Handbook of Filter Synthesis

Anatol I. Zverev is the author of Handbook of Filter Synthesis, published by Wiley.

Chapter 1 Filters in Electronics 1

1.1 Types of Filters 1

1.2 Filter Applications 3

1.3 All-Pass Filters 5

1.4 Properties of Lattice Filters 6

1.5 Filter Building Blocks 9

1.6 Higher Order Filters 17

1.7 Coil-Saving Bandpass Filters 17

1.8 Frequency Range of Applications 20

1.9 Physical Elements of the Filter 21

1.10 Active Bandpass Filters 22

1.11 RC Passive and Active Filters 22

1.12 Microwave Filters 25

1.13 Parametric Filters 29

Chapter 2 Theory of Effective Parameters 31

2.1 Power Balance 32

2.2 Types of General Network Equations 33

2.3 Effective Attenuation 35

2.4 Reflective (Echo) Attenuation 36

2.5 Transmission Function as a Function of Frequency Parameter, s 37

2.6 Polynomials of Transmission and Filtering Functions 38

2.7 Filter Networks 39

2.8 Voltage and Current Sources 41

2.9 The Function D(s) As an Approximation Function 42

2.10 Examples of Transmission Function Approximation 45

2.11 Simplest Polynomial Filters in Algebraic Form 49

2.12 Introduction to Image-Parameter Theory 50

2.13 Bridge Networks 52

2.14 Examples of Realization in the Bridge Form 53

2.15 Hurwitz Polynomial 54

2.16 The Smallest Realizable Networks 55

2.17 Fourth-Order Networks 57

2.18 Fifth-Order Networks 58

Chapter 3 Filter Characteristics in The Frequency Domain 60

3.1 Amplitude Responses 60

3.2 Phase-and Group-Delay Responses 61

3.3 Group Delay of an Idealized Filter 61

3.4 Group-Delay—Attenuation Relationship 61

3.5 The Chebyshev Family of Response Characteristics 62

3.6 Gaussian Family of Response Characteristics 67

3.7 A Filter with Transitional Magnitude Characteristics 74

3.8 Legendre Filters 74

3.9 Minimum-Loss Characteristics 76

3.10 Synchronously Tuned Filters 76

3.11 Arithmetically Symmetrical Bandpass Filters 77

3.12 Attenuation Characteristics of Image Parameter Filters 78

3.13 Other Types of Filter Characteristics 80

3.14 Plots of the Attenuation and Group Delay Characteristics 81

Chapter 4 Elliptic Functions and Elements of Realization 107

4.1 Double Periodic Elliptic Functions 107

4.2 Mapping of s-Plane into u-Plane 109

4.3 First Basic Transformation of Elliptic Functions 110

4.4 Filtering Function in z-Plane 112

4.5 Graphical Representation of Parameters 114

4.6 Characteristic Values of D(s) 115

4.7 An Example of Filter Design 116

4.8 Consideration of Losses 119

4.9 Introduction of Losses by Frequency Transformation 119

4.10 Highpass Filters with Losses 120

4.11 Transmission Functions with Losses 121

4.12 Conclusions on Consideration of Losses 123

4.13 Realization Process 124

4.14 Bandpass Filter with a Minimum Number of Inductors 125

4.15 The Elements of a Coil-Saving Network 127

4.16 Consideration of Losses in Zig-Zag Filters 128

4.17 Realization Procedure 129

4.18 Numerical Example of Realization 131

4.19 Full and Partial Removal for a Fifth-Order Filter 132

Chapter 5 The Catalog of Normalized Lowpass Filters 137

5.1 Introduction to the Catalog137

5.2 Real Part of the Driving Point Impedance146

5.3 Lowpass Filter Design148

5.4 Design of Highpass Filters151

5.5 Design of LC Bandpass Filters154

5.6 Design of Narrowband Crystal Filters160

5.7 Design of Bandstop Filters163

5.8 Catalog of Normalized Lowpass Models168

Chapter 6 Design Techniques for Polynomial Filters 290

6.1 Introduction to Tables of Normalized Element Values 290

6.2 Lowpass Design Examples 292

6.3 Bandpass Filter Design 295

6.4 Concept of Coupling 296

6.5 Coupled Resonators 298

6.6 Second-Order Bandpass Filter 300

6.7 Design with Tables of Predistorted k and q Parameters 305

6.8 Design Examples using Tables of k and q Values 306

6.9 Tables of Lowpass Element Values 310

6.10 Tables of 3-dB Down k and q Values 311

Chapter 7 Filter Characteristics in The Time Domain 380

7.1 Introduction to Transient Characteristics 380

7.2 Time and Frequency Domains 380

7.3 Information Contained in the Impulse Response 383

7.4 Step Response 383

7.5 Impulse Response of an Ideal Gaussian Filter 384

7.6 Residue Determination 385

7.7 Numerical Example 385

7.8 Practical Steps in the Inverse Transformation 388

7.9 Inverse Transform of Rational Spectral Functions 389

7.10 Numerical Example 390

7.11 Estimation Theory 391

7.12 Transient Response in Highpass and Bandpass Filters 392

7.13 The Exact Calculation of Transient Phenomena for Highpass Systems 393

7.14 Estimate of Transient Responses in Narrowband Filters 395

7.15 The Exact Transient Calculation in Narrowband Systems 397

7.16 Group Delay Versus Transient Response 398

7.17 Computer Determination of Filter Impulse Response 398

7.18 Transient Response Curves 400

Chapter 8 Crystal Filters 414

8.1 Introduction 414

8.2 Crystal Structure 414

8.3 Theory of Piezoelectricity 414

8.4 Properties of Piezoelectric Quartz Crystals 415

8.5 Classification of Crystal Filters 421

8.6 Bridge Filters 423

8.7 Limitation of Bridge Crystal Filters 425

8.8 Spurious Response 427

8.9 Circuit Analysis of a Simple Filter 428

8.10 Element Values in Image-Parameter Formulation 429

8.11 Ladder Filters 431

8.12 Effective Attenuation of Simple Filters 434

8.13 Effective Attenuation of Ladder Networks 437

8.14 Ladder Versus Bridge Filters 439

8.15 Practical Differential Transformer for Crystal Filters 440

8.16 Design of Narrowband Filters with the Aid of Lowpass Model 443

8.17 Synthesis of Ladder Single Sideband Filters 453

8.18 The Synthesis of Intermediate Bandpass Filters 483

8.19 Example of Band-Reject Filter 490

8.20 Ladder Filters with Large Bandwidth 491

Chapter 9 Helical Filters 499

9.1 Introduction 499

9.2 Helical Resonators 499

9.3 Filter with Helical Resonators 505

9.4 Alignment of Helical Filters 513

9.5 Examples of Helical Filtering 518

Chapter 10 Network Transformations 522

10.1 Two-Terminal Network Transformations 522

10.2 Delta-Star Transformation 528

10.3 Use of Transformer in Filter Realization 530

10.4 Norton’s Transformation 530

10.5 Applications of Mutual Inductive Coupling 536

10.6 The Realization of LC Filters with Crystal Resonators 540

10.7 Negative and Positive Capacitor Transformation 545

10.8 Bartlett’s Bisection Theorem 546

10.9 Caucr’s Equivalence 549

10.10 Canonic Bandpass Structures 552

10.11 Bandpass Ladder Filters Having a Canonical Number of Inductors without Mutual Coupling 553

10.12 Impedance and Admittance Inverters 559

10.13 Source and Load Transformation 567

Bibliography 569

Index 573