8 Perform ances of the Active RC Filters .' 199

3.8.1 Active Filter Noise 199

3.8.2 Active Filter Dynam ic Range 201

3.8.3 Sensitivity 206

3.8.4 Standard Com ponent Values

;

208


References 211


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4 Transmission Lines 2 1 3


4.1 Definitions 213

4.2 Telegraphist Equation of the Uniform Multicoupled

Transmission Lines 216

4.3 Adm ittance M atrix of the TEM Multicoupled Lines 223

4.4 Isolated Transm ission Lines 228

4.4.1 Loss-Free Isolated Transm ission Lines 228

4.4.2 Design Equations for Some Comm on

Transmission Lines 230

4.4.3 High-O rder M odes 236

4.4.4 Com mon Properties of Finite-Length

Transm ission Lines 239

4.4.5 Lossy Transm ission Lines 244

4.5 Sym metrical Coupled Lines 250

4.5.1 Even and Odd Modes . , 251

4.5.2 Imm ittance Matrices 254

4.5.3 Equivalent Circuits 257

4.5.4 Design Equations for Sym metrical Coupled

Lines 264

4.6 Additional Analyses of M ulticoupled Lines 268

4.6.1 Equivalent Circuits 268

4.6.2 Distributed Capacitance 277

4.7 Additional Considerations About Transm ission

Lines 286


References 288

5 Low Pass and Band Stop Distributed Filters . . . 2 8 9

5.0 Introduction /. 289

5.1 Semi-Lumped Low -Pass Filters 290

5.1.1 Design Principle 290

5.1.2 Semi-Lumped Filter Design 294

5.1.3 Lim itations of the Semi-Lumped Filters 312


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5.2 Richards Transform 315

5.3 Redundant Networks 319

5.3.1 Impedance Inverters 319

5.3.2 Kuroda Identities 323

5.4 Band-Stop Filters 326

5.4.1 Com mensurate Band-Stop Filters 326

5.4.2 Non-Com mensurate Band-Stop Filters 328

5.4.3 Examples of Distributed-Constant Filters 331


References 336

6 High Pass an d Band Pass Distributed F ilters... 3 3 7


6.1 Semi-Lum ped High-Pass Filters 338

6.1.1 Semi-Lumped High-Pass Elements 338

6.1.2 Sem i-Lumped High-Pass Filter Synthesis 341

6.1.3 Sem i-Lumped High-Pass Filter Design 344

6.2 Comb-Line Filters 347

6.2.1 Synthesis of the Comb-Line Filters 349

6.2.2 Analysis of the Com b-Line Filters 352

6.2.3 An Exam ple of a Com b-Line Filter 353

6.3 Periodic Band-Pass Filters 357

6.4 Interd igital Filters 362

6.4.1 Synthesis Formulae for the Interdigital Filters 363

6.4.2 An Example of a Narrow-Band Interdigital

Filter 369

6.5 Direct-Coupled Stub Filters 372

6.5.1 Direct-Coupled Stub Synthesis Formulae 373

6.5.2 Exam ples of Direct-Coupled Stub Filters 374

6.6 Edge-Coupled Filters 381

6.6.1 Narrow-Band Edge-Coupled Filters 382

6.6.2 W ide-Band Edge-Coupled Filters 385

6.6.3 Spurious Response in Edge-Coupled Filters 391

6.7 Other Types of Pass-Band Filters and Design

Techniques 395


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6.7.1 Pass-Band Filter Synthesis with the Coupling

Coefficients 396

6.7.2 Hairpin Filters 398

6.7.3 Tapped Filters 402


References 409

7 Special Designs of High Frequency Filters 4 1 1


7.1 M ultiplexers 411

7.1.1 An Exam ple of a Noncontiguous Diplexer 413

7.1.2 An Example of a Contiguous Triplexer 417

7.2 Tunable Filters 420

7.2.1 Varactor Characterization 420

7.2.2 Tunable Com b-Lines 428

7.2.3 Tunable Notch 435

7.3 Active Filters 439

7.3.1 Gallium Arsenide Field Effect Transistors 439

7.3.2 Filters with Automatic Loss Com pensation 443

7.3.3 Filters with Automatic Frequency Control 448

7.4 Pseudo-Elliptic Filters 449

7.5 High-Power Filters _ 452


References 456

8 Discrete Time Filters 4 5 7


8.1 M athematical Background 457

8.1.1 Z-Transform 457

8.1.2 Discrete Fourier Transform 459

8.1.3 Fourier Series . , 460

8.2 Digital Signal Processing 462

8.2.1 Sam pling 464

8.2.2 Quantization 468


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8.2.3 Quantization Distortion 471

8.2.4 AD C Pulse Shaping 474

8.2.5 Signal Interpolation 480

8.2.6 Response of the Analog Channel 482

8.3 Digital Filters 483

8.3.1 Basic DSP W orking Principles 483

8.3.2 IIR Filters 484

8.3.3 FIR Filters 499

8.4 Sw itched-Capacitor Filters 518


References 525

9 Waveguide Filters 527


9.1 Propagation in W aveguides 529

9.1.1 TE and TM M odes 530

9.1.2 Phase Constant 530

9.1.3 Dom inant M ode 531

9.1.4 Guided W avelength 531

9.1.5 Phase and Group Velocities 531

9.1.6 Wave Impedance and Characteristic

Impedance 532

9.1.7 Rectangular Waveguide 532

9.1.8 Ridge Waveguide 533

9.1.9 Circular W aveguide 534

9.2 Reactive Elem ents in W aveguide 535

9.2.1 Shunt-Inductive Obstacles 535

9.2.2 Shunt-Capacitive Obstacles 535

9.3 Shunt-Inductive Loaded Filter 538

9.3.1 Design Procedure ; 538

9.3.2 Design Exam ple 544

9.3.3 Design Procedure for W ide-Band Filter 547

9.3.4 Design Example 549


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9.4 Cross-Coupled Cavity Filters 552

9.4.1 Elliptic and Generalized Chebysheff Filtering

Functions 553

9.4.2 Coupling M atrix Description for Narrow-Band

Cross-Coupled Filters 554

9.4.3 Rec tangular Waveguide Realization 563

9.4.4 Design Procedure of H-Plane and E-Plane

Folded Filters 564

9.4.5 Design Exam ples 566

9.5 Dual-M ode Cavity Filters 574

9.5.1 Dual-M ode Circular and Rectangu lar Cavity

Filters 575

9.6 Low -Pass Filters 579

9.6.1 Tapered Corrugated Waveguide Filters 580

9.6.2 Evanescent-Mode Ridged Waveguide Filters 586


References 591

Appendixes 593

Appendix A Calculation of the Polynomial

Coefficients from a Factorized Expression 593

Appendix B Reflection Coefficients Zeroes of a

Polynom ial All-Pole Low -Pass Filter 595

Appendix C Complementarity of the Singly

Terminated Low-Pass and High-Pass Filters

with the Same Cutoff Frequency, Order, and

Load Resistance 599

n ex 601

electronic filter simulation and design

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