Design and realizations of miniaturized fractal RF and microwave filters

Engineers are continually searching for design methods that can satisfy the ever-increasing demand for miniaturization, accuracy, reliability, and fast development time. Design and Realizations of Miniaturized Fractal RF and Microwave Filters provides RF and microwave engineers and researchers, advanced graduate students, and wireless and telecommunication engineers with the knowledge and skills to design and realize miniaturized fractal microwave and RF filters. This book is an essential resource for the realization of portable and cellular phones, WiFi, 3G and 4G, and satellite networks.

The text focuses on the synthesis and fabrication of miniaturized fractal filters with symmetrical and asymmetrical frequency characteristics in the C, X and Ku bands, though applications to other frequency bands are considered. Readers will find helpful guidance on:

Miniaturized filters in bilevel fashion

Simplified methods for the synthesis of pseudo-elliptic electrical networks

Methods for extracting coupling coefficients and external quality factors from simulations of the RF/microwave structure

Methods for matching theoretical couplings to couplings of structure

Including studies of the real-world performance of fractal resonators and sensitivity analyses of suspended substrate realizations, this is a definitive resource for both practicing engineers and students who need timely insight on fractal resonators for compact and low-power microwave and RF applications.

Author Notes

Pierre Jarry graduated from the University of Limoges. As a professor at University of Brest, he directed the Laboratory of Electronics and Telecommunication Systems (LEST), affiliated with the French National Center for Scientific Research (CNRS). He later joined the University of Bordeaux and the CNRS laboratory IMS. He has published 300 technical papers in microwave and RF circuit synthesis, and is a senior member of the IEEE.
Jacques Deneat received his PhD in electrical and computer engineering from Worcester Polytechnic Institute with a focus in advanced microwave structures for satellite communications, and a doctorate degree from the University of Bordeaux with Mention Trs Honorable avec flicitations du Jury. He was a research scientist at the Center for Wireless Information Network Studies at WPI and is currently Associate Professor of Electrical and Computer Engineering at Norwich University.
Pierre Jarry and Jacques Beneat are the authors of the bestselling book Advanced Design Techniques and Realizations of Microwave and RF Filters, published by Wiley-IEEE Press and available also in electronic form.

Foreword	p. ix
Preface	p. xi
1 Microwave Filter Structures	p. 1
1.1 Background	p. 2
1.2 Cavity Filters	p. 3
1.2.1 Evanescent-Mode Waveguide Filters	p. 3
1.2.2 Coupled Cavity Filters	p. 5
1.2.3 Dielectric Resonator Filters	p. 9
1.2.4 E-Plane Filters	p. 12
1.3 Planar Filters	p. 13
1.3.1 Semi-lumped Filters	p. 14
1.3.2 Planar Transmission Line Filters	p. 14
1.4 Planar Filter Technology	p. 19
1.4.1 Microstrip Technology	p. 19
1.4.2 Coplanar Technology	p. 20
1.4.3 Suspended Substrate Stripline Technology	p. 20
1.4.4 Multilayer Technology	p. 21
1.5 Active Filters	p. 22
1.6 Superconductivity or HTS Filters	p. 23
1.7 Periodic Structure Filters	p. 24
1.8 SAW Filters	p. 25
1.9 Micromachined Filters	p. 27
1.10 Summary	p. 28
References	p. 29
2 In-Line Synthesis of Pseudo-Elliptic Filters	p. 35
2.1 Introduction	p. 35
2.2 Approximation and Synthesis	p. 36
2.3 Chebyshev Filters	p. 36
2.4 Pseudo-elliptic Filters	p. 37
2.4.1 Pseudo-elliptic Characteristic Function	p. 38
2.4.2 Pseudo-elliptic Transfer Functions	p. 40
2.4.3 Cross-Coupled and In-Line Prototypes for Asymmetrical Responses	p. 41
2.4.4 Analysis of the In-Line Prototype Elements	p. 45
2.4.5 Synthesis Algorithm for Pseudo-elliptic Lowpass In-line Filters	p. 49
2.4.6 Frequency Transformation	p. 50
2.5 Prototype Synthesis Examples	p. 52
2.6 Theoretical Coupling Coefficients and External Quality Factors	p. 59
References	p. 61
3 Suspended Substrate Structure	p. 63
3.1 Introduction	p. 63
3.2 Suspended Substrate Technology	p. 64
3.3 Unloaded Quality Factor of a Suspended Substrate Resonator	p. 66
3.4 Coupling Coefficients of Suspended Substrate Resonators	p. 69
3.4.1 Input/Output Coupling	p. 69
3.4.2 Coupling Between Resonators	p. 69
3.5 Enclosure Design Considerations	p. 73
References	p. 75
4 Miniaturization Of Planar Resonators Using Fractal Iterations	p. 79
4.1 Introduction	p. 79
4.2 Miniaturization of Planar Resonators	p. 81
4.3 Fractal Iteration Applied to Planar Resonators	p. 82
4.4 Minkowski Resonators	p. 84
4.4.1 Minkowski's Fractal Iteration	p. 84
4.4.2 Minkowski Square First-Iteration Resonator	p. 85
4.4.3 Minkowski Rectangular First-Iteration Resonator	p. 86
4.4.4 Minkowski Second-Iteration Resonators	p. 88
4.4.5 Sensitivity of Minkowski Resonators	p. 90
4.5 Hibert Resonators	p. 92
4.5.1 Hilbert's Curve	p. 92
4.5.2 Hilbert Half-Wavelength Resonator	p. 93
4.5.3 Unloaded Quality Factor of Hilbert Resonators	p. 94
4.5.4 Sensitivity of Hilbert Resonators	p. 96
References	p. 98
5 Design and Realizations of Meandered Line Filters	p. 101
5.1 Introduction	p. 102
5.2 Third-order Pseudo-elliptic Filters with Transmission Zero on the Right	p. 102
5.2.1 Topology of the Filter	p. 102
5.2.2 Synthesis of the Bandpass Prototype	p. 103
5.2.3 Defining the Dimensions of the Enclosure	p. 103
5.2.4 Defining the Gap Distances	p. 105
5.2.5 Further Study of the Filter Response	p. 107
5.2.6 Realization and Measured Performance	p. 110
5.2.7 Sensitivity Analysis	p. 114
5.3 Third-order Pseudo-elliptic Filters with Transmission Zero on the Left	p. 117
5.3.1 Topology of the Filter	p. 117
5.3.2 Synthesis of the Bandpass Prototype	p. 118
5.3.3 Defining the Dimensions of the Enclosure	p. 118
5.3.4 Defining the Gap Distances	p. 118
5.3.5 Realization and Measured Performance	p. 122
5.3.6 Sensitivity Analysis	p. 125
References	p. 127
6 Design and Realizations of Hilbert Filters	p. 129
6.1 Introduction	p. 129
6.2 Design of Hilbert Filters	p. 130
6.2.1 Second-Order Chebyshev Responses	p. 130
6.2.2 Third-Order Chebyshev Responses	p. 134
6.2.3 Third-Order Pseudo-elliptic Response	p. 136
6.2.4 Third-Order Pseudo-elliptic Responses Using Second-Iteration Resonators	p. 144
6.3 Realizations and Measured Performance	p. 148
6.3.1 Third-Order Pseudo-elliptic Filter with Transmission Zero on the Right	p. 149
6.3.2 Third-Order Pseudo-elliptic Filter- with Transmission Zero on the Left	p. 154
References	p. 159
7 Design And Realization of Dual-Mode Minkowski Filters	p. 161
7.1 Introduction	p. 161
7.2 Study of Minkowski Dual-Mode Resonators	p. 162
7.3 Design of Fourth-Order Pseudo-elliptic Filters with Two Transmission Zeros	p. 166
7.3.1 Topology	p. 166
7.3.2 Synthesis	p. 167
7.3.3 Design Steps	p. 168
7.4 Realization and Measured Performance	p. 176
References	p. 182
Appendix 1 Equivalence Between J and K Lowpass Prototypes	p. 183
Appendix 2 Extraction of the Unloaded Quality Factor of Suspended Substrate Resonators	p. 189
Index	p. 193

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