Dual-Band Bandstop Filter (Dbbsf) Using Spurline & Stepped-Impedance Resonator with Tunable Devices

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DUAL-BAND BANDSTOP FILTER (DBBSF) USING SPURLINE & STEPPED-IMPEDANCE RESONATOR WITH TUNABLE DEVICES

HAMAD GHAZI S ALRWUILI

B. E., Al-Jouf University, 2005

M. E., University of Denver, 2008

A dissertation submitted to the Graduate Faculty of the

University of Colorado Colorado Springs

in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy

Department of Electrical and Computer Engineering

2018

This dissertation for the Doctor of Philosophy degree by

Hamad Ghazi S Alrwuili

has been approved for the

Department of Electrical and Computer Engineering

Thottam S. Kalkur, Chair

Heather Song

Charlie Wang

John Lindsey

Anatoliy Glushchenko

12.10.2018 Date

Alrwuili, Hamad Ghazi S (Ph.D., Engineering) Dual-Band Bandstop Filter (DBBSF) Using Spurline & Stepped-Impedance Resonator with Tunable Devices Dissertation directed by Professor Thottam S. Kalkur

ABSTRACT

Bandstop filters are very important components in RF microwave systems by virtue of their effective suppression of spurious signals. They are used widely as key components in transmitter and receiver systems. They can be used to block the interfering signals which might affect the transmitted signal. Recently, Dual-Band Bandstop filters (DBBSFs) have become an attractive research field because of their suitability for treating the undesirable double-sideband spectrum in high-power amplifiers and mixers. This feature can be achieved using only a single filter which can reduce both the circuit size and cost of the proposed filter. In addition, this kind of filter has low insertion loss and group delay because of its ability to resonate in the stopband rather than in the passband.

This dissertation will present a novel methodology for designing Dual-Band Bandstop Filter with tunable devices. The new filter design will be compact and will integrate two different filter techniques into one. It will use a spurline section with a stepped impedance resonator to approach the performance of dual-band bandstop filter. Both resonators will be fabricated and tested by using microstrip transmission lines.

Ferroelectric Capacitors will be modeled and fabricated to be used as tunable elements for the Dual-Band Bandstop filter. These capacitors show low loss, ability to handle power and low distortion when performing isolation or intermodulation. In addition, they have demonstrated a very good tunability while maintaining a comparatively low bias voltage. They can be easily integrated with filter components because of their small size.

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In this work, chapter one will introduce briefly the importance of the different microwave filter technologies. It will briefly highlight the applications in RF microwave systems.

Also, it will provide a brief introduction about tunable technologies that are commonly used in RF systems.

Chapter two will present a literature review about the development of Dual-Band Bandstop filters. It will focus more on the microstrip methodology and tunable elements that are used in the application of tunability to bandstop filters.

In chapter three, the new design of a Dual-Band Bandstop filter will be introduced. It will integrate a spurline section and a stepped impedance resonator into one compacted filter. The modeling of the new filter design will be presented by using microstrip transmission lines.

Chapter four will deal with the tunable devices that are used to tune the new compact filter design. The compact dual-band bandstop filter design will be tuned by using p-n junction varactor diodes at 2.4 GHz and 3.5 GHz. In addition, the same filter design will be tuned by using ferroelectric materials at 2 GHz and 3.5 GHz. The P-n junction varactor diodes will be modeled and simulated by using ADS software. Ferroelectric material will be fabricated and used as tuning elements. The measurement results will be provided along with a comparison between modeling and fabricated filter designs.

Finally, in chapter five we are going to discuss the conclusion of this work with some recommendations for future work.

DEDICATION

The effort behind this dissertation is dedicated to my family and my friends. I am grateful to my loving parents for their great and unending support throughout my career as a student. And this is a timely opportunity for me to thank them for their sincere prayers.

I also dedicate this dissertation to my brothers, Ahmad, Mohammad and Yousuf who supported me throughout my studies. On my behalf and on behalf of my family, they have my sincere gratitude.

This work is also dedicated to my dear wife, Hoda Alrowili whose support, patience and dedication have been indispensable throughout this long journey. My beautiful daughters, Hdeel and Jenna, and my wonderful sons, Alharth, Ghazi, Rawad and Eyad have also been part of this journey which has seen my career grow and them flourish.

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my academic advisor Dr. Thottam

S. Kalkur for his great support and outstanding guidance throughout this work. His encouragement, patience and great expertise have been instrumental in motivating me through difficulties and keeping me on the right track.

I would also like to thank the distinguished members of the Committee, Dr.

Heather Song, Dr. Charlie Wang, Dr. John Lindsey and Dr. Anatoliy Glushchenko for their insightful comments and indispensable recommendations, which enabled my research and helped me conduct it to its completion.

I am also thankful to all the professors, students and staff at the Faculty of

Engineering whom I had the pleasure of meeting and would like to express my deep appreciation for all the friends in the United States for having been a second family to me.

And last but never least, I am utterly grateful to my Government for providing me with the generous support and assistance needed to complete my studies. It is my humble wish and my hope to be able to contribute to the renaissance of my country in many decisive ways.

TABLE OF CONTENTS

CHAPTER 1 FILTERS IN RF MICROWAVE SYSTEMS ...... 1

1.1 Introduction ...... 1

1.2 Microwave Communication Systems...... 1

1.2.1 Microwave Frequency Bands ...... 3

1.3 Filter applications in Microwave systems ...... 3

1.3.1 Filter Types in RF Microwave Systems...... 4

1.3.2 Passive Filters ...... 5

1.3.3 Active Filters ...... 6

1.3.4 Specification of RF Microwave Filters ...... 6

1.3.5 Fractional Bandwidth and Classification of Microwave filters ...... 7

1.3.6 Filter Frequency Specifications ...... 8

1.3.7 Filters Transmission Media and their classification ...... 8

1.4 Resonators in Microwave Systems ...... 9

1.4.1 Helical Resonator, Bulk Wave, Surface Acoustic Wave ...... 10

1.4.2 Coaxial, Dielectric, Waveguide and Stripline Resonators ...... 10

1.4.3 Planar Resonators...... 11

1.5 RF Tunable Devices ...... 16

1.5.1 Semiconductor Devices ...... 18

1.5.2 MOSFET Devices ...... 20

1.5.3 MEMS Devices ...... 20

1.5.4 Mechanical Varactor Devices ...... 22

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1.5.5 Ferrites Devices ...... 22

1.5.6 Ferroelectric Materials ...... 23

1.5.7 Ferroelectric Capacitors ...... 27

1.5.8 Characterizations and comparison of RF competing technologies ...... 28

CHAPTER 2 LITERATURE REVIEW ON TUNABLE DUAL-BAND BANDSTOP FILTER CIRCUITS ...... 32

2.1 Introduction...... 32

2.2 Single-band bandstop filter ...... 33

2.3 Dual band-bandstop filters ...... 35

2.3.1 Dielectric resonators ...... 35

2.3.2 Composite right/left-handed metamaterial transmission lines ...... 37

2.3.3 Stepped impedance resonators (SIRs) ...... 39

2.3.4 Split ring resonators (SRRs) ...... 41

2.3.5 TRI-Section stepped impedance resonators ...... 44

2.3.6 Square patch resonator ...... 46

2.3.7 Open and short stub-loaded resonators ...... 48

2.3.8 Defected ground structure (DGS) ...... 49

2.3.9 Stepped impedance hairpin resonators...... 51

2.3.10 E-Shaped Resonators ...... 52

2.3.11 Coupled line resonators...... 53

2.4 Tunable bandstop filter...... 55

2.4.1 Tunable BSF using varactor diodes ...... 56

2.4.2 Tunable BSF using lumped elements ...... 65

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2.4.3 Tunable BSF using ferroelectric materials ...... 67

2.4.4 Tunable BSF using liquid crystal material...... 69

CHAPTER 3 DESIGN, SIMULATION AND IMPLEMENTATION OF DUAL-BAND BANDSTOP FILTER ...... 76

3.1 Introduction ...... 76

3.2 Single band bandstop filter ...... 78

3.2.1 Theoretical design of bandstop filter and design simulation ...... 79

3.3 Compact Design for a single band bandstop filter ...... 84

3.3.1 Spurline Filter Design ...... 84

3.3.2 Bandstop filter using stepped impedance resonator (SIR) ...... 92

3.3.3 Analysis of the compact design of a single band filter ...... 102

3.4 Dual-band bandstop filter using spurline & stepped impedance resonator ...... 112

CHAPTER 4 TUNABLE DUAL-BAND BANDSTOP FILTER USING SPURLINE AND STEPPED IMPEDANCE RESONATOR ...... 121

4.1 Introduction ...... 121

4.2 Principles of designing RF filters based on coupled-lines ...... 122

4.3 Principles of designing microstrip filters using coupled-lines ...... 129

4.4 Principles of designing a microstrip filter using stepped impedance resonator (SIR)...... 134

4.5 Analysis of the compact design of a dual-band filter ...... 138

4.5.1 Simulation of a compact dual-band filter using ADS ...... 139

4.5.2 Simulation of a compact dual-band filter using MATLAB ...... 141

4.6 Tuning a single-band bandstop filter ...... 145

4.6.1 Tunable spurline filter using p-n varactors ...... 146

4.6.2 Tunable stepped impedance resonator filter using p-n varactors...... 147

4.7 Tunable of a compact DBBSF using a modeling of varactor diodes ...... 149

4.8 Fabrication of a tunable dual-band bandstop filter using varactor diodes ...... 151

4.9 Ferroelectric capacitors ...... 155

4.9.1 Fabrication of the ferroelectric-based capacitors ...... 156

4.10 Tunable of a compact DBBSF using a modeling ferroelectric capacitor ..... 161

4.11 Fabrication of a tunable dual-band bandstop filter using BST capacitors .... 164

CHAPTER 5 CONCLUSION AND FUTURE WORK ...... 169

5.1 Conclusion ...... 169

5.2 Future work ...... 170

REFERENCES ...... 172

APPENDICES ...... 178

A: MATLAB Code for S-Parameter of DBBSF Without Tuning ...... 178

B: MATLAB Code for S-Parameter of DBBSF With Tuning by Varactor Diodes ...... 180

C: MATLAB Code for S-Parameter of DBBSF With Tuning by BST Capacitors ...... 182

LIST OF TABLES

Table 1-1 Assignment of frequency bands according to various applications [2], [3]...... 3

Table 1-2 Most popular topologies for designing Dual-Band Bandstop Filter...... 27

Table 1-3 Characterizations and comparison of RF competing technologies [27]...... 28

Table 2-1 Most popular topologies for designing Dual-Band Bandstop Filter...... 55

Table 2-2 Comparison of different methods for tuning BSFs [22]...... 72

Table 3-1 Element Values table for maximally flat low-pass filter [1]...... 80

Table 3-2 Prototype filter transformations [1]...... 81

Table 3-3 Element values for equal-ripple low-pass filter [1]...... 88

Table 4-1 Measurements for dual-band bandstop filter...... 152

Table 4-2 Measurement results of tunable dual-band bandstop filter...... 155

Table 4-3 Measurement results of tunable dual-band bandstop filter...... 168

LIST OF FIGURES

Figure 1.1. The frequency response of all four filter types: a. Low pass, b. High pass, c. bandpass and d. bandstop [4]...... 5

Figure 1.2 Definitions of the figures of merit as shown by a high pass filter response [4]. 7

Figure 1.3 Stepped Impedance Resonators [5]...... 12

Figure 1.4 (a) Layout of shunt Series Resonance, (b) layout of shunt Parallel Resonance [2]...... 13

Figure 1.5 Layout of half Wavelength Resonator [2]...... 14

Figure 1.6 Structure of Circular and Square Closed Ring Resonator [2]...... 14

Figure 1.7 Structure of Circular and Square λg0/2 open-loop resonators [2]...... 15

Figure 1.8 Structure of Circular and Square Split Ring Resonators [2]...... 15

Figure 1.9 Tuning Frequency by Circuit Capacitor and Inductor [7]...... 17

Figure 1.10 Structure of a Cantilever MEMS Varactor [12]...... 20

Figure 1.11 Crystal Structure of a Ferroelectric Material of a Perovskite ABO3 [7]...... 24

Figure 1.12 Dielectric Polarization for Paraelectricity and Ferroelectricity [7]...... 25

Figure 1.13 Energy Barrier of Ferroelectric State and Paraelectric State [7]...... 25

Figure 1.14 Dielectric Constant Versus Temperature [7]...... 26

Figure 2.1 Basic circuit of the bandstop filter using lumped elements [22]...... 34

Figure 2.2 Bandstop filter design. (a) Prototype LPF (b) single bandstop filter [24]...... 36

Figure 2.3 Dual-band bandstop filter [24]...... 37

Figure 2.4 Conventional (a) bandpass (b) bandstop filters using quarter-wave short- circuited and open circuited (c) DBBPF (d) DBBSF (e) CRLH transmission lines [25]. 38

Figure 2.5 Dual-band bandstop filter using CRLH transmission lines [25]...... 39

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Figure 2.6 DBBSF using SIRs (a) Schematic of the proposed filter (b) Equivalent circuit using lumped components with the ideal J inverter [26]...... 39

Figure 2.7. (a) The equivalent circuit of DBBSF using shunt-connected series LC resonators and SIR. (b) Configuration of DBBSF admittance converter [26]...... 40

Figure 2.8 (a) Measured and simulated result of DBBSF. (b) Fabricated filter design [26]...... 40

Figure 2.9 Bandstop filter using split ring resonator SRR. (a) proposed filter layout. (b) simulated signal response [27]...... 41

Figure 2.10. (a) lumped element circuit of DBBSF using SRRs. (b) Simulated and measured result [27]...... 42

Figure 2.11. (a) Fabrication design of DBBSF using SRRs. (b) Measured and simulation result [27]...... 43

Figure 2.12. (a) quarter-wavelength stub, (b) two section-stepped impedance, (c) tri- section stepped impedance resonator [23]...... 44

Figure 2.13 Dual-band bandstop filter, (a) filter measurement results (b) fabrication design [23]...... 45

Figure 2.14 Dual-band bandstop filter, (a) filter response (b)filter fabrication [23]...... 45

Figure 2.15. DBBSF using a square loop with double-patch resonators [28]...... 46

Figure 2.16. The measurement result of DBBSF using double-patch [28]...... 47

Figure 2.17. Fabricated design of DBBSF using square patch resonators [28]...... 47

Figure 2.18. Structure of bandstop filter. (a) Open stub-loaded resonator. (b) Short stub- loaded resonator [29]...... 48

Figure 2.19 Simulation and measured results of DBBSFs. (a) Fabrication Filters. (b) Open stub-loaded resonators filter result. (c) Short stub-loaded resonator filter result [29]...... 49

Figure 2.20 Defected ground structure of DBBSF. (a) T-shaped structure. (b) DBBSF layout. (c) Measured result [30]...... 50

Figure 2.21 Simulated result of DBBSF using two-stages, T-shaped and U-shaped with DMS [30]...... 50

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Figure 2.22. DBBSF using stepped impedance hairpin resonators. (a) Filter layout. (b) Simulation result [31]...... 51

Figure 2.23. DBBSF using hairpin resonators. (a) Fabrication filter. (b) Measurement result [31]...... 52

Figure 2.24 DBBSF using E-shaped resonators. (a) Filter layout. (b) Simulation result [32]...... 53

Figure 2.25. (a) The ideal circuit of DBBSF using coupled line resonators. (b) Even-mode equivalent circuit. (c) Odd-mode equivalent circuit [33]...... 54

Figure 2.26 Simulation and Measurement results of DBBSF using coupled line resonators [33]...... 54

Figure 2.27 Parallel coupled tunable BSF. (a) equivalent circuit of the resonator (b) fabrication filter design [35]...... 56

Figure 2.28. (a) Simulation and measurement results without varactor diode (b) tunable results [35]...... 57

Figure 2.29. (a) bandstop filter using open-circuited stubs (b) filter response without tuning [36]...... 58

Figure 2.30. (a) varactor model with a biasing circuit (b) tunable circuit of open-circuited with stubs resonator [36]...... 58

Figure 2.31. (a) BSF with open-circuited stubs loaded with varactor diode (b) fabrication filter design [36]...... 59

Figure 2.32 Tunable bandstop filter response [36]...... 59

Figure 2.33 Tunable bandstop filter using E-shaped dual mode resonator. (a) without biasing circuit (b) with biasing circuit [37]...... 60

Figure 2.34 Tunable bandstop filter using E-shaped dual mode without biasing (a) forward biasing (b) reverse biasing [37]...... 61

Figure 2.35 Tunable bandstop filter using E-shaped dual mode with biasing (a) forward biasing (b) reverse biasing [37]...... 62

Figure 2.36 Bandstop filter layout using (OSRRs) and (OCRRs) [39]...... 63

Figure 2.37 Tunable bandstop filter using (OSRR) with diode varactor [38]...... 63

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Figure 2.38 Bandstop tunable filter. (a, b) the layout consists of a varactor-loaded transmission line. (c, d) S-Parameter of tuning center frequency and bandwidth [39]. ... 64

Figure 2.39 Tunable bandstop filter. (a) tuning center frequency (b) tuning bandwidth [39]...... 65

Figure 2.40 Tuning bandstop filter using lumped element [40]...... 65

Figure 2.41 Equivalent circuit of the lumped element using a quarter-wave microstrip line [40]...... 66

Figure 2.42 Tunable bandstop filter using a single varactor diode and back to back varactor diode [40]...... 67

Figure 2.43. (a) Profile layers of fabrication of the BST interdigital varactor chip (b) fabricated tunable BSF using BST varactor (c) BSF signal response [19]...... 68

Figure 2.44 Tunable bandstop filter using BST. (a) Fabricated filter. (b) Measurement result [22]...... 69

Figure 2.45 Bandstop filter using meander loop resonator. (a) Filter layout. (b) Filter result [43]...... 70

Figure 2.46 Structure of bandstop filter using Liquid Crystal (LC) technology [43]...... 71

Figure 2.47 Simulated result of TBSF using LC technology. (a) S21. (b) S11 [43]...... 71

Figure 3.1 Bandstop filter using Lumped Components...... 79

Figure 3.2 Lumped circuit for the low-pass filter using ADS...... 80

Figure 3.3 Low-pass maximally flat filter with lumped elements...... 83

Figure 3.4 Bandstop filter using ADS...... 83

Figure 3.5 Development of the spurline section using coupled line method...... 86

Figure 3.6 Spurline filter. (a) coupled line section (b) equivalent circuit of the spurline filter [50]...... 87

Figure 3.7 Coupled line structure for the bandstop filter...... 90

Figure 3.8 Spurline section using coupled line method...... 90

Figure 3.9 Spurline bandstop filter. (a) conventional structure (b) simulation design. .... 91 xv

Figure 3.10 Simulation result for the spurline bandstop filter...... 91

Figure 3.11 Attenuation versus normalized frequency for maximally flat prototype filter [1]...... 92

Figure 3.12 Low-pass filter using ADS...... 93

Figure 3.13 Bandstop filter with a circuit of the lumped components...... 95

Figure 3.14 Bandstop filter result using lumped components...... 95

Figure 3.15 Bandstop filter using microstrip transmission lines...... 96

Figure 3.16 (a) bandstop filter layout, (b) converting inductor and capacitor to the transmission line...... 98

Figure 3.17 Bandstop filter using stepped impedance resonator SIR...... 99

Figure 3.18 bandstop filter result using stepped impedance resonator SIR...... 99

Figure 3.19 Compact Bandstop filter design using spurline and SIR...... 100

Figure 3.20 Compact bandstop filter using spurline & stepped impedance resonator. .. 101

Figure 3.21 Comparison result for the bandstop filter...... 101

Figure 3.22 Comparison between conventional spurline filter and new compact filter. 102

Figure 3.23 Spurline equivalent circuit using lumped element components...... 104

Figure 3.24 (a) Spurline Filter Using Microstrip lines, (b) Filter layout...... 105

Figure 3.25 Comparison Results of Bandstop Filter...... 105

Figure 3.26 Equivalent Circuit of Bandstop Filter...... 106

Figure 3.27 (a) Stepped impedance filter using Microstrip Lines, (b) Layout of the stepped impedance filter...... 107

Figure 3.28 Comparison among the three bandstop filter results (EM simulation, lumped element simulation and microstrip simulation)...... 107

Figure 3.29 Compact Bandstop Filter Design Using Spurline and Stepped Impedance Resonator...... 108

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Figure 3.30 Comparison Results of The Compact Bandstop Filter For A Single Band. 108

Figure 3.31 Equivalent circuit with two shunt RLC resonators...... 109

Figure 3.32 Dual-band bandstop filter using spurline and stepped impedance resonator...... 113

Figure 3.33 Spurline bandstop filter at 2.4 GHz...... 114

Figure 3.34 Simulation result of spurline bandstop filter...... 114

Figure 3.35 Equivalent Circuit of BSF using SIR...... 115

Figure 3.36 Lumped element circuit of BSF...... 116

Figure 3.37 Bandstop filter using transmission-lines...... 116

Figure 3.38 Bandstop filter using SIR...... 118

Figure 3.39 Stepped impedance resonator at 3.5 GHz...... 118

Figure 3.40 Bandstop filter at 3.5 GHz using SIR...... 119

Figure 3.41 Compact dual-band bandstop filter...... 119

Figure 3.42 Dual-band bandstop filter using spurline & SIR ...... 120

Figure 4.1 symmetrical and equivalent circuit of even-mode and odd-mode of coupled line structure [58]...... 123

Figure 4.2 General structure of a coupled line filter using transmission lines [58]...... 124

Figure 4.3 Coupled line sections (a) bandpass structure, (b) lowpass structure [58]. .... 124

Figure 4.4 (a) Parallel coupled line structure, (b) equivalent circuit [59]...... 127

Figure 4.5 Open- and short-circuited resonators of microstrip coupled line filters [58]. 130

Figure 4.6 Short-circuited bandstop coupled line resonator with its equivalent circuit [58]...... 133

Figure 4.7 layout of a half-wavelength open-circuited transmission line using SIRs [59]...... 135

Figure 4.8 Configuration of SIR with its equivalent circuit [59]...... 136 xvii

Figure 4.9 The resonant condition of the SIR at the first resonance [59]...... 138

Figure 4.10 Dual-band filter using lumped element components...... 139

Figure 4.11 Compact dual-band filter using transmission lines...... 139

Figure 4.12 Comparison of the dual-band filter...... 140

Figure 4.13 EM simulation result of a dual-band filter...... 140

Figure 4.14 Circuit Element for quadrupole [60]...... 142

Figure 4.15 Two cascaded quadrupoles [60], [61]...... 144

Figure 4.16 MATLAB filter result of the dual-band bandstop filter...... 145

Figure 4.17 Spurline tunable filter using p-n varactor diode...... 146

Figure 4.18 Simulation result for the spurline filter...... 147

Figure 4.19 Tunable bandstop filter using SIR...... 148

Figure 4.20 Result of tuning SIR filter using varactor diode...... 148

Figure 4.21 Tuning of lumped element circuit of the dual-band filter...... 149

Figure 4.22 Tuning of microstrip lines dual-band filter...... 149

Figure 4.23 Tuning the momentum layout design of the dual-band filter...... 150

Figure 4.24 Comparison of tuning dual-band filter using varactor diodes...... 150

Figure 4.25 MATLAB tunable result of the dual-band bandstop filter...... 151

Figure 4.26 Tunable dual-band bandstop filter using varactor diodes...... 152

Figure 4.27 Fabrication design of tunable dual-band bandstop filter...... 153

Figure 4.28 Measurement result (S21) of the dual-band tunable filter...... 154

Figure 4.29 Measurement result (S11) of the dual-band filter...... 154

Figure 4.30 BST capacitor, (a) cross section (b) plan view of the capacitor [22]...... 157

Figure 4.31 Measurements of the fabricated BST capacitors...... 158 xviii

Figure 4.32 Measurement of the BST modeling capacitors...... 159

Figure 4.33 Fabrication and modeling results of the BST capacitors, (a) capacitor for low frequency (b) capacitor for high frequency...... 160

Figure 4.34 BST tunability variation with applied voltage, (a) simulation modeling (b) fabrication capacitor...... 161

Figure 4.35 Tuning of lumped element circuit of the dual-band filter...... 162

Figure 4.36 Tuning of a transmission lines circuit of the dual-band filter...... 162

Figure 4.37 Tuning the momentum layout design of the dual-band filter...... 163

Figure 4.38 Comparison of tuning dual-band filter using BST capacitor modeling...... 163

Figure 4.39 MATLAB tunable result of the dual-band bandstop filter...... 164

Figure 4.40 Dual-band bandstop filter Response at 2GHz and 3.5GHz...... 165

Figure 4.41 Fabrication of tunable DBBSF using BST capacitors...... 166

Figure 4.42 Measured variation of S11 with frequency for various applied voltages for the DBBSF filter...... 166

Figure 4.43 Measured variation of S21 with frequency for various applied voltages for DBBSF...... 167

Figure 4.44 Tunable dual-band bandstop filter result using BST...... 167

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CHAPTER 1

FILTERS IN RF MICROWAVE SYSTEMS

1.1 Introduction

Filters command great importance in RF microwave systems as a result of the essential roll which they play in the majority of communication systems. They operate by confining RF microwave signals, which they can do by sharing a limited EM spectrum.

Applications in wireless communications place higher demands on RF microwave filters.

Such filters are required to be smaller in size, lower in weight, perform up to a high standard while being cost effective. RF microwave filters have been studied and developed with a view to the requirements listed above. It was necessary to speed up the process, which prompted the emergence of new methodologies and new technologies such as waveguide, coaxial line or microstrip line. This dissertation discusses the means by which a compact dual-band bandstop filter is developed and the contribution to this development by spurline section with a stepped impedance resonator in a microstrip configuration.

1.2 Microwave Communication Systems

The field of RF and microwave engineering analyze the behavior of current signals between 100 MHz to 1000 GHz. As indicated in table 1.1 the frequency range of

RF is from VHF (30-300) MHZ to UHF (300-3000) MHz. And we note that the term microwave typically refers to frequencies in the range 3-300 GHz which corresponds to a wavelength range between λ=c/ =10cm and λ=1 mm [1]. Therefore, microwaves are a form of EM radiation that ranges푓 from several hundred MHz to several hundred GHz. 1

Technologies for microwaves have been evolving since World War II to which they owe their birth where they were implemented in early radars [2]. UHF/microwave bands required more intensive research and development, which resulted in many attempts at solving the problem; and one of those attempts was the conventional vacuum tube which was a novelty at the time. The functionality of vacuum tubes was limited because of the shortening of high frequencies and because of the long transit time. We note that the vacuum tube approach was proposed in 1920 by H. Barkhausen and K. kurz who was able to invent a new type of vacuum tube which was able to generate high frequency signals, but it came with a limited power output [2]. Their accomplishment was conducive to the creation of a new microwave device which they called magnetron. This invention was followed by Klystron vacuum tube. And as a result of this success radar technology became commercially available. Meanwhile and for many decades microwave systems were used by telephone companies in a commercial manner only.

Microwave systems were applied by telephone companies only and within commercial sectors. By the beginning of the 1960’s, microwave communications had already replaced 40% of the telephone circuitry that linked major cities. In the 1990’s, the technical revolution continued to grow and expanded into the consumer market. Direct high frequency services via satellites to people’s homes were available. Since then, microwave technologies have continued to grow in the private and commercial sectors.

Microwave application technologies have been very significant in areas other than communications; they have been applied in medicine as well. Microwave technologies have become of essential importance in all aspects of human life [2].

1.2.1 Microwave Frequency Bands

Table I.I represents the assignment of different microwave frequencies based on applications, which is used as a reference for microwave systems [2], [3].

Table 1-1 Assignment of frequency bands according to various applications [2], [3].

1.3 Filter applications in Microwave systems

Filters are two-port devices designed to allow through specified frequencies with very low attenuation and to reject unwanted frequencies [4]. Filters have a wide range of applications in many areas including military which relies on filters for communication systems, control systems, radar and scanner operations, sorting and separation of signals out of a massive bombardment of EM radiation. Also, the civilian sector relies heavily on filters for all kinds of communications. The components of transmission lines vary a lot;

their components are rectangular waveguides, strip lines and microstrip lines.

Multiplexers which are used in wireless communications require filters for their operations [2]. It is important to know that microwave filters embody the same design as low-frequency filters, the difference being in the structure of the circuitry. There are different ways to realize filters; it can be done with microstrip forms, waveguide forms or coaxial forms. It is true that microstrip filters fall short regarding high performance compared to waveguide filters, but their great advantage is in their planar structure which allows them to be flexible and, therefore, applicable in printed circuit and thin film technologies. The theory of filters is based on some aspects of classical network theory.

Filters represent highly accurate synthesis procedure that are addressed heavily within network theories. The advent of computer systems has accelerated the evolution of network theories, which has allowed the subject to grow fast and yield different designs which have prompted increasingly new configurations [4].

1.3.1 Filter Types in RF Microwave Systems

The classification of filters represents the actual operations of each filter. A low pass filter allows frequencies up to a certain upper limit to pass through while attenuating all frequencies above that limit. A high pass filter allows frequencies beyond a lower limit to pass through while attenuating all frequencies that are below that limit. A bandpass filter is designed to allow frequencies in a certain range that has a lower limit and an upper limit to pass through while rejecting all frequencies below the lower limit and all those above the upper limit. A bandstop filter is the opposite of a bandpass filter because it allows through all frequencies above a certain limit and below a certain limit while

blocking all frequencies in between the lower and upper limit. We note that the range between a lower and an upper limit is what we refer to as bandwidth. The responses of all four filters are illustrated in Figure 1.1 [4].

Figure 1.1. The frequency response of all four filter types: a. Low pass, b. High pass, c. bandpass and d. bandstop [4].

1.3.2 Passive Filters

Passive filter design consists mainly of inductors and capacitors arranged in such a configuration as give a specific filtering operation. RF signals pass through such a filter and lose some of their energy which gets absorbed by the device owing to the reactive nature of the signals and of the structure of the passive filter. As a result, energy loss of a

pass-band is unavoidable, which allows us to quantify how good a filter is. Therefore, a good filter causes a small energy loss on the order of 0.1 dB to 0.2 dB [4].

1.3.3 Active Filters

Active filters embody amplifiers which are their active elements. Active filters rely on operational amplifiers to manipulate voltages, control gain, compensate for loss due to attenuation at the edges. Such active elements allow active filters to accomplish a higher Q-value and higher space saving capabilities as required of MMIC [4]. It is an exciting thing that gain can compensate for the insertion loss, which is part of passive filters, but in order for the filter to be effective the insertion loss must be constant.

Therefore, if the loss can be minimized then we can enhance the bandwidth. In microwave active filters are found MESFET or HEMT transistors. Active microwave filters also utilize diodes which produce negative resistance. Examples of such diodes are

Gunn and tunnel diodes. Passive transmission structures are also found in active filters such as microstrip tapers, half wave sections and directional couplers. The main purpose of the structure is impedance matching and coupling resonance [4].

1.3.4 Specification of RF Microwave Filters

Filter design must take into account certain specifications which are illustrated by the figures of merit (FOM) as can be seen in 1.2. Those figures of merit are presented by bandstop and bandpass ripple and also by passband insertion loss and attenuation by stopband. They also show other specifications such as center frequency, cut-off frequency, group delay, rejection, bandwidth and the capabilities of the device at power handling. Microwave applications incorporate filters that operate between a source and 6

load impedance that represent 50 Ω of resistance. It is important that microwave passband filters operate at a very small attenuation level but when it comes to stopband filters the attenuation needs to be high. Good rejection ratio is exhibited by high attenuation at the passband edges. It is necessary that the filter be able to select high- frequency signals if interference with adjacent bands is to be prevented [4]. A concern of paramount importance is signal degradation that occurs as signals are being “filtered”. In order to minimize the degradation (or the “damage” to the signal) the filter is required to have a small group delay and the variation in the amplitude of the signal, also known as ripple, must be minimized [4].

Figure 1.2 Definitions of the figures of merit as shown by a high pass filter response [4].

1.3.5 Fractional Bandwidth and Classification of Microwave filters

One of the most important specifications in microwave filter design is the fractional bandwidth which is a measure of how wide a frequency band the component

can handle. The following equation can be used to calculate the percentage of bandwidth

[1]:

(1) BW BW% = × 100 Where BW stands for absolute bandwidth whilefc is the center frequency.

fc Filters can be classified based on two things, the center frequency and fractional bandwidth as follows:

▪ The narrow band filter type which is below 5%

▪ The moderate band filter type which is between 5% and 25%

▪ The wide band filter type that exceeds 25%

1.3.6 Filter Frequency Specifications

▪ Center frequency and bandwidth for BPF and BSF

▪ Cut-off frequency for low-pass and high-pass filter

▪ Passband insertion loss

▪ Signal preservation as indicated by flatness or ripple level

▪ Rejection levels

▪ Selectivity

▪ Harmonic rejection

1.3.7 Filters Transmission Media and their classification

Transmission media in microwave systems fall in two main categories, lumped elements and distributed elements. If a circuit element such as a resistor, inductor or

capacitor is presented by means of a simple linear equation then it is called a lumped element which is restricted to lower frequencies because they are smaller in size than a quarter-wavelength [2].

There are certain guiding factors that are essential for the design of any microwave filter. Those factors are necessary for the appropriateness and accuracy of the design. They help us choose the proper material and the proper measurements of the filter such as length, width, the thickness of the metal and how closely it can be incorporated into the ground plane. The following transmission media are used in RF microwave systems [2]:

▪ Coaxial transmission lines

▪ Microstrip lines

▪ Strip lines

▪ Waveguides

1.4 Resonators in Microwave Systems

Some component elements in microwave systems can contain an oscillating EM field which is a form of resonance. Such elements are, therefore, called resonators. Since there is a very wide range of possible frequencies it stands to reason that there must be and there is a wide variety of microwave resonator types. Resonators respond to certain frequencies, which means they can be changed and improved by changing the frequency.

Therefore, the frequency that a certain type resonates with dictates the frequency response of the corresponding filter. Following is a classification of resonators:

1.4.1 Helical Resonator, Bulk Wave, Surface Acoustic Wave

These three types are implemented for frequencies below 1 GHz and they are suitable for the purposes of minimization and low loss. Helical resonators in particular are an excellent choice for high power operations. Another excellent characteristic of these resonators is their high temperature tolerance and their ability to give good results for narrow band filters [2].

1.4.2 Coaxial, Dielectric, Waveguide and Stripline Resonators

There are many advantages that are offered by coaxial resonators and one of those advantages is their EM shielding. Coaxial resonators are also characterized by low loss, temperature tolerance and a small size, but their extremely small size makes them difficult to manufacture accurately for the purposes of applications above 10 GHz.

Dielectric resonators too have some notable advantages; they are small in size, they demonstrate temperature stability and low loss. Furthermore, waveguide resonators have advantages such as practicality of application, feasibility with up to 100 GHz and low loss. Despite the advantages of the three previous resonators, research has proven that the planar or stripline resonators are a superior choice. Their advantages consist of small size and similarity of characteristics to active elements. Also, they are structurally compactable with photolithography. It is to be noted that the best advantage offered by stripline resonators is a wide frequency range which can be achieved with a variety of substrate materials. However, a disadvantage of stripline resonators is increased loss as opposed to the other three kinds, which disqualifies it for use with narrow band filters [2].

1.4.3 Planar Resonators

One of guiding principles to adhere to when figuring out filter design is minimizing the structure in size and weight. In the case of planar resonators which can be fabricated with ease by virtue of printed circuit technologies we can expect optimal elements because such resonators maintain a small and lightweight structure. When it comes to microwave filters, the smallest EM filters are microstrip filters. Microstrip filters are small in dimension, reliable and easy to be fabricated; thus, they are widely used. Experimental data have shown these filters to be capable of fast and steady response in many complex design structures. Several methods are being used to reduce the size of microstrip filters which include folded strip line conductors, formation of irregularities in the conductors and substrates with high permittivity [2].

To improve the response of a filter the amplitude frequency should have a steeper slope and the bandstop attenuation should be large. Achieving this goal depends on how many filter resonators are involved and it also depends on many other parameters. In specifying the effect of resonators on filter frequency response it is important to study some filter parameters such as fractional bandwidth, permittivity of the substrate as well as other parameters. Much good research has been dedicated to the determination of limits to applicability and viability of design and to the creation of optimized MSFs. Also stripline resonators are categorized as transmission-lines and stepped-impedance resonators [2].

• Stepped Impedance Resonators

Stripline resonators demonstrate non-uniform impedance properties which are referred to as stepped impedance resonators. They have a simple structure, many features and offer many possibilities for applications. They have wide use in applications of filters, mixers and oscillators. They can be easily fabricated with printed circuit technologies. Different kinds of stepped impedance resonators are shown in figure 1.3.

[2].

Figure 1.3 Stepped Impedance Resonators [5].

• Transmission-Line Resonators

Transmission line resonators have recently gained a lot of popularity especially in

RF microwave systems. Their wide use is owed to their great features such as simple structure design, small size and their applicability in various devices. Coaxial and stripline resonators are the most widely used line resonators in transverse EM modes.

Their applicability ranges from 100 MHz to several 100 GHz [2]. They are suitable filters in wireless communications. They do not have a high-quality Q factor and their loss

properties are not low, but it is easy to integrate them with other active circuit designs.

This property is made possible by photolithography of metallic film on thin dielectric substrate. Microstrip resonators are distributed within a circuit as quarter-wavelength or half-wavelength line resonators and are classified as lumped elements or quasi-lumped elements. Transmission-lines resonators are built according to the type of the filter, Q- factor, the operating frequency and the desired power handling capability [2]. Figure 1.4 illustrates how the structure design of a quarter wavelength line resonator is fabricated and shows the physical length of (the guided wavelength) which pertains to the

푔0 fundamental frequency [2]. 휆 /4

푓0

Figure 1.4 (a) Layout of shunt Series Resonance, (b) layout of shunt Parallel Resonance [2].

Figure 1.5 illustrates the structure of half wavelength resonator with a physical length of

and it can resonate at , for [2].

휆푔0/2 푓 = 푛 푓0 푛 = 2,3, …

Figure 1.5 Layout of half Wavelength Resonator [2].

There are many different design shapes which can be assumed by a transmission-lines resonator and a shape or form can be chosen according to what is needed as well as other specifications. Each design can be a closed or open loop as needed as in the case of a close ring resonator which, as can be seen, is close loop resonator. The structure of such resonator is presented in figure 1.6 and, as can be inferred, this ring loop is activated at its fundamental where the median circumference , and r stands for the radius of

0 푔0 the ring. Modes푓 of higher resonance occur at 2휋푟 =for 휆 [2].

푓 = 푛푓0 푛 = 2,3, …

Figure 1.6 Structure of Circular and Square Closed Ring Resonator [2].

Figure 1.7 is an open loop resonator with a fundamental that is half of the resonant frequency of a closed resonator but the fundamental of the rectangular ring can be calculated by the average of the perimeter [2].

Figure 1.7 Structure of Circular and Square λg0/2 open-loop resonators [2].

Figure 1.8 is a type of transmission resonator with a split parameter that consists of two coupled conducting open loops achieved by printing them onto a dielectric slab [2].

Figure 1.8 Structure of Circular and Square Split Ring Resonators [2].

Split-ring resonators embody a small structure compared to other line resonators. They afford a high-quality Q and have many applications where a short notch is required or where the resonator is required to pass a desired frequency band. The size of the filter can be made smaller by allowing it to assume a different configuration that involves folding

[2].

1.5 RF Tunable Devices

Filters are essential circuit components in the majority of RF microwave systems.

These devices are used extensively for converting frequencies which is what happens in receivers and tuning elements. In fact, filters are building blocks with high-Q resonators of different kinds such as dielectric pucks and more. Systems that are designed for transmission and receiving require tunability which is done by the switching of multiple tuned circuit. The advantage of using a tunable filter is manifest in the significant reduction of losses which could otherwise occur with complex multiband systems.

Fortunately, frequency response is controllable by increase or decrease in the DC- voltage, which can change the inductor and capacitor of the tuning device [5]. It is by using tuning devices that voltage control can be achieved; such tuning devices are called varactors. Some of the characteristics of tunable varactors are a wide bandwidth accomplished by wide tuning range, linear functionality and low parasitic resistance which insures low loss. There are various kinds of tuning devices which can be categorized as P-n junction diodes, MEMS varactors and MOS varactors. There are also ferroelectric capacitors with high capacitance density, high-quality Q, reduced phase noise, high linear dependence of the frequency tuning on the bias and independence of operation with respect to voltage polarity [5]. Implementing tunability to a given RF circuit design can be done in two different ways, one is a tunable capacitor and the other by a tunable inductor. Figure 1.9 illustrates a tank circuit being tuned by means of a tunable capacitor and tunable inductor [6].

Figure 1.9 Tuning Frequency by Circuit Capacitor and Inductor [7].

The resonance frequency of the parallel tank circuit in the figure above is expressed as 푓푟푒푠

(2) 1 푓푟푒푠 = 2휋√퐿퐶 where L is the inductance and C is the capacitance of the circuit.

Inductance tuning can be accomplished be means of ferrite ferromagnetic devices and mechanical varactors, but inductance tuning is difficult to accomplish. On the other hand, technologies exist that can be used to tune capacitors, which is done by means of semiconductor varactors, MEMS varactors, PIN diodes and ferroelectric capacitors. For a parallel plate capacitor the capacitance is given by [6]

(3) ε0εrA C= Where, d

A is effective area of each plate. d is the plate separation.

is the electric constant and is ≈ 8.854× F . −12 −1 휀0 10 푚 is the relative static permittivity of the material sandwiched between the plates.

휀푟 We achieve tunability simply by changing the dielectric constant (the relative static permittivity of the material sandwiched between the plates) of the capacitor, which we can do be means of ferroelectric materials. Also, the distance between the plates can be mechanically changed, which would change the capacitance; for our purposes we would require an MEMS approach.

In order to choose an appropriate tunable device, we have to take into account many factors such as desired applications, system specifications, level of reliability, cost and integrability with other existing technologies. Similarly, the manner in which we select tunable devices is based on such certain desired characteristics as low cost, high tunability, high tuning speed and high-Q value for high frequencies. Most of the prementioned characteristics can be addressed by ferroelectric materials. One of those materials is known as BST and is one of the most attractive materials in this field and is leading the way to exciting future developments in this new technology.

1.5.1 Semiconductor Devices

The simplest kind of semiconductor devices is the diode and semiconductor materials which are utilized in electronic devices for the simple purpose of conducting electric signals according to a preconceived plan [7]. Semiconductors deliberately incorporate impurities that affect their conductivity and their temperature characteristics.

The process by which impurities are incorporated is called doping. For more than five 18

decades semiconductor varactors have been very popular devices as they have been used for tuning RF microwave filters [8]. LED conductor materials consist typically of aluminum-gallium-arsenide (AlGaAs) in which atoms form perfect bonds such that electrons are prevented from being transferred across the material. Therefore, material conductivity becomes a variable which can be affected by the addition of a few atoms that can disturb the balance of electrons thus making the material conductive [7].

Advantages and Disadvantages of Semiconductor Devices

A Semiconductor device can be part of a circuit by having all components integrated into it or on top of it. It is this feature of semiconductors that offers a great advantage. In order to fabricate an RF circuit, we require a structure that is small and compact; semiconductors offer the solution. A fully integrated single wafer in RF systems can be fabricated with semiconductors. Semiconductor devices are designed to be integrable with a direct gap of semiconductor material for optical communication systems. They are also adaptable in the sense that they can be modulated around the operating frequency in order to increase switching speed. A disadvantage of semiconductors is apparent in some varactor diodes that demonstrate a significant loss in response to high frequencies [6]. Certain materials like Gallium arsenide (GaAs) offer a high-Q but produce higher flicker noise due to increased electron mobility within the material. In some cases, noise results from collisions between electrons and positive holes. In those cases, the device requires high tuning voltages but their ability to handle power is low compare to some other devices [6].

1.5.2 MOSFET Devices

MOSFET devices have the advantage of being fabricated by a standard CMOS; this advantage has accelerated the MOSFET research and the production cycle of such devices [6]. The switches of CMOS are characterized by low voltage (3V), high linearity and a large tuning range on sapphire and silicon. These features of CMOS switches are useful in the insulator (SOI) technology [9],[10]. MOSFET devices have realized the impedance matching networks at a frequency ranging from 1 GHz to 20 GHz. When

CMOS devices are used as tuning elements, they implement control logic and mismatch detectors in the circuit under construction [11]. There are some issues when the circuit is required to operate at high frequencies such as dielectric and metal losses [6].

1.5.3 MEMS Devices

MEMS are tiny devices; they are mechanical in nature and have been in use as chromometers for more than two decades [12]. Their size is 20 micrometers to one millimeter, they are powered by electricity and are manufactured according to the same techniques as semiconductors [12]. One of the most common features of MEMS is called cantilever which is a varactor that has a structure capable of being actuated by its own electric charge as shown in figure 1.10.

Figure 1.10 Structure of a Cantilever MEMS Varactor [12].

The figure above illustrates a structural layer situated on a ceramic substrate which has a conductive path that leads to the backside of the substrate [12]. Voltage-controlled oscillators (VCOs) are demanded by wireless communications in this modern ege. The demands on voltage-controlled oscillators are that they provide wide tuning range, save on power, reduce phase noise and offer a high-qulity factor in the GHz range. It is importnant that the tuning range be wide enough to accommodate all the desired frequncies. In order to tune a VCO we usually require a varactor at the tank circuit and the phase noise can be handled by increasing the Q factor. Therefore, realizing a variable capacitor that is sitiuated on a chip is very difficult if it is to have low phase noinse and at the same time afford a high Q factor and still perform over a wide frequency range and over temperatrue variation [13]. To overcome this deficiency, the on-chip MOS varactors are replaced by MEMS-based varactors. MEMS varactors can satisfy the low-loss condition and possess the required high Q factor for dealing with wide process and variations in temperature. Another advantage to MEMS varactors is that they behave with more linearity and are better able to handle swings in output voltage than p-n junction varactors. Also, some MEMS-based varactors exhibit variation in capacitance below 6% over a wide temperature range [13].

Advantages and Disadvantages of MEMS

MEMS switches make possible very low loss as oposed to PIN diodes and other devices such as GaAs and MOS-based switches [6]. This advantage makes MEMS switches more practical when it comes to multi-band communcation devices. Another advantage of MEMS is their applicability to verious systems which include transmission 21

lines, antennas, filters, inductors and attenuators. Their ability to handle power is great and it does not sacrefice intermodulation or high isolation performance [14]. Despite their obvious advantages, MEMS devices exhibit certain issues that have to do with reliability, cost and lifetime maintenance which can be up to 30 years. On top of that there are issues with their switching speed as well as high actuation voltage (10-60V), where their switching time is 2-50μs compared to only 30 ns for semiconductors devices [6], [15].

1.5.4 Mechanical Varactor Devices

Mechanical varactor devices have been commonly used for tuning because their ability to handle power is high and they exhibit low insertion loss. Such devices have been used for channel selection and radio communications since channel selection is a tuning process. These mechanical varactors can be controlled by microprocessors and they can also be handled directly by an electric motor. However, being mechanical in nature their weight becomes an issue and researchers lose interest [6].

1.5.5 Ferrites Devices

Ferrites are tunable devices which are made of oxide materials. They are utilized in RF systems where their losses in the GHz range are very low due to high resistivity.

They exhibit absorption of a ferromagnetic resonance nature which happens within a line width and they operate at a saturation level because of their ferrite material. We can apply a magnetic field by means of a DC voltage which produces a net magnetic vector that causes the ferrimagnetic device vector to be aligned with the applied magnetic field.

Application of a bias field which generates a magnetic field controls the frequency of the magnetic dipole, which allows us to determine the operating frequency of microwave 22

devices [1], [6]. The linearity of ferrites regarding small signals allows them to be utilized in many important devices such as circulators, tunable filters, isolators, tunable oscillators and phase shifters. In the case of large signals, ferrites exhibit nonlinear behavior properties which make them useful in power enhancers as well as power-limiter devices

[16]. These devices show a unique ability to select and attenuate signals. This property promises potential solutions to interference problems in current and projected designs which suffer from increasing signal density and “over-crowded” RF bandwidth [16].

Most developments that are based on ferrite materials are applied in the construction and design of devices for high-frequency applications. Some applications demand higher frequencies and bandwidth of up to 100 GHz and require control components below 40 GHz. An application of that sort is a radar system which operates in the microwave band [17]. Ferrimagnetic oxide materials exhibit very high resistivity, which induces them to resonate in the micro- and mm-wave regions. This feature elevates them to the status of best choice for absorber devices in the micro- and mm-wave regions.

The importance of these devices is growing as is the demand on their use, which is a natural response to the progress in telecommunication technologies [17].

1.5.6 Ferroelectric Materials

Ferroelectric materials are dielectric materials that have a spontaneously induced polarization which can be reversed in the presence of an electric field; their relative permittivity is a nonlinear function that depends on the electric field E. Figure 1.11 illustrates the휖푟 hysteresis of ferroelectric materials as polarization P versus the characteristics of the electric field E [18]. 23

Figure 1.11 Crystal Structure of a Ferroelectric Material of a Perovskite ABO3 [7].

The above figure illustrates (a) the ferroelectric material in response to a downward applied electric field and (b) in response to an upward applied electric field [6].

Barium Strontium Titanite capacitors (BST) are among the most likable and popular ferroelectic devices that are utilized in the development of tunable RF cirucits by their use of electric power [19]. They became increasigly popular because of the low-cost fabrication process. In addition, they are able to handle power without affecting performance and offer high tuning speeds compared to other devices [20]. BST varactors can be fabricated by either metal-insulator-metal parallel plate structue (MIM) or by interdigital capcitor form (IDC) [19], [20]. The BST-type varactor that is based on IDC allows only a small capacitance tunability because of additional fringing capacitance and it happens to be less senstive to DC voltages. All these characteristics make them desirable tuning elements when we need lower capacitance and simpler fabrecation [20].

Figure 1.12 shows the dielectric polarization for both paraelectricity and ferroelectricity.

Figure 1.12 Dielectric Polarization for Paraelectricity and Ferroelectricity [7].

The above figure iullstrates the reversal of the external field when the domains are reversed to the oppsite direction and then fall behinde the electric polarization, which is a response to the change in the electric field. The ferroelectric hysteresis has memory effects on the input because of its time delay [6]. The relationship between paraelectricity and the electric field is linear or almost linear compared to the ferroelectric vs. the electric field. The energy barrier between the ferroelectric state and paraelectic state is iullsteated in figure 1.13.

Figure 1.13 Energy Barrier of Ferroelectric State and Paraelectric State [7].

Fig 1.13 shows the different configurations of ions in ferroelectric and paraelectric materials. The paraelectric state is one state of equilibrium but the ferroelectric state allows two different equilibrium states [6]. In the ferroelectic state, ions would have to overcome the energy barrier ∆ϵ before they can migrate to the other equilibrium position, which implies that there is a point between the two positions where the derivative of the dielectric with respect to position = 0. This point is related to the dielectric 푑휖 푑푦 displacement D and the polarization P [6].

Figure 1.14 Dielectric Constant Versus Temperature [7].

Fig 1.14 iullstreates the transition of the material from ferroelctric to paraelectric state, which happens at the Curie temperature . At the Curie tempreature the dipoles will have been heated enough to be able to overcome푇푐 forces and then get aligned [6]. Table

1.2 compares the two phases, ferroelectric and paraelectric, and points out their propoerties.

Table 1-2 Most popular topologies for designing Dual-Band Bandstop Filter.

1.5.7 Ferroelectric Capacitors

Ferroelectic capacitors have a distintctly high capacitance density compared to what we find with more common capcitor types. Their ferroelecticity allows them to be used in random access memories which is called (RAM). They are also used in analog electronics as tunable components because of their non-linear deielectric property.

Ferroelectic capacitors are suitable in designing thick ferrelectric films that are uilized in large industrial capacitors. In addition, ferroelectic capacitors are used in the desing and fabrication of thin film ferroelectric elements that ensure a high capcitance density.

Advantages and disadvantages of ferroelectric materials

Ferroelectirc materials have been very attractive recentaly in RF mcrowave systems. Increased fruitful research has been done on these materials with the intention of improving their effects as participants in RF devices. They are charectrized by low loss as well as low controll voltages compared to other commonly used materials. Another good feature of ferroelectics is their ability to handle high power and their high-speed tunabitiy

[6], [18]. Ferroelectic capcitors can be integreated into a single wafer by virtue of their

high density. Their dielectric constant is so high that the area of the device could be reduce by a factor of 10 compared to standard dielectric capacitors. All they require is a voltage controlled change instead of mechanical manipulation as is the case with MEMS devices. This non-mechanical feature makes them a much easier choice to be applied in certain technologies [6].

1.5.8 Characterizations and comparison of RF competing technologies

Various technologies have been utilized in RF microwave systems and have produced different designs. Each one of these technologies is based on different parameters and has different featrues that could make it a deirable choice for a cirtain desing. Most technological characterizations are a response to certain parameters such as

Q-factor, linearity, size, cost and tunability, to name a few. Table 1.3 is a comparsion between technologies that are indispensable in RF devices [21].

Table 1-3 Characterizations and comparison of RF competing technologies [27].

According to table 1.3, each technology is based on verious parameters that make it unique. For example semiconductors, when compared to other types of technology, offer a much lower Q factor at high microwave frequencies. Their linearity is moderate and it is limited to the range of (15-25 dB), which imposes limitations on their usefulness in communication systems. Their small size and light weight allow them to be integrated with other types of technology. What is more, semiconductor varactors command superior reliability over all other technologies. But MEMS and mechnical varactors are the best choices for linearity compared to all other types. Also, MEMS afford a large tuning range, which makes it stand out among other technologies and it has demonstrated a great power handling capability at very low loss [6], [12]. On the other hand, ferroelectric varactors are free of junction noise issues, which makes them one of the best choices compared to semiconductor varactors [6]. Ferroelectric varactors show low loss, are able to handle power well, demonstrate high isolation and low intermodulation distortion, all of which make them attractive for new research and development. They afford very good tunability at a relatively low bias voltage. Also, their small size coupled with very good linearity makes them a great choice for RF microwave applications.

This dissertation will present and study a new methodology for designing Dual-

Band Bandstop Filter With Tunable Devices. The proposed novel filter will be developed and approached by using two different methodologies; spurline section and stepped impedance resonators which will be integrated into one compact filter. A detailed investigation of parameters affecting the new novel design with a tunable ferroelectric capacitor is also carried out. Microstrip transmission line techniques for reducing size in

bandstop filter by compact structure using spurline section and stepped impedance resonators are developed. The configurations of the new tunable filter design are simulated by using advanced system design (ADS). Fabrication circuit designs of a compact dual-band bandstop filter and experimental results are presented based on synthesis equations. Chapter one gave a brief introduction to the relevance of microwave filters design methodologies, it briefly explained their applications and uses in RF microwave systems. Also, it provided a brief introduction to RF tunable technologies with tuning-element devices. Chapter two will present a literature review of the RF microwave filter designs and developments of Dual-Band Band Stop Filters. It will concentrate more on the methodologies of using microstrip filter theories and experiments. There are various types of microstrip filter which will be studied based on the use of spurline section and stepped impedance resonators. All these technologies are presented to motivate the approach to the present work. In chapter three, a new methodology will be described for novel Dual-Band Band Stop filter design. Various microstrip techniques will be utilized to design new and compact dual-band bandstop filter. The new approach filter design will integrate spurline section with stepped impedance resonator using the coupling line method. All experimental results, simulations and fabrication circuits are designed by using ADS software. Chapter four will concentrate on the tunable devices that are used to tune the new compact filter design. The compact dual-band filter design will be tuned by using p-n junction varactor diodes at 2.4 GHz and 3.5 GHz. The P-n junction varactor diodes will be modeled and simulated by using ADS software. The design of a tunable dual-band bandstop filter using p-n junction varactor diodes will be fabricated and measured with a Agilent vector 30

network analyzer. The measurement results will be provided along with a comparison between modeling and fabricated filter designs. Chapter four will also present the design modeling of ferroelectric capacitors by using ADS. It will show the procedure for fabricating Barium Strontium Titanium capacitors for low frequency and high frequency.

The dual-band bandstop filter will be tuned at 2 GHz and 3.5 GHz by BST capacitors.

Chapter five presents proven conclusions and points out the important advantages and features of this dissertation along with some recommendations for future work.

CHAPTER 2

LITERATURE REVIEW ON TUNABLE DUAL-BAND BANDSTOP FILTER CIRCUITS

2.1 Introduction.

This chapter will present a literature review of some techniques that have been approached in the design Dual-Band Bandstop filter. In recent years, many different methodologies have been developed substantially to enhance the performance of dual- band filters. Some research was carried out to improve the rejection band level. Some researchers tried to reduce the circuit size while maintaining the actual performance of the filter. Expanding and improving filter bandwidth was one of the main interesting areas for researchers. Recently, many different types of resonators were used to improve and develop the characteristics of the dual-band filters. Some resonators were developed to be a suitable choice for a miniaturization filter design with a low loss performance such as bulk wave, coaxial, waveguide, dielectric and surface acoustic wave resonators

(SAW) [2]. Also, some other resonators were developed to provide a small size with light weight structure like planer resonators. Other filters, such as helical resonators, were developed especially in response to the demand for a high level of power handling [2]. In general, developing a new type of filter imposes demands on filter size, low loss, fractional bandwidth, the permittivity of the substrate and on the capability of power handling.

One of the most popular miniature filters in R/f microwave systems is microstrip filters. They are used widely because of their small size, reliability and ease of

manufacturing. They have a high-speed quasi-static analysis compared to another topologies design. The stripline lines that are used to design the microstrip filter are classified into transmission lines and stepped impedance resonators (SIRs).

Moreover, designing tunable circuits has become an attractive research area in microwave system designs. It is possible to execute the performance of the conventional filter using tunable components with voltage or current control [22]. Using tunable components instead of the fixed lumped components with a reconfigurable adaptive circuit will help to reduce size and fabrication cost [22]. Many different tunable components such as p-n junction varactors, micro electro mechanical systems (MEMS), ferroelectric material and liquid crystal cells have been developed to apply tunability to

RF circuit blocks. They have been used as replacement elements of the fixed frequency circuit to apply tunability in many devices such as voltage-controlled oscillators, matching networks for power amplifiers, tunable filters, active and passive phase shifter and tunable antennas [22]. This chapter will investigate the development approaches for designing the dual-band bandstop filter DBBSF with a concentration on microstrip methodology and on different tunable components.

2.2 Single-band bandstop filter

Bandstop filter is a very important device that is used in both transmission and receiving systems. It is used to suppress unwanted signals in the specified band of frequencies. Also, it is used widely to prevent interfering signals in receiving systems.

Previously, bandpass filters were used to attenuate unwanted signals in their stop-band

[4]. In some cases, we might need to suppress unwanted interference signals that are 33

caused by nearby devices. The attenuation stop-band of bandpass filter may not be effective or practical against the strong interfering signals. The stopband of the bandpass filter is too large to stop unwanted signals at certain frequencies [4]. In contrast, we must use a bandstop filter with a narrow band or special performance characteristics to suppress interfering signals [4].

Figure 2.1 shows the basic circuit of band stop filter using lumped elements. There are many improved topologies for the bandstop filter design. Most of these topologies use a conventional structure to enhance the performance of the bandstop filter. The conventional bandstop filter is achieved by transforming low pass filter into bandstop filter. It is a basic LCR circuit that can be designed for a single band, dual-band and multiband filters. In microwave communication systems many methodologies are used to approach the performance of the conventional bandstop filter such as parallel-coupled lines and stepped impedance resonators. The resonators of these coupling lines can be either λ/2 long at the mid-band frequency with open-circuit at both ends, or λ/4 long and short-circuit at one end [4].

Figure 2.1 Basic circuit of the bandstop filter using lumped elements [22].

2.3 Dual band-bandstop filters

Dual-band bandstop filters (DBBSFs) are extensively used to suppress the double- sideband spectrum in high-power amplifiers and mixer devices [23]. They can be used to reduce the circuit size and cost with a good rejection band performance. There are numerous designs and methods that have been implemented to realize a dual-band bandstop filter. The dual-band performance can be achieved by applying two-step frequency-variable transformation to the low-pass prototype [23].

2.3.1 Dielectric resonators

Dual-band bandstop filter can be realized with dielectric resonators at L-band by using lumped element components. This topology is practical in the design of two closely-spaced rejection bands having good passband between them. It can show a rejection band filter with lower loss compared to a bandpass filter with the same number of resonators and at the same desired frequency. Moreover, it is a method applicable to distortion reduction filter in RF transmissions. Figure 2.7 shows the development of designing a dual-band bandstop filter. It shows the circuit synthesis of BSF with L-band using high-Q dielectric resonators where a low loss and low group delay features are verified and proven experimentally. The design of dual-band bandstop filter starts with the circuit of low pass filter as shown in figure 2.2 (a). The second step is to design the bandstop filter using the lumped circuit as shown in 2.2 (b) [24].

Figure 2.2 Bandstop filter design. (a) Prototype LPF (b) single bandstop filter [24].

According to [24] the following equations will be used to apply a frequency-variable transformation to the low pass filter. This formula can be used to obtain a conventional bandstop filter for the first rejection band.

(4) −1 ∆휔 휔 휔0 휔 → ( − ) The same method will be used to obtain휔0 another휔0 휔 frequency-variable transformation for designing the second rejection band.

(5) 휔0 휔1휔2 휔 → (휔 − ) For휔 2( − 휔1 휔

휔1 < 휔0 < 휔2) Where and are center frequencies of the bandstop filter while is the center frequency휔1 of pass-bnad.휔2 is the rejection bandwidth and can be given 휔by0

∆휔푟

(6) 2휔0∆휔푟 ∆휔 ≈ 36휔2 − 휔1

The lumped element values can be given by the following formulas.

(7) 휔2 − 휔1 푔1휔0∆휔 퐿12 = , 퐶12 = 푔2휔0휔1휔2∆휔 휔2 − 휔1

휔0 푔2∆휔(휔2 − 휔1) 퐿21 = , 퐶21 = 푔2∆휔(휔2 − 휔1) 휔0휔1휔2

(8) 휔0(휔2 − 휔1) 푔2∆휔(휔2 − 휔1) 퐿22 = , 퐶22 = By connecting two lumped circuits푔2휔1휔 2 of∆휔 the single bandstop휔0(휔2 − 휔filter1) as seen in the above figure, we can get the final dual-band bandstop filter. Figure 2.3 shows the final dual- band bandstop filter design approach by applying a two variable-frequency at two different cut-off rejection bands. This design provides lower transmission loss and group delay variation compared to BPF that has the same number as unloaded Q with the same frequency selectivity around the pass-band [24].

Figure 2.3 Dual-band bandstop filter [24].

2.3.2 Composite right/left-handed metamaterial transmission lines

The performance of dual-band bandstop filter can be realized using composite right/left-handed (CRLH) metamaterial transmission lines (TLs). This method has been

developed to replace the microstrip line of conventional dual-band bandstop filters. It has been developed by using the conventional bandstop filter and a quarter-wave short- circuited and open-circuited stubs. Then the dual-band can be easily approached by replacing the microstrip lines with the CRLH metamaterial transmission lines [25]. The rejection dual-band filter is experimentally demonstrated at 1 GHz and 1.9 GHz. The measured results show a good rejection dual-band filter with 12.2% and 6.9% stop bandwidth with 30 dB as attenuation level. The main advantage of this method is the ease in design procedures that lead to arbitrary dual-band bandstop filter; however, it has relatively large circuit size. Figure 2.4 shows the design structure of dual-band bandstop filter using a quarter-wave short-circuited and open-circuited stubs.

Figure 2.4 Conventional (a) bandpass (b) bandstop filters using quarter-wave short- circuited and open circuited (c) DBBPF (d) DBBSF (e) CRLH transmission lines [25].

The design of dual-band bandstop filter using CRLH transmission lines are shown in figure 2.5

Figure 2.5 Dual-band bandstop filter using CRLH transmission lines [25].

2.3.3 Stepped impedance resonators (SIRs)

Stepped impedance resonators method is one of the most important and famous topologies that are used in the design of dual-band bandstop filters. It helps to approach two controllable stopbands at desired frequencies. The filter size can be reduced by up to

12.6%, which cannot be accomplished with a conventional and standard DBBSFs [26].

Figure 2.6 shows the circuit design of DBBSF using stepped impedance resonators [26].

Figure 2.6 DBBSF using SIRs (a) Schematic of the proposed filter (b) Equivalent circuit using lumped components with the ideal J inverter [26].

The previous layout was fabricated on the FR-4 substrate with , tan δ and a thickness of 1.524 mm. The dual-band filter was designed at휀푟 1.5= 4.3and 3.15= GHz 0.02 with bandwidths of and . The dual-band frequencies of and can be

푓 푠 푓 푠 derived by transferring∆ = 70% LC elements∆ = 35% of the low-pass prototype filter to휔 bandstop휔 circuit.

Figure 2.7 shows the transferring of the lumped element circuit to a stepped impedance resonator using transmission lines.

Figure 2.7. (a) The equivalent circuit of DBBSF using shunt-connected series LC resonators and SIR. (b) Configuration of DBBSF admittance converter [26].

Figure 2.8 shows the simulated and measured results of DBBSF using stepped impedance resonators instead of the conventional lumped component filter.

Figure 2.8 (a) Measured and simulated result of DBBSF. (b) Fabricated filter design [26].

The previous layout can be used to realize dual-band bandstop filter with two controllable center frequencies and bandwidths. A single SIR can be adopted to reduce the total length of the resonators instead of using two parallel-connected stubs. Based on that, the physical length can be reduced by more than 24% [26].

2.3.4 Split ring resonators (SRRs)

The performance of the dual-band bandstop filter can be achieved by using two split ring resonators (SRRs). This method helps to design a compact dual-band filter by placing two resonators on the same transverse plane realizing two different rejection bands. Figure 2.9 shows the configuration of a single bandstop filter realized by using split ring resonator [27].

Figure 2.9 Bandstop filter using split ring resonator SRR. (a) proposed filter layout. (b) simulated signal response [27].

The scattering parameters in the previous figure are L1 = L2 = 2.9 mm, g = 0.2 mm and

W = 0.15 mm. The coupling effect in the proposed filter can be eliminated by aligning the distance between two resonators on the transverse plane. Moreover, the resonant frequency of the dual-band filter can be determined by the total length and physical width of the resonator [27]. The substrate of the split ring resonator filter is RT/Duroid 5880 with the thickness of 31 mils, the relative dielectric constant of 2.2, and loss tangent

0.0009. Figure 2.10 shows the simple lumped element circuit that is used in the design of the layout of the dual-band resonator.

Figure 2.10. (a) lumped element circuit of DBBSF using SRRs. (b) Simulated and measured result [27].

The dimensions of the first band resonator at 9.8 GHz (

) and for the second band resonator퐿1 = at 2.7 11.4 푚푚 GHz, 퐿2 = (

2.4 푚푚, 푊 = 0.3 푚푚, 푔 = 0.2 푚푚 42

). Figure 2.11 shows the

퐿measurement1 = 3.5 푚푚 ,result 퐿2 = of 2.4 the 푚푚 dual-band, 푊 = 0.3 bandstop 푚푚, 푔 =filter 0.2 using푚푚 split ring resonators [27].

Figure 2.11. (a) Fabrication design of DBBSF using SRRs. (b) Measured and simulation result [27].

As seen in the above structure design, dual-band bandstop filter was designed and has been demonstrated experimentally at 9.8 GHz and 11.4 GHz with a good rejection band.

The coupling effect between two resonators is neglectful because of the large distance between the resonators. Thus, both rejection bands can be controlled independently.

2.3.5 TRI-Section stepped impedance resonators

Dual-band bandstop filter can be designed by using two shunt-connected tri- section stepped impedance resonators with a transmission line in between. The tri-section method helps to design a compact size filter with a wide range of realizable frequency ratio and more realizable impedance. Figure 2.12 shows the layout of stepped impedance resonator with three different structures [23].

Figure 2.12. (a) quarter-wavelength stub, (b) two section-stepped impedance, (c) tri- section stepped impedance resonator [23].

The stepped impedance resonators can be used to reduce the size of the filter with a very good dual-band performance. Figure 2.13 shows the dual-band bandstop filter design at

1.5 GHz and 3.15 GHz with a bandwidth of 70% and 35%. The measurement results are achieved at 1.49 and 3.11 GHz with a bandwidth of 55% and 27% respectively.

Figure 2.13 Dual-band bandstop filter, (a) filter measurement results (b) fabrication design [23].

Also, stepped impedance resonators help to design dual-band filter with a fully controllable center frequency and bandwidths. Figure 2.14 shows the design of the same filter at 2.4 and 5.8 GHz. The results were measured at 2.35 and 5.58 GHz with a bandwidth of 40% and 18% respectively.

Figure 2.14 Dual-band bandstop filter, (a) filter response (b)filter fabrication [23].

According to figure 2.13 and figure 2.14, both center frequency and bandwidth can be tuned by using stepped impedance resonators. The structure of the proposed filter can be miniaturized with many different shapes to approach a compact size with a very good dual-band bandstop filter performance. The dual-band bandstop filter can be tuned with a good tunable range for center frequency and bandwidth.

2.3.6 Square patch resonator

The square loop resonator has been developed to realize the performance of dual- band bandstop filter. This method split the dominant mode and the degenerate mode by using double inner corner cuts which act as a perturbation. It has been improved to achieve the performance of dual-band bandstop filter. It shows a very simple design with a compact structure design for dual-mode and tri-band bandstop filter with the help of defected ground structure DGS. The filter size can be decreased by up to 64% compared with the standard filter designs [28]. Figure 2.15 shows the dual-mode bandstop filter using a square loop with double-patch resonators.

Figure 2.15. DBBSF using a square loop with double-patch resonators [28].

Figure 2.16 shows the measurement and simulation results of the square patch resonators for dual-band bandstop filter using Agilent vector network analyzer E5071C, which matches the simulation results.

Figure 2.16. The measurement result of DBBSF using double-patch [28].

Figure 2.17 shows the fabrication results of the DBBSF by using square patch resonators.

Figure 2.17. Fabricated design of DBBSF using square patch resonators [28].

2.3.7 Open and short stub-loaded resonators

The performance of the dual-band bandstop filter can be approached by using open and short stub-loaded resonators. This method uses even-mode resonant frequencies to maintain stopbands, while the odd-mode frequencies achieved by open and short stub- loaded resonators are used to suppress transferring signals. For the even-mode, the second harmonic filter response of the open stub-loaded resonator is used as the second stopband. In the same way, the third harmonic filter response of the short stub-loaded resonator is used as the second stopband. The resonators of the open and short stub- loaded filter have been developed by using two parallel transmission paths to achieve bandstop performance [29].

Figure 2.18. Structure of bandstop filter. (a) Open stub-loaded resonator. (b) Short stub- loaded resonator [29].

The above structure design uses folded loops resonators to enhance the loading effect that appears between filter resonators and the main transmission line. The results of dual-band bandstop filter have been measured by using IE3D and 8753ES network analyzer. The center frequencies of the first filter that use open stub-loaded resonators are 2.89 GHz

and 5 GHz as shown in figure 2.19. The filter has a 28-dB attenuation at the first rejection band and 16 dB for the second rejection level. Also, the center frequencies of the second filter that use short stub-loaded resonators are 1.16 GHz and 3.5 GHz. It has a rejection level of 29 dB and 28 dB respectively.

Figure 2.19 Simulation and measured results of DBBSFs. (a) Fabrication Filters. (b) Open stub-loaded resonators filter result. (c) Short stub-loaded resonator filter result [29].

2.3.8 Defected ground structure (DGS)

The defected ground structure is one of the most popular topologies that are used to design dual-band bandstop filter. It can be combined with other structures such as microstrip stepped impedance resonator, square patch resonators and spurline sections.

Moreover, there are many shapes that are used by defected ground structures such as T- shaped and U-shaped structures. The filter size can be realized at a minimal area with a very compact structure. Figure 2.20 shows the proposed dual-band filter with two center frequencies located at 3.825 GHz and 5.325 GHz with 3 dB fractional bandwidth of

14.6% 16.3% respectively. The attenuation level is more than 25 dB for both rejection bands. The rejection bands can be controlled separately or together [30].

Figure 2.20 Defected ground structure of DBBSF. (a) T-shaped structure. (b) DBBSF layout. (c) Measured result [30].

Figure 2.21 shows a new structure for DBBSF with two stages where one utilizes a T- shaped and the other a U-shaped microstrip defected ground DMS methodology. It has a good rejection band level at 49 dB.

Figure 2.21 Simulated result of DBBSF using two-stages, T-shaped and U-shaped with DMS [30].

2.3.9 Stepped impedance hairpin resonators

Stepped impedance hairpin resonators are used widely in RF microwave system to design dual-band bandstop filter. Figure 2.22 shows a structure design of DBBSF embedding two open stubs at 2 and 5.92 GHz. Both stopbands can be adjusted by changing the dimensions of the open stub-loaded resonators [31].

Figure 2.22. DBBSF using stepped impedance hairpin resonators. (a) Filter layout. (b) Simulation result [31].

The design of the hairpin resonators consists of two transmission zeroes in each one. The final layout of the proposed filter has only one hairpin resonator with a physical size of

15 mm 23.1 mm. Also, this filter can be tuned by changing the physical length of open

× 51

stub-loaded resonators. Figure 2.23 shows the final layout of the proposed filter with the measurement results.

Figure 2.23. DBBSF using hairpin resonators. (a) Fabrication filter. (b) Measurement result [31].

2.3.10 E-Shaped Resonators

The architecture of E-shaped resonator has been developed to approach the performance of dual-band bandstop filter at 1.8 and 5.2 GHz. This method was improved to achieve a small filter size with a good rejection band level at 54.03 dB and 42.57 respectively. The proposed filter was approached using E-shaped resonators and a microstrip feeding line. The dual-band bandpass filter was developed utilizing a quadruple-mode square ring loaded resonator (SRLR). This filter resonator provides a

very narrow rejection band with a simple structural design. Figure 2.24 shows the structural design with the simulation results [32]. Moreover, the proposed filter was demonstrated and experimentally provides controllable center frequencies and bandwidths.

Figure 2.24 DBBSF using E-shaped resonators. (a) Filter layout. (b) Simulation result [32].

2.3.11 Coupled line resonators

The microstrip coupled lines are used widely to design dual-band bandstop filter.

This method consisted of open and shorted coupled lines. Figure 2.25 shows the ideal circuit of the dual-band bandstop filter using even-mode and odd-mode equivalent circuits. The proposed filer of this method has nine transmission poles that are used to realize stopbands by coupled lines and transmission lines. It has two adjustable rejection bands which can be achieved by changing the even/odd-mode of the coupled line. The full- wavelength transmission lines have been used to avoid any increment in the

cascaded open stubs. This will promote the out-of-band selectivity and the filter suppression as well. The center frequencies of the dual-band bandstop filter are located at

1.5 GHz and 2.4 GHz. The design was achieved by using a prototype bandstop filter that was constructed on the dielectric substrate , mm, and tan

[33]. 휀푟 = 2.65 ℎ = 0.5 훿 = 0.003

Figure 2.25. (a) The ideal circuit of DBBSF using coupled line resonators. (b) Even-mode equivalent circuit. (c) Odd-mode equivalent circuit [33].

Figure 2.26 shows the simulation results and measurement results are matching each other with a very good rejection band level at both center frequencies.

Figure 2.26 Simulation and Measurement results of DBBSF using coupled line resonators [33].

Table 2.1 shows the most popular topologies that are used to approach the performance of dual-band bandstop filter.

Table 2-1 Most popular topologies for designing Dual-Band Bandstop Filter.

2.4 Tunable bandstop filter

Tunable microwave filters became an attractive topic for scientists due to the rapid developments in satellite technologies [34]. They have triggered great interest because they can be used to build blocks of multifunction communication systems. In this section, we will study the different approaches that are used to apply tunability to band stop filters. There are many approaches to achieving tunable microstrip filter in the literature; however, there are only a few tunable microstrip bandstop filters [34]. Most tunable materials and tuning devices were applied to the bandpass filter because of their applicability to the bandstop filter. The motivation for this trend is the fact that the bandpass filter and bandstop filter perform opposite functions. The rejected band in the bandpass filter was used as a stopband filter; however, this stopband was too large and unable to suppress interfering signals. Also, it was not effective enough in suppressing

unwanted signals in transceiver systems. Thus, new topologies have been developed to provide a bandstop filter with narrow bands that could be used to suppress the strong interference from nearby devices [4]. For all these reasons, the bandstop filter has become a more popular field in microwave system design. The development of bandstop filters coincided with the development of tuning filters.

2.4.1 Tunable BSF using varactor diodes

Varactor diodes have been used widely to apply tunability to bandstop filter with many different methods. The parallel coupled line resonators use varactor diodes and quarter wavelength stubs to tune the band stop filter as seen in figure 2. 27. The parallel coupled line resonator is loaded with a varactor diode into a quarter wavelength stubs to achieve a bandstop response [35].

Figure 2.27 Parallel coupled tunable BSF. (a) equivalent circuit of the resonator (b) fabrication filter design [35].

The proposed design in the above figure shows a filter with a 50 Ω of SMA connector that is soldered to excite the signal. The cut off frequency was 4.7 GHz and the resonator

dimensions were established by using CST Microwave studio. The bandwidth of the proposed filter at -10 dB reference level is 0.1 GHz (4.67-4.77 GHz). Figure 2.28 shows the tunable bandstop filter response with the different bias voltage conditions. The resonance frequency will be changed from 1.04 GHz to 3.13 GHz when the reverse bias is decreased [35].

Figure 2.28. (a) Simulation and measurement results without varactor diode (b) tunable results [35].

Other methods to tune bandstop filter have been approached by using a varactor diode located at an open-circuited stub. The electrical length of the open-circuited stub has been tuned by embedding a varactor diode into the bandstop resonator. The proposed filter design was realized by using a microstrip as a transmission line on FR4 substrate.

The tunable percentage of the center frequency can be approach by up to 84%. Figure

2.29 shows the insertion of varactor diode with a proposed filter [36].

Figure 2.29. (a) bandstop filter using open-circuited stubs (b) filter response without tuning [36].

Figure 2.30. (a) varactor model with a biasing circuit (b) tunable circuit of open-circuited with stubs resonator [36].

Figure 2.31 shows the layout of the proposed filter with dimensions of mm,

mm, mm and mm. The specifications퐿 of1 = the31 substrate.32

퐿are:2 = 15.3 , tan푊 1 == 0.02 2.68 and h = 푊 1.52 = mm. 4.2 The proposed filter was tuned using a

Skyworks휀푟 = 4.1SM1232 varactor diode as shown in [36].

Figure 2.31. (a) BSF with open-circuited stubs loaded with varactor diode (b) fabrication filter design [36].

Figure 2.32 Tunable bandstop filter response [36].

The proposed filter was tuned from 0.907 to 1.666 GHz and achieved 84% tuning range by applying a DC voltage from 0 V to 6 V.

In addition, the tunability of the bandstop filter can be achieved by using E- shaped dual mode resonator. The basic bandstop circuit is modified utilizing E-shaped mode in order to tune the bandstop filter with two discrete frequencies of 5 and 6 GHz with the same fractional bandwidth of 5%. The tunable bandstop filter was achieved by modifying the open stub inverter length loaded with PIN diode. The controlling of filter bandwidth can be obtained by selecting an appropriate value for the resonator width, the spacing between the filter resonator and the main line and by controlling the normalized reactance slope parameter of the resonator [37].

Figure 2.33 Tunable bandstop filter using E-shaped dual mode resonator. (a) without biasing circuit (b) with biasing circuit [37].

The modified design consists of an E-shaped resonator embedded above a microstrip transmission line using an open-stub inverter. The transmission line has 50 Ω as characteristic impedance. The gap between the transmission line and open-stub is modified as coupling structure. The benefit of utilizing the dual mode filters is that they must reduce the number of the switching elements [37]. As shown in figure 2.33 (a) the filter configuration is modified to a reconfigurable design by embedding PIN diode between the open-sub inverter and stub s. The total physical length of the open stub is

10 mm when the diode is in forward퐿푐 bias and 7 mm while in reverse bias. Figure 2.34 shows the signal response of the tunable bandstop filter using the E-shaped dual mode resonator without biasing.

Figure 2.34 Tunable bandstop filter using E-shaped dual mode without biasing (a) forward biasing (b) reverse biasing [37].

The center frequency is 5.066 GHz with a – 35.4 dB rejection band level while the return loss is – 2 dB in the forward bias. In the reverse bias, the center frequency is 5.880 GHz with a – 21.3 dB rejection band while the return loss – 0.9 dB.

Figure 2.35 Tunable bandstop filter using E-shaped dual mode with biasing (a) forward biasing (b) reverse biasing [37].

The center frequency is 5.23 GHz with a – 20.90 dB rejection band level while the return loss is – 1.9 dB in the forward bias. In the reverse bias, the center frequency is 5.982 GHz with a – 21.9 dB rejection band while the return loss – 0.677 dB.

Moreover, tuning bandstop filter can be realized by using open split ring resonators (OSRRs), and open complementary split ring resonators (OCSRRs) loaded with varactor diodes in coplanar waveguide (CPW) technology. The center frequency can be tuned with a very good range of 120% by varying the applied voltage between 0 to 28

V. Figure 2.36 shows the layout of the fabricated structure for the bandstop filter using

(OSRRs) and (OCSRRs). The dimensions of designing a bandstop filter are

푊 =

2.1 푚푚, 퐺 = 0.7 푚푚, 푟표 = 2.[38].29 푚푚 The, 푐substrate = 푑 = 0.of38 the 푚푚, proposed 퐿 = 23 filter, ℎ1 =is Rogers RO3010 62 6.14 푚푚 푎푛푑 ℎ2 = 5.9 푚푚

with a dielectric constant , thickness mm and the loss tangent tan δ

푟 . The tunable bandstop휀 = 10filter.2 was achievedℎ = 1.using27 the ‘Infineon BB833’ varactor=

0.diodes0023 with a varying of the capacitor range from 9.3 to 0.75 pF and control voltages from 1 to 28 V [38].

Figure 2.36 Bandstop filter layout using (OSRRs) and (OCRRs) [39].

Figure 2.37 shows the fabrication of tunable bandstop filter using open-split range resonator tuned with a varactor diode based on coplanar waveguide technology (CPW) with varying voltage control from 1 to 28 V.

Figure 2.37 Tunable bandstop filter using (OSRR) with diode varactor [38].

On the other hand, the bandstop filter can be tuned by developing the architecture of the coupling topology. This type of design allows for tuning both center frequency and bandwidth. The new architecture consists of a varactor-loaded transmission line resonator designed using odd symmetry with one axis coupled twice to a transmission line. This structure has no tuning elements placed in the signal through a path and it concentrates mainly on the development of the filter resonator based on coupling topology. The bandwidth of the proposed filter is determined by using the strength of the coupling and the electrical length associated with the transmission line [39]. Figure 2.38 shows the development of the bandstop tunable filter using a new architecture method.

Figure 2.38 Bandstop tunable filter. (a, b) the layout consists of a varactor-loaded transmission line. (c, d) S-Parameter of tuning center frequency and bandwidth [39].

The tunability of the filter bandwidth is achieved differentially by two varactors embedded at the opposite ends of the resonator while the center frequency is tuned by tuning both varactors simultaneously. The measurement results of the proposed filter

show a tuning range of 1.2 to 1.6 GHz of the center frequency and tuning range of 70 to

140 MHz of the filter bandwidth as seen in Figure 2.39.

Figure 2.39 Tunable bandstop filter. (a) tuning center frequency (b) tuning bandwidth [39].

2.4.2 Tunable BSF using lumped elements

Tuning of bandstop filter also achieved by using lumped elements. Figure 2.40 shows the tunable bandstop circuit by using variable capacitors [40].

Figure 2.40 Tuning bandstop filter using lumped element [40].

Lumped elements method uses variable capacitors to apply tunability to the center frequency and bandwidth control. The proposed filter is tuned by using two different methods: with a single varactor diode and with back to back varactor diodes. Figure 2.41 shows the equivalent circuit of the lumped element using a quarter-wave microstrip line and simulated amplitude and phase versus frequency [40].

Figure 2.41 Equivalent circuit of the lumped element using a quarter-wave microstrip line [40].

Figure 2.42 shows the tunable range of the proposed bandstop filter using a single varactor diode and back to back varactor diode. The center frequency was tuned from 470 to 730 MHz using the method of the single varactor diode. By using the back-to-back varactor diode method, the center frequency was tuned from 511 to 745 MHz. The insertion loss in both methods was 0.3 dB to 0.5 dB [40].

Figure 2.42 Tunable bandstop filter using a single varactor diode and back to back varactor diode [40].

2.4.3 Tunable BSF using ferroelectric materials

Recently, ferroelectric materials such as barium strontium titanium (BST) become more attractive in the development of tuning microwave circuits. The tunable varactor of these materials can be designed in the form of metal-insulator-metal (MIM) capacitor or by using an interdigital capacitor (IDC). Figure 2.43 shows a new design of tunable bandstop filter using slotted ground structure tuned by BST varactor. It consists of 2-pole bandstop filter that is measured at 1.2 and 1.4 GHz with the rejection band being more than 15 dB. The insertion loss of the proposed filter is less than 1 dB, and the bandwidth is 100 MHz with a measuring tuning range of 14% [19].

Figure 2.43. (a) Profile layers of fabrication of the BST interdigital varactor chip (b) fabricated tunable BSF using BST varactor (c) BSF signal response [19].

The layout of the tunable bandstop filter was converted into a microstrip transmission line structure with a dielectric constant and a height of 1.5 mm. The dimensions of bandstop filter with a slotted휀 푟 ground= 3.05 structure are 5.0 by 2.5 . The 2 measurement results have been achieved by using Agilent 8510B network analyzer푐푚 over the frequency range of 0.5 to 2.5 GHz with a controlling voltage of 0 to 35 V [19].

Figure 2.44 (a) shows the design of tunable bandstop filter using microstrip topology. This design uses the microstrip lines printed on FR-4 substrate with indium ribbons by pressure bonding. Barium Strontium Titanium BST capacitor was embedded in the microstrip filter to apply tunability to a bandstop filter on 0.5 GHz. The bandstop filter can be tuned from 600 MHz to 810 MHz by applying a tuning voltage of 0 to 6 V.

The attenuation level is about 13 dB with a good insertion loss of the pass band at 2.3 dB.

Figure 2.44 (b) shows the result of a tunable bandstop filter that uses BST capacitor [22].

Figure 2.44 Tunable bandstop filter using BST. (a) Fabricated filter. (b) Measurement result [22].

2.4.4 Tunable BSF using liquid crystal material

The bandstop filter can also be tuned by Liquid Crystal (LC) technology. Figure

2.45 shows a meander loop resonator of the tunable bandstop filter with two open- circuited stubs. The proposed filter shows a good rejection band performance because it was realized by using two additional open-circuited stubs with a compact size. Metal vias

connect both input and output of the proposed filter. The tunability is applied to this filter using the property of LC by applying low AC voltages [43]. This technology provides a very cheap filter with low power consumption and small size.

Figure 2.45 Bandstop filter using meander loop resonator. (a) Filter layout. (b) Filter result [43].

Figure 2.46 shows the schematics and fabrication of bandstop filter which was designed using liquid crystal technology. It shows Nematic liquid crystals that belong to the organic compounds designed by larger diameter long cylindrical molecules. This structure has no layers like semectic LC with a limited design of nematic LC molecules which cause less viscosity. The dielectric constant could be changed by adding an external electric field when there is change to the birefringence and polarization transfer function. It can be tuned by a control voltage which causes change to the effective permittivity of LC. This change applies tunability to the proposed filter and can be adjusted to a certain frequency. Figure 2.47 shows the scattering parameters of the

proposed filter ( ) with a center frequency of 3.4 GHz. The insertion loss is more than 65 dB with a푆 21return, 푆11 loss less than 0.4 dB.

Figure 2.46 Structure of bandstop filter using Liquid Crystal (LC) technology [43].

The above layout of the liquid crystal technology is designed based on the loop resonator with a patch that uses two open-circuited stubs into the input and output ports. The rejection band filter is shown in Figure 2.47.

Figure 2.47 Simulated result of TBSF using LC technology. (a) S21. (b) S11 [43].

The tunability of the bandstop filter is achieved by many different methodologies. Some of these topologies are used to tune the center frequency while others are used to apply tunability to the bandwidth. Table 2.2 shows a comparison of tuning BSFs utilizing different types of tuning methodologies.

Table 2-2 Comparison of different methods for tuning BSFs [22].

The above table illustrates some important scattering parameters associated with the tuning of the bandstop filter. It shows the parameters of the transferring signal such as tuning range, insertion loss, return loss and bandwidth. In addition, it shows the tuning change of bandstop signal by using many different methods of tuning elements. In this chapter, we have seen the most important methods that have been approached in the design of dual-band bandstop filter and we have also seen the different topologies that have been used to apply tunability to the single rejection band filter and dual-band

bandstop filter. In general, tunability could be applied by using tuning elements such as diode varactors, lumped elements, ferroelectric materials and liquid crystal materials.

In this dissertation, the main objective is to design a bandstop filter using a new and unique methodology for a single band and dual-band. In this methodology, we are going to use two different topologies; spurline section and stepped impedance resonator.

The lumped element components will be utilized to design a bandstop filter based on

LCR circuit for both single band and dual band filters. All the components that are used in the lumped element design will be transferred to transmission line components by using microstrip technology. The spurline sections will be designed based on the coupled lines topology while designing stepped impedance resonator based on the lumped element component using transmission lines. Both techniques will be designed at 2.4

GHz to obtain a single bandstop filter. To design a dual-band bandstop filter, the spurline sections will be designed at 2.4 GHz to obtain the first rejection band filter, while designing a stepped impedance resonator at 3.5 GHz to obtain the second rejection band filter. The final design of the dual-band bandstop filter will be achieved by connecting the cascading of both topologies in one compact filter. The new methodology will provide very good performance of the bandstop filter with many different advantages comparing with the previous design approaches. For the single bandstop filter, the novel design will provide the following:

- A Compact structure design that can be used to reduce filter size with a good

rejection band performance.

- A controllable bandwidth filter which helps to increase or reduce the

bandwidth by adjusting stepped impedance resonator (SIR).

- The attenuation level can be controlled by embedding more stepped

impedance resonators (SIRs) at the same center frequency.

- Designing the bandstop filter with multiple transmission poles by using more

stepped impedance resonators (SIRs) with the spurline sections.

On the other hand, the new methodology provides many advantages for the dual-band bandstop filter as follows:

- A very compact structure to design DBBSF using spurline section and stepped

impedance resonator in one transmission line filter.

- Two independent and controllable stopbands at desired frequencies.

- Combine a fully controllable narrow bandwidth filter and wide bandwidth

filter into one compact filter.

- Practical filter design to insert tunable components such as varactor diodes, a

ferroelectric material, and lumped elements.

Microstrip lines will be used to realize bandstop performance for both filters; single bandstop filter and dual-band bandstop filter. The microstrip technology is one of the most popular types of planar transmission lines in microwave system technologies. They are attractive devices in microwave systems because they can be easily miniaturized and integrated with passive and active devices. A photolithographic process can be used to fabricate the resonators of the microstrip line filters.

Moreover, this dissertation will provide an extensive study on a tunable dual-band bandstop filter by using spurline sections and stepped impedance resonators (SIRs). The focus of this study will be on the novel tuning design of the controllable dual-band bandstop filter. The tunability will be applied to DBBSF using varactor diodes and

Barium Strontium Titanate capacitors (BST).

CHAPTER 3

DESIGN, SIMULATION, AND IMPLEMENTATION OF DUAL-BAND BANDSTOP FILTER

3.1 Introduction

Bandstop filters are used widely in RF wireless communication systems for their effective suppression of spurious signals. They are very important components that are used in both receivers and transmitters [23]. Dual-band bandstop filters (DBBSFs) have recently become an attractive research field for scientists. This attraction is due to the ability of these filters to treat the unwanted double-sideband spectrum of high power amplifiers and mixers utilizing one single filter to reduce both the size and cost of proposed filters [26]. They have low insertion loss and group delay because their resonators are resonating in the stopband rather than in the passband [26], [44].

In the literature, many different approaches have been proposed to realize dual- band bandstop filters [23]. These filters can be designed by applying a two-step frequency-variable transformation using low-pass prototype filter methods [23], [24].

Chen et al. developed a different method which integrates two stacked loops into a module filter design for dual-mode dual-band operation [45]. Kuo et al. proposed a different structure design of DBBSFs by using parallel-coupled and vertical-stacked configurations utilizing stepped impedance resonators [46]. Another new method has been developed using composite right/left-handed metamaterial transmission lines to replace the microstrip lines of conventional bandstop filters [47]. DBBSFs have also been designed by using stepped impedance resonators (SIRs) instead of two parallel-connected

stubs [26]. Recently, a filter design was proposed using parallel connected stubs, usually known as dual-behavior resonators, as composite shunt resonators to match dual-band performance [48], [49]. Another method to design dual-band bandstop filters is by using split ring resonators (SRRs) [27]. This method uses two square split ring resonators to be placed on the same transverse plane realizing two independent stop bands. DBBSFs can also be designed by using spurline sections that utilize a coupled line approach [50].

This chapter proposes a new and unique type of dual-band bandstop filter using spurline section and stepped impedance resonator. The new structure filter compacts spurline section with stepped impedance into one filter realizing two independent rejection bands. This novel design combines a spurline section and stepped impedance resonator to be tuned by a P-n varactor diodes and ferroelectric capacitors. The two stopbands can be controlled and tuned independently in one filter while reducing circuit size and cost. The new design will provide two rejection bands with two different controllable bandwidths. Also, it can be used to realize a single bandstop filter with the ability to tune and increase the bandwidth.

Spurline filter is a microstrip bandstop filter that is used to moderate bandwidths on the order of 10% [51]. It provides many advantages compared to other types of microstrip filters. It has significantly lower radiation compared to conventional shunt stub and coupled filter types [51]. It has a suitable compact structure that enables it to be easily embedded in the microstrip antenna edges without increasing the overall filter size [51].

The inherently compact characteristics of the spurline section can be utilized to approach a good rejection performance band without any increase in structure size [52]. Spurline 77

section can also be utilized for a second resonance frequency to accomplish dual bands

[50]. Furthermore, using stepped impedance resonators (SIRs) has many advantages in microstrip filter structure designs. They are a suitable choice for various structures, harmonic suppression, controlling structure parameters and creating miniaturization filter structures [52]. Recently, stepped impedance resonators have been used to reduce the size of the filter without any penalty of changing the quality factor [52]. According to [26], the resonators' length can be reduced by 24% or more while using single SIR instead of using two parallel connected stubs. The compact structure design of spurline section and stepped impedance resonator can be achieved for both single band and dual-band bandstop filter. This chapter will focus on the design methodology of the compact bandstop filter for single and dual-bands with advantages for both designs.

3.2 Single band bandstop filter

The bandstop filter will be designed using spurline section and stepped impedance resonator at 2.4 GHz. The bandwidth is 20%, impedance of 50 Ohm, and at least 15 dB insertion loss at bandwidth. The advanced design system (ADS) will be used as a simulation software. Figure 3.1 shows the lumped component circuit of the bandstop filter using ADS.

Figure 3.1 Bandstop filter using Lumped Components.

FR-4 substrate has been selected to be used for designing a bandstop filter. The substrate has a relative dielectric constant ε while substrate thickness in length units is h =

60 mil. The filter design has a characteristicr = 4.25 impedance of a microstrip line of

. The thickness of the copper line is T = 0.5mil with a dielectric loss of TanDZc ==

500.02. Ohm All element values for maximally flat low pass filter prototypes can be defined for a

3 order N=3 to be transferred as bandstop filter elements. The filter can be designed based on bandstop lumped element components which utilize capacitors and inductors concerning the LCR model of microwave transmission lines.

3.2.1 Theoretical design of bandstop filter and design simulation

To design a bandstop filter (BSF), we should start with a lowpass maximally flat filter circuit. Figure 3.2 shows the lumped component circuit of the low pass filter with order number three (N = 3).

Figure 3.2 Lumped circuit for the low-pass filter using ADS.

All components that are used in the above lumped circuit should be calculated and determined.

With , , , ,

푅0 = 푔0 = 1 퐿1 = 푔1 퐶2 = 푔2 퐿3 = 푔3 푅퐿 = 푔4 = 1 According to [1], all the previous characteristics of the proposed bandstop filter will be determined and calculated for the low-pass maximally flat filter. Table 3.1 will be used to identify the elements of the low-pass filter that will transform it into bandstop filter.

Table 3-1 Element Values table for maximally flat low-pass filter [1].

The values of the elements of the low-pass filter are: , , ,

, . Table 3.2 will be used to transform푅0 = 푔 all0 = low-pass 1 퐿1 = components 푔1 퐶2 = 푔 to2

퐿bandstop3 = 푔3 filter푅퐿 = components. 푔4 = 1

Table 3-2 Prototype filter transformations [1].

The element values of the maximally flat low-pass filter can be converted in a such a way as to be bandstop filter values, which is achieved by using table 3.2. The fractional bandwidth of the prototype low pass filter is given by [1]

휔2 − 휔1 ∆ = = 0.2 휔0 Where , and the impedance-scaled is as follows:

푅0 = 50 ≠ 1 , , , ′ ′ 퐶 ′ 퐿 = 푅0퐿 퐶 = 푅081푅 = 푅0 푅퐿 = 푅0

According to [1], the series inductors of the low-pass prototype are converted into parallel LC circuits having element values given by

, (9) ′ ∆퐿푘 ′ 1 퐿푘 = 휔0 퐶푘 = ∆휔0퐿푘 Combined with the impedance-scaled:

, (10) ′ ∆푅0퐿푘 ′ 1 퐿푘 = 휔0 퐶푘 = ∆휔0푅0퐿푘 The shunt capacitor of the low-pass prototype is converted into series LC circuits having element values that are given by

, (11) ′ ∆퐶푘 ′ 1 퐶푘 = 휔0 퐿푘 = 휔0∆퐶푘 Combined with the impedance-scaled:

, (12) ′ ∆퐶푘 ′ 푅0 퐶푘 = 휔0푅0 퐿푘 = 휔0∆퐶푘 The impedance-scaled and frequency-transformed element values of the circuit in figure

3.1, calculated using the previous formulas of the low-pass filter at 2.4 GHz are:

′ ∆푅0퐿1 0.2 × 50 × 1 퐿1 = = 9 = 0.6631 푛퐻 휔0 2휋 × 2.4 × 10

′ 1 1 퐶1 = = 9 = 6.6315 푝퐹 ∆휔0푅0퐿1 0.2×2휋×2.4× 10 × 50 × 1

′ 푅0 50 퐿2 = = 9 = 8.2893 푛퐻 휔0∆퐶2 2휋 × 2.4 × 10 × 0.2 × 2

′ ∆퐶2 0.2 × 2 퐶2 = = 9 = 0.5305 푝퐹 휔0푅0 2휋 × 2.4 × 10 × 50 82

′ ∆푅0퐿3 0.2 × 50 × 1 퐿3 = = 9 = 0.6631 푛퐻 휔0 2휋 × 2.4 × 10

′ 1 1 3 9 퐶 = 0 0 3 = = 6.6315 푝퐹 Now, by using ADS∆휔 simulation푅 퐿 0.2×2휋×2.4×software, we verify10 results× 50 as× shown 1 in figure 3.3

Figure 3.3 Low-pass maximally flat filter with lumped elements.

Figure 3.4 shows the bandstop filter result that was achieved by using the transformations of low-pass filter elements.

Figure 3.4 Bandstop filter using ADS.

3.3 Compact Design for a single band bandstop filter

The new compact design which incorporates a spurline section with a stepped impedance resonator will be accomplished using the same lumped element theory of designing conventional bandstop filter at 2.4 GHz. The spurline section will be designed based on the coupled line method. Thus, the first step in our compact design consists of using a coupled line methodology to determine the spurline section at 2.4 GHz. As the second step, the bandstop filter will be designed using stepped impedance resonator SIR at the same center frequency. Finally, the spurline section and stepped impedance resonator will be combined by means of the microstrip transmission lines in order to approach the final compact design for a single band and dual-band bandstop filter.

3.3.1 Spurline Filter Design

The novel design will utilize a coupling line method to design a spurline section for the bandstop filter, then combine it with a SIR at the same center frequency of 2.4

GHz. According to [1], the spurline section of the bandstop filter at 2.4 GHz can be derived as:

(13) 2 푍0푒 = 푍0[1 + 퐽푍0 + (퐽푍0) ] (14) 2 푍0표 = 푍0[1 − 퐽푍0 + (퐽푍0) ]

Where and are the line impedance for the even-mode and odd-mode respectively.

Narrowband푍0푒 bandstop푍0표 filters can be made with cascaded coupled line sections. The filter

can be designed by calculating the image impedance and propagation constant of the equivalent circuit [60]. They must be equal to those of the coupled line section for θ =

π/2, which will correspond to the center frequency of the bandstop response. Equations

(13) and (14) are utilized for even-mode and odd-mode line impedances to derive the characteristics of the filter elements that transfer to the coupled line section. represents the admittance inverter that shows the necessary turns ratio , and it canJZ0 be determined by using equations (15), (16) and (17), according to N [1]. = TheJZ0 design of bandstop filters will be achieved if the impedance of the short-circuited series stub is infinity when . The bandstop filter design of coupled line section can be

푝표 created using equations푙 = 푉 /4푓 (15), (16) and (17).

(15) 휋∆ 푍0퐽1 = √ 2푔1 (16) 휋∆ 푍0퐽푛 = For n = 2,3, … . , N, 2√푔푛 − 1푔푛 (17) 휋∆ 푍0퐽푁+1 = √ 2푔푁푔푁 + 1 Where is the characteristic impedance and is the fractional bandwidth.푍0 The even- and odd-mode characteristic∆= impedances (푤1 − 푤2 for)/푤 each0 section of this design are found from equations (13) and (14). Figure 3.5 shows the procedure for the design and development of the bandstop filter based on coupled line section. It consists of the spurline section that is put together according to the coupled line method.

Figure 3.5 Development of the spurline section using coupled line method.

The design of the spurline filter procedure was developed by using coupled line sections as shown in Figure 3.5 (a). One section of that design will be converted to match the structure of a conventional spurline which is illustrated in Figure 3.5 (b). Finally, a conventional spurline design that consists of two identical parallel conductors was completed at 2.4 GHz which is shown in Figure 3.6 (a), according to [53] and [51].

Figure 3.6 (a) illustrates the area A that presents a section gap and that was designed by using an additional calculated length to the spurline section. According to figure 3.6 (b) and reference [50] the equivalent circuit of a spurline section is based on LCR circuit elements.

Figure 3.6 Spurline filter. (a) coupled line section (b) equivalent circuit of the spurline filter [50].

The spurline section was developed based on LCR simple design that is shown in Figure

3.6 (b). All circuit parameters can be found by using equations (18), (19) and (20) and according to [54].

(18)

푅 = 2푍0(1/|푆21| − 1) |푓 = 푓0 (19) 2 2 √0.5(푅 + 2푍0) − 4푍0 퐶 = 2.83휋푍0푅∆푓 (20) 1 퐿 = 2 4(휋푓0) 퐶 87

All the previous equations will be used to design a spurline bandstop filter at 2.4 GHz with N = 3 and the 0.5 dB equal-ripple response as seen in table 3-3. The bandwidth of the coupled line filter is 10 %, and the characteristic impedance is .

푍0 = 50Ω Table 3-3 Element values for equal-ripple low-pass filter [1].

By using the above table, we can determine the element values g1 = 1.5963, g2 = 1.0967 and g3 = g1 for the coupled line filter. The admittance inverter can be determined using equations (15), (16) and (17) which allow us to compute theJZ 0necessary turns ratio

N = JZ0

휋∆ 휋 × 0.1 푍0퐽1 = √ = √ = 0.3137 2푔1 2 × 1.5963 By using equation (16) the can be determined as

푍0퐽푛2 88

휋∆ 휋 × 0.1 푍0퐽푛2 = = = 0.1187 2√푔(푛 − 1)푔푛 2√1.5963 × 1.0967

휋 × 0.1 휋 × 0.1 푍0퐽3 = = = 0.1187 2√푔2. 푔3 2√1.0967 × 1.5963 The value of can be determined using equation (17) as the following

푍0퐽4 = ∆×0.1 푍0퐽4 √2×(1.5963)(1)(1) = 0.3137 Now, all the above values will be calculated by equations (13) and (14), which values will be assumed by and (the line impedance for the even-mode and odd-mode).

푍0푒 푍0표

2 푍0푒1 = 푍0[1 + 퐽1푍0 + (퐽1푍0) ] = 50 [ 1 + 0.3137 + ] 2 (0.3137)

푍0푒1 = 70.61 Ω

2 푍001 = 푍0[1 − 퐽1푍0 + (퐽1푍0) ] = 50 [ 1 - 0.3137 + ] 2 (0.3137)

푍001 = 39.24 Ω Then by using ADS, we add and values from the previous calculation to determine the values of the width푍0푒 and length푍00 of the spurline section (W, L) as shown in the figure 3.7.

Figure 3.7 Coupled line structure for the bandstop filter.

By using MACLIN from ADS, we find the values of the spurline section according to the coupled line method as

푤1 = 0.625 × 3 = 1.875 푚푚

푤2 = 0.25 × 3 = 0.75 푚푚

푠 = 0.125 × 3 = 0.375 푚푚 Figure 3.8 shows the spurline section which utilizes coupled line methodology for designing bandstop filter at 2.4 GHz, with all its values.

Figure 3.8 Spurline section using coupled line method.

Figure 3.9 shows the conventional structure of spurline section with the simulation filter that is based on ADS. Figure 3.10 shows the spurline bandstop filter result at 2.4 GHz.

Figure 3.9 Spurline bandstop filter. (a) conventional structure (b) simulation design.

Figure 3.10 Simulation result for the spurline bandstop filter.

3.3.2 Bandstop filter using stepped impedance resonator (SIR)

The design of bandstop filter utilizing stepped impedance resonator starts by transferring low-pass filter to a bandstop filter using table 3-2. The bandstop filter with a cutoff frequency of 2.4 GHz and a characteristic impedance of 50 Ω will be realized by using stepped impedance topology. The insertion loss of the proposed filter will be 15 dB at 3 GHz. By using figure 3.11, we can find the required order for the maximally flat filter that can satisfy appropriate insertion loss at 3 GHz for the proposed filter at 2.4

GHz.

Figure 3.11 Attenuation versus normalized frequency for maximally flat prototype filter [1].

; = 0.25 휔 3 |휔푐| − 1 = 2.4 − 1 From the above figure we found that the attenuation = 6 dB and the order number of the proposed designed filter is N = 3. 92

All the element values of the proposed filter can be determined by using table 3-1 at N =

3. The element values are: = , and . The lumped component circuit of the low-pass푔1 = filter 1 퐿 can1 be푔2 determined= 2 = 퐶2 by 푔3 = 1 = 퐿3

(21) 푍0푔 L = 휔푐 (22) 푔 C = 푍0휔푐

푍0푔1 50 × 1 퐿1 = = 9 = 3.3 푛퐻 휔푐 2휋 × 2.4 × 10

푔2 2 퐶2 = = 9 = 2.65 푝퐹 푍0휔푐 50 × 2휋 × 2.4 × 10

푍0푔3 퐿3 = = 퐿1 = 3.3 푛퐻 Figure 3.12 shows the lumped component휔푐 circuit for a low-pass filter that was used to approach the bandstop filter design.

Figure 3.12 Low-pass filter using ADS.

All the lumped components that are used to design the above low-pass filter will be transferred to a bandstop filter lumped circuit by means of table 3-2.

(23) 푔1∆푍0 퐿1 = = 퐿3 휔0 (24) 1 퐶1 = = 퐶3 휔0푔1∆푍0 (25) 푍0 퐿2 = 0푔2∆ 휔 (26) 2 2 푔 ∆ 퐶 = 0 0 휔 푍 1 × 0.1 × 50 퐿1 = 퐿3 = 9 = 0.33푛퐻 2.4 × 10 × 2휋

1 C1 = C3 = 9 = 13.263 pF 2π × 2.4 × 10 × 1 × 0.1 × 50

50 퐿2 = 9 = 16.58 푛퐻 2.4 × 2휋 × 10 × 2 × 0.1

2 × 0.1 퐶2 = 9 = 0.265 푝퐹 2.4 × 2휋 × 10 × 50

Figure 3.13 Bandstop filter with a circuit of the lumped components.

The simulation result of the bandstop filter design in the above figure is shown in figure

3.14.

Figure 3.14 Bandstop filter result using lumped components.

From the above design, we found that the bandwidth value is approximately the same for the filter calculation and the ADS simulation when .

95 ∆= 10% = 0.1

Bandwidth in calculation is 2.4

× 0.1 = 0.24 퐺퐻푧 Bandwidth in simulation is 2.53

− 2.28 = 0.25 퐺퐻푧 The impedance characteristics of the microstrip transmission line are and ° 0 푙 .To find out the dimension values (W, L) of the transmission lines,푍 we= compute50 them퐵 = ° 90by:

and Ω ° 퐵푙 = 44 푍ℎ = 130 and Ω ° 퐵푙 = 34.4 푍푙 = 15 By using an ADS program to transfer the lumped components, that are used for the bandstop filter, to microstrip transmission line, we found that; (W = 2.977 mm, L = 17.28 mm). Figure 3.15 shows the transferring of the characteristic impedance element from lumped component to transmission line structure.

Figure 3.15 Bandstop filter using microstrip transmission lines.

According to [1], the dimension values of the inductor and the capacitor in the above figure can be determined and transferred as transmission lines. The inductor can be 96

replaced by using a short-circuit stub of length and characteristic impedance L. In the same way, the capacitor also can be replaced 퐵 by푙 using open-circuited stub of and

푙 characteristic impedance1/C. When the value of is less than , we can assume퐵 that; ° . Using the scaling퐵푙 equations,45 we can calculate the electrical푍푙 = 15 표ℎ푚 length 푎푛푑 of 푍theℎ =inductor130 표ℎ푚 section and the electrical length of the capacitor.

(27) 퐿푅0 훽푙 = 푍ℎ (28) 퐶푍푙 훽푙 = Where is the filter impedance and L and C푅 0are the normalized element values of the low-pass푅 0 prototype filter. and represent the highest and lowest characteristic impedance. 푍ℎ 푍푙

2 × 50 ° 퐵푙 ( 푖푛푑푢푐푡표푟) = = 0.76 푟푎푑 = 44 , 130Ω 130 × 2.05

2 × 15 ° 퐵푙 ( 푐푎푝푎푐푖푡표푟) = = 0.6 푟푎푑 = 34.4 , 15Ω 50 × 2.05 The characteristic values of (W, L) can be determined by using the above scaling equation as

and Ω ° 퐵푙 = 44 푍ℎ = 130 and Ω ° 퐵푙 = 34.4 푍푙 = 15

푔2푍0 2 × 50 ° 퐵푙 ( 푖푛푑푢푐푡표푟) = = = 0.37 푟푎푑 = 21.5 , 13Ω 푍ℎ × 2.05 2.05 × 130

푔2푍푙 2 × 15 ° 퐵푙 ( 푐푎푝푎푐푖푡표푟 ) = = = 0.29 푟푎푑 = 16.77 , 15°Ω 푍0 × 2.05 2.05 × 50 For the Inductor: W = 0.292 mm and L = 9.06 mm.

For the Capacitor: W = 15.35 mm and L = 6.10 mm.

Figure 3.16 (a) shows the layout of the bandstop filter using SIR while (b) shows the transformation method for the values of the inductor and capacitor to be integrated into a system of transmission lines.

Figure 3.16 (a) bandstop filter layout, (b) converting inductor and capacitor to the transmission line.

Figure 3.17 shows the simulation design for the bandstop filter using stepped impedance resonator SIR at 2.4 GHz.

Figure 3.17 Bandstop filter using stepped impedance resonator SIR.

In the above figure (a) is the ADS simulation of bandstop filter using SIR while (b) is the

SIR modification that will be used in the new compact bandstop filter that incorporates spurline and stepped impedance resonator at 2.4 GHz.

Figure 3.18 shows the simulation result for the bandstop filter using stepped impedance resonator.

Figure 3.18 bandstop filter result using stepped impedance resonator SIR.

According to the previous procedure, the compact filter design of bandstop filter is developed by using two types of methodology; spurline section and stepped impedance resonator (SIR). The conventional spurline filter was designed at 2.4 GHz then it was combined with the stepped impedance resonator at the same desired cutoff frequency.

The main advantage of the new compact filter is in allowing us to control the bandwidth of the proposed filter. Also, it is a suitable compact structure which serves as a reduced- size filter with a good rejection band performance. Figure 3.19 shows the compact filter design for a single bandstop filter at 2.4 GHz. As a result of this new compact design, we have a filter that can be tuned and controlled by using tuning elements for both single band design and dual-band filter design.

Figure 3.19 Compact Bandstop filter design using spurline and SIR.

The above figure shows compact filter design that was achieved by using a spurline section and a stepped impedance resonator. The specifications of the spurline section are shown in figure 3.20 while figure 2.21 shows the simulation result of the compact filter using ADS.

100

Figure 3.20 Compact bandstop filter using spurline & stepped impedance resonator.

The design of the spurline filter implements a narrow band at 2.4 GHz. Embedding a stepped impedance resonator at the same center frequency offers a controllable rejection band performance. The stepped impedance resonator provides a varying capacitance and a varying inductance. Thus, the bandwidth can be increased or decreased by changing the capacitance of the stepped impedance capacitor. Figure 3.22 shows the comparison between a spurline filter and the new compact filter.

Figure 3.21 Comparison result for the bandstop filter.

101

Figure 3.22 shows the performance difference between the spurline filter and the new compact filter design based on the bandwidth values.

Figure 3.22 Comparison between conventional spurline filter and new compact filter.

The new compact filter shows a better rejection performance with a wider bandwidth compared to a conventional spurline filter. The bandwidth can be calculated as (

in both designs. The bandwidth of the new compact filter is 1.6 GHz while휔 2 the−

휔bandwidth1) of the conventional spurline filter is limited to 1.2 GHz for the same center frequency. The bandwidth of the compact spurline filter has been improved by using a stepped impedance resonator.

3.3.3 Analysis of the compact design of a single band filter

The new compact design of bandstop filter can be accomplished by many different methodologies. In this section, we are going to consider three mythologies; lumped

102

element components, microstrip transmission lines and EM simulation design. Figure

3.23 shows the equivalent circuit of spurline filter that uses lumped element components.

The equivalent circuit of a spurline filter can be calculated using the S-Parameters. The

RLC circuit is calculated for spurline filter using its S-parameters and according to the following expressions [50], [55].

(29) 1 푅 = 2푍0 ( − 1)| |푆21| 푓=푓0 (30) 푓0 푄푟푒푠 = ∆푓3푑퐵 (31) 푄푟푒푠 퐶 = 2휋푓0푅 (32) 1 2 퐿 = 0 Where f0 is the resonant frequency (minimum(2휋푓 value) 퐶 of S21), and f3dB is the bandwidth in which the minimum value of S21 is increased 3 dB. All the components of the proposed spurline filter are calculated by ADS as shown in figure 3.23. The S-parameters array for this quadrupole is given based on [56] as follows

푍01 + 푍푅퐿퐶 − 푍02 푍02 2 푍푅퐿퐶 + 푍01 + 푍02 푍푅퐿퐶 + 푍01 + 푍02 푆 = 푍02 푍01 + 푍푅퐿퐶 − 푍02 2 ( 푍푅퐿퐶 + 푍01 + 푍02 푍푅퐿퐶 + 푍01 + 푍02 )

푗휔푅퐿 푍푅퐿퐶 = 2 푅(1 − 휔 퐿퐶) + 푗휔퐿

푍01, 푍10302 = 50

The best choice for transmission line in ADS with a lossy /4 is to select a transmission line with /4; however, for the MATLAB we must use ideal /4 transmission line to calculate and simplify the MATLAB codes. In this case, transmission line has for the

0 resonant frequency, 50  for the characteristic impedance and 90 deg for the푓 electric length. The quadrupole is given by

−푗훽푙 푆 = ( −푗훽푙0 푒 ) 푒 0 휋 푓 훽푙 = ∙ 2 푓0

Figure 3.23 Spurline equivalent circuit using lumped element components.

We have used the same procedure and equations that we used previously for designing a spurline section. Figure 3.24 (a) shows the same filter design that uses microstrip transmission lines while figure 3.24 (b) shows the layout of the spurline section using EM simulation.

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Figure 3.24 (a) Spurline Filter Using Microstrip lines, (b) Filter layout.

Figure 3.25 shows the results of comparing all three methodologies that were used in the design of the 2.4 GHz bandstop filter.

Figure 3.25 Comparison Results of Bandstop Filter.

In the same way, figure 3.26 shows the equivalent circuit of the 2.4 GHz stepped impedance resonator filter. By using the same previous equations of RLC, we will find all

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components for the equivalent circuit of a stepped impedance resonator. The S- parameters array for this quadrupole for SIR design [56] are

푍02푍푅퐿퐶 − 푍01푍02 − 푍01푍푅퐿퐶 푍02푍푅퐿퐶 2 푍01푍02 + 푍01푍푅퐿퐶 + 푍02푍푅퐿퐶 푍01푍02 + 푍01푍푅퐿퐶 + 푍02푍푅퐿퐶 푆 = 푍02푍푅퐿퐶 푍02푍푅퐿퐶 − 푍01푍02 − 푍01푍푅퐿퐶 2 ( 푍01푍02 + 푍01푍푅퐿퐶 + 푍02푍푅퐿퐶 푍01푍02 + 푍01푍푅퐿퐶 + 푍02푍푅퐿퐶 )

1 푍푅퐿퐶 = 푅 + 푗 (휔퐿 − ) 휔퐶

푍01, 푍02 = 50

Figure 3.26 Equivalent Circuit of Bandstop Filter.

Figure 3.27 shows the filter design that uses microstrip transmission lines and the layout of the stepped impedance components.

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Figure 3.27 (a) Stepped impedance filter using Microstrip Lines, (b) Layout of the stepped impedance filter.

Figure 3.28 is a comparison among the three bandstop filter results (EM simulation, lumped element simulation and microstrip simulation) using stepped impedance resonator.

Figure 3.28 Comparison among the three bandstop filter results (EM simulation, lumped element simulation and microstrip simulation).

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Figure 3.29 shows both resonators in one compact filter design, a filter design for a single band using spurline section and stepped impedance resonator at 2.4 GHz.

Figure 3.29 Compact Bandstop Filter Design Using Spurline and Stepped Impedance Resonator.

The comparison results of the compact bandstop filter design using spurline and stepped impedance resonator are shown in figure 3.30.

Figure 3.30 Comparison Results of The Compact Bandstop Filter For A Single Band.

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According to figure 3.29, the parallel RLC circuit can be transformed using Norton’s theorem to be quarter-wavelength transmission line. It can be connected in series with a series RLC, shunt to the ground. The equivalent of the stepped impedance resonator is placed in cascade with this circuit, the new circuit will be as shown in figure 3.31.

Figure 3.31 Equivalent circuit with two shunt RLC resonators.

At the resonant frequency, both resonators have a resistive component and can be deducted for the first resonator as

2 1 − 휔 퐿1퐶1 푍1 = 푅1 − 푗 휔퐶1 In the same way it can be deducted for the second resonator as

2 1 − 휔 퐿2퐶2 푍2 = 푅2 − 푗 휔퐶2 And for both resonators as

푍1푍2 푍 = 푍1+푍2

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At  =0, both Z1 and Z2 are resistive and the total resistance is lower. It implies a higher insertion loss which can be expressed as

푅1푅2 푅 = 푎푡 휔 = 휔0 푅1+푅2 Based on that, we have two series RLC placed in parallel and the Q-factor is presented next [57]

1 1 1 = + 푄푇 푄1 푄2

휔0퐿1 휔0퐿2 푄1 = 푄2 = 푅1 푅2 Which means, the new compact filter gives a lower Q-factor with a greater bandwidth.

According to [1], and based on the binomial matching transformer, designing multi sections at the same center frequency will provide as flat as possible a signal response. The bandwidth of the proposed filter can be controlled and increased by inserting more sections at the desired center frequency. This is called a maximally flat filter, and it is determined for an N-section transformer by setting the first derivatives of equal to zero at the center frequency. The filter response can푁 − be 1 obtained by determining|Г(휃)| the reflection coefficient as

(33) −2푗휃 푁 So, the magnitude of the reflectionГ( coefficient휃) = 퐴(1 +is 푒 )

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(34) −푗휃 푁 푗휃 −푗휃 푁 |Г(휃)| = |퐴||푒 | |푒 + 푒 | 푁 푁 = 2 |퐴||푐표푠| In achieving a multi-section transformer, we should have N degrees of design freedom each of which corresponding to a which is the impedance for the nth characteristic. The multi-section filter can be described푍푛 by using the following reflection formula [1]:

−푗2휔푇 −푗4휔푇 −푗2푁휔푇 Г푖푛(휔) = Г0 + Г1푒 + Г2푒 + ⋯ + Г푁푒

푁 −푗2푛휔푇 = ∑ Г푛푒 푛=0 Where is the propagation time through one section. According to the previous 푙 푇 = 푉푃 equation, we should define N independent design equations to be used in determining the

N characteristic impedances referred to collectively as .

푍푛 Moreover, designing a bandstop filter with a single-section directional coupler affords only a limited bandwidth response; however, to increase this bandwidth we must cascade many sections, which is what we did in our design [58]. Adding more sections to the proposed휆/4 filter will increase bandwidth and provide more flat coupling characteristics to the proposed filter. The main theory behind this method is that the small amount of total incident power will be totally coupled at each inserted section. Which means that the total incident power will be transferred from the transmission section to the loaded section.

Also, it is important to note that there is an odd number of cascaded sections. The coupling of these sections can be expressed as [58]

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푀−1 (35)

퐶0 = 푠푖푛 휃 [∑ 2퐶푖 푐표푠(푁 − 2푖 + 1)휃 + 퐶푀] Where M = (N + 1)/2, and N is the푖=1 total number of odd-sections in the coupler, is the electrical length and stands for the coupling contributed in each section ( 휃 The overall desired coupling퐶푖 will be nominated by determining all couplings of each푖 ≠ section. 0).

Then, we should calculate the even-mode and odd-mode characteristic impedances for each section. Finally, all these sections will be cascaded and physically connected for the desired center frequency [58].

3.4 Dual-band bandstop filter using spurline & stepped impedance resonator

The novel design of the dual-band bandstop filter will utilize a coupling line method to design a spurline section for the first rejection band, then it will be combined with an SIR for the second frequency band. The dual-band design combines two controllable traditional approaches into one filter: spurline section and stepped impedance resonator at 2.4 and 3.5 GHz respectively. A prototype filter circuit is designed and developed according to synthesis equations. The same design procedure and equations that are used for a single band filter will be applied again to develop dual-band filter. This novel design will provide two controllable bandstop filter responses. Each response can be tuned and controlled separately. Figure 3.32 shows the layout of the compact dual- band bandstop filter at 2.4 GHz and 3.5 GHz.

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Figure 3.32 Dual-band bandstop filter using spurline and stepped impedance

resonator.

The design of the compact filter consists of a spurline filter at 2.4 GHz combined with a stepped impedance resonator filter at 3.5 GHz. The spurline section was developed based on equations (13) and (14). Spurline section provides narrowband bandstop filter that uses a cascaded coupled line section. Filters can be designed by calculating the image impedance and propagation constant of the filter equivalent circuit. The lumped elements of an equivalent circuit must be equal to those of the coupled line section for value of θ = π/2, that correspond to the desired filter center frequency. Both equations

(13) and (14) are used for even-mode and odd-mode line impedance in order to find out the characteristics of the filter elements to be transferred to the coupled line section. In these equations stands for the admittance inverter that shows the necessary turns ratio

N = and canJZ 0 be found by using equations 15, 16 and 17. In a proposed filter, the impedanceJZ0 of the short-circuit series stub is infinity when . Figure 3.33 shows

푙 = 푉푝표/4푓

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the design of the spurline bandstop filter at 2.4 GHz to be used for the compact dual-band bandstop filter while figure 3.34 shows the simulation result.

Figure 3.33 Spurline bandstop filter at 2.4 GHz.

Figure 3.34 Simulation result of spurline bandstop filter.

In the same previous procedure of designing a stepped impedance resonator, the second band will be achieved by using SIR and will be based on equations (27) and (28) 114

to find the inductor and the capacitor at 3.5 GHz. For designing a bandstop filter using stepped impedance resonator at 3.5 GHz, we are going to repeat same previous procedures. The component of the proposed filter can be found as follows:

, , , ,

푅0 = 푔0 = 1 퐿1 = 푔1 = 1 퐶2 = 푔2 = 2 퐿3 = 푔3 = 1 푅퐿 = 푔4 = 1 To convert to Stop-band filter, with 휔2−휔1 ∆ = 휔0 = 0.2 The equivalent circuit of stop-band filter is as follows:

Figure 3.35 Equivalent Circuit of BSF using SIR.

The impedance-scaled and frequency-transformed element values for the circuit of the figure above using the following formulas:

′ ∆푅0퐿1 0.2 × 50 × 1 퐿1 = = 9 = 0.45473 푛퐻. 휔0 2휋 × 3.5 × 10

′ 1 1 퐶1 = = 9 = 4.54728 푝퐹. ∆휔0푅0퐿1 0.2×2휋×3.5× 10 × 50 × 1

′ 푅0 50 2 9 퐿 = 0 2 = = 5.68411 푛퐻. 휔 ∆퐶 2휋 × 3.5 ×11510 × 0.2 × 2

′ ∆퐶2 0.2 × 2 퐶2 = = 9 = 0.36378 푝퐹. 휔0푅0 2휋 × 3.5 × 10 × 50

′ ∆푅0퐿3 0.2 × 50 × 1 퐿3 = = 9 = 0.45473 푛퐻. 휔0 2휋 × 3.5 × 10

′ 1 1 퐶3 = = 9 = 4.54728 푝퐹. ∆휔0푅0퐿3 0.2×2휋×3.5× 10 × 50 × 1

Figure 3.36 Lumped element circuit of BSF.

Figure 3.37 shows the transforming of lumped element to transmission line filter.

Figure 3.37 Bandstop filter using transmission-lines.

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With , to fabricate easily we select the minimum width of ′ ′ transmission퐿1 = 퐿3 line= 11which.36825 is 0.15 푛퐻 mm, 5.9055 mil ( ).

푍0 = 153.084 Ω

′ 9 −9 ′ 휔퐿1 2휋 × 3.5 × 10 × 11.36825 × 10 푍푖푛 = 푗푍0 tan 훽푙 = 푗휔퐿1 = tan 훽푙 = = 푍0 153.084

= 1.633. 1.021 rad = 58.518 degree. So, l = 8.344 mm.

훽푙 = With select ′ ′ 퐶1 = 퐶3 = 0.18189 푝퐹 , 푍0 = 25 Ω.

1 1 ′ 푍푖푛 = −푗푍0 cot 훽푙 = −푗 ′ ⟺ cot 훽푙 = ′ ⟺ tan 훽푙 = 푍0휔퐶1. 휔퐶1 푍0휔퐶1

9 −12 = 25 × 2휋 × 3.5 × 10 × 0.18189 × 10 = 0.1 Ω. 0.0997 rad = 5.713 degree. So, l = 0.71188mm, w = 8.191mm.

훽푙 = With , to fabricate easily we select the minimum width of transmission ′ line which퐿2 = is 5. 0.1568411 mm푛퐻 = 5.9055 mil ( ).

푍0 = 153.084 Ω

′ 9 −9 ′ 휔퐿2 2휋 × 3.5 × 10 × 5.68411 × 10 푍푖푛 = 푗푍0 tan 훽푙 = 푗휔퐿2 ⟺ tan 훽푙 = = 푍0 153.084

= 0.8165. 0.6847 rad = 39.233degree. So, l = 5.594mm.

훽푙 = With select ′ 퐶2 = 0.36378푝퐹 , 푍0 = 25 Ω. 117

1 1 ′ 푍푖푛 = −푗푍0 cot 훽푙 = −푗 ′ ⟺ cot 훽푙 = ′ ⟺ tan 훽푙 = 푍0휔퐶2 휔퐶2 푍0휔퐶2 . 9 −12 = 25 × 2휋 × 3.5 × 10 × 0.36378 × 10 = 0.2 0.1974 rad = 11.31 degree. So, l = 1.4093mm, w = 8.191mm. Figure 3.38 shows

훽푙the =simulation design of bandstop filter at 3.5 GHz using stepped impedance resonator.

Figure 3.38 Bandstop filter using SIR.

Figure 3.39 shows the design of stepped impedance resonator at 3.5 GHz using transmission-lines with only one resonator.

Figure 3.39 Stepped impedance resonator at 3.5 GHz.

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The simulation result of bandstop filter at 3.5 GHz using SIR is shown in figure 3.40.

Figure 3.40 Bandstop filter at 3.5 GHz using SIR.

Figure 3.41 shows the compact dual-band bandstop filter design at 2.4 GHz and 3.5 GHz.

Figure 3.41 Compact dual-band bandstop filter.

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The characteristic impedance of the transmission line is Ω. The dual-band bandstop filter dimensions and specifications from port 1 to Zport0 = 250 are W 2.97767mm and L 17.280mm. Spurline section specifications are , = ,

=and . The dimensions of the steppedW1 =impedance 1mm W 2 resonator= 1.47mm wereS as = follows:0.5mm the Lvalues = 17 of.3mm the inductor are and ; and the capacitor values are and W =. 0.15mm The simulationL = result 5.59mm of the proposed dual- band bandstopW = filter 8.19mm using spurlineL = 1.40mm and stepped impedance resonator is shown in figure

3.42.

Figure 3.42 Dual-band bandstop filter using spurline & SIR

The first rejection band was achieved by spurline section at 2.4 GHz while the second rejection band was achieved by stepped impedance resonator at 3.5 GHz with different bandwidths and different rejection band levels.

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CHAPTER 4

TUNABLE DUAL-BAND BANDSTOP FILTER USING SPURLINE AND STEPPED IMPEDANCE RESONATOR

4.1 Introduction

The tuning methodology of electronic circuits for RF communication systems become an attractive field of research because a single tuning-methodology device can handle multiple frequency bands. Using tunable devices for reconfigurable circuits helps to reduce cost while maintaining circuit performance. The tunability process in the microwave filters has used many different approaches. Some researchers used a new type of circuit structure by improving the architecture of the proposed circuit. Other researchers used tunable devices such as p-n junction diode varactors, Micro Electro

Mechanical Systems (MEMS), liquid crystal cells and ferroelectric varactors [22].

Barium Strontium Titanate capacitors (BSTs) are one of the most attractive ferroelectric materials used in the development of electronically tunable microwave circuits [42]; they became more popular because of their low cost of fabrication and because they can be integrated with a variety of substrates. Moreover, they provide a suitable handling power capability and fast tuning speed compared to other tunable elements, which makes them desirable in research and development despite their high dielectric loss and low tunability [20]. There are two different methods for designing a

BST varactor; one is by metal-insulator-metal form (MIM), the other by interdigital capacitor form (IDC) [20], [42]. The BST varactors that are designed by IDC usually exhibit a small capacitive tunability due to additional fringing capacitance. Also, they are

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less sensitive to the applied DC voltages. These characteristics make them a suitable choice when a lower capacitance and simpler fabrication process are desired. This chapter is concered mainly with the tunability of dual-band bandstop filter that is implemented by using p-n junction varactor diodes and ferroelectric materials [20].

The design of a dual-band bandstop filter (DBBSF) will incorporate tunability by using two types of tuning material: varactor diodes and BST capacitors. The p-n junction varactor diodes will be used to tune dual-band filter at 2.4 GHz and 3.5 GHz, the ferroelectric material will be used to tune the dual-band filter at 2 GHz and 3.5 GHz.

4.2 Principles of designing RF filters based on coupled-lines

Designing filters based on coupled transmission lines is very important in RF microwave systems. They are extensively used in the design of the directional couplers and electric filters. Using rectangular waveguides in directional couplers was a very good development for microwave systems because of their ability of separating forward and backward transmitted waves. One of the most important innovative devices that was based on directional couplers was the reflectometer. This device enabled engineers and developer to envision other important devices such as power detectors and network analyzers [58].

The theory of coupling lines was developed by Hans Albrecht Bethe while he was working at the Massachusetts Institute of Technology during World War II [58]. The design of waveguide directional couplers was the result of studies in coupling mechanisms which utilized small apertures between two waveguides. In addition, the

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rectangular waveguides were commonly used in designing directional couplers, TEM structures and coaxial lines. The coupled TEM or quasi-TEM structures become very important and extensively used following the innovation of the printed circuits board machine. This technology enabled the design of a cost-effective compact filter by using microstrip and stripline structures. The theory of coupled line is practical and had wide impact on designing digital and telecommunication circuits. The design of microwave filter has four-port sections based on the coupled line method and matching networks.

Figure 4.1 shows two uniform symmetrical TEM coupled lines which terminated with a resistive load. This equivalent circuit shows two modes for the coupled line method that is known as either even-mode or odd-mode, depending on the electric field patterns of each section mode [58].

Figure 4.1 symmetrical and equivalent circuit of even-mode and odd-mode of coupled line structure [58].

Figure 4.2 shows the coupled line structure with its Z-parameters of the four-ports.

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Figure 4.2 General structure of a coupled line filter using transmission lines [58].

Most microwave filters utilize a two-port circuit to describe the four terminals of the coupled line circuit. The two-port filter has two different types of termination filter structure: short circuit and open circuit with different characteristics. Figure 4.3 (a,b) shows two structures of coupled line section with their transmission line equivalents. The first structure is commonly used to approach the performance of a bandpass filter while the second structure is used for lowpass filter. The short circuit in the second structure can be replaced by a quarter-wavelength open circuit in order to eliminate via-holes [58].

The design of bandpass filter using this coupled line structure can be remodeled to approach the performance of bandstop filter.

Figure 4.3 Coupled line sections (a) bandpass structure, (b) lowpass structure [58].

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The above structures of open-circuited and short-circuited coupled lines are used to transfer filter networks from lumped element prototype to distributed equivalents using transmission lines. All lumped element components will be replaced with their equivalent transmission lines. Then, the network of the transmission lines will be converted to a coupled line equivalents to approach the final design of the distributed filter which can be easily printed by using printed circuit board technology. The Z-parameters description of the coupled line structures will be as follows and according to [58].

(36) 푍푐1푐표푡ℎ(훾푐푙) 푍휋1푐표푡ℎ(훾휋푙) 푍11 = 푍22 = + (1 − 푅푐/푅휋) (1 − 푅휋/푅푐) (37) 2 2 푅푐 푍푐1푐표푡ℎ(훾푐푙) 푅휋푍휋1푐표푡ℎ(훾휋푙) 푍33 = 푍44 = + (1 − 푅푐/푅휋) (1 − 푅휋/푅푐) (38) 푍푐2푐표푡ℎ(훾푐푙) 푍휋1푐표푡ℎ(훾휋푙) 푍13 = 푍31 = 푍24 = 푍42 = − 푅휋(1 − 푅푐/푅휋) 푅푐(1 − 푅휋/푅푐) (39) 푅푐푍푐1 푅휋푍휋1 푍14 = 푍41 = 푍23 = 푍32 = − (1 − 푅푐/푅휋)푠푖푛ℎ(훾푐푙) (1 − 푅휋/푅푐)푠푖푛ℎ(훾푐푙) (40) 푍푐1 푍휋1 푍12 = 푍21 = + (1 − 푅푐/푅휋)푠푖푛ℎ(훾푐푙) (1 − 푅휋/푅푐)푠푖푛ℎ(훾푐푙) (41) 2 2 푅푐 푍푐1 푅휋푍휋1 푍34 = 푍43 = + (1 − 푅푐/푅휋)푠푖푛ℎ(훾푐푙) (1 − 푅휋/푅푐)푠푖푛ℎ(훾푐푙) (42) 1 2 푅푐 = [(푎2 − 푎1) + √(푎2 − 푎1) + 4푏1푏2] 2푏1 (43) 1 2 푅휋 = [(푎2 − 푎1) − √(푎2 − 푎1) + 4푏1푏2] 2푏1

푎1 = 퐿11퐶11 + 퐿푚퐶푚

2 22 22 푚 푚 푎 = 퐿 125퐶 + 퐿 퐶

푎2 = 퐿22퐶22 + 퐿푚퐶푚

푏2 = 퐿22퐶푚 + 퐿푚퐶11 Where and are the mode propagation constants. Also , , and are the characteristic훾푐 impedance훾휋 for each line. The symmetrical lines,푍푐1 푍휋1 푍푐2 푍휋2, are the impedances of the two modes which correspond to the even and odd푅푐 modes.= −푅휋 According= 1 to

[58] , the previous equations can be simplified as

(44) 푍0푒푐표푡ℎ(훾푒푙) 푍0표푐표푡ℎ(훾표푙) 푍11 = 푍22 = 푍33 = 푍44 = + 2 2 (45) 푍0푒푐표푡ℎ(훾푒푙) 푍0표푐표푡ℎ(훾표푙) 푍13 = 푍31 = 푍42 = 푍24 = − 2 2 (46) 푍0푒 푍0표 푍23 = 푍32 = 푍14 = 푍41 = − 2푠푖푛ℎ(훾푒푙) 2푠푖푛ℎ(훾표푙) (47) 푍0푒 푍0표 푍12 = 푍21 = 푍43 = 푍34 = + Where is the characteristic impedance of2푠푖푛ℎ the even-mode(훾푒푙) 2푠푖푛ℎ and (훾표푙) is the characteristic impedance푍0푒 of the odd-mode. , stand for even-mode and푍0표 odd-mode of the propagation constant and is the훾 length푒 훾표 of the coupled line section. Based on the above

Z-parameters and according푙 to [58], the Z-parameters of the two coupled line sections can be determined into two types:

Type A,

(48) 푍0푒 + 푍0표 푍11 = 푍22 = 푐표푡ℎ(훾푙) 2 126

(49) 푍0푒 − 푍0표 1 푍21 = 푍12 = Type B, 2 푠푖푛ℎ(훾푙)

(50) 2 푍0푒 + 푍0표 1 (푍0푒 − 푍0표) 푍11 = 푐표푡ℎ(훾푙) − 푐표푡ℎ(훾푙) 2 2 (푍0푒 + 푍0표)

2푍0푒푍0표 = 푐표푡ℎ(훾푙) 푍0푒 + 푍0표

(51) 2 푍0푒 + 푍0표 1 (푍0푒 − 푍0표) 1 푍22 = 푐표푡ℎ(훾푙) − 2 2 (푍0푒 + 푍0표) 푠푖푛ℎ(훾푙)푐표푡ℎ(훾푙)

2 2푍0푒푍0표 1 (푍0푒 − 푍0표) = + 푡푎푛ℎ(훾푙) 푍0푒 + 푍0표 푡푎푛ℎ(훾푙) 2(푍0푒 + 푍0표)

(52) 2 푍0푒 − 푍0표 1 1 (푍0푒 − 푍0표) 1 푍21 = 푍12 = − 2 2 푠푖푛ℎ(훾푙) 2 (푍0푒 − 푍0표) 푠푖푛ℎ(훾푙)

2푍0푒푍0표 1 = 푍0푒 + 푍0표 푠푖푛ℎ(훾푙) Figure 4.4 shows the structure of the parallel coupled line resonator with its equivalent circuit.

Figure 4.4 (a) Parallel coupled line structure, (b) equivalent circuit [59].

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To verify the equivalent circuit of parallel coupled line in the above figure by using

ABCD matrices, we should use the characteristics of its even-mode and odd-mode (

as [59]

푍0푒, 푍0표)

2 2 2 푍0푒 + 푍0표 (푍0푒 − 푍0표) − (푍0푒 + 푍0표) 푐표푠 휃 (53) 푐표푠휃 푗 퐴 퐵 푍0푒 − 푍0표 2(푍0푒 − 푍0표)푠푖푛휃 [ ] = 퐶 퐷 푎 2푠푖푛휃 푍0푒 + 푍0표 푗 푐표푠휃 The ABCD matrix of [the 푍electrical0푒 − 푍0표 length in the 푍transmission0푒 − 푍0표 line can be ]determined with its characteristic impedance as 휃

푍0

(54) 푐표푠휃 푗푍0푠푖푛휃 [푗푠푖푛휃 ] 푐표푠휃 The ABCD matrix of the J- inverter in 푍the0 above figure can be expressed as

(55) −푗 0 [ 퐽 ] Based on the above, the ABCD matrix of− the푗퐽 entire0 J-inverter circuit can be found by cascading the ABCD matrices of three element blocks as follows

(56) 푐표푠휃 푗푍0푠푖푛휃 −푗 푐표푠휃 푗푍0푠푖푛휃 퐴 퐵 0 [ ] = [푗푠푖푛휃 ][ 퐽 ][푗푠푖푛휃 ] 퐶 퐷 푎 푐표푠휃 푐표푠휃 푍0 −푗퐽 0 푍0 2 2 2 0 1 0 푐표푠 휃 (퐽푍 + 0) 푠푖푛휃푐표푠푛휃 푗 (퐽푍 푠푖푛 휃 − ) 퐽푍 퐽 = 1 2 2 1 푗 ( 2 푠푖푛 휃 − 푗푐표푠 휃) (퐽푍0 + ) 푠푖푛휃푐표푠푛휃 [ 퐽푍0 퐽푍0 ] 128

By using the equations matrix of the even-mode and the odd-mode with the description of the J-inverter matrix, we can simplify them as

(57) 푍0푒 + 푍0표 1 푐표푠휃 = (퐽푍0 + ) 푠푖푛휃푐표푠휃 푍0푒 − 푍0표 퐽푍0 (58) 2 2 2 2 (푍0푒 − 푍0표) − (푍0푒 + 푍0표) 푐표푠 휃 2 2 푐표푠 휃 = 퐽푍0 푠푖푛 휃 − 2(푍0푒 − 푍0표)푠푖푛휃 퐽 (59) 2푠푖푛휃 1 2 2 2 0푒 0표 = 푠푖푛 휃 − 퐽푐표푠 휃 according to which we can푍 determined− 푍 퐽푍 the0 characteristic impedance of the even-mode and odd-mode of the parallel coupled line filter to be

(60) 2 2 푍0푒 1 + 퐽푍0푐푠푐휃 + 퐽 푍0 = 2 2 2 푍0 1 − 퐽 푍0 푐표푡 휃 (61) 2 2 푍0푒 1 − 퐽푍0푐푠푐휃 + 퐽 푍0 2 2 2 0 = knowing the value of , 푍where sin1 − 퐽 푍0 and푐표푡 cos휃 , we can simplify the above equation into 휃 = 휋/2 휃 ≈ 1 휃 ≈ 0

(62) 2 2 0푒 0 0 0 푍 = 푍 (1 + 퐽푍 + 퐽 푍 ) (63) 2 2 푍0표 = 푍0(1 − 퐽푍0 + 퐽 푍0 ) 4.3 Principles of designing microstrip filters using coupled-lines

According to the previous analysis of the coupled lines method, we can summarize the principle of designing coupled line microstrip filters. These filters are constructed by using cascaded sections known as coupled resonators. The design of bandstop filter can be realized using these resonators by modifying the even-mode and odd-mode 129

characteristic impedances of each resonator. Each resonator section will be designed using a quarter-wavelength at the desired center frequency. The length of these resonators must be adjusted to compensate for fringing fields because of the open ends and the quasi-TEM propagation [58]. In some cases, we must have a small gap between the conductors of some resonant elements. This might make it too diffecult to be printed and fabricated using PCB technology. We can use high-coupling resnoators in a stripline configuration with broadside coupling to avoid such issues [58]. The structure design of the coupled-line filters relies on the equivalent models of the open-circuited and short- circuited resonators. Figure 4.5 shows both resonators with their equivalent distributed models.

Figure 4.5 Open- and short-circuited resonators of microstrip coupled line filters [58].

The open-circuited resonators do not require ground via-holes, which makes them an attractive choice for designing coupled-line filters. They are designed using series stub

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with the approximate equivalent circuit of a series-tuned LC resonator while short- circuited shunt stub has an approximated equivalent circuit of a parllel-tuned LC resonator. Then, the design of bandpass filter or bandstop fitler will be achieved by convertig the lumped filter elements that provide the desired frequency response to a configureation containing either series or shunt resonators. That means the design of a coupled-line filter starts based on the lumped elements filter. The Z-parameters of the open-circuited coupled line filter can be expressed as [58]

(64) 푍11 푍21 푗 푍0푒푐표푡(휃푒) + 푍0표푐표푡(휃0) 푍0푒푐푠푐(휃푒) − 푍0표푐푠푐(휃0) [ 21 22] = − [ ] Where 푍 and 푍 represent2 the푍0푒 even-mode푐푠푐(휃푒) − 푍and0표푐푠푐 odd-mode(휃0) 푍 0푒repeectivaly.푐표푡(휃푒) + 푍For0표푐표푡 (휃0) , the previouse 푒 표expression can be simplfied into 휃푒 ≈ 휃표 ≈ 훽푙

(65) 푍11 푍21 푗 (푍0푒 + 푍0표)cot(훽푙) (푍0푒 − 푍0표)csc(훽푙) [ ] = − [ ] The coupled line푍21 resonator푍22 is separated2 (푍0푒 − by 푍0표 an)csc( impedance훽푙) (푍 0푒inverter+ 푍0표 )whichcot(훽푙 should) be added to the Z-parameter network as follows:

(66) ′ 푍1 푍2 푍11 = + 푗푡푎푛(훽푙) 푗푡푎푛(훽푙) (67) ′ 푍1 푍3 푍22 = + 푗푡푎푛(훽푙) 푗푡푎푛(훽푙) (68) ′ ′ ′ 1 ′ 푍12 = 푍21 = √(푍22 − ′ ) 푍11 푌22 Where

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2 (69) 푍 1 + 푗푍 tan(훽푙) 3 1 푗푡푎푛(훽푙) 푍 ′ = 푍1 + 22 푍2 푌 푍1 + 푗 푡푎푛(훽푙) 푗푡푎푛(훽푙) That can lead to 푗푡푎푛(훽푙)

(70) ′ 2 2 푍1 + 푍2 푍12 = √−푍1 [푡푎푛 (훽푙) + 1] 2 푡푎푛 (훽푙)(푍1 + 푍2)

푍1 = −푗 sin (훽푙) In the above equations is the characteristic impedance of the inverter section while

are the characteristic푍1 impedances of the resonator stubs. Considering the previous

푍equations,2, 푍3 the characteristic impedances of the inverter with the coupled line stubs in terms of even-mode and odd-mode can be found as follows:

For the open-circuited coupled lines

(71) 푍0푒 − 푍0표 푍1 = 2 (72)

For the short-circuited coupled lines 푍2 = 푍3 = 푍0표

(73) 푌0푒 − 푌0표 푌1 = 2 (74)

In the case of asymmetrical coupled 푌lines2 = 푌the3 = above 푌0표 equations become (71) and (72) for open-circuited-couple lines

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(75) 1 푎 푎 푏 푏 푍1 = √(푍0푒 − 푍0표)(푍0푒 − 푍0표) 2 (76) 1 푎 푎 푍2 = (푍0푒 − 푍0표) − 푍1 2 (77) 1 푏 푏 푍3 = (푍0푒 − 푍0표) − 푍1 And for short-circuited coupled lines 2the equations are

(78) 1 푎 푎 푏 푏 푌1 = √(푌0푒 − 푌0표)(푌0푒 − 푌0표) 2 (79) 1 푎 푎 푌2 = (푌0푒 − 푌0표) − 푌1 2 (80) 1 푏 푏 푌3 = (푌0푒 − 푌0표) − 푌1 Where a and b express the first and second2 lines with different widths. Figure 4.6 shows the coupled line resonator of bandstop filter with its equivalent configurations.

Figure 4.6 Short-circuited bandstop coupled line resonator with its equivalent circuit [58].

The above figure shows the relationship between the stub equivalent circuit and the coupled line impedances for the bandstop filter that can be expressed as

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(81) 2 푍0표 = 푍1 + 푍2 ± √푍2 + 푍1. 푍2 (82) 2 푍1 + 푍2 ± √푍2 + 푍1. 푍2 푍0푒 = 푍1 2 1 2 1 2 Where , stand for the even-mode푍 + 2푍 ± and 2√ 푍 odd-mode2 + 푍 . 푍 characteristic impedances repectivaly.푍0푒 푍 0표 is the characteristic impedance of the the inverter of the coupled transmission 푍line1 and is the characteristic impedance of the short-circuited stub [58].

푍2 4.4 Principles of designing a microstrip filter using stepped impedance resonator (SIR)

For the second band of our proposed filter, we are using a stepped impedance resonator. The lowpass filter performance can be achieved by stepped impedance resonator based on Richard’s transformation. This filter consists of a cascade connection between low-and high impedance of electrically short microstrip transmission lines. The lumped component elements of lowpass filter can be transferred to transmission lines. A short low-impedance transmission line can be approximated by using shunt capacitor connected to the ground while a short high-impedance transmission line is approximated by using a series inductor [58]. Stepped impedance resonators are used extensively in RF microwave systems because of their simple design implementation. They can be easily designed by using printed circuit board technology. Designing stepped impedance filters starts with determination of lowpass prototype filter. All lumped elements of lowpass filter will be transferred to the proposed filter such as bandpass or bandstop filters. The electrical lengths of low impedance and high impedance sections can be determined according to the following equations [58]. Figure 4.7 shows the configuration of a half-

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wavelength open-circuited transmission line using stepped impedance resonator with a different ratio of the characteristic impedances [59].

Figure 4.7 layout of a half-wavelength open-circuited transmission line using SIRs [59].

The resonances for a half-wavelength occur when

(83)

Where stands for the total electrical휃푇 = 휃2 +length 2휃1 +of휃 the2 = resonator푛휋 while is the number of the resonant휃푇 modes. The configuration of stepped impedance resonators푛 is shown in figure 4.8 with its equivalent circuit.

135

Figure 4.8 Configuration of SIR with its equivalent circuit [59].

In the above figure and are left and righ sides at the center of the SIR and must satisfy 푌퐿 푌푅

(84)

For the left side 푌퐿 + 푌푅 = 0

(85) 푌1푡푎푛휃1 + 푌2푡푎푛휃2 푌퐿 = 푗푌1 푌1 − 푌2푡푎푛휃1푡푎푛휃2 (86) 푅푧푡푎푛휃1 + 푡푎푛휃2 = 푗푌1 Where is the ratio of two characteristic푅푧 − impedances 푡푎푛휃1푡푎푛휃 that2 can be expressed as

푅푧 (87)

푅푧 = 푌1/푌2 = 푍2/푍1 136

Since both sides are symmetrical, then, the expression of both sides can be given as 푌퐿 = 푌푅

(88)

In the same way the 2푗푌expression1(푅푧 − 푡푎푛휃of the1푡푎푛휃 input2 )(admittance푅푧푡푎푛휃1 + 푡푎푛휃 of the2) =left 0 side to the right side can be derived as 푌푖푛

(89) 2(푅푧푡푎푛휃1 + 푡푎푛휃2)(푅푧 − 푡푎푛휃1푡푎푛휃2) 푌푖푛 = 푗푌2 2 2 2 That means, the resonant푅푧 (condition1 − 푡푎푛 휃lead1)(1s to − 푡푎푛 휃2) − 2(1 + 푅푧)푡푎푛휃1푡푎푛휃2

푌푖푛 = 0 Which implies

(for odd-mode frequencies)

푅푧 − 푡푎푛휃1푡푎푛휃2 = 0 (for even-mode frequencies)

푅푧푡푎푛휃1 + 푡푎푛휃2 = 0 The total electrical length of the SIR at the first resonance is written as

(90) −1 푅푧 휃푇 = 2휃1 + 2푡푎푛 ( ) Figure 4.9 shows the resonance condition for the SIR푡푎푛휃 at the1 first resonance [59].

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Figure 4.9 The resonant condition of the SIR at the first resonance [59].

From reference [58], the low-impedance of the SIR lines is expressed by

(91) 푍푙표푤 훽푙 = 푔푘 푍0 푘 = 1,3,5, … While, the high-impedance of the SIR lines is expressed by

(92) 푍0 훽푙 = 푔푘 푍ℎ푖푔ℎ 푘 = 2,4,6, … Where and are the characteristic impedances of both low and high impedance

푙표푤 ℎ푖푔ℎ lines. 푍 stands 푍for the normalization impedance while are the values of the lowpass prototype푍0 filter components [58]. 푔푘

4.5 Analysis of the compact design of a dual-band filter

The compact design of the dual-band bandstop filter will be achieved using coupled line synthesis equation for microstrip lines for the first rejection band at 2.4 GHz.

Similarly, the stepped impedance resonator that use open-circuited transmission lines will be used for the second rejection band at 3.5 GHz.

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4.5.1 Simulation of a compact dual-band filter using ADS

In this section we will compare the three prementioned methodologies for the new filter design. The comparison results will use lumped circuit elements, transmission lines and EM simulation of the compact dual-band filter. These three methodologies will be achieved according to the previous work analysis of both coupled-lines filter and SIR filters. Figure 4.10 shows a dual-band filter using lumped elements.

Figure 4.10 Dual-band filter using lumped element components.

In the same way, figure 4.11 shows the same filter design by using transmission lines.

Figure 4.11 Compact dual-band filter using transmission lines.

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Figure 4.12 shows the comparison results between all three technologies.

Figure 4.12 Comparison of the dual-band filter.

Figure 4.13 shows the EM response of a dual-band filter response that will be used to accomplish the simulation design of the MATLAB simulation.

Figure 4.13 EM simulation result of a dual-band filter. 140

4.5.2 Simulation of a compact dual-band filter using MATLAB

For the MATLAB work, the equivalent circuits of spurline section and stepped impedance resonator in figure 4.10 will be used by cascaded quadrupoles. The S-

Parameters ( will be used to find out the filter response by using MATLAB.

, representS11and the S21 insertion) loss and return loss of the proposed filter and they are

Sgiven11 S 21as [22]

(93)

Where is the load power and 퐼퐿 is= the −20 sourcelog ( power.푃푙/푃푖푛)

푃푙 푃푖푛 (94)

Where T is the transmission coefficient푅퐿 = −and20 islog given (푇) by:푑퐵

(95) 푍퐿 + 푍0 2푍퐿 푇 = 1 + Г = 1 + = Where is the voltage reflection coefficient 푍and퐿 + expressed 푍0 푍퐿 + as 푍 0

− (96) 0 퐿 0 푉+ 푍 + 푍 Г = 0 = 퐿 0 The equivalent circuit of the spurline has푉 two푍 quadrupoles:+ 푍 a parallel RLC and λ/4 ideal transmission line. The equivalent circuit of the stepped impedance is a shunt serial RLC.

The MATLAB simulation will use T-matrix (T1, T2 and T3) to characterize each quadrupole. The source and load impedance are Z1 and Z2 are 50Ω. The components of

RLC equivalent circuit of the spurline at 2.4 GHz are:

while the shunt equivalent circuit values푟1 = for1400 the. 74 stepped, 푐1 = −12 −9 2.18푒 푎푛푑 푙1 = 1.92푒 141

impedance at 3.5 GHz are: . The MATLAB −12 −9 result can be achieved by using푟2 = Z-parameters 1.47, 푐2 = 0.7푒 of spurline 푎푛푑 section푙1 = 2. 93in 푒figures (4.5 and 4.6).

Similarly, figure 4.8 will be used along with its Z-parameters to determine the filter response of a second band for a stepped impedance resonator. According to [1], [22] the insertion loss and return loss of the proposed filter, and by using S matrix can be found as

− (97) 푖 푖푗 푉+ 푆 = | + 푉푗 푉푘 =0 푓표푟 푘≠푗

− (98) 1 11 푉+ ∴ 푆 = | + 푉1 푉2 =0

− (99) 2 21 푉+ 푆 = | + 1 푉2 =0 The transmission line has a frequency dependence푉 as a function of its electrical length.

So, in order to make a MATLAB calculation, we should use the matrix calculations using quadrupoles. In this way the filter can be simulated using MATLAB codes. Thus, each equivalent circuit can be represented by a quadrupole because there are two incoming waves ( and ) and two outgoing waves, ( and ). Figure 4.14 shows the quadrupole푎1 for the푎 2circuit elements [60], [61]. 푏1 푏2

Figure 4.14 Circuit Element for quadrupole [60].

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The following matrix shows the S-parameters with the description of the filter losses in reflection and in transmission which are calculated based on [56], [60].

(100) 푏1 푆11 푆12 푎1 ( ) = ( )( 2) 푏2 푆21 푆22 푎 (101) 푏1 푆11 = | 푎1 푎2=0 (102) 푏1 푆12 = | 푎2 푎1=0 (103) 푏2 푆21 = | 푎1 푎2=0 (104) 2 22 푏 푆 = 2|푎1=0 Using S-parameters directly in the cascaded푎 quadrupole circuit is complex because is the wave transmitted for the output and is the reflected one which, as a result of푏 2the reflection becomes the inverse in the input.푎2 For that reason, the total S array is not the array product of each quadrupole array. Therefore, we can use T scattering transfer which is defined as follows [60], [61]

(105) 푎1 푇11 푇12 푎2 ( 1) = ( )( 2) 푏 푇21 푇22 푏 (106) 푎1 푇11 = | 푎2 푏2=0 (107) 푎1 푇12 = | 푏2 푎2=0 (108) 푏1 푇21 = | 143푎2 푏2=0

(109) 1 22 푏 푇 = 2|푎2=0 We can calculate the T-parameters using the푏 S-parameters by

푆11푆22 − 푆12푆21 푇11 = − 푆21

푆11 푇12 = 푆21

푆22 푇21 = − 푆21

1 푇22 = 푆21 The total T array can be determined by

푇 = 푇1 ∙ 푇2 Figure 4.15 shows the cascading of two quadrupoles.

Figure 4.15 Two cascaded quadrupoles [60], [61].

When we find out the total T array, the S array can be determined easily by the next transformation 144

푇12 푇11푇22 − 푇12푇21 푆11 = 푆12 = 푇22 푇22 1 푇21 푆21 = 푆22 = − 푇22 푇22 Figure 4.16 shows the filter result of the dual-band bandstop filter at 2.4 and 3.5 GHz using MATLAB.

Figure 4.16 MATLAB filter result of the dual-band bandstop filter.

4.6 Tuning a single-band bandstop filter

Tuning bandstop filter provides many advantages in RF communication systems. It can be used to implement the performance of the filter over a wide range of frequencies.

In some cases, the tuning devices are utilized to apply a rejection band with a different range of frequencies with lower cost and less effort. To accomplish this goal, p-n junction varactor diodes will be used to apply tunability to single band bandstop filter and dual-

145

band bandstop filter. The simulation and measurement results will be provided according to synthesis equations with a fabrication circuit design.

4.6.1 Tunable spurline filter using p-n varactors

A spurline tunable design is achieved by embedding a varactor diode at the gap G as shown in figure 4.17. Spurline length can be increased by controlling the voltage which tune the end gap in the microstrip filter design [50]. The following equations show the operation of the spurline resonator that is controlled by the odd mode [50].

(110)

퐶1 = 퐶푒푣푒푛/2 (111)

퐶12 = (푐표푑푑 − 퐶1)/2 (112)

표푑푑 푝표 ∞ The range of the capacitance will ∆퐿be =changed 퐶 × 푉when× 푍the varactor diode is inserted into the structure gap. Spurline length will be changed and controlled based on the voltage change. An SMV1233 Varactor∆L Diode (Sky-Works Co.) has been utilized to apply tunability to the proposed filter with a spurline section. The tunability result of the spurline filter was achieved by embedding the p-n junction diode into the gap of the transmission line. Figure 4.17 shows the layout of the spurline tunable filter which was achieved by using ADS and modeling of the varactor diode.

Figure 4.17 Spurline tunable filter using p-n varactor diode. 146

The simulation result of the spurline tunable filter is shown in figure 4.18. It shows the scattering parameter of the spurline filter ( ) of the designed filter at 2.4 GHz. The center frequency has been tuned by the control푆11, 푆 21voltage to be in the range 1.586 to 2.541

GHz.

Figure 4.18 Simulation result for the spurline filter.

4.6.2 Tunable stepped impedance resonator filter using p-n varactors

The bandstop filter was achieved by using a stepped impedance resonator at 3.5

GHz for a single band. The varactor diode will be embedded into stepped impedance resonator layout to increase the value of the proposed filter capacitance. The capacitance value of the varactor diode will be controlled when a DC voltage value is increasing. The initial capacitance value of the varactor diode at 0 V is 5.08 pF. This value will be decreased inversely with increased voltage. Figure 3.38 shows the tunability result of the stepped impedance resonator filter accomplished by using a varactor diode with a DC control voltage. Figure 4.19 shows the layout of the stepped impedance resonator

147

embedded with the varactor diode while figure 4.20 shows the tunable result of stepped impedance resonator filter at 3.5 GHz.

Figure 4.19 Tunable bandstop filter using SIR.

Figure 4.20 Result of tuning SIR filter using varactor diode.

The center frequency can be tuned from 3.5 GHz to 4.02 GHz by loading a p-n junction varactor diode fbetween0 the inductor and capacitor as seen in figure 4.20.

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4.7 Tunable of a compact DBBSF using a modeling of varactor diodes

This section will show the tunability of the new compact dual-band filter using lumped element circuit, transmission lines and EM layout of the proposed filter. Same previous design procedure will be applied with some changes by using ADS momentum to get matching between results and to avoid shifting in center frequency responses.

Figure 4.21 will show the lumped element circuit while figure 4.22 shows the transmission line circuit of the DBBSF. An SMV1233 Varactor Diode (Sky-Works Co.) has been utilized to apply tunability to the proposed filter with a spurline section and stepped impedance resonator.

Figure 4.21 Tuning of lumped element circuit of the dual-band filter.

Figure 4.22 Tuning of microstrip lines dual-band filter.

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Figure 4.23 shows the same varactor diodes that are embedded to the momentum layout of the dual-band filter while figure 4.24 shows the comparison results of all three methodologies.

Figure 4.23 Tuning the momentum layout design of the dual-band filter.

Figure 4.24 Comparison of tuning dual-band filter using varactor diodes.

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It is very important to mention that; the dimensions of the simulation designs will be changed corresponding to the embedding of the varactor diodes. The varactor diodes have a capacitance value at 0 V before applying any voltage which might change the center frequency response. For that reason, we must take this into account while designing our proposed filter. Figure 4.25 shows the MATLAB tunable result of the proposed filter using varactor diodes with variable capacitance values.

Figure 4.25 MATLAB tunable result of the dual-band bandstop filter.

4.8 Fabrication of a tunable dual-band bandstop filter using varactor diodes

The design of the dual-band bandstop filter was fabricated using microstrip transmission lines and printed on the FR-4 substrate with the same specifications that were mentioned before. Two varactor diodes will be embedded into spurline section and stepped impedance resonator as seen in figure 4.26. The fabricated design of the tunable dual-band bandstop filter was achieved with new different configurations considering 151

dimensions of the varactor diodes and as seen in figure 4.26. The new dimensions

bypass of the spurline and SIR of the DBBSF Care given as shown in Table 4.1.

Figure 4.26 Tunable dual-band bandstop filter using varactor diodes.

Table 4-1 Measurements for dual-band bandstop filter.

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The length value of the characteristic impedance (L) of the previous layout can be reduced and adjusted by using ADS momentum features. A capacitor was

bypass installed into a spurline section as a DC blocked capacitor, and its valueC is 1.2 pF. Section

A shows the specifications of the spurline section at 2.4 GHz based on the coupled line method. Section B shows the specification of the stepped impedance resonator at 3.5

GHz. Both methodologies were combined and fabricated in one compact filter as shown in figure 4.27. The compact filter design reduced the proposed filter size with a good rejection band performance. The fabrication filter design of dual-band bandstop filter is shown in figure 4.27 with p-n junction varactors loaded to a spurline section and a stepped impedance resonator. Figure 4.28 shows the tunability result (S21) of dual-band bandstop filter at 2.4 GHz and 3.5 GHz.

Figure 4.27 Fabrication design of tunable dual-band bandstop filter.

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Figure 4.28 Measurement result (S21) of the dual-band tunable filter.

Figure 4.29 shows the tunability result (S11) of the dual-band bandstop filter.

Figure 4.29 Measurement result (S11) of the dual-band filter.

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Table 4.2 shows the tunability results when the filter design is controlled by changing voltage values that are applied to the varactor diode.

Table 4-2 Measurement results of tunable dual-band bandstop filter.

The center frequency changed from 2.1GHz to 2.4 GHz by embedding a varactor diode into the spurline푓 0 filter. By embedding same varactor diode to SIR, the center frequency changed from 3.5 GHz to 4.48 GHz.

푓0 4.9 Ferroelectric capacitors

The dual-band bandstop filter can be tuned by using many different methods and tunable devices. In this section the focus is on using ferroelectric capacitors to tune the frequency of the dual-band bandstop filter at 2 GHz and 3.5 GHz. Ferroelectric capacitor with such a thin-film Barium Strontium Titanate (BST) and a voltage-dependent permittivity provide low-cost tunable component compatible with existing manufacturing methodologies. The BST capacitors offer relative ease of integration and embedding process with RF circuits. They become one of the most important tunable materials for

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microwave devices [62]. They have many advantages compared to other tunable materials such as small size, ease of handling voltage polarity, independent tuning characteristics, low voltage operation and high-quality factor [22].

4.9.1 Fabrication of the ferroelectric-based capacitors

The BST (Ba0.5Sr0.5TiO3) will be used as a tunable ferroelectric-based capacitor to be embedded into dual-band bandstop filter design. The fabrication of BST capacitors is realized by using silicon or sapphire substrates. The ultrasonic cleaning is used to degrease the wafers with acetone and methanol. The substrate of the proposed capacitor will have been degreased completely in a vacuum oven for 30 minutes. The sample added with many different layers such as platinum films with a thickness of 200 nm and adhesion layer of titanium with a thickness of 20 nm. These layers are deposited on a sapphire wafer by DC magnetron sputtering in an argon environment. The bottom electrodes of the proposed capacitor will be fabricated utilizing standard photolithographic technique and ion milling. Then, the capacitor films will be deposited using spin-on Metal Organic Decomposition (MOD) methodology. The films will be annealed in an oxygen environment at C for 30 minutes. The top electrode platinum ° film with a thickness of 200 nm will800 be deposited by DC magnetron sputtering and defined by photolithography and ion- milling as well. The area of the parallel plate of the proposed thin-film capacitor can be determined by the overlap area of the bottom and top electrodes [22]. The characteristics of the thin-film based capacitors can be determined by HP4275A LCR meter. The tunability of the BST capacitor can be defined as [22]:

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(113) 휀푟0 − 휀푟푏 푇푢푛푎푏푖푙푖푡푦 = = 100% Where is the dielectric constant at zero bias,휀푟0 and is the dielectric constant at the maximum휀푟0 bias [22]. The capacitive tunability of BST varactors휀푟푏 is defined as [19]:

(114) 퐶푚푎푥 − 퐶푚푖푛 퐶푎푝푐푖푡푖푣푒 푇푢푛푎푏푖푙푖푡푦 = = 100% where is the capacitive of BST varactor at 0-V퐶푚푎푥 bias; and is the capacitive that is obtained퐶푚푎푥 at non-zero DC bias. When the DC bias voltage 퐶 is푚푖푛 increased, the value of

will be decreased as well. Figure 4.30 (a) shows the cross section of the fabricated thin-film퐶푚푖푛 tunable capacitor, while figure 4.30 (b) shows the plan view of BST capacitor on Sapphire.

Figure 4.30 BST capacitor, (a) cross section (b) plan view of the capacitor [22].

Figure 4.31 shows the measurements of the fabricated BST capacitors. These capacitors were fabricated and measured for both low frequency filter and high frequency filter. The measurements show the ability of fabricating ferroelectric capacitor for many different

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tunability ranges. The fabricated BST capacitor samples show the variation of the tunability with a control voltage from to . At zero point, the capacitance of the BST capacitor will start at the maximum−5 푉 value+ 5 푉 . When we apply the voltage , the capacitance will start gradually to decrease to the퐶푚푎푥 value. Figure 4.32 shows 푉the푡 modeling measurements for the BST capacitors which 퐶have푚푖푛 been fabricated to find out an appropriate capacitor with a very low capacitance value to tune our proposed filter at 2

GHz and 3.5 GHz.

Figure 4.31 Measurements of the fabricated BST capacitors.

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Figure 4.32 Measurement of the BST modeling capacitors.

For our filter design, we have selected a BST capacitor that gives 1.4 pF to be used for low frequency band at 2 GHz. In the same way we have chosen a capacitor that gives 5.8 pF for the high frequency at 3.5 GHz. The compact dual-band filter has been refabricated to work at 2 GHz for the first rejection band and at 3.5 GHz for the second rejection band. For that reason, we have to fabricate a suitable BST capacitor that can be

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embedded into the filter. Figure 4.33 shows the fabricated BST capacitor for low and high frequency with its modeling results.

Figure 4.33 Fabrication and modeling results of the BST capacitors, (a) capacitor for low frequency (b) capacitor for high frequency.

Figure 4.34 shows the tunability variation of the BST capacitors with applied DC bias. Figure 4.34 (a) shows the modeling result with an applied voltage of the BST capacitor that was achieved by using ADS software. Figure 4.34 (b) shows the fabrication result of BST capacitor for the low frequency at 1.4 pF at 0 V. The result of the modeling part and fabrication design is a matching between the two, and they will be used to make a tunability for the low frequency at 2 GHz.

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Figure 4.34 BST tunability variation with applied voltage, (a) simulation modeling (b) fabrication capacitor.

The capacitors tunability is decreasing linearly with the increase of the applied voltage.

The maximum tunability approached 50% with applying voltage from 0 to 6 V.

4.10 Tunable of a compact DBBSF using a modeling ferroelectric capacitor

The new compact dual-band filter will be tuned by embedding BST capacitor modeling into lumped element circuit, transmission lines and EM layout of the proposed filter. Figure 4.35 shows the lumped element circuit while figure 4.36 shows the transmission line circuit of the DBBSF. BST modeling capacitors have been utilized to apply tunability to the proposed filter with a spurline section and stepped impedance resonator.

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Figure 4.35 Tuning of lumped element circuit of the dual-band filter.

Figure 4.36 Tuning of a transmission lines circuit of the dual-band filter.

Figure 4.37 shows the same modeling of BST capacitors that was embedded to the momentum layout of the dual-band bandstop filter while figure 4.38 shows the comparison results of all three methodologies.

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Figure 4.37 Tuning the momentum layout design of the dual-band filter.

Figure 4.38 Comparison of tuning dual-band filter using BST capacitor modeling.

For the previous circuits, we should consider the dimensions and configurations before and after inserting the capacitor modeling. The capacitor modeling has a capacitance value at 0 V which need to be considered to avoid signal shifting. Figure 4.39 shows the

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MATLAB tunable result of the DBBSF by using a BST capacitor modeling. This capacitor modeling was applied to the MATLAB configurations with variable capacitance values.

Figure 4.39 MATLAB tunable result of the dual-band bandstop filter.

4.11 Fabrication of a tunable dual-band bandstop filter using BST capacitors

The design of DBBSF will be calculated again to be fabricated and tuned by ferroelectric-material at 2 GHz and 3.5 GHz. Same layout in the figure 4.26 will be fabricated with different specifications and different dimensions. The characteristic impedance of the transmission line Ω. The dimensions and specifications from port 1 to port 2 are W = 2.97 mm andZ0 = L50 = 17.28 mm. Spurline section dimensions are

, , and the value of . The

Wdimensions1 = 1mm of W the2 = spurline 1.477mm gap S are = given0.5mm by L = 21.4 mm . The

W = 2.8126 mm and S = 0.5 mm 164

transmission line area that is under the gap and placed on lower transmission line has

W = 1.47 mm and L = 퐴12 mm. The transmission line of the has W = 1.4 mm and L = 1 mm. The dimensions of stepped impedance resonator are퐴1 as follows: the values of characteristics impedance from port 1 to port 2 are W = 2.977 mm and L = 17.280 mm.

The inductor dimensions are W = 0.15 mm and L = 5.59 mm. The capacitor dimensions are W = 8.19 mm and L = 1.39 mm. Figure 4.40 shows the dual-band bandstop filter frequency response at 2 GHz and 3.5 GHz utilizing spurline section and stepped impedance resonator.

Figure 4.40 Dual-band bandstop filter Response at 2GHz and 3.5GHz.

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The BST capacitors in figure 4.33 will be embedded into the microstrip layout of the

DBBSF to tune the proposed filter at 2 GHz and 3.5 GHz. Figure 4.41 shows the microstrip designed filter with the BST capacitors.

Figure 4.41 Fabrication of tunable DBBSF using BST capacitors.

Figure 4.42 shows the measurement of the S11 with the applied voltages from 0V to 6V.

Figure 4.42 Measured variation of S11 with frequency for various applied voltages for the DBBSF filter.

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Figure 3.43 shows the measurements of S21 with a frequency for various applied voltages of a dual-band filter from 0V to 6V. Figure 3.44 shows the scattering parameters

S11 and S21 for the proposed dual-band bandstop filter.

Figure 4.43 Measured variation of S21 with frequency for various applied voltages for DBBSF.

Figure 4.44 Tunable dual-band bandstop filter result using BST. 167

Table 4-3 Measurement results of tunable dual-band bandstop filter.

The above table shows the tunability range of using a BST capacitor with DC control voltage from 0V to 6V. The rejection first band filter that used a spurline section has been changed from 1.9 GHz to 1.99 GHz. Moreover, the second rejection band has been tuned and the center frequency changed from 3.3 GHz to 3.54 GHz.

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CHAPTER 5

CONCLUSION AND FUTURE WORK

5.1 Conclusion

In this dissertation we have designed a new circuit structure for bandstop filter using two different methodologies: spurline sections and stepped impedance resonator.

The novel design was simulated, fabricated and characterized. The expected performance of the bandstop filter was achieved for a single band and dual-band bandstop filter. In a single band, we used a compact structure to enhance and get wider bandwidth at 2.4 GHz.

For the dual-band, we have combined two methodologies to approach the performance of a dual-band bandstop filter at 2.4 GHz and 3.5 GHz with a practical and compact structure design. The new method provides good performance and good rejection level at the proposed low frequency and high frequency bands. We used p-n junction diode varactors and ferroelectric-materials to apply tunability for the dual-band filter. The experiment and measurement results show a good tunability performance for the proposed filter.

The center frequency of the first notch of DBBSF can be tuned from 2.1GHz to

2.4 GHz by embedding a varactor푓0 diode into the spurline filter. By embedding similar varactor diode to SIR, the center frequency of the second notch can be tuned from 3.5

GHz to 4.48 GHz. Similarly, the center frequency of a DBBSF푓0 can be tuned from 1.9

GHz to 1.99 GHz by embedding BST capacitor into푓0 the spurline filter. By embedding same capacitor to SIR, the center frequency can be tuned from 3.3 GHz to 4.54 GHz.

푓0 169

The new filter design has proven to be a good performance for a single bandstop filter and for dual-band bandstop filter. The fabricated filters show a good bandstop performance with a good tunability.

5.2 Future work

The design of a spurline section can be achieve using stepped impedance resonator instead of using coupled line method. In this way, we can avoid shifting in signal response if we apply tunable elements. The tuning elements can be embedded to the filter capacitor instead of using spurline transmission end-gap. This gap has a capacitance values that will change in conjunction with the new tuning materials.

In this work, we have applied tunability to the dual-band filter response; however,

I recommend to study how to introduce tunability into the filter bandwidth. Bandwidth is a very important parameter in RF filter characterization. Bandwidth can be tuned by studying the filter circuit structure or by involving tuning devices.

In addition, the spurline filter can be integrated with many different filter approaches other than stepped impedance resonators. It can be design with microstrip filters such as defected ground structure (DGS), split ring resonators and square patch resonators. It can be combined with many filter structures for a single band, dual-band and multi-bands.

The proposed filter design of this dissertation was achieved for dual-band bandstop filter and it can be used for bandpass filter, either for a single band or dual- band. In this filter structure we have used p-n varactor diodes and ferroelectric-materials 170

as tuning elements, but we can try other tunable components such as semiconductor devices, MEMS devices, lumped elements and liquid crystal materials.

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APPENDICES

A: MATLAB Code for S-Parameter of DBBSF Without Tuning

T11 = -(S11*S22-S21*S12)/S21 T12 = S11/S21 T21 = -S22/S21 T22 = 1/S21

The resultant T-matrix is calculated by

T = T1*T2*T3

The total S-matrix is calculated by

S11 = T12/T22 S12 = (T11*T22-T21*T12)/T22 S21 = 1/T22 S22 = -T21/T22

clear; clc;

Source and Load Impedance z01 = 50; z02 = 50;

Parallel RLC equivalent circuit for the spurline at 2.456GHz r1 = 1400.74; c1 = 2.18e-12; l1 = 1.92e-9;

Shunt serial equivalent circuit for the stepped impedance at 3.5GHz r2 = 1.47; c2 = 0.7e-12; l2 = 2.93e-9;

Initializing values fa = (1000e6:25e6:5000e6); S21 = zeros(1,length(fa)); S11 = zeros(1,length(fa)); for m = 1:length(fa) wa = 2*pi*fa(m); Impedance for the spurline z1 = 1i*r1*l1*wa/(r1*(1-wa^2*l1*c1)+1i*wa*l1);

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Calculation T matrix for spurline parallel RLC s11 = (z1+z01-z02)/(z01+z1+z02); s21 = 2*z01/(z01+z1+z02); s12 = s21; s22 = s11;

T1 = [-(s11*s22-s21*s12)/s21 s11/s21;-s22/s21 1/s21];

calculation T matrix for transmission line wres = 1/(2*pi*sqrt(l1*c1)); beta = 0.25/wres; s11 = 0; s21 = cos (beta*wa)-1i*sin(beta*wa); s12 = cos (beta*wa)-1i*sin(beta*wa); s22 = 0;

T2 = [-(s11*s22-s21*s12)/s21 s11/s21; -s22/s21 1/s21];

calculation T matrix for stepped impedance serial RLC z2= r2 + 1i*wa*l2 + 1/(1i*wa*c2); z2load=z2*z02/(z2+z02); s11 = (z2load-z01)/(z01+z2load); s21 = 2*z2load/(z01+z2load); s12 = s21; s22 = s11;

T3 = [-(s11*s22-s21*s12)/s21 s11/s21;-s22/s21 1/s21];

T matrix and S parameter calculations T = T1*T2*T3;

S11(m) = 20*log10(abs (T(1,2)/T(2,2))); S21(m) = 20*log10(abs(1/T(2,2))); end plot(fa,S11) hold on plot(fa,S21) axis ([1000e6 5000e6 -40 5]) grid;

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B: MATLAB Code for S-Parameter of DBBSF With Tuning by Varactor Diodes

T11 = -(S11*S22-S21*S12)/S21 T12 = S11/S21 T21 = -S22/S21 T22 = 1/S21

The resultant T-matrix is calculated by

T = T1*T2*T3

The total S-matrix is calculated by

S11 = T12/T22 S12 = (T11*T22-T21*T12)/T22 S21 = 1/T22 S22 = -T21/T22

clear; clc;

Source and Load Impedance z01 = 50; z02 = 50;

Varactor Diode Voltage vj = 5:2:13;

Parameters for the equivalent circuit of the varactor diode rs = 1.2; ls = 7e-10; cj = 5.08e-12./(1+vj/11.87).^6.43; cp = 8.1e-13;

Parallel RLC equivalent circuit for the spurline r1 = 4359.30; c1 = 2.737e-12; l1 = 1.218e-9;

Shunt serial equivalent circuit for the stepped impedance r2 = 1.47; c2 = 3.58e-13; l2 = 7.5e-9;

Initializing values fa = (1000e6:25e6:4000e6); 180

S21 = zeros(1,length(fa)); S11 = zeros(1,length(fa)); for m = 1:length(fa) for n = 1:length(vj) wa = 2*pi*fa(m); Impedance for the spurline zdiode = (rs + (1i*wa*ls) + 1/(1i*wa*cj(n))); zcp=1/(1i*wa*cp); zd = 1/(1/zdiode +1/zcp); z1 = 1/(1/r1+1/(1i*wa*l1)+(1i*wa*c1)+1/zd);

Calculation T matrix for spurline parallel RLC s11 = (z1+z01-z02)/(z01+z1+z02); s21 = 2*z01/(z01+z1+z02); s12 = s21; s22 = s11; T1 = [-(s11*s22-s21*s12)/s21 s11/s21;-s22/s21 1/s21];

calculation T matrix for transmission line wres = 1/(2*pi*sqrt(l1*c1)); beta = 0.25/wres; s11 = 0; s21 = cos (beta*wa)-1i*sin(beta*wa); s12 = cos (beta*wa)-1i*sin(beta*wa); s22 = 0;

T2 = [-(s11*s22-s21*s12)/s21 s11/s21; -s22/s21 1/s21];

calculation T matrix for stepped impedance serial RLC z2= zd + r2 + 1i*wa*l2 + 1/(1i*wa*c2); z2load=1/(1/z2+1/z02); s11 = (z2load-z01)/(z01+z2load); s21 = 2*z2load/(z01+z2load); s12 = s21; s22 = s11;

T3 = [-(s11*s22-s21*s12)/s21 s11/s21;-s22/s21 1/s21];

T matrix and S parameter calculations T = T1*T2*T2*T3*T2; S11(m,n) = 20*log10(abs (T(1,2)/T(2,2))); S21(m,n) = 20*log10(abs(1/T(2,2))); end end plot(fa,S11) hold on plot(fa,S21) axis ([1000e6 5000e6 -40 5]) grid; legend ('C1=5V','C2=7V','C3=9V','C4=11V','C5=13V')

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C: MATLAB Code for S-Parameter of DBBSF With Tuning by BST Capacitors

T11 = -(S11*S22-S21*S12)/S21 T12 = S11/S21 T21 = -S22/S21 T22 = 1/S21

The resultant T-matrix is calculated by

T = T1*T2*T3

The total S-matrix is calculated by

S11 = T12/T22 S12 = (T11*T22-T21*T12)/T22 S21 = 1/T22 S22 = -T21/T22

Rev. 2. Values of ferrocaps are changed to use 1-6V suppliy.

clear; clc;

Source and Load Impedance z01 = 50; z02 = 50;

Varactor Diode Voltage vj = 1:1:6;

Parameters for the equivalent circuit of the ferroelectric cap cj1 = 1.4e-12./(1+(vj/1.98).^2).^0.36; cj2 = 5.8e-12./(1+(vj/1.98).^2).^0.36;

Parallel RLC equivalent circuit for the spurline r1 = 4359.30; c1 = 2.74e-12; l1 = 1.40e-9;

Shunt serial equivalent circuit for the stepped impedance r2 = 1.47; c2 = 3.58e-13; l2 = 6.42e-9;

Initializing values fa = (1000e6:25e6:4000e6); 182

S21 = zeros(1,length(fa)); S11 = zeros(1,length(fa)); for m = 1:length(fa) for n = 1:length(vj) wa = 2*pi*fa(m); Impedance for the spurline z11 = (1i*wa*l1); z12 = (1/(1i*wa*c1)); z1 = 1i*wa*l1*r1/(r1*(1-wa^2*l1*(c1+cj1(n)))+1i*wa*l1);

Calculation T matrix for spurline parallel RLC s11 = (z1+z01-z02)/(z01+z1+z02); s21 = 2*z02/(z01+z1+z02); s12 = s21; s22 = s11; T1 = [-(s11*s22-s21*s12)/s21 s11/s21;-s22/s21 1/s21];

calculation T matrix for transmission line wres = 1/(2*pi*sqrt(l1*c1)); beta = 0.25/wres; s11 = 0; s21 = cos (beta*wa)-1i*sin(beta*wa); s12 = cos (beta*wa)-1i*sin(beta*wa); s22 = 0;

T2 = [-(s11*s22-s21*s12)/s21 s11/s21; -s22/s21 1/s21];

calculation T matrix for stepped impedance serial RLC z2= r2 + 1i*wa*l2 + 1/(1i*wa*c2)+1/(1i*wa*cj2(n)); z2load=z2*z02/(z2+z02); s11 = (z2load-z01)/(z01+z2load); s21 = 2*z2load/(z01+z2load); s12 = s21; s22 = s11;

T3 = [-(s11*s22-s21*s12)/s21 s11/s21;-s22/s21 1/s21];

T matrix and S parameter calculations T = T1*T2*T2*T3*T2; S11(m,n) = 20*log10(abs (T(1,2)/T(2,2))); S21(m,n) = 20*log10(abs(1/T(2,2))); end end plot(fa,S11) hold on plot(fa,S21) axis ([1000e6 4000e6 -40 5]) grid; legend ('C1=1V','C2=2V','C3=3V','C4=4V','C5=5V')

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