Radio Frequency and Microwave Design Methods for Mobile Communications

The University of New South Wales Sydney, Australia

RADIO FREQUENCY AND MICROWAVE DESIGN METHODS FOR MOBILE COMMUNICATIONS

Marian Gabriel Banciu

Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy

School of Electrical Engineering and Telecommunications 2003

RF and Microwave Design Methods for Mobile Communication

Abstract

The Global System for Mobile communications (GSM), which covers 54% of the world’s mobile market, evolved into the General Packet Radio Service (GPRS). The thesis addresses interference suppression using new radio frequency (RF) and microwave design methods for GSM and GPRS. The overall outcome is interference reduction and enhanced network capacity, leading to superior quality of service (QoS) for wider area coverage. The main results can be summarized as follows

• Design, manufacturing and characterisation measurements of new compact filters for GSM and GPRS base stations in order to reduce the out-of-band interference. It is shown that filters with novel microstrip resonators - dual mode filters and cross coupled filters - provide both a high degree of miniaturisation and narrow bandwidth.

• Development of a new 3-D Finite-Difference Time-Domain (FDTD) design method for new microstrip filters. A non-homogeneous Perfectly Matched Layer (NH-PML) was implemented for Absorbing Boundary Conditions (ABC) to increase the accuracy of the FDTD method. Signal estimation techniques were developed to speed up FDTD computations. A novel design method based on neural networks (NN) and FDTD was implemented to reduce the total design time.

• Investigation of High Temperature Superconductors (HTS) thin film resonators and antennas at microwave frequencies. High Q-factor HTS devices considerably enhance both the front-ends sensitivity and selectivity of wireless receivers.

• Design, manufacturing and testing of radio frequency (RF) electronics for 16 elements GSM and GPRS Smart Antenna for multipath fading mitigation and for in-band interference including co-channel interference (CCI) suppression.

i RF and Microwave Design Methods for Mobile Communication

Acknowledgments

First of all, I would like to express my gratitude to all the people in the Government of Australia, University of New South Wales, Faculty of Engineering and School of Electrical Engineering and Telecommunications who promoted research policies and maintained a research environment indispensable for this project. I would like to thank my supervisor Dr. R. Ramer for giving me the opportunity to work on microwave and RF design techniques for mobile communications at the University of New South Wales. I am grateful for all the given support and the essential guidance during my Ph.D. study. I wish to express my appreciation to my former co-supervisor Prof. T. Bao Vu and to Gary Jonas for their support during my two years long participation as a RF engineer in the “Smart Antenna for GSM” project. I would like to thank to Dr. E. Ambikairajah for his encouragements and for the inspiring lectures on Neural Networks and Applications. I am grateful to Dr. P. Rapajic for his encouragements and for his support during my activity as a tutor and laboratory demonstrator for the subject Mobile and Satellite Communications.

I dedicate this work to my family. Lucrare dedicată familiei mele (Mihai, Doina, Elena, Emil, Zoica)

Musical motto. Oedipus, challenging the Destiny, is defeating the Sphynx.

George Enescu, opera “Oedipe”

ii RF and Microwave Design Methods for Mobile Communication

List of Publications

[1] R. Ramer, M. G. Banciu, C. Constantin, G. J. Russell, T. B. Vu, “Superconducting Thin Films for Microwave Resonators”, Proceedings of the Asia-Pacific Microwave Conference, APMC ’97, 2-5 December 1997, pp. 121-123 [2] M. G. Banciu, R. Coca, R. Ramer, T. B. Vu, “Full Wave Computations for Microstrip Resonators and Antennas”, Proceedings of the 3rd Asia-Pacific Conference on Communications, APCC’97, 7-10 December, 1997, pp. 814-817 [3] M. G. Banciu, M. S. Pham, R. Ramer, T. B. Vu, “Preliminary Design and Fabrication of Microstrip HTS Antenna”, Proceedings of the 3rd Asia-Pacific Conference on Communications, APCC’97, 7-10 December, 1997, pp. 902-905 [4] M. G. Banciu, R. Ramer, “FDTD Method for Mobile Communicationss Filters”, Progress in Electromagnetics Research Symposium, PIERS 2000, Cambridge, Massachusetts, USA, July 2000 [5] M. G. Banciu, R. Ramer, “Analysis of Microstrip Circuits Using a Finite- Difference Time-Domain”, Proceedings of the 4th World Multiconference on Circuits, Systems, Communications and Computers, Proceedings CSCC 2000, Vouliagmeni, Greece, July 2000, ISBN 960-8052-19-X, pp 4611-4615 [6] M. G. Banciu, R. Ramer, “Analysis of Microstrip Circuits Using a Finite- Difference Time-Domain”, in Advances in Physics, Electronics and Signal Processing Applications, edited by N. E. Mastorakis, World Scientific and Engineering Society Press, Danvers, MA, USA, 2000, ISBN: 960-8052-17-3, pp. 156-160 [7] M. G. Banciu, R. Ramer, “A FDTD Method for Circuits on High Dielectric Constant Substrates”, Proceedings of the 5th International Symposium on Antennas, Propagation and Electromagnetic Theory, ISAPE 2000, Beijing, China, August 2000, pp. 219-222 [8] M. G. Banciu, R. Ramer, “Design of Microstrip Dual Mode Filters Using Finite-Difference Time-Domain Method”, Proceedings of the Asia-Pacific Microwave Conference – APMC 2000, December 2000, Sydney, vol. 1, pp. 975-978

iii RF and Microwave Design Methods for Mobile Communication

[9] R. Ramer, M. G. Banciu, “High Temperature Superconducting Thin Films for Microwave Devices”, Proceedings of the XV-th International Conference on Microwave Ferrites, Rokosowo, Poland, September 2000, pp. 120-123 [10] R. Ramer, M. G. Banciu, E. Dimitriu, M. S. Pham, T. B. Vu, “Design and Fabrication Preamble of a Microstrip HTS Antenna”, Industrial Ceramics, vol. 21, no. 2, ISSN 1127-7588, pp. 111-113 [11] M. G. Banciu, R. Ramer, A. Ioachim, “Microstrip Filters Using New Compact Resonators”, Electronics Letters, vol. 38, 2002, pp. 228-229 [12] M. G. Banciu, E. Ambikairajah, R. Ramer, “Microstrip Filter Design Using FDTD and Neural Networks”, Microwave and Optical Technology Letters, vol. 34, No. 3, 2002, pp. 219-224. [13] M. G. Banciu, R. Ramer, A. Ioachim, “Compact Microstrip Resonators for 900 MHz Frequency Band”, to appear in IEEE Microwave and Wireless Components Letters, May 2003 [14] M. G. Banciu, A. Ioachim, R. Ramer, “New Microstrip Resonators and Filters for GSM / GPRS”, Proceedings of the 25th Edition of the International Semiconductor Conference, CAS 2002, (IEEE Romania Section), Sinaia, Romania, 2002, vol. 1, pp. 41-44 [15] M. G. Banciu, A. Ioachim, R. Ramer, “New Microstrip Filters for GSM / GPRS”, to appear in the Proceedings of the EMFM 2002 (former ICMF), (IEE Slovakia Section), Bratislava, Slovakia, September 2002 [16] A. Ioachim, R. Ramer, G. Banciu, “X-Band High Peak Power Ferrite Devices“, presented to Progress in Electromagnetic Research, PIERS 2002, Cambridge, MA, July 2002 [17] M. G. Banciu, P. Rapajic, R. Ramer, “RF Electronics for GSM/GPRS Smart Antenna”, Proceedings of the 25th Edition of the International Semiconductor Conference, CAS 2002, (IEEE Romania Section), Sinaia, Romania, 2002, vol. 1, pp. 45-48

iv RF and Microwave Design Methods for Mobile Communication

Table of contents

1. Introduction …………………………………………………………………. 1 1.1. Thesis outline ………………………………………………………... 1 1.2. Summary of Thesis Contributions …………………………………… 3 References ………………………………………………………………… 4 Acronyms and Abbreviations in Chapter 1 …………………………….… 8

2. Background Knowledge …………………………………………....…..…… 9 2.1. Fundamental Concepts in Mobile Communications ………..….....…. 9 2.1.1. Global System for Mobile Communication ………...……... 15 2.1.2. General Packet Radio Service ………………………...….… 17 2.2. Finite Difference Time Domain Method …...... ………………… 18 2.3. Elements of Microwave Filters …………………………………..….. 24 2.3.1. Microstrip Filters …………….………………………..….… 30 2.4. High Temperature Superconductivity for Mobile Communications …………………………………………………….. 32 2.4.1. The Cryogenic Front Ends …...………………………..…... 34 2.4.2. HTS Antennas ……………...... ………………………..…... 38 2.5. Antenna Array Concepts…………………..…………………….…… 39 2.5.1. Smart Antennas……………...... ………………………..…... 42 2.6. Chapter Summary ……………………………………………….…… 46 References …………………………………………....…………….…….. 47 Acronyms and Abbreviations in Chapter 2 …………………….....……… 54

3. Designing of Microstrip Devices Using the FDTD Method ……..……..… 57 3.1. Introduction …………………………………………………….……. 57 3.2. Dispersion Effects …………………..………………………….……. 59 3.3. FDTD Analysis of Different Types of Microstrip Devices ….………. 60 3.3.1. Linear Low Impedance Microstrip Section ………….…….. 60 3.3.2. Gap End Coupled Linear Resonator ………………….…….. 62 3.3.3. Meander Lines ………………………………………….….. 63 3.3.4. Dual Mode Filters ………………………………………….. 66

v RF and Microwave Design Methods for Mobile Communication

3.4. Non-Homogeneous PML …………...... ………………………….. 69 3.5. FDTD Signal Estimation Technique ………………………………… 73 3.5.1. Signal Estimation for Meander Loop Dual Mode Filter Design ………………………………………………... 74 3.5.2. Signal Estimation for FDTD Analysis of Forward Coupled Filter ……………………………………………… 82 3.6. Microstrip Filter Design Using FDTD and Neural Networks ….……. 87 3.7. Chapter Summary …….…..………………………………….………. 93 References ……………………………………………………….....…….. 94 Acronyms and Abbreviations and Notations in Chapter 3 …………...…… 96

4. New Microstrip Filter Design …………………….…………………...... …… 97 4.1. Introduction ………………………………………………….....……. 97 4.1.1. Low Pass Filters ..………………………………...... ……… 97 4.1.2. Design of Edge Coupled Band Pass Filter …………...... … 99 4.2. Dual Mode Resonators and Filters ………………………….....……. 100 4.2.1. Quasi Fractal Dual Mode Resonators ………………...…… 115 4.3. Filters with Cross-Coupled Resonators ………………………...…… 121 4.3.1. Design of HTS Filter with Cross-Coupled Loop Resonators 122 4.3.2. Stubs Effect on Half-Wavelength Resonators and Stepped-Impedance Resonators ……….………….……… 123 4.3.3. Novel Microstrip Resonators ……………………………… 132 4.3.4. Filters with Novel Microstrip Resonators Coupled in Cascade …………………………………….… 137 4.3.5. Filters with Cross-Coupled Novel Microstrip Resonators … 141

4.4. The Influence of the Resonators' Unloaded Quality Factor Qu on the Filter Response ……………………………………………….. 147 4.5. Chapter Summary ………………………………………...... …….….. 149 References ………………………………………………………....……... 150 Acronyms and Abbreviations in Chapter 4 …………………………..…… 152

vi RF and Microwave Design Methods for Mobile Communication

5. High Temperature Superconducting Microwave Devices …………….…. 153 5.1. HTS Thin Film Fabrication ………………………………………….. 153 5.2. YBCO Microstrip Ring Resonator …………………………………… 155 5.3. HTS Slot Coupled Antenna ………………...………………………… 159 5.3.1. Design and Fabrication ………..………………………….… 159 5.3.2. Measurements ………………………………………………. 160 5.4. Chapter Summary ………………………………………………….…. 163 References ……………………………………………………………….... 164 Acronyms and Abbreviations in Chapter 5 ………………………………. 165

6. Low Noise RF Electronics for GSM / GPRS Smart Antenna …….…….…. 166 6.1. Introduction …………………………………………………………… 166 6.2. Development of GSM 900 Receivers ………………..……………..… 167 6.3. Design of DCS 1800 Receiver ………………..……………………… 179 6.4. Design of GSM 900 / DCS 1800 Transmitter …….…………………. 181 6.5. Testing the RF Electronics for GSM / GPRS Smart Antenna ……...… 184 6.6. Chapter Summary ……………………………………………………. 185 References ………………………………………………………………… 186 Acronyms and Abbreviations in Chapter 6 ……………………………….. 187

7. Conclusions and Future Trends …..…………………………………………. 188 7.1. Conclusion ……………………………………………………….…… 188 7.2. Proposed Further Research ….……………………………………….. 190 References ………………………………………………………………… 191

Appendices ……………………………………………………………………….. 192 Appendix 1. The Hata Model and the COST Model ……..………………. 192 Appendix 2. Elements of Global System for Mobile Communications (GSM) ……………………..……………… 193 Appendix 3. General Packet Radio Service (GPRS) ………..…………….. 197 Appendix 4. Evaluation of the RF electronics for GSM / GPRS Smart Antenna ………………..…………………………….. 202 References ……………………………………………………………….... 209 Acronyms and Abbreviations in Appendices ...…………………………… 210

vii Chapter 1 - Introduction

C H A P T E R 1 Introduction

The research summarized in this thesis refers to RF and microwave design methods that better utilize the available resources of the physical layer, which is the basis of the whole mobile communication concept. The main approached problem refers to techniques of minimizing the interference in mobile communications. This issue becomes more and more important with the rapid growth of wireless networks using an overcrowded electromagnetic spectrum. The estimations are that links, which might be interference free in the present, soon will encounter interference problems. A dynamic network design including adequate frequency and site planning or new coding and modulation techniques might increase the immunity to the interference. However, at the same time there is a necessity to enhance the performance of base stations (BSs) RF and microwave circuitry. Most of the research described in this work refers to designs directly applicable to base stations in the digital Global System for Mobile communications (GSM) standard, which is the cellular standard with the widest worldwide penetration, about 54% from the world’s cellular market. The imminent convergence between wireless networks and packet data networks, such as Internet, had as an effect the new standard of an intermediate generation (2.5G), the General Packet Radio Service (GPRS). GPRS shares with GSM physical resources and many properties of the physical transmission layer. Therefore the results of this research, even when initially designed for GSM, can be directly applied to GPRS.

1.1. Thesis outline

Chapter 2 provides the background information that will be used in the later chapters. Basic concepts on cellular communications, on Finite-Difference Time-Domain (FDTD) method, and microwave filters are introduced. The advantages of the

1 Chapter 1 - Introduction applications of high temperature superconductors (HTS) to mobile communications are explained. Chapter 2 introduces also the adaptive antenna concept to mitigate the in- band interference including the co-channel interference (CCI) with a simultaneous improved immunity to multipath fading. Chapter 3 presents the three-dimensional finite-difference time-domain (FDTD) method developed for microstrip circuits and devices. The implementation of the non- homogeneous Perfectly Matched Layer (NH-PML) is demonstrated. Signal estimation techniques are developed in order to reduce the number of FDTD iterations. A novel design technique using artificial neural networks (ANN) is demonstrated. Chapter 4 presents the development of new types of compact filters with improved characteristics in order to be used in GSM and GPRS base stations for an improved rejection of out-of-band interference. Investigations on dual mode filters (DMF) and filters with open loop cross-coupled resonators are discussed. Compact filters using novel microstrip resonators are presented. The effect of resonator unloaded

Qu factor on filters' characteristics is discussed and the High Temperature Superconductors (HTS) technology is recommended for an enhanced selectivity without compromising the insertion loss or the noise figure. In Chapter 5, the experimental investigation of superconducting YBCO thin film resonators is presented. The measurements demonstrate the good quality of the deposited HTS films. Preliminary design and measurements for a HTS microstrip slot- coupled antenna are also presented. Chapter 6 presents the investigations of noise reduction techniques for RF electronics (GSM-900 and DCS-1800 receivers and transmitter) developed for a GSM / GPRS adaptive antenna. The research was carried on at the University of New South Wales in the frame of the “Smart Antenna for GSM” project. Chapter 7 contains the conclusions and some proposed directions for a following research. The appendices refer to theoretical and experimental issues referenced in the main body of the thesis.

2 Chapter 1 - Introduction

1.2. Summary of Thesis Contributions

Most of the thesis contributions have been published [1-17] during the author's Ph.D. research. Some of these results are a continuation of his previous research activities [18-31] on microwave devices, measurement systems, and microwave interactions with materials and biologic solutions. The thesis contributions can be summarized as follows

• Design of new type of compact planar filters with improved characteristics for enhanced cellular base stations front-ends. • Investigation of novel microstrip resonators and their use for design of new cross-coupled and cascade type filters [11, 13-15]. • Design, manufacture and testing on a low-pass DCS-1800 microstrip filter [4]. • Development of meander line and square patch two- and four-pole band-pass dual mode filters (DMF) [8]. • Design of very low insertion loss HTS filter using square loop cross- coupled resonators [9]. The design approach was developed on the basis of previous research on filters with dielectric resonators (DR) [22-24, 26, 30] and on tunable single crystal YIG filters [25, 28]. • Development of a 3D FDTD method [4-8, 12] required by the accurate full wave analysis [2] of microstrip circuits and devices. • Implementation of a non-homogeneous Perfectly Matched Layer (NH-PML) for absorbing boundary conditions (ABC) to increase the FDTD results accuracy [4-8, 12]. • Development of signal estimation techniques to reduce the number of FDTD iterations [8, 12]. • Novel use of the artificial neural networks (ANN) for the reduction of the total FDTD design time [12]. • FDTD application to the design of non-conventional microstrip filters such as filters with dual mode resonators (DMR) [8] and with crossed coupled novel resonators etc. [12, 13].

3 Chapter 1 - Introduction

• Experimental investigation of high temperature superconducting (HTS) YBCO thin film devices. • Experiments on YBCO thin film resonators [1, 9], an essential step towards the cryogenic front-ends that could enhance cellular coverage and/or capacity and reduce the microwave effects on biological matter illustrated by previous research [19-20]. • Preliminary design and measurements of a HTS antenna [3, 10]. • Investigation of noise reduction techniques for RF electronics developed for a GSM / GPRS smart antenna for in-band (including co-channel) interference rejection and for multipath fading increased immunity. • Design, manufacturing and measurements of sixteen low-noise uplink receivers for a GSM adaptive array [17] with front-ends optimized for minimum noise figure based on earlier results [18, 21]. • Design of the low-noise DCS 1800 up-link receiver [17]. • Design of the GSM low-noise down-link receiver needed to fully test the radio channel. The test set-up for DCS 1800 receiver-transmitter chain required the use of a nonreciprocal device investigated conceptually by previous research [27, 29]. • Experimental investigation of the GSM 900 / DCS 1800 transmitter [17].

References

Papers published when M. G. Banciu was affiliated to University of New South Wales:

4 Chapter 1 - Introduction

[3] M. G. Banciu, M. S. Pham, R. Ramer, T. B. Vu, “Preliminary Design and Fabrication of Microstrip HTS Antenna”, Proceedings of the 3rd Asia-Pacific Conference on Communications, APCC’97, 7-10 December, 1997, pp. 902-905 [4] M. G. Banciu, R. Ramer, “FDTD Method for Mobile Communicationss Filters”, Progress In Electromagnetics Research Symposium, PIERS 2000, Cambridge, Massachusetts, USA, July 2000 [5] M. G. Banciu, R. Ramer, “Analysis of Microstrip Circuits Using a Finite- Difference Time-Domain”, Proceedings of the 4th World Multiconference on Circuits, Systems, Communications and Computers, Proceedings CSCC 2000, Vouliagmeni, Greece, July 2000, ISBN 960-8052-19-X, pp 4611-4615 [6] M. G. Banciu, R. Ramer, “Analysis of Microstrip Circuits Using a Finite- Difference Time-Domain”, in Advances in Physics, Electronics and Signal Processing Applications, edited by N. E. Mastorakis, World Scientific and Engineering Society Press, Danvers, MA, USA, 2000, ISBN: 960-8052-17-3, pp. 156-160 [7] M. G. Banciu, R. Ramer, “A FDTD Method for Circuits on High Dielectric Constant Substrates”, Proceedings of the 5th International Symposium on Antennas, Propagation and Electromagnetic Theory. ISAPE 2000, Beijing, China, August 2000, pp. 219-222 [8] M. G. Banciu, R. Ramer, “Design of Microstrip Dual Mode Filters Using Finite-Difference Time-Domain Method”, Proceedings of the Asia-Pacific Microwave Conference – APMC 2000, December 2000, Sydney, vol. 1, pp. 975-978 [9] R. Ramer, M. G. Banciu, “High Temperature Superconducting Thin Films for Microwave Devices”, Proceedings of the XV-th International Conference on Microwave Ferrites, Rokosowo, Poland, September 2000, pp. 120-123 [10] R. Ramer, M. G. Banciu, E. Dimitriu, M. S. Pham, T. B. Vu, “Design and Fabrication Preamble of a Microstrip HTS Antenna”, Industrial Ceramics, vol. 21, no. 2, ISSN 1127-7588, pp. 111-113 [11] M. G. Banciu, R. Ramer, A. Ioachim, “Microstrip Filters Using New Compact Resonators”, Electronics Letters, vol. 38, 2002, pp. 228-229 [12] M. G. Banciu, E. Ambikairajah, R. Ramer, “Microstrip Filter Design Using FDTD and Neural Networks”, Microwave and Optical Technology Letters, vol. 34, No. 3, 2002, pp. 219-224.

5 Chapter 1 - Introduction

[13] M. G. Banciu, R. Ramer, A. Ioachim, “Compact Microstrip Resonators for 900 MHz Frequency Band”, to appear in IEEE Microwave and Wireless Components Letters, May 2003 [14] M. G. Banciu, A. Ioachim, R. Ramer, “New Microstrip Resonators and Filters for GSM / GPRS”, Proceedings of the 25th Edition of the International Semiconductor Conference, CAS 2002, (IEEE Romania Section), Sinaia, Romania, 2002, vol. 1, pp. 41-44 [15] M. G. Banciu, A. Ioachim, R. Ramer, “New Microstrip Filters for GSM / GPRS”, to appear in the Proceedings of the EMFM 2002 (former ICMF), (IEE Slovakia Section), Bratislava, Slovakia, September 2002 [16] A. Ioachim, R. Ramer, G. Banciu, “X-Band High Peak Power Ferrite Devices“, presented to Progress in Electromagnetic Research, PIERS 2002, Cambridge, MA, July 2002 [17] M. G. Banciu, P. Rapajic, R. Ramer, “RF Electronics for GSM/GPRS Smart Antenna”, Proceedings of the 25th Edition of the International Semiconductor Conference, CAS 2002, (IEEE Romania Section), Sinaia, Romania, 2002, vol. 1, pp. 45-48

Papers with affiliations other than UNSW:

[18] M. G. Banciu, “A measurement method to determine the noise parameters of microwave transistors”, Technische Universiteit Eindhoven, Report EEA-477, August 1993 [19] C. Muntean, A. Ioachim, G. Banciu, “Effects on Macromolecular Concentration and of Polymer Aging on the Microwave Response of Dissolved DNA”, The 11-th International Congress of Biophysics, Budapest, Hungary, July 1993 [20] C. Muntean, G. Banciu, “Effects of Macromolecular Concentration on the Microwave Absorption of DNA in Aqueous Solution”, presented to the 9th Balkan Biochemical Biophysical Days, Thesaloniki, Greece, Abstracts, May 1992, pp 135

6 Chapter 1 - Introduction

[21] M. G. Banciu, J. J. M. Kwaspen, H. C. Heyker, “Correction for Mismatches in Measuring Low Noise Microwave Transistors”, Proceedings of the Annual Conference on Semiconductors, CAS’94, Sinaia, Romania, 1994, vol. 2, pp. 379-382 [22] M. G. Banciu, A. Ioachim, D. D. Sandu, F. Manolache, “Identification of Resonating Modes of a DR Using a Computer Aided Measurement System”, Proceedings of the 13th Hertzian Optics and Dielectrics Biennial Colloquium, OHD 1995, Zaragoza, Spain, September 1995, pp. 294-297 [23] G. Banciu, A. Ioachim, “Advanced Model for Dielectric Resonators”, The National Conference for New Materials, Bucharest, Romania, October 1995 [24] G. Banciu, A. Ioachim, “Computer Aided Measurements for High Dielectric Constant Materials”, The National Conference for New Materials, Bucharest, Romania, October 1995 [25] A. Ioachim, G. Banciu, “Computer Assisted Studies of Resonance Frequency Behaviour with Temperature in a Monocrystalline YIG”, presented to The National Conference for New Materials, Bucharest, Romania, October 1995 [26] G. Banciu, A. Ioachim, G. Nicoara, G. Filoti, “Computer Assisted Measurements for Microwave Resonators Materials”, Proceedings of the XIII-th International Conference on Microwave Ferrites, ICMF’96, Busteni, Romania, 1996, pp. 189-195 [27] G. Banciu, A. Ioachim, G. Nicoara, G. Filoti, “Simulation Model and Measurements for Nonreciprocal Structures”, Proceedings of the XIII-th International Conference on Microwave Ferrites, ICMF’96, Busteni, Romania, 1996, pp. 209-213 [28] A. Ioachim, G. Nicoara, G. Banciu, R. Coca, “Temperature Compensation for the Resonance Frequency in the Monocrystalline YIG”, Proceedings of the XIII-th International Conference on Microwave Ferrites, ICMF’96, Busteni, Romania, 1996, pp. 28-32 [29] G. Nicoara, G. Banciu, A. Ioachim, R. Coca, D. Fratiloiu, R. Ramer, “Microwave Absorbtion of the Ferrite-Based Nanocomposite Materials”, Proceedings of the XIII-th International Conference on Microwave Ferrites, ICMF’96, Busteni, Romania, 1996, pp. 196-200

7 Chapter 1 - Introduction

[30] A. Ioachim, M. I. Toacsen, G. Stoica, R. Coca, F. Vasiliu, G. Banciu,

“Microwave Characteristics of BaO-PbO-Nd2O3-TiO2 Dielectric Resonators”, Proceedings of the 16th Hertzian Optics and Dielectrics Biennial Colloquium, OHD 2001, Le Mans, France, September 2001, pp. 133-136 [31] C. Angelescu, M. Negosanu, A. Ioachim, M. I. Toacsan, R. Coca, G. Banciu, D. D. Sandu, “Frequency Dispersion in Dielectric-Magnetic Composites” Proceedings of the 16th Hertzian Optics and Dielectrics Biennial Colloquium, OHD 2001, Le Mans, France, September 2001, pp. 369-372

Acronyms and Abbreviations in Chapter 1

1G, 2G, 2.5G, 3G First, second, intermediate, third generation of standards in mobile communication ABC Absorbing Boundary Condition ANN Artificial Neural Networks BS Basestation CCI Co-Channel Interference DCS-1800 Digital Cellular System in 1800 MHz bandwidth DMF Dual Mode Filter DMR Dual Mode Resonator DR Dielectric Resonator FDTD Finite Difference Time Domain Method GSM Global System for Mobile communications GPRS General Packet Radio Service HTS High Temperature Superconductors LNA Low Noise Amplifier PML Perfectly Matched Layer

YBCO YBa2Cu3O7-δ YIG Yttrium Iron Garnet

8 Chapter 2 – Background Knowledge

C H A P T E R 2 Background Knowledge

This chapter provides background information, which will be used in later chapters. The main target of the thesis is the interference reduction in mobile communications using new RF techniques. Hence, basic elements of mobile communications are first introduced in Section 2.1. A 3-D Finite-Difference Time-Domain (FDTD) method developed for microstrip circuits will be discussed in Chapter 3. Therefore, fundamental elements of FDTD method are presented in Section 2.2. New preselect filters designed with FDTD method will be analyzed in Chapter 4. Consequently, elements of microwave filters are introduced in Section 2.3. The benefits of High Temperature Superconductors (HTS) technology to mobile communications are presented in Section 2.4. The experimental investigations on HTS devices discussed in Chapter 5 were motivated by the possibility of using HTS technology for receivers front ends with enhanced selectivity and sensitivity, and for high gain antennas. Finally, the antenna array concepts introduced in Section 2.5 will be used in Chapter 6, which presents the development of low-noise RF electronics for a GSM / GPRS smart antenna.

2.1. Fundamental Concepts in Mobile Communications

Mobile communications comprise various communications technologies, which can ensure portability and mobility. The technologies range from indoor infrared (IR) wireless local area networks (WLAN) to satellite systems [1-2]. Most of the research results performed for this thesis refer to cellular systems, which are the most prevalent part of terrestrial radio communications. The terrestrial communications include also cordless telephony, paging, professional mobile radio (PMR) [3]. A cellular system is realized as a network of radio cells, based on frequency reuse, which provides complete coverage of the service area [3]. From all the mobile

9 Chapter 2 – Background Knowledge terrestrial systems, the cellular technology offers voice and data communication services over very large coverage areas. Each cell contains a base station (BS) serving more mobile stations (MSs). The MS can be a handset, a computer seen as mobile office [4], etc. There is no strict geometric border between the cells. When the signal becomes too weak for being handled by a BS, a neighbor BS takes over the communication after a new radio frequency (RF) channel was assigned. This process is called handover or handoff. The time over which a call can be maintained within a cell without handoff is called the dwell time. The radio link in a cellular system is subjected to the specific propagation laws of the radio waves. There is a significant contrast between a transmission channel of a wired communication path and a radio mobile channel. Since the former is almost constant in time, the latter is random and undergoes shadowing and multipath fading. Even when a mobile user is stationary, ambient motion in the vicinity of the base station can produce fading. Shadowing, also called slow fading or long-term fading [5], designates the slow variation in the mean complex envelope of the receiver signal over a distance corresponding to tens of wavelengths. This is caused by variations in the local topography such as buildings, foliage, and hilly terrain. The effect of shadowing is reduced when the transmitter power is increased. The local means values of the received power measured in different points, but at the same separation distance d between BS and MS constitute a statistical ensemble obeying a lognormal distribution [5] with the probability density function (pdf)

  x    ln2    1 m ()xf = exp−    , (2.1) 2  2  x 2πσ  2σ    where m is the median value of the random variable x and σ is the standard deviation of  x  ln  . This pdf can be obtained by transforming a normal pdf via = ln()xy .  m  Therefore, if the measured values are plotted in dBs, they will follow a Gaussian distribution. Multipath fading, also referred to as fast fading, designates the rapid fluctuation of the envelope. Deep fades, up to 40 dB, can occur within a fraction of a wavelength. These fluctuations are caused by the interference of multiple copies of a transmitted

10 Chapter 2 – Background Knowledge signal, each with different amplitude, phase and delay [6]. The components suffer before the reception multiple reflections from fixed and mobile structures. Therefore multipath fading predominates in urban environment, heavily wooded areas etc. The scatterers local to a moving MS can cause Doppler spread, small delay spread and small angle spread. The scatterers local to BS contribute multipath rays with small delay spread and large angular spread. The remote scatterers can cause independent fading on paths and contribute multipath with large delay spread (frequency selective fading) and large angular spread. In macrocells, the case of isotropic scattering is very common since the MS is surrounded by local scatterers. In this case, the amplitude distribution of multipath fading is described by a Rayleigh distribution

r 2  r 2  rf = exp)( −  , (2.2) 2  2  σ  2σ  where r is the positive envelope, f(r) is the probability density function, r2 represents the instantaneous power and σ2 is the average signal power. In microcells, a line of sight (LoS) path is often possible; i.e. a direct path between BS and MS without any scattering, or a direction in which the received power strongly dominates the power in the scattered components. This type of multipath fading is described better by a Rician distribution

 + 22   ararr  rf = exp)( −    rafor ≥≥ 0,0, . (2.3) 2  2  I 0 2  σ  2σ  σ  where a denotes the peak amplitude of the dominant signal, I0 is the modified Bessel function of the first kind and zero-order. The Rician distribution is specified by the Rice factor.

maintheinorLoStheinPower component a2 Rice factor = = . (2.4) theinPower scattered components 2σ 2 Usually the Rice factor takes values between 5 to 30 dB. If the Rice factor is 0 dB, the multipath fading is described by a Rayleigh distribution. The fast fading rate depends on the mobile speed. The multipath fading cannot be improved by increasing the power but by diversity techniques, which can be achieved by time, frequency, space, angle (direction), field component, rake (multipath) and polarization. The diversity is based on the idea that the probability for almost two uncorrelated components to suffer simultaneous

11 Chapter 2 – Background Knowledge fading is much smaller than the probability that a single component will fade. The diversity gain is defined as the reduction in the required averaged output signal to noise ratio (SNR) for a given bit error rate (BER) in the presence of fading [7]. From the above discussion it can be deduced that the received power is a statistical variable. However, to describe the path loss we will focus on the average (50 percentile) values. Measurement campaigns showed an exponential variation of the received power with the distance

γ  d 0  r ()= ()dPdP 00   , (2.5)  d  where Pr is the ensemble average of received power at distance d, P0 is the ensemble average of the received power at a reference distance d0 and γ is the path loss exponent. In a cellular system γ spreads between 2 and 4. The path loss exponent can take large values when the signal propagation occurs over a terrestrial path having obstructions and reflecting objects; the smallest value 2 correspons to free space propagation. The path loss usually increases with carrier frequency. In the case of microcells and indoor picocells, the interference between the LoS wave and the reflected wave by a flat earth ground causes a breakpoint in the path loss variation. The path loss slope is γ = 2 up to a distance called the radius of the first Fresnel clearance zone, and γ = 4 beyond the Fresnel zone. Formula (2.5) is valid only if d and d0 belong to the same domain with the same γ, but the extension of (2.5) for a multiple breakpoint model is straightforward. Two of important models for propagation loss estimation, i.e. the Hata model and the COST model are presented in Appendix 1. The knowledge on propagation loss is essential in estimating the power at receiver side and for estimating the link budget. The multipath propagation will cause a delay spread, which represents the difference in propagation delays among the multiple paths. The delay spread limits the maximum data rate due to the intersymbol interference (ISI), which occurs especially when the delay spread is greater than 10 percent of the symbol period. Adaptive equalization can be used to mitigate ISI. In frequency domain the mobile channel shows a Doppler spread caused by the Doppler shift in frequency due to the movement of the mobile or of the reflectors causing multipath. The rms Doppler spread is sometimes used to measure the fading rate of the channel [3].

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The capacity of a cellular network depends on the mutual interference between users. A compromise between coverage and capacity often occurs when the number and size of cells during the network design is decided. A good coverage is the first requirement in cases where the system operates below the maximum capacity as in rural regions. On the contrary, in heavy traffic urban areas, the network evolves by splitting the larger cells in micro or picocells to accommodate more users. The interference is often regarded as a major impediment in increasing cellular network capacity. Due to the insufficient isolation between voice channels, cross-talk occurs and subscribers can hear another conversation in the background. Interference often wears the responsibility for dropped calls. Interference can be co-channel, near channel (commonly called adjacent-band interference) or far channel. The co-channel interference (CCI) results from frequency reuse. The same RF channel used in one cell is reallocated in a cell at a sufficient distance. Co-channel cells must be physically separated by a minimum distance to provide sufficient isolation due to propagation. Additional interference will be present at reduced strength from cells that are further away. In order to reduce the CCI, the base stations are usually equipped with 120o sectorized antennas rather than with omni-directional antennas. The adjacent channel interference takes place when close RF channels “bleed over” into the passband. The near-far effect occurs when a strong mobile transmits on a channel close to the desired channel being used by a weak mobile. Strong or weak mobile means a mobile which is near to BS or at the cell border respectively. In such a case, it is very hard for a BS to discern between the desired small signal and the leakage from a near channel. The receiver has to withstand another type of out of band interference due to the very high levels in transmitted power, compared to the levels of the received signals. Without an adequate transmitter and receiver isolation the receiver desensitization will occur. The interference is a major issue in mobile communication due to the increasing number of users and BS in the same area. How new base station technologies based on sharp low loss RF filters or smart antennas enhance the coverage keeping the capacity unchanged will be shown in the following chapters. The improvement in coverage can be specified by the range extension factor (REF) [8], the area extension factor (AEF), or can be translated to a reduction in the number of the base stations needed to cover a certain service area,

13 Chapter 2 – Background Knowledge expressed by the base stations reduction factor (BSRF). When using obvious notations, the index i taking the value 1 for the unimproved case and the value 2 for the improved case, then

R Area N BS 2 1 REF = 2 ; AEF 2 == REF 2 ; BSRF == . (2.6) R1 Area1 N BS 1 AEF The evolution of cellular networks objective is to obtain high capacity for limited radio spectrum, concomitant with large areas coverage and provision of enhanced services with increased data rates. Some predictions by Merill Lynch cited in [9], indicate that more than 400,000 cell sites (base stations) exist worldwide. By 2003, a forecasted per diem traffic of 7,000 Gigabytes (the voice will be one half of that) will be carried by more than 1 million base stations. By 2005 nearly 1 billion subscribers are worldwide estimated [10]. The wireless networks are standardized giving the service providers the possibility to acquire the same equipment from multiple suppliers to sustain competitive pricing. Digital cellular 2G standards in the second generation have offered an increase in capacity of one order of magnitude compared to the analog 1G systems. The looming convergence with the Internet determined a further evolution towards the third generation standards (3G). Some other 2G standards evolved to intermediate standards 2.5G providing packet switch services and, at the same time, taking the advantage of the already deployed equipment. The 3G Universal Mobile Telecommunication System (UMTS) is guaranteed to give new high-quality multimedia services and a global coverage [10]. The existent fixed and mobile networks will be integrated under UMTS and the users will be permitted a terminal mobility among them. The UMTS core network will evolve from the GSM / GPRS infrastructure [11]. The GSM and GPRS standards will be introduced in Sections 2.1.1 and 2.1.2 respectively. The development of wireless communications made possible the extendibility of the network node concept to the mobile network node. This can change its point-of- attachment to the Internet from one link to another without interrupting any ongoing communication [4]. The ongoing Internet Protocol version 4 (IPv4) was therefore extended to the Mobile Internet Protocol (MIP) [12]. The appropriate routing for mobile nodes led to the need of providing homogenous mobility [4] allowing a mobile node to move from one network link to another one of the same media type. The extension of mobility between different media

14 Chapter 2 – Background Knowledge types, while retaining the capability to communicate, caused the heterogeneous mobility implementation by mobile IP technology. As an example, the MIP permits a notebook computer to disconnect from a wired Ethernet and switch to a wireless network without encountering any disturbance in the network service. The use of MIP data packets has the ability to tunnel the packet data wireless networks. A tunnel is the path followed by a first packet, while is encapsulated within the payload portion of a second packet [4].

2.1.1. Global System for Mobile Communications

The Global System for Mobile communications (GSM) is the mobile communications standard with today’s highest penetration worldwide. GSM is a system of the 2nd generation using the benefits of a digital technology for an increased capacity. GSM covers 54% from the world’s mobile market followed by the Interim Standard 95 (IS-95), an American CDMA system, which covers 16.9% from the world’s market [6]. A GSM user can roam nationally and even internationally. GSM uses a time division multiple access (TDMA) technology. Each TDMA frame consists of 8 time slots (TS), of 577 µs each. Since there are 124 RF channels, the total number of communications channels is 992 [13]. As a full duplex system, GSM allows simultaneous radio transmission and reception between MS and BS. This is achieved using frequency division duplexing (FDD), the transmission and reception having allocated separated RF channels. The transmission from BS to MS occurs on the forward channel, called also downlink or downstream channel, and from MS to BS takes place on the reverse (uplink) channel. The BS uses separate antennas for the forward / reverse channels but at MS (subscriber unit) a single antenna is connected to a device called duplexer which enables simultaneous transmission and reception. An inexpensive duplexer can provide sufficient isolation between the two channels if their RF frequencies are separated by at least 5% of the nominal value [2]. The downlink channels spread between 935-960 MHz. The frequencies are given by the formula

Fd(N) = 935.2 + 0.2 (N-1) MHz, where N=ARFCN=1,2,… 124, (2.7a)

15 Chapter 2 – Background Knowledge where ARFCN represents the absolute frequency channel number. The lowest channel (935 to 935.2 MHz) serves as a guardband. The duplex spacing, defined by the frequency spacing between downlink and uplink bands is 45 MHz. Hence, the uplink (reverse) channels are positioned 45 MHz lower than their downlink correspondent, therefore they occupy the band 890-915 MHz. The uplink channels frequencies are given by the relation

Fu(N) = 890.2+0.2 (N-1) MHz, where N=ARFCN=1,2,… 124, (2.7b)

Again the lowest channel (890 to 890.2 MHz) is used as a guard band between GSM and other services on lower frequencies. The Digital Cellular System DCS 1800 is a variant of the GSM standard using the frequency ranges of 1710 to 1785 MHz for the uplink and 1805 to 1880 for the downlink, therefore the duplex spacing is 95 MHz. In the case of DCS 1800 the 374 channels of the same 200 kHz bandwidth as GSM-900 have ARFCN numbered from 512 to distinguish them from the other GSM bands and are given by the frequencies

Fd(N)=1805+0.2*(N-511) MHz, where N=ARFCN=512,..,885 (2.8a)

Fu(N)=Fd(N)-95 MHz. (2.8b)

TDMA allows frame-by-frame monitoring of bit error rates (BERs) depending on signal strength required by the handoff decisions. In the case of TDMA, the bandwidth is utilized more efficiently than in Frequency Division Multiple Access (FDMA) with no frequency guard bands between channels required. However, there is a guard time of 30.4 µs [14] between time slots, to adapt for the delay spread, the propagation delay, the clock instability effects and the transient response effects. The GSM frame duration is 4.615 ms. A multiframe consists of 26 frames of 8 TS, a superframe (6.12 s) contains 51 multiframes and a hyperframe (3.48 hours) contains 2048 superframes [13]. The GSM permits dynamic frequency allocation. In order to decrease the multipath effects, GSM uses frequency diversity based on frequency hopping technology. In GSM the MS is an active participant to the mobile assisted handover (MAHO).

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The GSM system architecture and the elements of the GSM logical system are presented in Appendix 2.

2.1.2. General Packet Radio Service

The General Packet Radio Service (GPRS) is the result of the global convergence strategy between GSM, the pan-European TDMA system and IS-136 the extension of the North American TDMA system. GSM, as a circuit switched system, is not able to properly handle the bursty traffic characteristic to the Internet or other protocol data networks and does not provide direct connection to the Internet. The packet switching technology is required by a dynamic bandwidth and resource allocation “on demand”, and by the possibility to easily multiplex and combine traffic from different resources. For a packet switched network, the billing is based on the actual volume of transmitted data rather than on the connection time as for the switched data transmission.

Local Area Network

Packet Host data 126.33.18.3 Host network 123.456.78.9 Router Router GPRS network 123.456.78 Subnetwork 126.33.18 Subnetwork 137.345.23 Router

Host 137.345.27.1

Figure 2.1. GPRS system from the user’s point of view.

GPRS preserves some of the GSM physical resources and many properties of the physical transmission layer such as TDMA, structure of time-slots, modulation techniques [14] etc.

17 Chapter 2 – Background Knowledge

The mobile terminals, such as those so-called “wireless PCs” or “mobile offices”, should support any conventional Internet-based applications, such as file transfer, e-mail or World Wide Web “navigation”. An emphasis is put on multimedia services with the video as a major component. From the user’s point of view, the GPRS network looks like in Fig. 2.1. An end system is treated as a host and a network element, as a rooter. The intermediate systems relay data packets from end systems and route them toward their destinations. In conclusion, the GPRS network looks like any normal IP network for a normal user and, in principle, all IP applications work on the top of GPRS, excepting at this stage those which use continuous data streams, such as IP phone. Other details on GPRS are presented in Appendix 2.

2.2. Finite Difference Time Domain (FDTD) Method

Basic elements of the Finite-Difference Time-Domain (FDTD) method are presented in this section. The 3-D FDTD method developed for novel filters design will be described in Chapter 3. The miniaturization of the high frequency integrated circuits requires more accurate design methods to control simultaneously effects such as packaging influence, cross coupling, surface waves, etc. Most of the commercial CAD software packages neglect the effects mentioned above. To go beyond the empirical model limits of microwave components, one needs to apply a full wave analysis method. The Finite-Difference Time-Domain method distinguishes itself from other numerical full wave analysis methods because of its accuracy and versatility. The FDTD method provides analysis with a high degree of accuracy and versatility of high frequency (RF, microwave etc.) components and circuits [15, 17]. Although FDTD is based on a simple concept, it is remarkably robust. It provides highly accurate modeling predictions and it can be applied for a wide variety of electromagnetic interactions problems. Due to its dimensionally reduced computational burdens and ability to simulate directly the dynamics of wave propagation, FDTD has became a viable alternative to frequency domain Method of Moments (MoM) and to Finite Element Method (FEM).

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Early finite-difference methods applied to Maxwell equations, as an attempt to describe the electromagnetic field propagation, leaded to spurious (non-physical) solutions. The FDTD method selects from all four Maxwell equations the two curl equations and solves them numerically by finite differences in time domain. The grid points where the electric and magnetic fields are calculated alternates in space forming the FDTD cell (Fig. 2.2). The FDTD algorithm discovered by Kane S. Yee [16] r describes the electromagnetic field in such a way that every electric field E component r r is surrounded by four circulating magnetic field H components, and every H r component is surrounded by four circulating E components. The Maxwell’s equations are simulated by the FDTD algorithm in both pointwise differential form and macroscopic integral form. The FDTD cells make obvious the Faraday’s Law and Ampère’s Law contours. The integral form is extremely useful in specifying field boundary conditions and singularities.

Figure 2.2. The FDTD cell.

r r The E and H components are centered in time in a leapfrog arrangement. The time and space derivatives in the curl equations are approximated with finite central finite-difference expressions of second order of accuracy.

19 Chapter 2 – Background Knowledge

Maxwell’s curl equations in the 3-D Cartesian system are

∂E 1  ∂H ∂H  x  z y  =  − −σ Ex  , (2.9a) ∂t ε  ∂y ∂z 

∂E y 1  ∂H x ∂H z  =  − −σ E y  , (2.9b) ∂t ε  ∂z ∂x 

∂E 1  ∂H ∂H  z  y x  =  − −σ Ez  , (2.9c) ∂t ε  ∂x ∂y 

∂H 1  ∂E ∂E  x  y z '  =  − − ρ H x  , (2.9d) ∂t µ  ∂z ∂y 

∂H y 1  ∂Ez ∂Ex '  =  − − ρ H y  , (2.9e) ∂t µ  ∂x ∂z 

∂H 1  ∂E ∂E  z  x y '  =  − − ρ H z  . (2.9f) ∂t µ  ∂y ∂x  Let us take the equation (2.9a) to see how these curl equations are transformed into finite difference equations. The discretized form of (2.9a) is

 n+ 21  1  n+ 21  1  n+1 n   , + , kji  −  , − , kji  ()− (),,,, kjikji 1 H z  2  H z  2  x EE x =  − ∆t ε (),, kji  ∆y   (2.10)  1   1   n+ 21 n+ 21  H y  ,, kji +  − H y  ,, kji −   2   2  n+ 21 − σ ().. (),, kjikji  ∆z E x   

The component n+ 21 ,, at time step n+1/2 is not calculated directly in E x (kji ) FDTD scheme, but it may be approximated by the arithmetic average between the components calculated at time steps n and n+1. The final result is an explicit expression of the component at time step n+1 when the components at previous time steps are already known: σ (),, ∆tkji ∆t 1 − ε (),,2 kji ε (),, kji n+1(),, kji = n (),, kji + × E x σ (),, ∆tkji E x σ (),, ∆tkji 1 + 1 + ε (),,2 kji ε (),,2 kji (2.11)

 n+ 21  1  n+ 21  1  n+ 21  1  n+ 21  1     , + , kji  −  , − , kji   ,, kji +  −  ,, kji −   H z 2 H z 2 H y 2 H y 2      −       ∆y ∆z     

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It can be easily seen that the leapfrog time-stepping is fully explicit, therefore it avoids completely the problems involving simultaneous equations and matrix inversion. The space step (cell size) is chosen as small as possible in order to describe accurately the device geometry. However, the total number of cells in the computational domain must be reasonably low in order to fit in the computer memory. The computation time is practically proportional with the total number of cells, therefore a too small cell size might lead to an excessive running time. The expected result accuracy is a very important criterion for choosing the cell size. It is largely accepted that 10 to 20 cells per the smallest wavelength of interest is a good choice. The selection of the time step is accomplished according to the stability criterion Courant-Friedrichs-Levy (CFL). It can be shown that the FDTD method is numerically stable, as far the time increment does not exceed a specific bound

−1 k  111  2 t ≤∆  + +  . (2.12)  2 2 2  c  ∆ ∆ ∆zyx  where k is the Courant-Friedrichs-Levy (CFL) factor and c is the speed of light. The time domain data provided by FDTD can be Fourier transformed in frequency domain. The ratio between the transmitted and reflected pulses at all the circuits ports over the incident pulse provide the scattering S parameters over the frequency bandwidth. The field excitation is often chosen as a Gaussian pulse

()−Tt 2 − 0 T z )( = z0eEtE . (2.13) where T is the pulse half width in time domain and T0=4T. The maximum frequency 1 from the Gaussian spectrum, on which we can rely, is f = [17]. max 2T A ‘hard’ voltage source it is not a good option for FDTD simulations on planar circuits, because the important quantity of electric charge deposited on FDTD grid [22]. Although the FDTD method is divergence free in a source free region, some excitation sources may produce a non-zero divergence field. The divergence of the electric field can be expressed as a non-physical charge, which cannot move itself along the grid, but which contributes to the input signal with a spurious DC tail. In [22], it is shown that not only voltage sources can deposit charges but also the current sources can produce temporary charges. These charges may be persistent when

21 Chapter 2 – Background Knowledge the current source has a DC component. As it will be shown in Chapter 3, our numerical experiments confirm that the geometry of the source dictates the amount of charging for a given temporal form. Numerical experiments have proved that the transparent ‘lumped’ source, occupying only one cell generates an insignificant numerical charge compared to the ‘hard’ source with a perfect electric conductor (PEC) below the microstrip line [23]. This fact is expressed in a less distortion (DC tail) of the excited pulse. In [25], it is recommended a “soft” source for planar circuits

∆tn 1 n V s () n− Rs (),, kji = + 2 , (2.14) E s sss ∆z I s ∆z where 1  1 1  n−  n− n−  s 2 =  HI x 2 (),1, kji sss −− H x 2 (),, sss  ∆⋅ xkji   (2.15)  1 1   n− n−  +  H y 2 (),, kji sss − H x 2 ()− ,,1 sss  ∆⋅ ykji   In FDTD algorithm, there is a half time step offset between the electric and the magnetic field. In the same way, when the Ohm’s law is applied, there will be a half time step offset between the voltage and the current. Therefore, in order to calculate the impedance, the current needs to be at the same point as the voltage Vk as Ik-1/2 [24]

k − 2/1 ()f = −1 ()III kk ()ff . (2.16) Then, the characteristic impedance can be calculated from π ∆− tfj k ()f eV Z = . (2.17) ff −1()II kk () The computational domain is always finite, therefore some boundary conditions need to be applied. Sometimes, very seldom, the analyzed structure has symmetry planes and the boundary conditions can be expressed as magnetic walls or perfect magnetic conductors (PMC). The metallic enclosure (housing), ground plane, etc. can be considered as perfect electric conductors (PEC). Besides PMC and PEC, a very important case is the absorbing boundary conditions (ABC). This is the case when the pulse should suffer a minimum spurious reflection at the boundary of the computational domain. The FDTD analysis depends drastically on the ABC quality. As it will be shown in Chapter 3, a poor ABC, such as the first-order Mur’s ABC [18], limits the method

22 Chapter 2 – Background Knowledge accuracy. Nevertheless, the Bérenger’s Perfectly Matched Layer (PML) [19-21] can increase the FDTD accuracy. The PML idea is to use a lossy material to match the incident waves. However, for a isotropic lossy material, the match occurs only at normally incidence, therefore such a material has only a limited applications as an ABC. A PML should match waves of arbitrary incidence, polarization, and frequency. The Bérenger’s innovation consits in a derivation of a split-field formulation of Maxwell’s equations; namely, each vector field component is split into two orthogonal components. The PML technique decomposes each field projections in two, and the wave incident to PML is attenuated via electric (σ) and magnetic (σ*) conductivity. The extremely small reflection is satisfied by the impedance matching condition perpendicularly to the PML layer. In a continuous space, the PML provides a perfect matching with the computational field. However, the FDTD space is discrete, therefore large reflections may result. On the FDTD grid, the electric and magnetic material properties are represented in a piecewise constant manner. As well, the electric and magnetic material properties are spatially staggered. Thus, large spurious reflections may result from discretization errors. The values of electric (σ) and magnetic (σ*) conductivities should satisfy the impedance matching condition.

σ * µ − j 2πf = const. , (2.18) σ ε − j 2πf where µ is the magnetic permeability, ε is the electric permitivity and f is the frequency. For a normal incidence on the PML layer, the matching conditions implies σ * µ = 0 . (2.19) σ 0εε r The conductivity inside PML increases with the distance from the PML – computational domain interface. For two-dimensional cases one of the best profile for the conductivity is the geometric series profile [20-21]. However, the computing algorithm for the 2-D PML parameters [20-21] cannot be straightforward applied to the 3-D case.

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In the PML layer, a linear discretization scheme was preferred to a exponential discretization scheme, as the wave decays in space inside PML, but not in time. The electric (magnetic) conductivity is obtained by the integration of the geometric profile between two electric (magnetic) field grid points. The electric conductivity σl on the electric field points is given by

l 0εσ r g − )1(  g  σ l =  l0 δδ l0 g +−+ )1)(1(  , (2.20) ln g  g  where l=0,1,2… represents the grid point index inside PML, σ0 is the electrical conductivity at PML interface, g is the geometric progression ratio and δl0 is the Kronecker symbol (equal to 1 when l=0, zero in all the other cases). The PML has nl distinct layers. The magnetic absorption is described by a magnetic conductivity applied on the magnetic field grid points, which are shifted half a cell relative to electric grid points εσ g − )1( σ * = 0 r g l , (2.21) l η 2 ln g where η is the plane wave free space impedance. For the input port, due to the association of the magnetic grid points to a cell number, the index l needs to be replaced by l-1. If the signal leaves the computational domain at both input / output ports along y

* 2 axis; then only σy and = yy /ησσ are non zero, and all the other components along the x and y axes cancel. It can be proved, that the domain of validity of the PML technique is bounded by a frequency fc, which depends on the numerical conductivity implemented in the first row of the layer, denoted by σn(0)

σ n )0( c 1− g f c == nl R )0(ln , (2.22) 0 42 ππε ∆x g −1 where R(0) is the apparent reflection coefficient at the normal incidence.

2.3. Elements of Microwave Filters

The notions on microwave and microstrip filters, introduced in this section, will be used in Chapter 4 to discuss the novel preselect filters developed for mobile communications front ends.

24 Chapter 2 – Background Knowledge

Filters are devices that take an input waveshape and modify the frequency spectrum to produce an output waveshape. Let Pin, PR, f, ω, Γ be the incident power, reflected power, signal frequency, angular frequency, and the reflection coefficient, respectively. The most important filter parameters can be listed as

PL • insertion loss IL −= log10 10 . (2.23) Pin

PR  2  • reflection loss RL −= log10 10 log10  Γ−=  . (2.24) Pin  

PL • in-band rejection RJ −= 10log10 − ILm . (2.25) Pin

• transmission phase (rads) φT = arg(IL) . (2.26)

dφT 1 dφT • the group delay τD (seconds) τ == . (2.27) D d 2πω df • maximum deviation from linear phase DLP

DLP max(T −= ωφ tK ), (2.28) where the constant K in (2.28) can been chosen to minimize the deviation from linear phase. The filter frequency response can be worse for a pulsed signal than for a steady state signal. Two dips in the curve IL(f), which appear for a pulsed input signal are called rabbit ears. Filters may be classified in many ways. One way is according to the type of construction used. Examples are the lumped element filters and transmission line filters. The lumped element filters are used at frequencies ranging from DC to few hundreds of MHz. Above these frequencies, transmission line filters are used. The filter function permits the clasification in low-pass filters (LPF), high-pass filters (HPF), band-pass filters (BPF), band stop filters (BSF) or all-pass filters. Filters can be also classified according to the realized transfer function. The transfer function is defined as the square magnitude of the forward transmission 2 coefficient S21 . The filter attenuation is then expressed by the transducer loss or by the insertion loss in the matched case

 1  L = log10   . (2.29) 10  2  S21   LS == ZZZ 0

25 Chapter 2 – Background Knowledge

The following discussion will refer to the transfer function of a low pass filter prototype. All the other filter types, such as BPF, HPF, etc., can be designed by an appropriate transformation of the low pass prototype filter. The prototype transfer 2 function S21()Ω' depends on the normalized (angular) frequency

ω ' '=Ω , (2.30) ' ω 1 where ω ’ and ω ’1 are the angular and the angular cut-off frequency of the prototype filter, respectively. The prototype filter is also designed for source and load impedances equal to unity. However, the filter can be easily generalized for arbitrary frequencies and arbitrary impedances. The low pass prototype filter response is exemplified in Fig. 2.3 for maximally flat design (Fig. 2.3a) and for equal-ripple design (Fig. 2.3b). A low-pass filter prototype filter can be transformed into a band-pass prototype using frequency transformations. The band-pass responses are illustrated in Fig. 2.3c and Fig. 2.3d. The low pass prototype filters are illustrated in Figs. 2.4a-b and their duals in Figs. 2.4c-d.

Figure 2.3. Prototype filter response. a) low pass maximally flat b) low pass equal-ripple c) band-pass maximally flat d) band pass equal-ripple.

26 Chapter 2 – Background Knowledge

a) Low pass prototype for odd n b) Low pass prototype for even n

c) Dual low pass prototype for even n d) Low pass prototype for odd n

Figure 2.4. Low-pass prototype filters and their duals.

An alternative description of prototype filters uses the modified impedance inverters (Fig. 2.5) and admittance inverters (Fig. 2.6), which are frequently used in microwave design.

Figure 2.5. Modified prototype filter using impedance inverters.

27 Chapter 2 – Background Knowledge

Using obvious notations from Fig. 2.4a and Fig. 2.5, the impedance inverter parameters can be calculated from

LR aS 1 K01 = , gg 10

L L ()ka +1 K = ak , kk +1, ntok −= 11 gk gk +1

anRL L K nn +1, = . gg nn +1

Figure 2.6. Modified prototype filter using admittance inverters.

In the same way as before, using notations from Fig. 2.4c and Fig. 2.6, the admittance inverter parameters are given by

CG aS 1 J01 = , gg 10

C C ()ka +1 J = ak , kk +1, ntok −= 11 gk gk +1

anGC L J nn +1, = . gg nn +1

The elliptic response is hard to implement for microwave filters. However, filters, using cross-coupling between resonators, can implement the generalized Chebyshev response [35, 41], which provides a transmission zero close to the cut-off frequency and a sharper profile. The generalized Chebyshev response is given by [35]

28 Chapter 2 – Background Knowledge

2 1 S ()' =Ω , (2.31) 21 22 1 ε FN ()Ω+ where ε is the pass-band ripple related to a given return loss LR (in dB) and 1 ε = . (2.32) 10−()LR 10 −1

For n even [35] the form Fn (Ω') becomes

 −1 −1 a −ΩΩ 1''  −1 a +ΩΩ 1''  Fn () (n −=Ω ) ()+Ω cosh'cosh2cosh'   + cosh   . (2.33)   a Ω−Ω ''   a Ω+Ω '' 

For n odd [41] the form Fn (Ω') becomes

  2    −1 a −Ω 1'  −1  Fn () (n −=Ω ) Ω'cosh1cosh'  ()Ω+ 'cosh . (2.34)   2 Ω−Ω '' 2     a   The generalized Chebyshev response is shown in Fig. 2.7 as a function of the normalized frequency Ω'. The response has been plotted for n = 4, 5, 6, 7 and

a =Ω 23.1' . The low-pass response from Fig. 2.7 can be converted to a band-pass response using the following frequency transformation

Ωr  Ω Ωr  '=Ω  −  . (2.35) Ω−Ω 12  Ωr Ω  The fractional bandwidth (FBW) is defined as Ω−Ω FBW = 12 . (2.36) Ωr

The locations of the two band-pass filter finite frequency attenuation poles Ω a and

Ω b in Fig. 2.3d are given by

Ωr  2  a =Ω  'a FBW ()'a FBW +⋅Ω+⋅Ω− 4  , (2.37) 2  

Ωr  2  b =Ω  'a FBW ()'a FBW +⋅Ω+⋅Ω 4  . (2.38) 2  

29 Chapter 2 – Background Knowledge

0 n=6 n=4 -20

-40 n=5

-60 Filter Response (dB) n=7

-80

-100

-120 0 0.5 1 1.5 2 2.5 3 ' Ω Ω0 = 1.23 Normalized frequency

Figure 2.7. Response of low-pass generalized Chebyshev filter of order n.

2.3.1. Microstrip Filters

Microstrip filters take advantage of the planar technology. All the filter configurations (low pass, high pass, etc.) can be manufactured using microstrip technology. The most popular types of microstrip filters include end-coupled filter (Fig. 2.8a), parallel coupled filter (Fig. 2.8b), staggered resonator filter (Fig. 2.8c), step-impedance resonator filter (Fig. 2.8d), interdigital filter (Fig. 2.8e), hair-pin resonator filter (Fig. 2.8f), and comb- line filter (Fig. 2.8g). The dual mode concept, which has been used for a while in waveguide cavities [29], initiated the apparition of microstrip dual mode filters (DMF). Dual mode resonators (DMR) are perturbed resonators, in such a way that two resonating modes, initially degenerate, can couple each other offering a dual mode filter (DMF). The first investigation of a microstrip DMR was made by Wolff [30]. Since then DMF evolved towards new designs [31-34]. Another interesting solution to improve the filter skirt is the cross coupling between resonators. The cross-coupling mechanism [35-36] makes quasi-elliptical filter response [37-40]. Solutions to improve the microstrip filters characteristics, considered the use of HTS materials the unloaded quality factor enhancement.

30 Chapter 2 – Background Knowledge

New designs of meander loop DMF and filters with cross-coupled compact resonators developed for GSM / GPRS basestations will be presented in Chapter 4.

Figure 2.8. Few examples of microstrip band-pass filters a) end-coupled filter [27], b) parallel-coupled (also called edge-coupled) filter [45], c) forward-coupled filter, also called staggered resonator filter or pseudo-interdigital filter [43, 44], d) step-impedance resonator (SIR) filter [46], e) interdigital filter [28], f) hair-pin resonator filter [46, 47], g) comb-line filter [28].

31 Chapter 2 – Background Knowledge

2.4. High Temperature Superconductivity for Mobile Communictions

Basic concepts in High Temperature Superconductors (HTS) technology and its advantages for mobile communications are presented in this Section. The HTS technology benefits for the base stations front ends and antennas motivated the preliminary experimental investigations on HTS devices, which are described in Chapter 5. A material is called superconductor if its thermodynamic state is inside the volume shown in Fig. 2.9. The volume is limited by three key parameters, which are: the critical temperature Tc, the critical magnetic field Hc and the critical current density

Jc. A material is superconductor as far the temperature, magnetic field applied and current flowing through do not overpass the critical values specific to that material [48].

Figure 2.9. The thermodynamic state diagram of a superconducting material.

The J. G. Bednorz and K. A. Müller discovery in 1986 triggered researches on a new class of materials with high Tc. These materials, with critical temperatures usually above the temperature of liquid nitrogen (77K), are called high temperature superconductors (HTS). Examples of few HTS materials are given in Table 2.1.

Table 2.1. Examples of HTS materials [48, 49].

HTS Material TC (K) Notation

YBa2Cu3O7-δ 85 – 93 (in thin film form) Y-123 (YBCO)

YBa2Cu4O8 80 Y-124

Tl2Ba2Ca2Cu3O10 125 - 127 Tl-2223

Tl2Ba2CaCu3O8 100-106 (in thin film form) Tl-2212

(La2-xSrx)CaCu2O6 60 --

Bi2Sr2Ca2Cu3O10 110 Bi-2223

32 Chapter 2 – Background Knowledge

Due to the DC zero resistance of the superconductors, a current induced in a superconductor ring will flow forever. The AC resistance slowly increase with the frequency increase is presented in Fig. 2.10. In cellular band, the AC resistance is one thousandth of that in the best ordinary conductor.

Figure 2.10. The AC losses [48] in HTS films compared to Copper (dashed line). Filled circles represent high quality YBCO epitaxial films and open circles designate the polycrystalline samples.

HTS materials can be obtained using different technological methods. Bulk materials are manufactured mainly using ceramic technology or crystal growth. HTS crystal growth is a technique for obtaining materials with very good properties but is very expensive. An alternative approach is the thick film technology. The copper microwave components, such as resonant cavity filters are coated with a paste of superconductor precursor material and then fired to form a ceramic superconducting coating. Nevertheless, the crystalline quality of the resultant material is poor and the maximum handled power is low, when compared with HTS thin films. Thin film technology [50-52] is the best solution for compact HTS devices. Thin film technology was available mainly due to the advancements in semiconductor industry. The thin films are grown or deposited on crystalline, high dielectric constant substrates. Examples of substrates for HTS thin films are given in Table 2.2. There are

33 Chapter 2 – Background Knowledge several techniques of obtaining thin films. Laser ablation [51, 52] is a technique currently used for obtaining good quality, uniform and relatively large, 2 inches in diameter or more, thin films. A less expensive deposition technique is the RF deposition. YBCO thin film devices fabricated by RF deposition will be presented in Chapter 5.

Table 2.2. Examples of substrates for HTS thin films [53, 54]. Substrate Dielectric constant ε at RF Notation

Lanthanum Aluminate (LaAlO3) 23 LAO Yttria Stabilized Zirconia 25 YSZ

Magnesium Oxide (MgO) 8 to 9.87

Sapphire (Al2O3) 8.4 to 11.5

A typical HTS thin film is thicker than the superconducting penetration depth, which is about 0.3 microns at 77 K [48]. Double sided deposition is required by very low loss devices. An HTS device is fabricated by a standard photolithographic processing. Electric contacts are normally made by depositing of 0.5 µm thick gold film. Finally, the HTS device is mounted into a microwave housing with the input and output ports electrically joined with SMA-connectors using silver paint.

2.4.1. The Cryogenic Front Ends

After the above short introduction in high temperature superconductors, the HTS technology application to base stations receivers is discussed. The receiver front-end plays a very important role in the receiver operation no matter the receiver architecture. It selects and amplifies the signal received in a certain frequency band. It also rejects any signal out-of-band, which can cause interference with the desired signal leading to the apparition of the intermodulation (or IM) products (IMP) or can even saturate the amplifiers. The quality of a signal can be expressed through signal to noise ratio (SNR). Along the amplification and downconversion chain, active devices add noise to the

34 Chapter 2 – Background Knowledge incident noise. The noise figure (NF) express in dB how much a circuit or component affects the SNR.

NF = 10 ()F ;log10 = ()in ()NSNSF out , (2.39) where F is called the noise factor and is a number greater than 1. S represents the signal power and N is the noise power. A passive device does not add noise power, then

out = NN in . However, out < SS in and SNRout < SNRin due to the losses in the passive component. Hence, the noise figure of a passive component is equal to its insertion loss. The noise figure of a receiver chain consisting of N elements is given by the Friis formula

F2 −1 F3 −1 Fk FN total FF 1 += + L++ L++ , (2.40) G1 GG 21 LGGG k −121 LL GGGG Nk −− 1121 where Fk and Gk are the noise factor and the available gain respectively, of the k component in the chain. This formula is derived in condition of neglecting any mismatches between the components; therefore, the total available gain of the receiver is assumed to be the product of the available gain of all components. The first device in the receiver chain is typically a preselect filter, a multiplexer, a chanalizer, etc. The noise figure of this passive device has to be very low for a good overall receiver noise performance. In conclusion, advantage can be taken from the low loss of HTS devices not only for gain increase, but also for noise figure improvement. For the maximum benefit, the HTS device should be connected in the receiver front-end, as the first component in the receiver noise chain. It can been seen from equation (2.40) that the noise figure of the first device in the chain has a very important role. In most of the cases the first device connected to the antenna is a passive device which has its NF equal to IL. This first device is typically a preselect filter (or multiplexer, chanalizer) providing to the low noise amplifier (LNA) only the desired band of spectrum otherwise the amplifier could be blocked (saturated) by the all incoming signals. In conclusion, the noise floor in the BS receiver can be kept very low if that receiver uses an HTS device as preselector filter or multiplexer. The outstanding noise performance of the HTS devices is derived from their very high quality factors. If the noise is expressed in terms of noise temperatures rather than noise factors, the enhancement of the receiver sensitivity due to the use of HTS device can be written as:

35 Chapter 2 – Background Knowledge

+ TT (without HTS) Sensitivity improvement = BSa . (2.41) + BSa HTSwithTT )( From formula (2.6) the range extension factor (REF) is given by

Noise unimproved−Noise improved REF =10 10*γ , (2.42) where γ is the path loss exponent, as defined by (2.5). However, to take advantage of the improvement of the cryogenic front-end noise figure a low antenna noise temperature (150

36 Chapter 2 – Background Knowledge performance arises from having two signals near the band edge where the group delay is greater. The cryogenic front-ends have found already industrial applications for the analog (1G) wireless networks such as the North American analog system AMPS [65-67]. There are installed (since 1996) even now hundreds of HTS subsystems in 1G networks to provide coverage and sensitivity enhancements. The field trials proved an enhancement of the voice quality enhanced. For 1G networks the high selectivity of the HTS filters found an outstanding applications in the interleaved AMPS spectrum [86]. There are also strategies to use the benefit of the HTS for 3G networks [55-60]. For areas with higher traffic, the maximum cell radius is not limited by the link budget considerations, but rather by capacity considerations (interference-limited system). Here, the reduction of receiver noise under certain circumstances can be transformed into increased capacity. This is especially true for 3G WCDMA systems, where a given signal-to-interference-and-noise ratio (SINR) reduced (thermal) noise allows a higher multiple-access-noise level and, therefore, more simultaneous users per area [55]. The normal operation of the HTS devices requires low temperatures such as 77 K. This can be obtained using liquid nitrogen available because its routine use in medicine, food processing and other industries. Another way to operate with HTS is to use physically small, closed-cycle cryogenic refrigeration systems. These coolers have orders of magnitude smaller weight, volume and electrical input power requirements than those for conventional superconducting materials, which must be operated below 20 K [72-73]. A cryocooler is a refrigerating system capable of achieving temperatures in the cryogenic range (less than 120 K) [72]. The cryocoolers are also used for infrared-imaging systems on remote-sensing satellites and military platforms.

37 Chapter 2 – Background Knowledge

Based on the “fit and forget” design philosophy [59], the cryocoolers are made invisible to the BTS operator requiring d.c. or a.c. supply from BTS site and minimal service utilities. They allow a low mean time between maintenance (MTBM) periods providing 40000 hour maintenance free cycle. The cryocooler are compact allowing the tower mounting due to their small mass and small wind resistance. They are capable to operate in all atmospheric conditions and ambient temperatures from a –40oC to +65oC. The base station (BS) cryocoolers are required to present an operational cool down time less than 2 hours. They provide a very stable cryogenic temperature, typically <0.5 K, medium capacity heat lift, typically 5 watts at 60 K into a +65oC reject temperature, “vibrationless” cold head, to eliminate induced microphonic effect in the RF components. The Striling cooler, which is considered to have the highest efficiency and the smallest size of any cryogenic cooling technology [59], can satisfy all the mentioned requirements. Another option is a highly-reliable closed-cycle Gifford-McMahon compressor/refrigeration unit, a design widely used in the semiconductor manufacturing industry.

2.4.2. HTS Antennas

First of all, some antenna parameters are defined for a better examination of the HTS antenna benefits. The antenna pattern is a mathematical function of coordinate, which describes the antenna properties in space [74]. A directional antenna receives or transmits the electromagnetic energy more efficient in some directions than in others. The opposite of directional antenna is the omnidirectional antenna. The power radiated by an antenna per unit solid angle in a certain direction is called radiation intensity. Directivity of an antenna is the ratio of the radiation intensity in a given direction to the radiation intensity averaged in all directions. The maximum directivity is obtained when the maximum radiation intensity is used [74]. Antenna gain is the ratio of the total radiated power to the total input (accepted) power. The relative gain is the ratio of the power gain in a given direction to the power gain of a referenced antenna (dipole, horn, etc.) in its referenced direction. The term

38 Chapter 2 – Background Knowledge dBi is used to reference the antenna gain with respect to an isotropic radiator. When referenced to a half-wave dipole, the term used is dBd (0 dBd = 2.1 dBi). The gain does not include losses arising from impedance mismatches (reflection losses) and polarization mismatches. These types of losses are included in antenna efficiency. The total efficiency e0 is the product of reflection efficiency er, conduction efficiency ec, and dielectric efficiency ed.. The antenna radiation efficiency is η = ee dc , and is used to relate the gain and directivity. The microstrip antennas are easy to integrate miniaturized microwave antennas [75]. However, from the mismatches point of view, the best feeding technique uses a coaxial feed (please refer to the technology discussed in Chapter 6), which is very difficult for HTS technology. In addition, microstrip antenna designed on thin high dielectric constant substrate have a narrow bandwidth. A promising feeding technique is used for aperture coupled, or slot coupled antennas [74]. The HTS antennas can provide an increased radiation efficiency [76] by reducing the conduction efficiency ec,. Loss reduction in feed lines, couplers, etc. makes HTS technology attractive for beam forming networks (BFN) [76] for advanced phased array antennas (please also refer to section 2.5). When normal conductors are used for BFN, the conduction losses increase drastically with frequency. Therefore the most advantageous use of the HTS BFNs and antennas is at higher frequencies when the reduced dimensions of the microwave circuits allow HTS thin film deposition and patterning on small areas without difficulty.

2.5. Antenna Array Concepts

The notions related to the antenna pattern and antenna gain have been introduced in Section 2.4.2. The maximization of the overall link budget requires a highly directive antenna. For a fixed antenna this is realized at the expense of a reduced coverage. Therefore, there is a need to steer the antenna main beam towards the direction of the desired signal. Mechanical steering is slow and less reliable. Fortunately, a fast and reliable electronic steering can be accomplished using antenna arrays. The simplest case of an antenna array is the linear array when all the antennas as array elements are positioned on a single axis. A linear array along Oz direction with M

39 Chapter 2 – Background Knowledge identical elements equally spaced with distance d is presented in Fig. 2.11. The mutual coupling between elements is neglected. The incident signal is assumed to be narrowband, i.e. with a bandwidth very small compared to the carrier frequency, and generated by a source far from the array in such a way all the elements receive a planar wave front with constant polarization, under the same angle θ with the array axis. For the beginning any noise is neglected. If the signal received by the first element is taken as a reference a1()θ = 1, then the signal an ()θ = ,..,2, Nn received by the element n will be phased due to the time delay required for the wave front to reach that element. The vector having as elements the signals received by each array element is termed the steering vector or array response vector [89] T a()θ = [1 a2 ()θ L aN ()θ ] , (2.43) where T refers to matrix transposition. The calculated or measured values of steering vectors for all the angular values constitute the array manifold. When the elements are identical, the signals received by antenna array elements have the same amplitude but different phase ψn. Then T  jψ j N 1 jψψ N  a()θ = 1 e 2 L − ee . (2.44)   When the antenna’s elements are equally spaced 2πd ψ n −= θ )cos()1( . (2.45) n λ The signals from all elements are then combined after being weighted with the

αn weights wn, which are in general complex numbers nn ⋅= eww . All the weights form the weighting vector T w = [21 L www N ]. (2.46)

If the weights wi have the same magnitude but the phase is different, then the array is called a phased array. These weights are physically implemented by using phase shifters. If the phase shift between two consecutive elements is constant, for example

321 === K φαφαφφ N −1 N φα N N )1(,)2(,,2,,0 ⋅−=⋅−= α , (2.47) then the linear phased array is called linear uniform array.

40 Chapter 2 – Background Knowledge

Figure 2.11. Outline of a receiving linear antenna array.

After combining the antenna array response, the so-called the array factor (AF) is obtained as a complex number N H AF()θ aw == ∑ aw nn , (2.48) n=1 where by H it was indicated the Hermitian transposition. The beamforming is the process of modifying the antenna pattern by changing the weights. The antenna array behaves as a filter in spatial domain, rejecting the undesired signals and steering the main beam in the direction of the desired signal. The array pattern can be tailored even further, by steering the nulls in the direction of the interference sources in order to increase the immunity to interference. Relatively simple techniques are available to implement beamforming networks using cascaded 90o hybrid couplers as in the Butler matrix [79]. An alternative definition of the array factor is expressed by the AF(θ) magnitude normalized by its maximum value. For a uniform linear array the normalized array factor is given by

41 Chapter 2 – Background Knowledge

 Nψ  sin  1 2 AF()θ =   . (2.49) N ψ  sin   2 

In this case, the main beam can be steered towards any direction M ,,0 M ≤≤ πθθ just by electronically changing the phase shift α to the value 2πd α −= cos(θ ). (2.50) λ M When the array is not linear, the array factor will contain the dependence of the azimuth angle φ. The actual response of the antenna array y(θ) depends also on the pattern of each element called the unit pattern. It can be shown that the pattern of the antenna array is the product between the array factor and the unit pattern The advantage of phased arrays is that they require commonly available RF hardware and have been used in radar systems for quite a while. However, they do not have the ability to place nulls independently of the main beam direction. In the case of the even more simple and inexpensive alternative, of beamforming only by amplitude control wn [80-82], without changing the phase of wn, the nulls can be steered only in pairs. The application of the phased arrays and amplitude controlled arrays for mobile communications are decreased due to the inadequacy to consistently combine multipath sources.

2.5.1. Smart Antennas

By smart antenna is usually understood a multibeam or adaptive antenna [7]. The multibeam antenna is based on a finite set of weighting vectors, therefore the cell sector is covered by a number of predetermined main beams. By switching between the multibeams, the BS can choose that beam who suits the MS the best. The gain decreases with as much as 2 dB between beams due to the beam shape. This effect is termed as scalloping. The interference can be suppressed only if is not in the same beam. The interference or multipath can also make multibeam antennas lock onto the wrong beam.

42 Chapter 2 – Background Knowledge

The adaptive antennas do not have the problems of the multibeam antennas. In the case of an adaptive antenna shown in Fig. 2.12, the weights are continuously changed by an adaptive algorithm aiming to minimize the error function ε, which is the difference between the desired output (reference) and the actual array response.

Figure 2.12. Outline of a receiving adaptive linear antenna array.

There is a clear distinction between an adaptive antenna and a Maximal Ratio

Combiner (MRC) [83], which adjusts the complex wn to maximize the signal to noise ratio of the output. On one side, the MRC has wide separation between the elements in order to implement spatial diversity. On the other side, the adaptive array typically uses element separations of a fraction of a wavelength to avoid grating lobes. There is no feedback loop in the case of MRC, and the weights wn are adjusted separately in each diversity branch. MRC can achieve optimal performance in the presence of noise, but it does not provide the ability to reject interference or multipath.

43 Chapter 2 – Background Knowledge

For the beginning, we will consider a number M, (M < N), of pointwise signal sources sm(t) containing the complex modulation functions, (m=1,M) assumed zero mean and stationary. The signal induced by the nth element is M n )( = ∑ () (θ mnm )+ n ()tvatstx , (2.51) m=1 2 where vn(t) is the additive white noise with zero mean and variance (power) σ noise . The mean output power will be

= tytyEP )](*)([ = wHRw , (2.52) where E[.] signifies the expectation operator and R is the array correlation matrix [78] in such a way that the matrix element Rnl denotes the correlation between the signals received by the nth and lth elements of the array. M H H 2 H 2 = xx )]()([ = ∑ pttER ()()mm aa m σθθ noiseI ASA +=+ σ noiseI , (2.53) m=1 th where pm represents the power of the m signal source. The M by M matrix S denotes the source correlation, therefore for uncorrelated sources has zero nondiagonal elements, and the diagonal contains the signal powers. The N by M matrix A has the columns formed of the steering vectors corresponding to the directions of all point sources

= [()aaA 21 (θθ 21 )L a (θ MM )]. (2.54)

The signals xn(t) can be coherentely combined by the beamforming network, but the noise power remains unchanged if the noise sources are uncorrelated. Therefore, the antenna array provides an SNR improvement by the number of elements

out ⋅= SNRNSNR in . As shown in Fig. 2.12, the adaptive algorithm aims to minimize the mean square error (MSE) between the output of the antenna array and the reference signal. There are several algorithms, which can be used. One of the simplest, but not very attractive in practice, is the least mean square (LMS) algorithm. The error function describes a surface in the N dimensional weight space. The LMS algorithm calculates the gradient aiming to find a path to the global minimum of that surface. The weights are updated according to the procedure * n n +=+ µε n ()(2)()1( kxkkwkw ), (2.55)

44 Chapter 2 – Background Knowledge where k is the time step, µ is a constant called step size, ε is the error between the array output and the desired output, and * means the complex conjugation. Other algorithms as MUSIC or ESPRIT [78] are used for direction of arrival (DoA) estimation. The number of degrees of freedom for an antenna array is equal to the number of elements. It can be proved that such an adaptive array can cancel out up to N-1 interference sources, dramatically improving signal to interference plus noise ratio (SINR). Therefore, the smart antenna system has the ability to isolate the co-channel signals with the upshot an improved SINR. Interference reduction leads to an improved capacity [9]. When the gain and the phase of each antenna element is changed to obtain a maximum signal-to-interference plus noise ratio (SINR), an adaptive antenna is called optimal. However, the mobile communication environment cannot be accurately described by a number of point signal sources, due to the multipath and delay spread as discussed above. In a multipath environment the wanted signal and interference are no longer single point sources. Instead, there are many correlated sources due to the multipath reflections. The number of sources when considering multipath waves appear to be greater than the number of degrees of freedom of the antenna array, that is greater than number of antenna elements. th Let us assume that the m user transmits a signal gm(t) which is the baseband signal um(t) modulated with the carrier frequency fc

2πfj ct ()= mm ()etutg . (2.56) th The signal sm(t) coming from the m user is a sum of all the Qm multipath waves. If a single multipath wave is indexed by q then

Qm fj c t −τπ mq )(2 m ()ts = ∑ β )( ()−τ mqmmq etut q=1 (2.57) Qm 2πfj ct = ∑α )( ()−τ mqmmq etut q=1 where τmq is the time delay and βmq is the attenuation factor of the mq multipath wave. The factor

− 2 fj τπ mqc = βα mqmq e , (2.58) is the complex path fading with the magnitude obeying the Rayleigh distribution and phase uniformly distributed over [0, 2π].

45 Chapter 2 – Background Knowledge

Assuming that from all M users, only the jth user transmits the signal of interests, this signal can be separated from the co-channel interference (CCI) produced by other users. Then (2.51) becomes

Q j 2πfj ct )( = ()θ jnn eatx ∑α )( ()tut τ jqjjq +− q=1 14244444 4344444 Desired signal . (2.59) M Qm 2πfj ct ()θ mn ea α )( ()τ mqmmq +− n tvtut )( ∑∑ { ==11, ≠ jmm q noise 14244444444 4344444444 CCI From this perspective, it is clear that only a spatial processing is not satisfactory for the mobile channel. Better performance can be obtained by space-time processing [84-90] when the multipath environment can be beneficial. The local objects to MS act as a huge reflector antenna allowing an angular resolution far superior to the beamwidth [7]. Due to the enhanced immunity to multipath fading, smart antenna gives the possibility to configure the coverage of each BS to match the cell specific propagation conditions. The benefits of the smart antennas are attractive to 3G systems. Examples are the European project SUNBEAM (Smart Universal BEAMforming) [91], which builds on the work of TSUNAMI project (Technology in Smart antennas for UNiversal Advanced Mobile Infrastructure). This project studied the requirements implied by adaptive antenna in software radio base stations for 3G and beyond 3G systems. Also, the smart antenna allows the implementation of the space division multiple access (SDMA) concept [8], working as a dynamic sectorization when users within the same cell can operate on the same time and RF channel.

2.6. Chapter Summary

The chapter presents the fundamentals, which will be used in later chapters of the thesis. Since the main goal of the work is to provide solutions for RF interference reducing in mobile communications, some important concepts in mobile communications are presented. The GSM and the GPRS are also introduced. The Finite-Difference Time-Domain method is introduced as a powerful tool. The development of an efficient 3-D FDTD method for planar circuits will be discussed

46 Chapter 2 – Background Knowledge in Chapter 3. Concepts of microwave and microstrip filters are also presented in order to discuss, in Chapter 4, the development of new compact preselect filters for base station front-ends. The HTS technology is introduced as an attractive option to enhance the coverage and / or Quality of Service in Mobile Communications Services. The preliminary investigations of HTS devices presented in Chapter 5 were motivated by the possibility of using HTS technology for receiver front ends. Finally, the adaptive antennas are introduced as a promising technology to enhance SINR, to reduce the CCI and to provide a better coverage.

References Chapter 2

[1] M. J. Miller, B. Vucetic, L. Berry, “Satellite Communications – Mobile and Fixed Services”, Kluwer Academic, Boston, 1993 [2] T. S. Rappaport, “Wireless Communications – Principles and Practice”, Prentice Hall, Upper Saddle River, NJ, 1999 [3] J. Dunlop, “The Terrestrial Trunked Radio System (TETRA)”, presented at the “Workshop on 3G Wireless Networks: Technology and Advances”, Newcastle (NSW), Australia, August 2000 [4] J. D. Solomon, “Mobile IP – The Internet Unplugged”, PTR Prentice Hall, Upper Saddle River, New Jersey, 1998 [5] William C. Y. Lee, “Mobile Communications Engineering”, McGrawHill, New York, 1998 [6] R. Steele, L. Hanzo (Eds.), “Mobile Radio Communications – Second and Third Generation Cellular and WATM Systems”, John Wiley, Chichester 2000 [7] J. H. Winters, “Smart Antennas for Wireless Systems”, IEEE Personal Communications, Feb. 1998, pp. 23-27 [8] G. V. Tsoulos, “Smart Antennas for Mobile Communication Systems: Benefits and Challenges”, Journal of Electronics & Communication Engineering, vol. 11, April 1999, pp. 84 –94 [9] R. Simon, “Expanding Opportunities for HTS Technology in the Wireless Industry”, Superconductor and Cryoelectronics, Spring 2000, pp. 9-14

47 Chapter 2 – Background Knowledge

[10] R. Prasad, W. Mohr, W. Konhäuser editors, “Third Generation Mobile Communications Systems”, Artech, Boston, 2000 [11] H. Aghvami, B. Jafarian, “A Vision of UMTS/IMT 2000 Evolution”, Electronics and Communication Engineering Journal, vol. 12, 2000, pp. 148-152 [12] C. N. Yap, M. Kraner, N. A. Fikouras, S. R. Cvetkovic, “Novel and Enhanced Mobile Internet Protocol for Third Generation Cellular Environments Compared to MIP and MIP-LR”, First Conference on 3G Mobile Communications Technologies, London, 2000, pp. 143-147 [13] A. Mehrotra, “GSM System Engineering”, Artech, Boston, 1997 [14] J. Cai, D. J. Goodman, “General Packet Radio Service in GSM”, IEEE Communications Magazine, October 1997, pp. 122-131 [15] A. Taflove (Editor), “Advances in Computational Electrodynamics – The Finite- Difference Time-Domain Method”, Artech House, Boston, London, 1998 [16] K. S. Yee, “Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media,” IEEE Trans. Antennas Propagat., vol. AP-14, May 1966, pp. 302-307 [17] B. Houshmand, T. Itoh, M. Piket-May, “Advances in Computational Electrodynamics: The Finite-difference Time-Domain Method”, Norwood, MA, Artech House, 1998 [18] G. Mur, “Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic Field Equations”, IEEE Trans. Electromagnetic Compatibility, vol. EMC-23, Nov. 1981, pp. 377-382 [19] J.-P. Bérenger, “A Perfectly Matched Layer for Absorption of Electromagnetic Waves”, Journal of Computational Physics, vol. 114, 1994, pp. 185-200 [20] J.-P. Bérenger, “Perfectly Matched Layer for the FDTD Solution of Wave- Structure Interaction Problems”, IEEE Trans. Antennas and Propagation, vol. AP-44, 1996, pp.110-117 [21] J.-P. Bérenger, “Improved PML for the FDTD Solution of Wave-Structure Interaction Problems”, IEEE Trans. Microwave Theory and Techniques, vol. 45, 1997, pp. 466-473 [22] C. L. Wagner, J. B. Schneider, “Divergent Fields, Charge, and Capacitance in FDTD Simulations”, IEEE Transactions on Microwave Theory Tech., vol. 46, 1998, pp. 2131-2136

48 Chapter 2 – Background Knowledge

[23] R. J. Luebbers, H. S. Langdon, “A Simple Feed Model that Reduces Time Steps Needed for FDTD Antenna and Microstrip Calculations”, IEEE Trans. on Antennas and Propag., vol. AP-44, 1996, pp. 1000-1005 [24] J. Fang, D. Xue, “Numerical Errors in the Computation of Impedances by FDTD Method and Ways to Eliminate Them”, in IEEE Microwave and Guided Wave Lett., vol. 5, 1995, pp. 6-8 [25] J. B. Schneider, C. L. Wagner, O. M. Ramahi, “Implementation of Transparent Sources in FDTD Simulations”, IEEE Trans. Antenna and Propagation, vol. AP 46, 1998, pp. 1159-1168 [26] A. Taflove (Editor), "Computational Electrodynamics – The Finite-Difference Time-Domain Method", Artech House, Boston, London, 1995 [27] D. M. Pozar, “Microwave Engineering”, Adison-Wesley, Reading MA, 1990 [28] G. L. Matthaei, Young L., and E. M. T. Jones, “Microwave Filters, Impedance- matching Networks, and Coupling Structures”, McGraw-Hill, New York, 1964 [29] R. J. Cameron, “Dual-mode Realisations for Asymmetric Filter Characteristics”, ESA Journal, vol. 6, 1982, pp. 339-356 [30] I. Wolff, “Microstrip Bandpass Filter Using Degenerate Modes of a Microstrip Ring Resonator”, Electron. Lett., 1972, vol. 8, (12), 302-303 [31] M. Guglielmi, G. Gatti, “Experimental Investigation of Dual-Mode Microstrip Ring Resonator”, Proceedings of the 20th European Microwave Conference, Budapest, Sept. 1990, pp. 901-906 [32] R. R. Mansour, “Design of Superconductive Multiplexers Using Single-Mode and Dual-Mode Filters”, IEEE Trans. on Microwave Theory and Techniques, vol. 42, 1994, pp. 1411-1418 [33] J. A. Curtis, S. J. Fiedziuszko, “Miniature Dual Mode Microstrip Filters”, Digest of IEEE Microwave Theory and Techniques Symposium, 1991, pp. 443-446 [34] J. S. Hong, M. J. Lancaster, “Bandpass Characteristics of New Dual-Mode Microstrip Square Loop Resonators”, Electron. Lett., 1995, vol. 31, (11), pp. 891-892 [35] J.-S. Hong, M. J. Lancaster, “Design of Highlty Selective Microstrip Bandpass Filters with a Single Pair of Attenuation Poles at Finite Frequencies”, IEEE Trans. on Microwave Theory and Tech., vol. MTT-48, 2000, 1098-1107 [36] J.-S. Hong, M. J. Lancaster, “Cross-Coupling Hairpin-Resonator Filters”, IEEE Trans. on Microwave Theory and Techniques, vol. 46, 1998, pp. 118-122

49 Chapter 2 – Background Knowledge

[37] M. Reppel, J.-C. Mage, “Superconducting Microstrip Bandpass Filter on LaAlO3 with High Out-of-Band Rejection”, IEEE Microwave and Guided Wave Letters, vol. 10, no. 5, 2000, pp. 180-182 [38] M. Reppel, H. Chaloupka, S. Kolesov, “Advanced Lumped-Element Bandpass Filters”, in Applied Superconductivity 1997, Inst. Phys. Ser. No. 158, Edited by H. Rogalla and D. H. A. Blank, Bristol 1997, vol. 1, pp. 323-326 [39] I. Awai, T. Yamashita, “Theory on a Circular Dual-Mode Resonator and Filter with Internal Coupling Scheme”, Asia-Pacific Microwave Conference, APMC’97, 2-5 December 1997, Hong-Kong, 817-820 [40] R. Levy, “Synthesis of General Asymmetric Singly- and Doubly Terminated Cross-Coupled Filters”, IEEE Transactions on Microwave Theory and Techniques, vol. 42, 1994, pp. 2468-2471 [41] J. D. Rhodes, S. A. Alseyab, "The Generalized Chebyshev Low-Pass Prototype Filter", Circuit Theory Applicat., vol. 8, 1980, pp. 113-125 [42] G. L. Matthaei, C. Rautio, B. A. Willemsen, “Concerning the Influence of Housing Dimensions on the Response and Design of Microstrip Filters with Parallel-Line Couplings”, IEEE Transactions on Microwave Theory and Techniques, vol. 48, 2000, pp. 1361-1368 [43] G. L. Matthaei, G. L. Hay-Shipton, “Novel Staggered Array Superconducting 2.3-GHz Bandpass Filter”, IEEE Trans. on Microwave Theory and Tech., 1993, vol. 41, pp. 2345-2352 [44] G. L. Matthaei, G. L. Hey-Shipton, “Concerning the Use of High-Temperature Superconductivity in Planar Microwave Filters”, IEEE Trans. on Microwave Theory and Tech., 1994, vol. 42, pp. 1287-1294 [45] A. F. Sheta, J. P. Coupez., G. Tanné, S. Toutain, J. P. Blot, “Miniature Microstrip Stepped Impedance Resonator Bandpass Filters and Diplexers for Mobile Communications”, IEEE Microwave Theory and Techniques Symposium Digest, pp. 607-610, 1996 [46] K. Takahashi, M. Sagawa, M. Makimoto, “Miniaturized Hair-Pin Resonator Filters and Their Applications to Receiver Front-End MICs”, IEEE Microwave Theory and Techn. International Microwave Symposium Digest, 1989, vol. 2, pp.667-670

50 Chapter 2 – Background Knowledge

[47] A. Enokihara, K. Setsune, K. Wasa, M. Sagawa, M. Makimoto, “High Tc Bandpass Filter Using Miniaturised Microstrip Hairpin Resonators”, Electron. Lett., 1992, vol. 28, (20), pp. 1925-27 [48] M. Hein, “High Temperature-Superconductor Thin Films at Microwave Frequencies”, Springer, Berlin Heidelberg, 1999 [49] G. Burns, “High-Temperature Superconductivity”, Academic Press, Boston, USA, 1992 [50] J. George, “Preparation of Thin Films”, Marcel Dekker Inc., 1992 [51] J. C. Miller, “Laser Ablation, Principles and Applications”, Springer Verlag, Berlin, 1994. [52] D. B. Chrisey, G. K. Hubler, editors, “Pulsed laser deposition of thin films”, John Wiley, New York, 1994 [53] J. M. Phillips, “Substrate Selection for High-Temperature Superconducting Thin Films”, Journal of Applied Physics, vol. 79, 1996, pp. 1829-1848

[54] J. Talvacchio, G. R. Wagner, S. H. Talisa, “High TC Film Development for Electronic Applications”, Microwave Journal, 1991, pp. 105-114 [55] M. Klauda, T. Kässer, B. Mayer, C. Neumann, F. Schnell, B. Aminov, A. Baumfalk, H. Chaloupka, S. Kolesov, H. Piel, N. Klein, S. Schornstein, M. Bareiss, “Superconductors and Cryogenics for Future Communications Systems”, IEEE Trans. Microwave Theory and Techniques, vol. 48, No. 7, 2000, pp. 1227-1239 [56] J.-S. Hong, M. J. Lancaster, R. B. Greed, D. Jedamzik, J.-C. Mage, H. J. Chaloupka, “A High-Temperature Superconducting Duplexer for Cellular Base-Station Applications”, IEEE Microwave Theory and Techniques, vol. 48, 2000, pp. 1336-1342 [57] J.-S. Hong, M. J. Lancaster, R. B. Greed , D. Voyce, D. Jedamzik, J. A. Holland, H. J. Chaloupka, J.-C. Mage, “Thin Film HTS Passive Components for Advanced Communication Systems”, IEEE Transactions on Applied Superconductivity, 1999, pp. 3893-3896 [58] D. Jedamzik, R. Menolascino, M. Pizarroso, B. Salas, “Evaluation of HTS Sub- Systems for Cellular Basestations, ” IEEE Trans. Applied Superconductivity, vol. 9, 1999, pp. 4022-4025, [59] B. Greed, D. C. Voice, D. Jedamzik, J. S. Hong, M. J. Lancaster, M. Reppel, H. J. Chaloupka, J. C. Mage, B. Marcilhac, R. Mistry, H. U. Häfner, G. Auger,

51 Chapter 2 – Background Knowledge

W. Rebernak, “An HTS Transceiver For Third Generation Mobile Communications”, IEEE Trans. Applied Superconductivity, vol. 9, 1999, pp. 4002-4005 [60] H. Chaloupka, D. Jedamzik, “HTS-Technology for UMTS Radio Basestation”, IEEE Internat. Symposium on Personal, Indoor and Mobile Radio Communications, vol. 3, 1998, pp. 1255-1259 [61] T. Nojima, S. Tarahashi, T. Mimura, K. Satoh, Y. Suzuki, “2-GHz Band Cryogenic Front End for Mobile Communications Base Stations Systems”, IEICE Trans. Commun., vol. E83-B, 2000, 1834-1843 [62] R. B. Hammond, D. J. Scalapino, J. R. Schrieffer, B. A. Willemsen, “HTS Wireless Filters: Past, Present and Future Performance”, Microwave Journal, vol. 41, 1998, pp. 94-107 [63] G. Koepf, “Superconductors Improve Coverage in Wireless Networks”, Microwaves and RF, 1998, pp. 63-73 [64] D. G. Smith, V. K. Jain, “Superconducting Filters for Wireless Communications: A Reappraisal”, IEEE Trans. Applied Superconductivity, vol. 9, 1999, pp. 4010- 4013 [65] SCT Inc., “A Receiver Front End For Wireless Base Stations”, Microwave Journal, 1996, 116-122 [66] A. I. Braginski, “Superconducting Electronics Coming to Market”, IEEE Trans. Applied Superconductivity, vol. 9, 1999, pp. 2825-2836 [67] E. R. Soares, K. F. Raihin, A. A. Davis, R. L. Alvarez, P. J. Marozik, G. L. Hey- Shipton, “HTS AMPS-A and AMPS-B Filters for Cellular Receive Base Stations”, IEEE Trans. Applied Superconductivity, vol. 9, No. 2, 1999, pp. 4018-4021 [68] T. Dahm, D. J. Scalapino, “Analysis and Optimization of Intermodulation in

High-TC Superconducting Microwave Filter Design”, IEEE on Applied Superconductivity, vol. 8, 1998, pp. 149-157

[69] K. Setsune, A. Kenokihara, “Elliptic-Disk Filters of High-TC Superconducting Films for Power Handling Capability Over 100W”, IEEE Microwave Theory and Techniques, vol. 48, 2000, pp. 1256-1264 [70] A. C. Anderson, H. Wui, et. al., “Transmit Filters for Wireless Basestations”, IEEE Trans. Applied Superconductivity, vol. 9, 1999, pp. 4006-4009

52 Chapter 2 – Background Knowledge

[71] MITEQ Inc., “Miniature, Low Noise Cryogenic Amplifiers“, Microwave Journal, 1999, pp.128-130 [72] G. Walker, “Nomenclature and Classification of Cryocoolers”, in Proceedings of the Symposium on “Low Temperature Electronics and High Temperature Superconductors”, The Electrochemical Society, 1988, pp. 221-218 [73] G. Walker, “Cryocoolers-Part I: Fundamentals and Part II: Applications”, Plenum Press, New York, 1983 [74] C. A. Balanis, “Antenna Theory”, John Wiley, New York, 1997 [75] M. A. Richard, K. B. Bhasin, P. C. Claspy, “Superconducting Microstrip Antennas: An Experimental Comparison of Two Feeding Methods”, IEEE Transactions on Antennas and Propagation, vol. 41, 1993, pp. 967-974 [76] H. Kobeissi, D. J. Drolet, K. Wu, M. G. Stubbs, G. Larralde, S. K. Rao, “High- Temperature Superconducting Beam Forming Network for Communication System Applications”, IEEE on Applied Superconduc., vol. 7, 1997, pp. 33-38 [77] L. C. Godara, “Applications of Antenna Arrays to Mobile Communications, Part I: Performance Improvement, Feasibility, and System Considerations”, IEEE Proceedings, vol. 85, 1997, pp. 1031-1060 [78] L. C. Godara, “Applications of Antenna Arrays to Mobile Communications, Part II: Beam Forming and Direction of Arrival Considerations”, IEEE Proceedings, vol. 85, 1997, pp. 1195-1245 [79] J. B.-Yen Tsui, “Digital Microwave Receivers - Theory and Concepts”, Artech, Norwood, MA, 1989 [80] T. B. Vu, “Method of Null Steering without Using Phase Shifters”, IEE Preceedings, vol. 131, Pt. H, 1984, pp. 242-246 [81] T. B. Vu, “Pattern Nulling in Difference Pattern by Amplitude Control”, IEEE Trans. Antennas and Propagation, vol. AP. 33, 1985, pp. 669-671 [82] T. B. Vu, “Simultaneous Nulling in Sum and Difference Patterns by Amplitude Control”, IEEE Trans. Antennas and Propagation, vol. AP. 34, 1986, pp. 214- 218 [83] J. C. Liberti, T. S. Rappaport, “Smart Antennas for Wireless Communications. IS-95 and Third Generation CDMA Applications”. Prentice Hall PTR, Upper Saddle River, NJ, 1999

53 Chapter 2 – Background Knowledge

[84] H. M. Jones, P. B. Rapajic, R. A. Kennedy, “Bound on Capacity Improvements Using Spatial Filtering”, Proceedings of the Fifth International Symposium on Signal Processing and its Application, ISSPA ’99, vol. 2, 1999, pp. 987-991 [85] B. Xu, T. B. Vu, “Effective Interference Cancellation Scheme Based on Smart Antenna”, Electronics Letters, vol. 33, 1997, pp. 1114-1116 [86] K. Sheikh, D. Gesbert, D. Gore, A. Paulraj, “Smart Antennas for Broadband Wireless Access Networks”, IEEE Communications Magazine, November 1999, pp. 100-105 [87] L. C. Godara, M. R. S. Jahromi, “Limitations and Capabilities of Frequency Domain Broadband Constrained Beamforming Schemes”, IEEE Trans. on Signal Processing, vol. 47, Sept. 1999, pp. 2386-2395 [88] G. V. Tsoulos, M. A. Beach, “Calibration and Linearity Issues for an Adaptive Antenna System”, The IEEE 47th Vehicular Techn. Conf., 1997, vol. 3, 1997 [89] A. J. Pulraj, C. B. Papadias, “Space-Time Processing for Wireless Communications – Improving Capacity, Coverage, and Quality in Wireless Networks by Exploiting the Spatial Dimension”, IEEE Signal Processing Magazine, 1997, pp. 49-83 [90] S. Anderson, B. Hagerman, H. Dam, U. Forssén, J. Karlsson, F. Kronestedt, S. Mazur, K. J. Molnar, “Adaptive Antennas for GSM and TDMA Systems”, IEEE Personal Communications, 1999, pp. 74-86 [91] A. Pérez-Neira, X. Mestre, “Smart Antennas in Software Radio Base Stations”, IEEE Communications Magazine, vol. 39, 2001, pp.166-173

Acronyms and Abbreviations in Chapter 2

1G, 2G, 2.5G, 3G First, second, intermediate, third generation of standards in mobile communication AEF Area Extension Factor AF Array Factor ABC Absorbing Boundary Condition AMPS Advanced Mobile Phone Service BER Bit Error Rate

54 Chapter 2 – Background Knowledge

BFN Beam Forming Network BPF Band-Pass Filter BS Base Station BSF Band Stop Filter BSRF Base Stations Reduction Factor BTS Base Transceiver Station CCI Co-channel Interference CDMA Code Division Multiple Access CFL criterion Courant-Friedrichs-Levy criterion COST (European) Co-operative for Scientific and Technical research DCS-1800 Digital Cellular System in 1800 MHz bandwidth DMF Dual Mode Filter DMR Dual Mode Resonator DoA Direction of Arrival FBW Fractional Bandwidth FDD Frequency Division Duplexing FDMA Frequency-Division Multiple Access FDTD Finite Difference Time Domain Method FEM Finite Element Method GSM Global System for Mobile communications GPRS General Packet Radio Service HPF High Pass Filter HTS High Temperature Superconductors IDM Inter-Modulation Distortion IF Intermediate Frequency IL Insertion Loss IPv4 Internet Protocol version 4 IR Infrared IMP Inter-Modulation Products IS-95 Interim Standard 95 ISI Inter-Symbol Interference

LAO LaAlO3 LoS Line of Sight LMS Least Mean Square

55 Chapter 2 – Background Knowledge

LNA Low Noise Amplifier LPF Low Pass Filter MAHO Mobile Assisted Handover MIP Mobile Internet Protocol MoM Method of Moments MRC Maximal Ratio Combiner MS Mobile Station MSE Mean Square Error MTBM Mean Time Between Maintenance NF Noise Figure PMC Perfect Magnetic Conductor PEC Perfect Electric Conductor PML Perfect Matched Layer PMR Professional (Private) Mobile Radio Q-factor Quality Factor QoS Quality of Service REF Range Extension Factor SDMA Space Division Multiple Access SINR Signal to Interference and Noise Ratio SNR Signal to Noise Ratio TDD Time Division Diplexing TDMA Time Division Multiple Access TS Time Slot

TBCCO Tl2Ba2Ca2Cu3Ox

Tl-2212 Tl2Ba2CaCu2O8

Y-123 YBa2Cu3O7-δ

YBCO YBa2Cu3O7-δ YSZ Yttria Stabilized Zirconia UMTS Universal Mobile Telecommunications System WCDMA Wideband Code Division Multiple Access WLAN Wireless Local Area Network

56 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

C H A P T E R 3 Designing of Microstrip Devices Using the FDTD Method

The Finite-Difference Time-Domain (FDTD) method introduced in Section 2.2 is a powerful tool for solving various electromagnetic (EM) problems. The development of a 3-D FDTD method for planar devices is presented in this chapter. This method offers an accurate design technique for new type of microstrip filters, which will be discussed in Chapter 4. A signal estimation technique, discussed in Section 3.5, was developed in order to reduce the FDTD computation time. By using this signal estimation technique, the number of FDTD iterations was reduced up to five times [1]. A design algorithm, which uses FDTD and Neural Networks [1], is presented in Section 3.6. This is much faster than the FDTD method alone.

3.1. Introduction

The FDTD signal excitation contains a voltage source below the microstrip line. The signal needs to propagate a certain distance along the line to let the transient modes to vanish and reach their true modal nature. In order to minimize the computational domain, the pulse propagation along a simple input microstrip line is first simulated. After the signal acquires the correct transversal profile, the pulse is copied at the input of the microstrip device in order to be analyzed. The same input signal can be used in several simulations of various planar structures with the substrate and the FDTD grid not changed. FDTD method allows the analysis of the electromagnetic field in the planar structure at different time instances. As expected, the FDTD simulations expose the concentration of the electromagnetic energy just underneath the microstrip lines and patches. The analysis in time domain, easily illustrates the incident, reflected and transmitted signals. For example, the plot of the electric field component Ez in Fig. 3.1 and Fig. 3.2 shows the propagation of a pulse along a bent microstrip line. After 550

57 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method time steps, the incident pulse is still on the input line (Fig. 3.1) [2]. After additional 400 time steps (∆t=0.27 ps), the pulse turned left, and propagated along a wider microstrip. TS=550

Figure. 3.1. The pulse is guided by the microstrip line along Oy axis [2, 3].

Figure 3.2. The pulse changes direction after a mittered corner and reaches wider microstrip [2, 3].

58 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

3.2. Dispersion Effects

The fundamental propagation mode for the microstrip line is considered as approximating the Transversal Electric and Magnetic (TEM) mode, when the fields are oscillating only in a perpendicular plane on the direction of propagation. For an ideal TEM mode, not including the material effects, the pulse should not encounter any dispersion. In practice, the microstrip properties are considered frequency independent for a frequency bandwidth up to 2 GHz, when designing on low (εr=2.55) dielectric constant substrate [4]. However, the dispersion effect increases with the increase of the dielectric constant and the working frequency [5].

1.8 y=90 y=130 1.6 y=50 1.4 y=30 1.2 y=0 1 0.8 0.6 0.4 0.2 Pulse amplitude (relat. units) 0 -0.2 0 200 400 600 800 1000 1200 Time steps

Figure 3.3. The dispersion effect of the “quasi-TEM” mode, while propagating along a microstrip line. The distance y from the source is given in ∆y units and the time in ∆t units [2, 3].

The FDTD simulations clearly illustrate the dispersion effects in time domain

[3]. The Ez field just underneath a straight microstrip line versus time at different locations is shown in Fig. 3.3. The distances y from the source plane to the measuring

59 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

points are given in ∆y units. In this case, the substrate was alumina (Al2O3) having a dielectric constant εr=9.98 and thickness h=0.635 mm. The 50 Ω line width was w50=0.635 mm. The FDTD grid had ∆x=∆y=0.1525 mm and ∆z=0.127 mm. The time step ∆t=0.27 ps and the incident Gaussian pulse had T=38 ∆t in width and T0=4 T as initial delay. While at the source position, the pulse is an undistorted Gaussian, after propagating a certain distance, the amplitude decreases and the pulse broadens with a strong negative tail. Since the dielectric layers were considered non-dispersive and the numerical dispersion of FDTD is negligible, the pulse distortion observed along a microstrip line is intrinsic to the fundamental “quasi-TEM” propagating mode.

3.3. FDTD Analysis of Different Types of Microstrip Devices

Several microstrip devices have been analyzed to verify accuracy of the developed FDTD method. The method was applied to numerous microstrip devices manufactured on substrates having different values for dielectric constant and thickness. In some simple cases, the simulated scattering S parameters were compared with the S parameters provided by commercial software. In other cases, the simulated response was compared with measurements or data taken from literature.

3.3.1. Linear Low Impedance Microstrip Section

A linear low impedance resonator on a substrate a dielectric constant of εr=3.38 and a thickness of h=0.81 mm was simulated using the developed FDTD method [2]. The

50 Ω line had the width of w50=1.87 mm. The resonator line width was wreson=4.07 and the resonator length was lreson=15.54 mm. For such a simple device, a commercial software, such as Touchstone [6], modeled the step discontinuities and could provide accurate S parameters. For the initial FDTD analysis, the first-order Mur’s ABC was used as boundary conditions at input and output ports. The FDTD simulated S parameters were compared against the S parameters provided by Touchstone. Fig. 3.4 shows a good fit between FDTD results and Touchstone results up to 17 GHz. The shift in resonance frequencies

60 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method is negligible, therefore the discretization error is unimportant. However, in the actual model, the dielectric and conductor losses were not yet included, as they led to the deeper resonances compared to the data obtained from Touchstone. The FDTD accuracy was limited mainly by the poor absorbing boundary conditions (ABC). The first-order Mur’s ABC assume a non-dispersive mode propagating perpendicularly to the boundary plane. The dispersive effects increase with frequency, therefore these absorbing boundary conditions gave spurious numerical reflections at higher frequency.

-10 (dB) 11 -20

-30

(dB) and S -40 21 S -50

-60 0 5 10 15 20 25 30 Frequency (GHz)

Figure 3.4. Scattering S parameters for a low impedance section [2, 3].

FDTD S21 (continuous line), Touchstone S21 (dotted line), FDTD S11 (dashed

line) and Touchstone S11 (solid line) in deciBells versus frequency (GHz).

To improve the FDTD accuracy, a non-homogeneous perfectly matched layer (NH-PML) was developed [7-9]. The non-homogeneous PML, which will be described in Section 3.4, is not restricted to non-dispersive modes and gave very good results even for microstrip lines on higher dielectric constant substrate. In order to prove this, a similar linear low impedance resonator as before was simulated. The substrate was alumina (Al2O3) with a dielectric constant of εr=9.8. The linear resonator width was wreson=1.68 mm, and the resonator length was lreson=10.06 mm. The simulated S21

61 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method shown in Fig. 3.5, presents no unexpected drop at 30 GHz as happened in the previous case (Fig. 3.4). The results accuracy clearly increased by using the non-homogeneous PML.

-10

) -20 dB ( 11 -30 and S

) -40

dB (

21 -50 S

-60 0 5 10 15 20 25 30 Frequency (GHz)

Figure 3.5. S11 (dashed line) and S21 (continuous line) parameters for low impedance linear microstrip resonator on alumina substrate [2, 3].

3.3.2. Gap End Coupled Linear Resonator

An end coupled linear resonator presents a higher overall quality factor (Q-factor) than the linear low impedance section discussed above. Consequently, the output signal decays slowly and the FDTD simulation requires a large number of time steps to complete the simulation. The gap end coupled linear resonator was designed as having the line width wreson=w50= 0.61 mm, the length lreson=10 mm and the coupling gap s=0.3 mm. The used substrate had dielectric constant of εr=9.98 and thickness of h=0.635 mm. The used FDTD grid had ∆x=∆y=0.1525 mm and ∆z=0.127 mm and the time step was ∆t=0.27 ps. The S parameters shown in Fig. 3.6 were calculated using a number of time steps of TS=16,384. Truncation of the observation time, i.e. time steps number reduction, would decrease the simulation accuracy, when a ripple can be noticed in

62 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method frequency data. A signal estimation technique used to reduce the number of iterations without affecting the accuracy will be presented in Section 3.5.

10 0 -10

(dB) -20 11 -30

-40 (dB) S and

21 -50 S -60 -70 0 5 10 15 20 25 30 Frequency (GHz)

Figure 3.6. S21 (continuous line) and S11 (dotted line) versus frequency for a linear gap end coupled resonator [2, 3].

3.3.3. Meander Lines

The majority of commercial computer aided design (CAD) software for microwave planar circuits [6] is based on models for circuit elements valid for a limited variety of low dielectric constant substrates. However, the present developed FDTD method can provide accurate data for microwave planar circuits designed on high dielectric constant substrates. In order to test the present developed FDTD method, two meander lines were simulated on two different substrates: alumina (Al2O3) with a dielectric constant of

εr=9.98, and lanthanum aluminate (LaAlO3) with a dielectric constant of εr=23.6. The geometry of the meander line on the FDTD grid is shown in Fig. 3.7. The alumina substrate had thickness of h=0.635 mm and line width of w50= 0.635 mm. The FDTD grid had ∆x=∆y=0.1525 mm and ∆z=0.127 mm. The computational domain was

63 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method chosen to be larger than necessary for the meander line, but ready to fit more complex circuits. It had the dimensions of 137 cells on x and y axes and 49 cells on z axis. The time step must satisfy the Courant condition and was chosen to be ∆t=0.27 ps. The incident Gaussian pulse had T=38 ∆t and T0=4 T. The number of time steps until the convergence was TS=6000. For a better accuracy in frequency domain, the vectors were filled in with zeros up to a total number of 32768 elements, before applying the Fourier transform.

Figure 3.7. The geometry of a meander line on FDTD grid. The geometry has ∆x=∆y=0.1525 mm [7].

For a rough discretization of only four cells per microstrip width, as shown in Fig. 3.7, the performed numerical experiments showed that a straight transition from the lumped source to the microstrip line provides a better matching than using a tapered line. The accuracy and the consistency of the present developed FDTD method were proved by comparing the results of a simulation on a meander line to the measurements [10]. The FDTD data fit very well the measured data, as shown in Fig. 3.8.

64 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

Meander Meander line on Al2O3 5

-5

-10

-15

-20

[dB] -25 11 -30 , S

21 -35 S -40

-45

-50 0 5 10 15 20 Frequency [GHz]

Figure 3.8. Calculated S21 (dotted line) and S11 (continuous line), and measured

[10], S11 (*) for a meander line on Al2O3 with εr=9.98, h=0.635 mm, w = 0.61 mm [7].

Fig. 3.9 shows the magnitude of the S parameters for a meander line designed on

Lanthanum Aluminate (LaAlO3) substrate. Lanthanum Aluminate, having dielectric constant of εr=23.6 and thickness of h=0.508 mm, is a commonly used substrate for high temperature0 superconducting (HTS) devices. The 50 Ω line width was 0.17 mm. The geometry of the meander line was chosen as before (Fig. 3.7), except that the FDTD grid was modified: ∆x = ∆y = 0.0425 mm and ∆z = 0.1016 mm. Comparison of Fig. 3.8 with Fig. 3.9 shows that the meander line on Lanthanum Aluminate has a pass-band more than two times wider than the pass-band on alumina. However, the in-band ripple of the meander line on lanthanum aluminate increases.

65 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

Meander line on LaAlO3 εr=23.6 h=0.508mm w=0.17mm 5

-5

-10

-15 [dB]

11 -20

, S -25 21

S -30

-35

-40

-45

-50 0 5 10 15 20 25 Frequency [GHz]

Figure 3.9. Calculated S21 (dark continuous line) and S11 (dashed line) for the

meander line on LaAlO3 (εr=23.6) [7].

3.3.4 Dual Mode Filters

The 3-D FDTD method was used to design square patch and meander loop dual mode filters (DMF) [9]. The layouts of the square patch DMF and the meander loop DMF are shown in Fig. 4.8. The design of dual mode filters will be discussed in Section 4.2. The FDTD method provides the full information about the field components at each time step. Given the evolution in time of the field distribution, the propagation effects are easyly analyzed. In the case of the meander loop DMF, the distribution of the electric field Ez just under the dielectric air interface after 1200 time steps is shown in Fig. 3.10. Fig. 3.10 shows the way the signal is guided under the microstrip line. The same thing is illustrated in Fig. 3.12 for the square patch dual mode filter. In this case, the field distribution corresponds to 2000 time steps.

66 Chapter 3–Designing ofMicrostrip Devices Using the FDTDMetho 67

Figure 3.10. Surface plot of the Ez component below the dielectric air-interface after 1200 iterations for the meander loop d 2 pole DMF.

Chapter 3–Designing ofMicrostrip Devices Using the FDTDMetho

68 Figure 3.11. Surface plot of the Ez component below the dielectric air-interface after 2000

iterations for two-pole square patch DMF. d

Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

3.4. Non-Homogeneous PML

The importance of the absorbing boundary condition (ABC) quality on the accuracy of the FDTD results was discussed in Section 3.3.1. The Bérenger’s Perfectly Matched Layer (PML) introduced in Section 2.2 is a wideband ABC. Previous implementations of the three-dimensional (3-D) PML [11, 12] cannot be used for microstrip devices analysis, due to the extension outside the computational domain of microstrip lines and different dielectric layers. A non-homogenous PML (NH-PML) [1-3, 7-9] is described in this section. In the following, we use notations defined previously in Section 2.2. Assuming that nld dielectric layers cross the PML perpendicularly, using the notations defined in Section 2.2. The matching condition (2.19) for the ld th dielectric layer becomes σ * ()ld µµ ()ld = 0 r . (3.1) σ ()ld 0εε r ()ld

For the frequent case of planar circuits on nonmagnetic substrates, µ r ()ld = 1

* * and ld = σσ = 1for,)( Knldld . In the following, the FDTD equations for all 12 filed components in the PML layer are presented. Let us imagine a fully-open computational domain. In Cartesian space, this domain will be fully covered by PMLs as shown in Fig. 3.12.

Figure 3.12. Regions for a) a conventional PML and for b) a non-homogeneous PML (NH-PML) surrounding a (completely open) computational domain.

69 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

∗ Let us designate by εr(ld), µr(ld), σ(ld), σ (ld) the dielectric constant, relative magnetic permeability, and electric conductivity respectively. The electric conductivity σ(ld) and the magnetic conductivity σ∗(ld) are designated by the low-indices x, y, and z indicating the losses in direction Ox, Oy, and Oz, respectively. The NH-PML regions can be classified from the point of view of FDTD equations which applies to them.

• region A is perpendicular to Ox

* σ x ()ld σ x ld)( * * = ;0 σσσσ zzyy ====≠ 0 . r ld)( εε 0 r ()ld µµ 0 electric and magnetic field components

,.,,,,,,,, HHHHHEEEEE zyzxyzyxxzyzxyzyxx

• region B is perpendicular to Oy

* σ y ()ld σ y ld)( * * = ;0 σσσσ zzxx ====≠ 0 . r ld)( εε 0 r ()ld µµ 0 electric and magnetic field components

,.,,,,,,,, HHHHHEEEEE zyzxyxzxyzyzxyxzxy • region C is perpendicular to Oz * * * z ≠≠ ;0 σσσσσσ yyxxz ==== 0 . electric and magnetic field components

,.,,,,,,,, HHHHHEEEEE zyzyxxzxyzyzyxxzxy

• region ab is a combination of regions A and B

* * σ x ()ld σ x ld)( σ y ()ld σ y ld)( * = ≠ ;0 = ;0 σσ zz ==≠ 0 . r ld)( εε 0 r ()ld µµ 0 r ld)( εε 0 r ()ld µµ 0 electric and magnetic field components

,.,,,,,,,,,, HHHHHHEEEEEE zyzxyzyxxzxyzyzxyzyxxzxy

• region ac is a combination of regions A and C

** * * σσ xx nld 0)( =≠≠= xx nld z ;0);( σσσσσσ yyz ==≠≠ 0 . electric and magnetic field components

,.,,,,,,,,,, HHHHHHEEEEEE zyzxyzyxxzxyzyzxyzyxxzxy

70 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

• region bc is a combination of regions B and C

** * * σσ yy nld 0)( =≠≠= yy nld z ;0);( σσσσσσ xxz ==≠≠ 0 . electric and magnetic field components

,.,,,,,,,,,, HHHHHHEEEEEE zyzxyzyxxzxyzyzxyzyxxzxy • region abc is a combination of regions A, B and C

** ** σσ xx nld 0)( =≠≠= xx nld σσσσ yy nld 0)();( =≠≠= σσ yy nld);(

* z 0 ≠≠ σσ z . electric and magnetic field components

,.,,,,,,,,,, HHHHHHEEEEEE zyzxyzyxxzxyzyzxyzyxxzxy The FDTD updating equations take into account the non-homogeneous distribution of the dielectric constant and magnetic permeability in the NH-PML. For instance, the 12 field components in the edge region ab in Fig. 3.12(b) are computed by the equations (3.2-3.13).  σ )( ∆tld  exp1 −− y   σ )( ∆tld   ε  n+1 kji exp,, −= y  n ,, kji +  0  × E xy ()   E xy () (3.2)  ε 0  r σε y )()( ∆yldld n + n n n −−−− ,1,,1,,,,, kjikjikjikji []zx ()()()()zy HHH zx H zy

n+1 n ∆t = ,,,, kjikji − × xz ()EE xz () r )( 0σεε z ∆zld (3.3) n + n − n kjikjikji −− n kji −1,,1,,,,,, []yx ()yz ()HHH yx ( )H yz ( )

 σ x )( ∆tld  exp1 −−  n+1  σ )( ∆tld  n ε kji exp,, −= x  ,, kji −  0  × E yx ()   E yx () (3.4)  ε 0  r σε x )()( ∆xldld n + n ,,,, n ,,1 n −−−− ,,1 kjikjikjikji []zx ()xy ()HHH zx ( )H zy ( )

n+1 n ∆t = ,,,, kjikji + × yz ()EE yz () r )( εε 0 ∆zld (3.5) n + n − n kjikjikji −− n kji −1,,1,,,,,, []xy ()()()()xz HHH xy H xz

 σ x )( ∆tld  exp1 −−  n+1  σ )( ∆tld  n ε kji exp,, −= x  ,, kji +  0  × E zx ()   E zx () (3.6)  ε 0  r σε x )()( ∆xldld n + n ,,,, n ,,1 n −−−− ,,1 kjikjikjikji []yx ()yz ()HHH yx ( )H yz ( )

71 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

 σ y )( ∆tld  exp1 −−  n+1  σ )( ∆tld  n ε kji exp,, −= x  ,, kji −  0  × E zy ()   E zy () (3.7)  ε 0  r σε x )()( ∆yldld n + n n n −−−− ,1,,1,,,,, kjikjikjikji []xy ()()()()xz HHH xy H xz

 σ * )( ∆tld  exp1 −− y  *    σ )( ∆tld  µ0 n+1 ()kji exp,, −= y  n (),, kji −   × H xy   H xy * (3.8)  µ0  ()σµ yr )( ∆yldld n n −+++ n − n ,,,,,1,,1, kjikjikjikji []zx ()()()()zy zx EEEE zy

n+1 n ∆t ,, = ,, kjikji + × xz ()HH xz () r ()µµ 0 ∆zld (3.9) n kji ++ n kji −+ n − n ,,,,1,,1,, kjikji []E yx ()()()(yz yx EEE yz )

 σ * )( ∆tld  exp1 −− x  *   n+1  σ ()∆tld  n µ0 kji exp,, −= x  ,, kji +   × H yx ()   H yx () * (3.10)  µ0  r σµ x )()( ∆xldld n ,,1 n −+++ n − n ,,,,,,1 kjikjikjikji []zx ()()()()zy zx EEEE zy

n+1 n ∆t ,, = ,, kjikji − × yz ()HH yz () r )( µµ 0 ∆zld (3.11) n kji ++ n − n − n ,,,,,,1,, kjikjikji []E xy ( )xz ()zy ()EEE xz ()

 σ * )( ∆tld  exp1 −− x  *   n+1  σ )( ∆tld  n µ kji exp,, −= x  ,, kji −  0  × H zx ()   H zx () * (3.12)  µ0  r σµ x )()( ∆xldld n ,,1 n −+++ n − n ,,,,,,1 kjikjikjikji []E yx ()()()()yz yx EEE yx

 σ * )( ∆tld  exp1 −− y  *   n+1  σ )( ∆tld  n µ0 kji exp,, −= x  ,, kji +   × H zy ()   H zy () * (3.13)  µ0  r σµ y )()( ∆yldld n n −+++ n − n ,,,,,1,,1, kjikjikjikji []E xy ()()()()xz xy EEE xz

The absorption profile of the NH-PML was established after empirical investigations. Satisfactory results are found for σ0=1 mS, g=2.3, nl=13.

72 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

3.5. FDTD Signal Estimation Technique

The required long computation time is a major drawback of the FDTD method. Previous researches [13-15] attempted to use signal estimation techniques to reduce the number of FDTD iterations. However, some of the spectral techniques such as the multiple signal classification (MUSIC) algorithm [15], while appropriate for finding the eigen-frequencies, they are less suitable for S parameters estimation. Other techniques, such as autoregression (AR) method [14], or Prony-Pisarenko method [13], often require very high-order models. In this section, the present developed estimation technique based on autoregressive moving average (ARMA) algorithm [1] is discussed. Let us consider y1(n) the FDTD signal at an output port of a microstrip device. The bandwidth of this signal is often much larger than the bandwidth of interest. Moreover, the signal y1(n) is oversampled. Therefore, the signal y1(n) needs to be processed into a replica more suitable for signal estimation. A signal y2(n), can be obtained by passing y1(n) through a sixth-order digital low-pass elliptic filter with 10 GHz cut-off frequency. A new signal y3(n) is then obtained by desamplig the signal y2(n) with a certain desampling rate desra. This signal y3(n) can now be modeled using an autoregressive moving-average (ARMA) process.

For the ARMA modeling, only the initial nmin samples of y3(n) are considered.

The signal y3(n) is affected by white Gaussian noise due to the spectral limitation of the FDTD method and the rounded numbers of the calculation. Given an input sequence x(n), the ARMA modeling requires to find the impulse response h(n) of a recursive infinite impulse response (IIR) filter in order to minimize the signal error err(n) between the IIR filter output y4(n) and the given output signal y3(n).

3 4 3 −=−= (*)()()()()( nxnhnynynynerr ). (3.14)

Let X(z), Y3(z), H(z) and ERR(z) be the z-transforms of the x(n), y3(n), h(n), and err(n) respectively. The transfer function H(z) can be written as

−1 −M ()zB 10 ... +++ M zbzbb zH )( == −1 −K . (3.15) ()zA 1 1 ... +++ K zaza Then, the z-transform of (3.14) is

73 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

zB )( zYzERR )()( −= = − zBzXzAzYzX )()(')()(')( . (3.16) 3 zA )( 3

3 zY )( zX )( where zY )(' = and zX )(' = . Let the sequences y3’(n) and x’(n) be the 3 zA )( zA )( inverse z-transforms of Y3’(z) and X’(z) respectively. Signals y3’(n) and x’(n) are the 1 replica of y3(n) and x(n) prefiltered by a filter with the transfer function . The zA )( inverse z-transform of (3.16) becomes

K M 3 )(' −= ∑ k 3 +− ∑ m +− nemnxbknyany )()(')(' . (3.17) k =1 m=0

The coefficients ak (k = 1,…, K) and bm (m = 0,…, M) are iteratively calculated. Given the A(z) from the previous iteration, the coefficients (, ba mk ) are simultaneously computed using a least-square procedure on the error. Finally, the long FDTD sequence is described by few coefficients (), ba mk . The behavior of the microstrip device is completely known when the coefficients (, ba mk ) are found. The ARMA coefficients constitute a parameterization of the device response in time and frequency domain. Example of the signal estimation technique used for FDTD analysis is its application to the design of the meander loop dual mode filter and forward coupled filter.

3.5.1. Signal Estimation for Meander Loop Dual Mode Filter Design

Dual mode filters are narrow-band. An incident FDTD signal decays very slowly, therefore, the simulation of these devices requires a very large number of iterations (up to 100,000 time steps). The signals in time domain are illustrated in Fig. 3.13. The iteration process was stopped after TS = 60,000 iterations [9].

The incident signal yin can be obtained without any reflection along a simple microstrip line with non-uniform PMLs at both ends. The total signal yt is measured at the input port of the filter, therefore it is the superposition of the yin and the reflected signal yrefl. The output signal yout is the transmitted signal after passing through the filter.

74 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

2.5 yout = y1

yrefl 1.5

yin 0.5

0 yt -0.5 FDTD Signals (arbitrary units)

-1

-1.5 0 500 1000 1500 2000 2500 3000

Time step

Figure 3.13. Total yt, incident yin, reflected yrefl, and transmitted yout signals from the meander loop dual mode filter.

The signal yout played the role of the signal y1 in the estimation procedure, hence

1 = yy out . The frequencies beyond fC =10 GHz were of no interest for the filter design. Moreover, they could act as a strong noise in the estimation procedure. Consequently, the signal components with frequencies greater than fC were rejected by using a digital filter. The first nskip=1000 samples of the filtered signal were skipped and the signal y2 was obtained.

The decimation of y2 with the desampling rate desra=200 corresponded to an increase in the time step. The very small FDTD time step was required by the stability Courant criterion, but it could cause a coarse frequency step, when translated in frequency domain. The signal y3 resulted from decimation was provided to the ARMA algorithm. The obtained ARMA coefficients could be considered as the coefficients of an Infinite Impulse Response (IIR) filter, which could identify the estimated signal. In this case, the order of the IIR filter was K = M = 16.

75 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

s21[dB], s11[dB] 10

-10

-20

-30

-40

-50

-60

-70

-80 0 5 10 15 20 25 30

Figure 3.14. S parameters (in dB) versus frequency (GHz) of the meander loop dual mode filter.

-20

-40

-60 Magnitude (dB)

-80 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized Angular Frequency (×π rads/sample) 200

-200

-400

Phase (degrees) -600

-800 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized Angular Frequency (×π rads/sample)

Figure 3.15. IIR filter response for desra = 200, K = M =16, nmin=100, nskip=1,000.

76 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

It can be easily seen the similarity between the S21 up to 10 GHz in Fig. 3.14 and the IIR filter response in Fig. 3.15. This suggests the possibility of using the processing of the truncated signal y1 in time domain to estimate the S parameters in frequency domain. Fig. 3.16 presents the poles and zeros of the IIR filter. The two poles in the first quadrant correspond to the two-mode resonances of the microstrip filter. These poles are situated between two zeros, which correspond to the attenuation poles on both sides of the microstrip filter pass-band.

0.8

0.6

0.4

0.2

-0.2 Imaginary Part -0.4

-0.6

-0.8

-1

-1 -0.5 0 0.5 1 Real Part

Figure 3.16. Poles and zeros location for the IIR filter.

In Fig. 3.17 the predicted response is compared with the response simulated by FDTD. There are only minor differences for large number of steps. The vertical line indicates the number nmin=200 of training data. This corresponds to 20,000 FDTD iterations. After the training, and after the coefficients (, ba mk ) are found, the method predicts accurately the FDTD data up to n=300 corresponding to TS = 60,000.

77 Prediction of FDTD signal using a 16 order IIR filter 0.01 FDTD response Predicted response

0.005 Chapter 3–Designing ofMicrostrip Devices Using the FDTDMetho

-0.005 Output signal DMF from

-0.01

-0.015 0 50 100 150 200 250 300 78 Time steps/200 d Figure 3.17. Comparison between the FDTD simulated signal and the ARMA predicted signal.

Chapter 3 – Designing of Microstrip Devices by Using the FDTD Method

The values of the IIR filter coefficients are:

i a(i) b(i) 0 1.0000 0.0061 1 1.0921 0.0100 2 3.0173 0.0153 3 1.9015 0.0083 4 4.3264 0.0108 5 2.7306 0.0067 6 5.2155 0.0080 7 2.2481 -0.0080 8 3.4874 -0.0137 9 0.2861 -0.0202 10 1.7993 -0.0158 12 -0.4641 -0.0196 13 0.4162 -0.0186 14 -0.9538 -0.0156 15 -0.2911 -0.0080 16 -0.3646 -0.0028 17 -0.0178 -0.0008

When the order of the IIR filter is reduced from 16 to 6 (Fig. 3.18-3.19) the prediction loses its accuracy. The same happens when the number of training data nmin is reduced from 100 to 90 (Fig. 3.20 –3.21). The difference between the traces becomes clear for n is close to 300 (Fig. 3.21).

79 Chapter 3 – Designing of Microstrip Devices by Using the FDTD Method

K=M=6, nskip=1000, desra=200, nmin=100

0.8

0.6

0.4

0.2

-0.2 Imaginary Part Imaginary -0.4

-0.6

-0.8

-1 -1.5 -1 -0.5 0 0.5 1 Real Part

Figure 3.18. IIR filter Zeros and poles position for K = M = 6.

K=M=6, nskip=1000, desra=200, nmin=100 0.01

4 y 0.005

0 and predicted signal and predicted signal 3 -0.005 y (arbitrary units) units) (arbitrary -0.01 FDTD signal

-0.015 0 50 100 150 200 250 300 Time step / desra

Figure 3.19. Comparison between ARMA predicted signal for K = M = 6 and nmin = 100, and the FDTD simulated signal.

80 Chapter 3 – Designing of Microstrip Devices by Using the FDTD Method

K=M=16, nskip=1000, desra=200, nmin=90

0.8

0.6

0.4

0.2

-0.2

Imaginary Part Imaginary -0.4

-0.6

-0.8

-1 -1 -0.5 0 0.5 1 Real Part

Figure 3.20. IIR filter Zeros and poles position for nmin = 90.

K=M=16, nskip=1000, desra=200, nmin=90 0.0

4 y 0.00

0 and predicted signal signal and predicted 3 -0.005 (arbitrary units) (arbitrary -0.01 FDTD signal y

-0.015 0 50 100 150 200 250 300

Time step / desra Figure 3.21. Comparison between ARMA predicted signal for K = M = 16 and nmin = 90, and the FDTD simulated signal.

81 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

3.5.2. Signal Estimation for FDTD Analysis of Forward Coupled Filter

Let us consider a non-optimized forward coupled filter with s = 0.56 mm, d = 3.92 mm, l = 11.2 mm (Fig.3.22). The device was designed on a substrate having dielectric constant of 10.8 and thickness of 0.635 mm. The spatial grid had ∆x = ∆y = 0.14 mm and ∆z = 0.127 mm. The time step was chosen small enough to satisfy the Courant condition, i.e. ∆t=0.25 ps. The FDTD analysis of this filter required usually 64,000 time steps. The way to use the signal estimation technique [1] in order to reduce the number of FDTD iterations is presented in the following.

Fig. 3.22. Microstrip forward coupled filter geometry [1].

The procedure for optimization of the filter illustrated in Fig. 3.22 will be presented in Section 3.6. The output signal y1 at the port 2 of the filter is presented in

Fig. 3.23. The signal y1 follows the same procedure of low-pass filtering with the cut- off frequency fC = 10 GHz and desampling at a rate desra = 120. The order of ARMA procedure is kept the same as before, namely K = M = 16.

82 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

0.1

(n) 1

0 Output signal y

-0.1 1 2 3 4 5 6 Time step n [ x 10-4 ]

Figure 3.23. Initial output FDTD signal y1 for the non-optimized filter in Fig. 3.22 with s = 0.56 mm, d = 3.92 mm, l = 11.2 mm [1].

0.05

(n) 4

y y3 y4 and (n) 3

y 0 Signals

-0.05 100 200 300 400 500 600 Time step n

Figure 3.24. FDTD signal y3(n) and the signal y4(n) resulted from

ARMA(16,16) modeling using only the first nmin=100 samples of y3(n) [1].

83 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

0.001

(n) 3 (n)-y 4

0 err(n)=y Error signal -0.001 100 200 300 400 500 600

Time step n

Figure 3.25. The ARMA modeling error err(n)=y3(n)-y4(n)

y3(n) is computed from FDTD up to 533 samples [1].

It can be seen that, the ARMA modeled signal y4(n) follows very closely the initial signal y3(n) (Figs. 3.24-3.25). Practically, signals y3(n) and y4(n) in Fig. 3.24 cannot be distinguished from each other. The nmin=100 region is emphasized by a continuous line in Fig. 3.24 and Fig. 3.25. The signal y4(n) is able to extrapolate very well the signal y3(n), even far beyond nmin (Fig. 3.24). Therefore, the FDTD computation time can be reduced by more of five times.

Let S11(1) be the reflection coefficient at port 1 of the microstrip filter in

Fig. 3.22, computed from the signal y1(n). Also, let S21(1), S21(3), S21(4) be the S21 parameters calculated using the Fast Fourier Transform (FFT) of the signals y1(n), y3(n), y4(n), respectively. Fig. 3.26 shows the good accord between S21(4) obtained as the result of ARMA modeling and S21(1) from the unaltered initial FDTD data.

84 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

-10 [dB] 11 -20

-30

S21(1) [dB] and S

21 -40 S21(3) S S21(4) S (1) -50 11 3 4 5 6 7 8 9 10 11 12 Frequency [GHz]

Figure 3.26. Magnitude of S parameters versus frequency for the non-optimized microstrip filter in Fig. 3.22 with s = 0.56 mm, d = 3.92 mm, l = 11.2 mm [1].

S21(1) – is |S21| calculated using the full 64000 samples FDTD signal y1(n),

S21(3) – is |S21| calculated using all the 533 samples of y3(n),

S21(4) – is |S21| calculated using ARMA modeled signal y4(n),

S11(1) – is |S11| calculated using the signal y1(n).

The filter frequency response in Fig. 3.26 proves that the initial set of geometric parameters is not optimal. The central frequency is higher than desired, the 5 dB pass- band ripple is unacceptably large and the 4 dB in-band return loss is inappropriately low. Additional FDTD – ARMA analysis are required in order to find the optimal design parameters. The poles and zeros of the ARMA(K, M) process are shown in Fig. 3.27. The presence of poles, very close to the unit circle, proves that the ARMA modeling is a better choice than a MA modeling. For poles close to the unit circle, the MA modeling requires a very large number of coefficients in order to keep the same accuracy. The ARMA modeling does not guarantee that all zeros and poles will be obtained inside the

85 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method unit circle. However, for all the studied cases, a stable ARMA process was obtained.

When a zero zk of the ARMA process has zk > 1, then zk can be replaced by its inverse

1 zk without any changes in the magnitude characteristic of the process.

1 p1

0.8 p2 ωc n1 0.6 0.4 p3 0.2 0 -0.2

Imaginary part Imaginary -0.4 -0.6 -0.8 -1 -1 -0.5 0 0.5 1

Real part

Figure 3.27. Poles and zeros of the IIR filter B(z)/A(z). The 10GHz cut-of

frequency fC of the elliptic filter corresponds to ωC = 0.6 π [1].

The pass-band ripple peaks shown in Fig. 3.26, correspond to the three poles p1, p2 and p3 in Fig. 3.27. The zero n1 in Fig. 3.27, corresponds to the transmission zero at 5.6 GHz in Fig. 3.26. The poles p1, p2, p3 and the zero n1 positions in Fig. 3.27 are very important for the pass-band response of the microstrip filter.

86 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

3.6. Microstrip Filter Design Using FDTD and Neural Networks

A new design technique [1] using FDTD and artificial neural networks (ANN) was developed and applied to design of a forward coupled microstrip filter shown in Fig. 3.22. Designing with ANNs makes use of the ANN propensity for storing knowledge, generalizing patterns in data and offering computational efficiency. The ANN can model nonlinearities better than multidimensional polynomials and require less computer memory than the look-up table approach. It is known that, for the look table approach, the size of the table grows exponentially with the problem dimensions. In conventional approaches [16-19], the ANN learns the relationships between input and output data at certain discrete frequency points. On the contrary, a major particularity of the method presented here consists in training an ANN to provide a model, which describes a microstrip filter in continuous frequency band and also in time domain. The ANN learns the relationships between the input geometric parameters and the output ARMA coefficients obtained during the signal estimation procedure used to reduce the required FDTD computation time. Once trained, the ANN provides the microstrip filter response parameterized by the estimated ARMA coefficients. As a peculiarity of the design method, the frequency is not an input parameter of the neural network. This is an additional distinct characteristic between the newly developed design method and precious approaches [16-19]. The ARMA modeling reduces up to five times the FDTD computation time. The use of ANN model eliminates a large number of time-consuming FDTD simulations leading to a substantial reduction of the total design time. The design goal of the forward-coupled microstrip filter shown in Fig. 3.22 is to determine the optimal geometrical parameters, namely the spacing s between the resonators, the resonators length l, and the position d of the input and output coupling lines. Due to the symmetry, we will consider only values for d, which satisfy

−< wld 0 2)( , where w0 is the width of the input and output coupling lines in Fig. 3.22. The device was designed on a 0.635 mm thick substrate having dielectric constant of 10.8. As the geometric parameters vary, the ARMA poles and zeros move about the unit circle and the microstrip filter response changes. Let us have a close look to the

87 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method shift of poles p1, p2, p3 and zero n1, as each of the parameters s, d and l varies once at a time. As the space gap s between the resonators increases, the microstrip filter pass- band becomes narrower, therefore the poles are approaching each other as shown in Fig. 3.28. As the distance d increases, the pass-band ripple of the microstrip filter increases. The poles p1, p2, p3 in Fig. 3.29 approach the circle border and the zero n1 moves towards smaller frequencies. The increase of the microstrip resonator length l results in the resonance frequency decrease. The microstrip filter pass-band moves to lower frequencies, therefore all the poles p1, p2, p3 and the zero n1 move towards smaller frequencies, as shown in Fig. 3.30. Similar position shifts occur for the complex conjugates of p1, p2, p3 and n1.

0.9 n1 unit circle 0.85

0.8 p1 0.75

Imaginary part Imaginary 0.7 p2 0.65

0.5 0.55 0.6 0.65 Real part

Figure 3.28. Poles p1, p2, p3 and the zero n1 shift as s is varied [1], (d = 2.24 mm, l = 11.2 mm). The arrows indicate the increase in s. (+) s = 0.28 mm, (x) s = 0.56 mm, (*) s = 1.12 mm.

88 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

n1 0.84 unit circle

0.8

p1 0.76

0.72 Imaginary partImaginary p2

0.68 p3

0.45 0.55 0.65 0.75 Real part

Figure 3.29. Position shift for poles p1, p2, p3 and zero n1 as the distance d varies (s = 0.24 mm, l = 44.8 mm) [1]. The arrows indicate the increase in d from 2.24 mm to 4.48 mm.

0.9 n1

0.8 p1 unit circle

Imaginary part part Imaginary p 0.7 3

0.6 0.4 0.5 0.6 0.7 Real part

Figure 3.30. Position shift for poles p1, p2, p3 and zero n1 when the resonator length l varies (s = 2.24 mm, d = 11.2 mm) [1]. The arrows indicate the increase of l. (+) l = 10.08 mm, (x) l = 11.2 mm, (*) l = 12.32 mm.

89 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

The existence of a three-layer feedforward ANN, which can map the geometric parameters into the space of ARMA coefficients, is a result of the Kolmogorov’s theorem [20]. However, this theorem does not show how to build the required ANN.

Figure 3.31. The architecture of the neural network used for microstrip filter design process [1].

The ANN shown in Fig. 3.31 has Nin, Nhid, Nout neurons at the input, hidden and output layer respectively. The input neurons do not perform any calculations, but just forward the input data to the hidden layer. The input layer dimension is given by the number of the geometric parameters, therefore is Nin=3 in this case. The ANN outputs are the ARMA (, ba mk ) coefficients, therefore Nout = K+M+1 = 33. The number of hidden neurons is determined empirically. The output y vector of the ANN shown in Fig. 3.31 is given by

g()2 f ()1 ++⋅⋅= bbxwwy 21 where x is the input data vector, w1 and w2 are the weight matrices of the hidden and output layers respectively, b1 and b2 are the thresholds (biases) of hidden and output

90 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method layers respectively. The activation function f of the hidden layer is the hyperbolic tangent sigmoid and the activation function g of the output layer is a linear function. The ANN was trained during a supervised learning procedure using 13 input data sets for geometric parameters lying in the intervals 0.28 mm ≤ s ≤ 1.12 mm, 10.8 mm ≤ l ≤ 12.32 mm and 2.24 mm ≤ d ≤ 4.48 mm. During the learning process, all the N in N hid hid ×+× NN out weights and N hid + N out biases are adjusted until the output of the ANN matches the target response within a certain error. The ANN generalization capability was verified with three data sets and one final test was performed for ANN validation. The ANN was trained using two efficient variants of the error back-propagation algorithm: the Levenberg-Marquardt algorithm [20] and the resilient back-propagation (RPROP) algorithm [21].

-10

-20 [dB] [dB] 11 -30

-40

[dB] and S S21 21

S -50 S11

2 3 4 5 6 7 8 9 10 11 12

Frequency [GHz]

Figure 3.32. The magnitude of the S parameters for the designed filter [1].

When Nhid = 50 with weights and biases initialized to small random numbers, the Levenberg-Marquardt training required 1000 epochs for a 4 4. ×10−4 training performance of the mean square error (MSE). The RPROP training performed

91 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

3.7 ×105 epochs in approximately the same amount of computation time for a 7.4 ×10 −6 final performance. Once the training / verification procedure was accomplished, the ANN was able to provide the microstrip filter response via ARMA coefficients in virtually no time. This is a significant achievement of the method when compared with numerous hours required by a conventional FDTD analysis. The selection of the most advantageous number of hidden neurons and training procedure is still currently under investigation.

Scatter plot 1

0.8

0.6

0.4

FDTD and ANN 21

S 0.2

0 0 0.2 0.4 0.6 0.8 1 S FDTD analysis 21

Figure 3.33. The linear values of the |S21| calculated by using ANN

model versus the |S21| calculated from the FDTD with the 5% correlation bonds [1].

The ANN modeling provided the following parameters s = 0.7 mm, l = 12.18 mm and d = 3.22 mm for the design. The filter response is given in Fig. 3.32. As a verification of the ANN modeling, this filter was also analyzed by using conventional FDTD method. A good agreement between the S parameters provided by both methods was found as shown in Fig. 3.33.

92 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

3.7. Chapter Summary

A 3-D FDTD method for planar microwave devices was developed. Various microstrip circuits on substrates with different thickness and dielectric constants have been analyzed in order to test the method. The method was validated by a very good matching between simulated data and measurements, literature data or, for simple cases, comparisons with commercial software (Touchstone). The time domain analysis of microstrip devices reveals interesting aspects of the electromagnetic field configuration as the pulse propagates through the structure. An example is the dispersive character of the microstrip lines. This is easily illustrated by the FDTD analysis. The accuracy of the FDTD results depends on the quality of the absorbing boundary conditions (ABC). As a consequence, a non-homogeneous perfectly matched layer (NH-PML) was developed in order to minimize any spurious reflection. In addition, the source geometry was optimized for a minimum generated numerical charge. An iterative ARMA signal estimation technique was developed in order to reduce the FDTD computation time. This is of importance especially in the case of the analysis of narrowband resonating structures. Therefore, with the present technique, the required number of iterations can be reduced up to five times, keeping the same accuracy of the results. Finally, a new design technique using FDTD method and Neural Networks was developed and applied to a microstrip filter. The total design time was reduced twofold. The ARMA signal estimation technique was first utilized to reduce the computation time for each FDTD run. Secondly, the number of FDTD simulations was decreased using the device model provided by a neural network with the ARMA coefficients at the output. The trained network was then incorporated in an optimization procedure for a microstrip filter design.

93 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

References

[1] M. G. Banciu, E. Ambikairajah, R. Ramer, “Microstrip Filter Design Using FDTD and Neural Networks”, Microwave and Optical Technology Letters, vol. 34, No. 3, August 5, 2002, pp. 219-224. [2] M. G. Banciu, R. Ramer, “Analysis of Microstrip Circuits Using a Finite- Difference Time-Domain”, Proceedings of the 4th World Multiconference on Circuits, Systems, Communications and Computers, Proceedings CSCC 2000, Vouliagmeni, Greece, July 2000, ISBN 960-8052-19-X, pp. 4611-4615 [3] M. G. Banciu, R. Ramer, “Analysis of Microstrip Circuits Using a Finite- Difference Time-Domain”, in Advances in Physics, Electronics and Signal Processing Applications, edited by N. E. Mastorakis, World Scientific and Engineering Soc.Press, Danvers, MA, 2000, ISBN: 960-8052-17-3, pp. 156-160 [4] E. H. Fooks, R. A. Zakarevicius, “Microwave Engineering Using Microstrip Circuits”, Prentice Hall, 1989 [5] R. L. Veghte, C.A. Balanis, Dispersion of Transient Signals in Microstrip Transmission Lines, IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No. 12, 1986, pp. 1427-1436 [6] HP-Eesof Microwave & RF Circuit Design – Circuit Element Catalog, HewlettR-Packard, March 1994 [7] M. G. Banciu, R. Ramer, “A FDTD Method for Circuits on High Dielectric Constant Substrates”, Proceeding of the 5th International Symposium on Antennas, Propagation and Electromagnetic Theory, August 2000, Beijing, China, August 2000, pp. 219-222 [8] M. G. Banciu, R. Ramer, “FDTD Method for Mobile Communicationss Filters”, Progress In Electromagnetics Research Symposium, PIERS 2000, Cambridge, Massachusetts, USA July 2000 [9] M. G. Banciu, R. Ramer, “Design of Microstrip Dual Mode Filters Using Finite- Difference Time-Domain Method”, Proceedings of the Asia-Pacific Microwave Conference – APMC 2000, Sydney, Australia, vol. 1, December 2000, pp. 975-978 [10] I. Wolff, “Applications of Finite-Difference Time-Domain Technique to Planar Microwave Circuit Design”, in “Time-Domain Methods for Microwave

94 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

Structures”, Eds. T. Itoh, B. Honshmand, IEEE Press, New York, USA, 1988, pp. 381-402 [11] J.-P. Bérenger, “Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves”, Journal of Computational Physics, vol. 127, 1996, pp. 363-379 [12] D. S. Katz, E.T. Thiele, A. Taflove, “Validation and Extension to Three Dimensions of the Bérenger PML Absorbing Boundary Condition for FD-TD Meshes”, IEEE Microwave and Guided Wave Lett., vol. 4, 1994, pp. 268-270 [13] J. L. Dubard, D. Pompei, A. Papiernik, J. Le Roux, “Characterization of Microstrip Antennas Using the TLM Simulation Associated with a Prony- Pisarenko Method”, International Journal of Numerical Modeling: Electronics Networks, Devices and Fields, vol. 3, 1990, pp. 269-285 [14] V. Jandhyala, E. Michielssen, R. Mittra, “FDTD Signal Extrapolation Using the Forward-Bacward Autoregressive (AR) Model”, IEEE Microwave and Guided Wave Letters, vol. 4, 1994, pp. 163-165 [15] Z. Bi, Y. Shen, K. Wu, J. Litva, “Enhancing Finite-Difference Time-Domain Analysis of Dielectric Resonators Using Spectrum Estimation Techniques”, Digest of IEEE Microwave Theory and Techniques Symp., 1992, pp. 263-266 [16] J. W. Bandler, M. A. Ismail, J. E. Rayas-Sánchez, Qi-Jun Zhang, “Neuromo- deling of Microwave Circuits Exploiting Space-Mapping Technology”, IEEE Trans. Microwave Theory Tech., vol. MTT-47, 1999, pp. 2417-2427, [17] M. M. Vai, S. Wu, B. Li, S. Prasad, “Reverse Modeling of Microwave Circuits with Bidirectional Neural Network Models”, IEEE Trans. Microwave Theory Tech., vol. MTT-46, 1998, pp. 1492-1494 [18] P. M. Watson, K. C. Gupta, and R. L. Mahajan. “Development of Knowledge Based Artificial Neural Network Models for Microwave Components”, MTT-S International Microwave Symposium Digest, vol. 1, 1998, pp. 9-12 [19] G. L. Creech, B. J. Paul, C. D. Lesniak, T. J. Jenkins, M. C. Calcatera, “Artifi- cial Neural Networks for Fast and Accurate EM-CAD of Microwave Circuits”, IEEE Trans. Microwave Theory Tech., vol. MTT-45, 1997, pp. 794-802 [20] S. Haykin, “Neural Networks – A Comprehensive Foundation”, MacMillan, 1994

95 Chapter 3 – Designing of Microstrip Devices Using the FDTD Method

[21] M. Riedmiller, H. Brown, “A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm”, in H. Ruspin (Ed.), Proceedings of the ICNN 93, San Francisco, 1993, pp. 586-591

Acronyms, Abbreviations and Notations in Chapter 3

ABC Absorbing Boundary Condition ANN Artificial Neural Network ARMA Autoregressive Moving Average CFL criterion Courant-Friedrichs-Levy criterion FDTD Finite Difference Time Domain Method FFT Fast Fourier Transform IIR Infinite Impulse Response NH-PML Non-Homogeneous Perfectly Matched Layer RPROP Resilient back-propagation algorithm ld Index of dielectric layer in NH-PML

σk(ld) Electric conductivity in NH-PML for the dielectric layer ld and direction k (k = x, y, z) ∗ σ k(ld) Magnetic conductivity in NH-PML for the dielectric layer ld and direction k (k = x, y, z) n n Ek (or Hk ) Electric (or magnetic) field in NH-PML at the time iteration n and in direction k (k=x, y, z, xy, xz, yx, yz, zx, zy) desra Desampling rate

K Order of the IIR denominator polynomial (in ak)

M Order of the IIR numerator polynomial (in ak) nmin Number of samples of y3 to obtain the predicted signal y4 nskip Number of samples skipped to obtain y2 y1 The initial FDTD signal (yout) y2 The signal obtained by low-pass filtering y1 by an elliptic filter

with the cut-off frequency fC y3 The y2 signal after desampling at a rate desra y4 The predicted signal obtained from the first nmin samples of y3

Nin, Nhid, Nout Number of neurons in the input layer, hidden layer, and output layer respectively

96 Chapter 4 – New Microstrip Filter Design

C H A P T E R 4 New Microstrip Filter Design

4.1. Introduction

Mobile communications systems require preselect filters with enhanced properties. This chapter presents the research on novel microstrip filters. The technology required by the newly developed filters is economical, no short-circuit elements and no lumped components are needed. The designs can be easily extended for planar HTS technology. In this chapter, an emphasis is put on the development of dual mode filters and filters with cross-coupled novel resonators. This introductive section presents the work on low-pass and band-pass conventional filters.

4.1.1. Low Pass Filter

The layout of a 7 pole Chebyshev low-pass filter with 0.25 dB in-band ripple [1] is shown in Fig. 4.1.

Figure 4.1. Picture of the low pass filter simulated with FDTD.

The filter can be used in a mobile communication receiver in the DCS 1800 standard. The filter was design and manufactured on a substrate with dielectric constant

εr=2.55 and thickness h=0.762 mm.

97 Chapter 4 – New Microstrip Filter Design

The newly developed FDTD method was used for accurate design of the above low-pass filter. An uniform rectangular FDTD grid was used with mesh sizes: ∆x=0.3016 mm, ∆y=0.4525 mm and ∆z=0.1905 mm. The time step was ∆t=0.28 ps and the Gaussian pulse half bandwidth was T=15 ps, with the initial delay T0=60 ps. The computational domain was bordered by the ground plane as a perfect conductor at one side and by perfectly matched layers (PML) on the other sides. All non-homogeneous perfectly matched layers (NH-PML) were identical. The NH-PML was 16 cells thick and its parameters g=2 and σ=2.2 mS/m.

-10

-20

S21 [dB] -30

-40

-50 0 2 4 6 8 10 12 Frequency [GHz]

Figure 4.2. Response (S21) of the low pass filter for DCS1800 – simulated (continuous line) and measured (dotted line).

Fig. 4.2 shows that the method provides a good accuracy in a large frequency band. The differences between the simulated and the measured responses are mainly due to the fact that, in the actual version of the method, the losses are not included. The measured response shows an in-band insertion loss of 0.5 dB at 1.8 GHz and very good rejection for the first two harmonics: 38 dB at 3.6 GHz and 40 dB at 5.4 GHz

98 Chapter 4 – New Microstrip Filter Design

4.1.2. Design of Edge Coupled Band Pass Filter

Fig. 4.3 illustrates the layout of a HTS five poles Chebyshev edge-coupled band-pass filter developed using a conventional design technique [2]. The central frequency was chosen 1.265 GHz, so that the filter could have applications to the Australian L-band mobile satellite. The filter sections impedances have been kept close to 50 Ω. However, there is also the constraint that the width of an HTS line shouldn’t be less than 170 microns. Consequently the filter response showed in Fig. 4.4 presents an increased ripple in the pass-band. The layout dimensions extended to a 4 inches substrate made the HTS deposition difficult and emphasized the need to look for new type of more miniaturized filters.

Figure 4.3. Layout of the L band (1.265 GHz) five poles Chebyshev filter. It requires HTS deposition on 4 inches diameter substrate.

Figure 4.4. The simulated response of the HTS filter showed in Fig. 4.3 (continuous line) compared to a filter made of normal conductor (dashed line).

99 Chapter 4 – New Microstrip Filter Design

4.2. Dual Mode Resonators and Filters

Dual mode resonators (DMR) are resonators perturbed in such a way that two resonating modes, initially degenerate, can couple each other. A DMR offers a dual mode filter (DMF) behavior, when certain conditions on the input and output couplings are satisfied. As discussed in Section 2.2, the planar DMFs evolved towards new designs [3-15].

Figure 4.5. Symmetry planes suitable for perturbations for a DMR

A planar design of dual mode filters was presented [7] using λ meander resonators. A resonator forms a 2-pole filter and consists of a meander loop with the input and output structures, two optional stubs for independent tuning of the resonant frequencies of the orthogonal modes, and a stub providing a coupling between modes. Two types of filter are possible depending on the stubs location. For the symmetric filter, the stub is located on the AA' plane in Fig. 4.5 and the frequency response has two transmission zeros located on both sides of the passband [9]. The asymmetric filter has the stub on BB' plane and does not present any transmission zero. Four pole elliptic filters, also exhibit transmission zeros, but, unlike in the 2-pole symmetric filter, the position of the zeros can be fully controlled. Each of these two rings has three lines attached: an input (or output) line, a line providing major coupling between rings, and a line providing minor coupling. Moreover, each ring has a stub for tuning of the center frequency of one of the modes and obviously a stub providing coupling between orthogonal modes. The input/output structure can be realized in many

100 Chapter 4 – New Microstrip Filter Design ways, but for optimized sensitivity they have been carried out as sections of coupled transmission lines. Coupling between rings have been realized by using capacitive gaps. The lines between rings and coupling elements provide appropriate transformations from the gaps or in/out structures as well as a spatial separation between rings. With symmetrical input/output couplings and without perturbations, resonators like those in Fig. 4.6 allow two orthogonal modes to resonate at the same frequency. Adding a perturbation, the modes frequencies shift and the modes couple each other. The coupling coefficient between the two modes is proportional with the frequency separation between them. When the input and output couplings are neglected, the input admittance for the resonator is

= jBY inin , (4.1) where Bin is the input susceptance. The susceptance slope parameter is ω dB b = 0 in . (4.2) 2 dω ω0

Figure. 4.6 a) Layout and b) equivalent circuit of meander loop DMR – unperturbed case.

The DMR is modelled by using nondispersive transmission lines (TL). This

101 Chapter 4 – New Microstrip Filter Design analytical simplified model will be followed by a FDTD analysis in order to accurately evaluate the effects of dispersion, bents, spurious couplings, etc. A symmetrically coupled resonator has a total effective electrical length of 4π ( + ll 21 ) , where the lengths l1 and l2 are defined in Fig. 4.7. Let us denote by β0 and ω0 the resonance propagation constant and resonance angular frequency respectively. Then, the resonance condition will be given by

ll 021 =+ 2)(2 πβ . (4.3) Therefore

ω 0 π β 0 == , (4.4) ν + ll 21 where v is the wave propagation speed along the transmission line. β and ω are the off- resonance, propagation constant and angular frequency respectively ωπω β == . (4.5) + llv ω 021 If a perturbation with susceptance B is added on the symmetry axis as shown in Fig. 4.7a, then the degeneracy between the two modes is risen. The perturbance can be a shunt capacitor B>0 or a shunt inductor B<0.

Figure 4.7. a) Layout of Perturbed DMR b) Equivalent circuit for even mode c) Equivalent circuit for odd mode

102 Chapter 4 – New Microstrip Filter Design

For the even mode, the equivalent circuit is presented in Fig. 4.7b. The resonance condition imposes Yin = 0 , therefore )2()1( YY inin =+ 0 , (4.6) where the index (1) represents the branch of length l1 and the index (2) refers to the branch of length l2. Let us consider a transmission line section of characteristic impedance Yc, propagation constant β and the length l connected to a load with the admittance YL. The input admittance is given by the relation

+ cL tan(βljYY ) = YY cin . (4.7) + Lc tan(βljYY )

For the branch (l1) in Fig. 4.7, the load has an impedance B = jY . (4.8) L 2 Therefore B j + c tan()β ljY 1 )1( = YY 2 . (4.9) in c B Y − tan()β l c 2 1 If we define the normalized susceptance as B b = , (4.10) Yc then (4.9) becomes b j + tan()β lj 1 )1( = YY 2 . (4.11) in c b 1− tan()β l 2 1 Furthermore, if we define the angle ϕ such that b tan()ϕ = , (4.12) 2 then )1( in = c tan()ljYY 1 + ϕβ . (4.13)

If we apply the formula (4.7) for the branch (l2), then )2( in = c tan()β ljYY 2 . (4.14)

103 Chapter 4 – New Microstrip Filter Design

At resonance the formula (4.6) becomes

tan()()l1 ++ tan βϕβ l2 = 0 , (4.15) or equivalently

−1 b  β ()ll 21 πϕπ −=−=+ tan   . (4.16)  2 

The propagation constant, which satisfies (4.16) is labeled β e corresponding to the even mode, and  b  π − tan−1  2π f e 2 β e ==   . (4.17) v + ll 21 The unperturbed mode can be obtained by letting b=0. Next, we define

2π f0 π β0 == . (4.18) + llv 21 Therefore

e  1 −1 b  ββ 0 1−= tan   , (4.19)  π  2  and the resonant frequency for the even mode is

e  1 −1 b  ff 0 1−= tan   . (4.20)  π  2  The perturbation does not affect the odd mode. Therefore the odd mode resonant frequency f o remains the same as in the unperturbed case

o = ff 0 . (4.21) The central resonant frequency is oe + ff  1 −1 b  fc = f0 1−= tan   . (4.22) 2  2π  2  The coupling coefficient of the two modes, defined as the absolute value of the frequency shift between both even and odd modes over the central frequency, becomes

1 −1 b  − ff oe tan   2π  2  k = = . (4.23) f 1  b  c 1− tan−1  2π  2 

104 Chapter 4 – New Microstrip Filter Design

The configuration with only one perturbation in the symmetry plane shown in Fig. 4.7 is a very common case in literature [15]. However in [8-12], two perturbations with normalized susceptances b in A and b’ in A' are analyzed. The values corresponding to this case will be labeled with the index 2. The central frequency is given [10] by oe + ff 22  1 −1 b  fc2 = f0 1−= tan   , (4.24) 2  π  2  and the coupling coefficient is

2 −1 b  − ff oe tan   22 π  2  k2 = = . (4.25) f 1  b  c2 1− tan−1  π  2  The values corresponding to the case where the two different susceptances are connected to points B and B' (Fig. 4.5) will be indexed with index 3. The central frequency in this case is given [10] by

oe    '  + ff 33 1  −1 b  −1 b  fc3 = f0 1−= tan   + tan  , (4.26) 2  2π  2  2        and the coupling coefficient between the modes is

' 1 −1  b  −1  b  oe tan   + tan   − ff 33 π  2   2  k = = . (4.27) 3 ' f c3 1   b   b   −1 −1   1−  tan   + tan   2π   2   2  The above relations can be used for design of dual mode filters as far the propagation constants and the normalized susceptances b and b’ are known. The results obtained by using the transmission line model described above constitute a good starting point for an accurate design of DMF by using the FDTD method. Fig. 4.8 shows the layout of 2 and 4 pole meander line DMF and of 2 pole square patch DMF. The meander loop line DMF can be initially approximated by a dual mode ring resonator more studied in the literature [8-15]. The output of the full wave FDTD method will include all the discontinuities effects as the 900 bends, coupling gaps etc. All the filters presented are Chebyshev type filters. For an improved quasi-elliptic response of the 4 pole DMF, an extra coupling between modes belonging to different resonators can be added.

105 Chapter 4 – New Microstrip Filter Design

Figure 4.8. The layout for 3 types of designed dual mode filters a) patch square resonator 2 pole dual mode filter for DCS 1800, the perturbation is not shown, b) 4 pole meander loop dual mode filter for GSM 900, c) 2 pole meander loop dual mode filter for GSM 900.

The simulated response of the meander loop DMFs shown in Figs. 4.9 - 4.12 does not take into account any losses. In Section 4.4, it will be shown that a limited unloaded quality factor has a significant effect on the narrowband filters. Generally, DMFs are narrowband filters, therefore the limited quality factor can cause substantial in-band insertion loss. In addition, the filter response is very sensitive to the input and output couplings. The in-band response in Fig. 4.10 and Fig. 4.12 shows a return loss better than 10 dB with 0.1 mm input/output space gaps. To improve the return loss, stronger input and output capacitive couplings are required. However, narrower coupling gaps are very hard to realize by using the conventional photolithography technology, especially when filters are designed on high dielectric constant materials.

106 Chapter 4 – New Microstrip Filter Design

Figure 4.9. Simulated response for the two-pole meander loop DMF in Fig. 4.8c. (Wide frequency range).

Figure 4.10. Simulated response for the two-pole meander loop DMF in Fig. 4.8c. (Reduced frequency range).

107 Chapter 4 – New Microstrip Filter Design

Figure 4.11 Simulated response for the four pole meander loop DMF in Fig. 4.8b. (Wide frequency range).

Figure 4.12 Simulated response for the four pole meander loop DMF in Fig. 4.8b. (Reduced frequency range).

108 Chapter 4 – New Microstrip Filter Design

Figure 4.13. The experimental set-up for measurement on dual mode filters using the HP 8720A Vector Network Analyser (VNA) [7].

The filters have been characterized using an HP 8720A VNA shown in Fig. 4.13. For the un-tuned two-pole DMF, the central frequency was 878 MHz as shown in Fig. 4.14. The filter bandwidth was found to be 16.7 MHz. The transmission zeros are clearly shown on both sides of the filter pass-band. The response of the un-tuned four-pole meander loop DMF is depicted in Fig. 4.15. The filter band-pass is centred at 880 MHz and the insertion loss is about 12 dB before tuning. The final rejection of the four-pole filter cold not be measured accurately due to the limitation in the network analyser dynamic range. Consequently the presence and the position of the attenuation poles shown by the simulated response shown in Fig. 4.11 could not be checked.

109 Chapter 4 – New Microstrip Filter Design

Figure 4.14. Meander loop two-pole DMF before tuning.

Figure 4.15. Meander loop four-pole DMF before tuning.

110 Chapter 4 – New Microstrip Filter Design

The measured responses after tuning can be also compared with the simulated responses given in Fig. 4.16. The four-pole DMF displays a better rejection and a steeper filter skirt. However, both two-pole and four-pole DMFs present a spurious pass band at about twice the central frequency.

0 -10 -20 -30 -40 -50 S21 [dB] S21 -60 -70 -80 -90 0.2 0.4 0.6 0.8 1 1.2 1.4 Frequency [GHz]

Figure 4.16. The calculated and measured dual mode filters response after

tuning [7]. a) heavy solid line: calculated S21 for 2-pole meander loop DMF;

b) x and dashed line: measured S21 for 2-pole meander loop DMF;

c) solid line: calculated S21 for 4-pole filter;

d) o and dashed line: measured S21 for 4-pole filter.

For the patch DMF, the coupling between modes is fulfilled by a small perturbation, mitering the corner situated on the symmetry axis at 45o with both input and output. The perturbation size a effect on the on the filter response is shown in Figs. 4.17–4.21. When a is increased from 2 mm to 5.5 mm (Figs. 4.17-4.19), the insertion loss decreases from 30 dB to 17 dB. Increasing a to 7 mm as in Fig.4.20, the insertion loss does not significantly decrease, but a pass-band ripple occur due to the two peaks corresponding to the two coupled modes. The coupling between modes can increase further as the perturbation a is increased, generating the enlarging of the in- band ripple.

111 Chapter 4 – New Microstrip Filter Design

Figure 4.17. Patch DMF with perturbation a = 2 mm.

Figure 4.18. Patch DMF with perturbation a = 5 mm.

112 Chapter 4 – New Microstrip Filter Design

Figure 4.19. Patch DMF with perturbation a = 5.5 mm.

Figure 4.20. Patch DMF with perturbation a = 7 mm.

113 Chapter 4 – New Microstrip Filter Design

Figure 4.21. Patch DMF with perturbation a = 7mm, wide scope view.

Figure 4.22. Patch DMF with metallic post as perturbation.

114 Chapter 4 – New Microstrip Filter Design

The patch DMF has a very interesting response shown in Fig. 4.22 when is perturbed with a metallic post positioned on the same location with the cut corner. In this case, the response presents two transmission zeros on both sides of the pass-band, similar to the meander loop DMF response shown in Fig. 4.14. Although the 2 pole meander line DMF occupies a smaller surface than the square patch DMF, its central bandwidth frequency is about half of the central bandwidth frequency of the square patch DMF. However, the square patch DMF is preferred in situations when there is a need to increase the maximum handling power. This might be the case for some high temperature superconducting (HTS) filters. HTS resonators and filters have been reported as an opportunity to reduce the conductive losses for planar microwave devices. It was shown [18, 19], that the current distribution on a square patch DMF allows a handling maximum power approximately 4 times greater than for all studied line filters.

4.2.1. Quasi Fractal Dual Mode Resonators

We already discussed that, the DMF patch filters have good power handling properties but they occupy a larger surface area. In order to reduce the patch size, a technique from microstrip antenna design was borrowed. When slots are cut in the square patch, as shown in Fig. 4.23, the resonance frequency can be substantially reduced [4, 5].

Figure 4.23. Patch dual mode filter [4, 5].

The perturbation required for the dual mode effect is provided by the slots’ asymmetry. The coupling between the modes can be controlled by the difference in the length of the diagonal slots.

115 Chapter 4 – New Microstrip Filter Design

Our research showed, that the patch size can be further reduced by practicing more slots. The current cannot flow across the patch as for the simple square patch of Fig. 4.8a, but it is forced to flow along a longer line, which looks like a Koch's fractal curve. For that reason, the novel resonator shown in Fig. 4.24 is called quasi-fractal. The newly developed quasi-fractal resonator is more compact than the previously slotted patch DMF [4, 5].

Figure 4.24. Novel quasi-fractal dual mode patch resonator.

QFfil01

S -10 11 S 21

-20 [dB] 21

-30 and S and 11 S -40

-50

-60 0 0.5 1 1.5 2 2.5 Frequency [MHz]

Figure 4.25. S parameters for the non-perturbed quasi-fractal dual mode resonator of Fig. 4.24.

A small asymmetry to control the coupling between modes is required by the quasi-fractal resonator in order to behave as two-pole dual mode filter. Initially, the

116 Chapter 4 – New Microstrip Filter Design resonator was designed symmetrically and the resonance around 800 MHz illustrated in Fig. 4.25 is caused only by the presence of the asymmetry in coupling lines. Several tuning experiments have been conducted to investigate dual-mode response of the quasi-fractal resonator.

a) b) c)

d) e)

Figure 4.26. Tuning experiments on quasi fractal resonators.

For the tuning configuration in Fig. 4.26a, the insertion loss decreased to approximately 12 dB. The filter presents two transmission zeros on each side of the pass-band as shown in Fig. 4.27, similar to those of the loop DMF. The insertion loss can be further decreased as shown in Fig. 4.28 if another dielectric post is added on the opposite corner of patch as shown Fig. 4.26b. The filter response in Figs. 4.29-4.30 is made symmetrical in the tuning experiment shown in Fig. 4.26c. The configurations represented in Fig. 4.26d-e offer a smaller insertion loss as it can be seen in Fig. 4. 31 and Fig. 4.32. The conclusion drawn from these experiments is that the design should be symmetrically perturbed along the diagonal slots to obtain a low loss DMF response. For smaller insertion loss, a stronger input and output coupling is required, therefore a smaller coupling gap.

117 Chapter 4 – New Microstrip Filter Design

QFfil02

-10 S 11 S 21 -20 [dB] 21

-30 and S and 11 S -40

-50

-60 0 0.5 1 1.5 2 2.5 Frequency [MHz]

Figure 4.27. Quasi-fractal filter response in tuning configuration of Fig. 4.26a.

QFfil03

S 0 11 S 21

-10

-20 [dB] 21

-30 and S and 11 S -40

-50

-60 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Frequency [GHz]

Figure 4.28. Quasi-fractal filter response in tuning configuration of Fig. 4.26b.

118 Chapter 4 – New Microstrip Filter Design

QFfil04

S 0 11 S 21

-10

-20 [dB] 21

-30 and S and 11 S -40

-50

-60 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 Frequency [GHz]

Figure 4.29. Quasi-fractal filter response in tuning configuration of Fig. 4.26c. (wide frequency range).

QFfil05

S 0 11 S 21

-10

-20 [dB] 21

-30 and S and 11 S -40

-50

-60 0.7 0.75 0.8 0.85 0.9 0.95 Frequency [GHz]

Figure 4.30. Quasi-fractal filter response in tuning configuration of Fig. 4.26c. (Reduced frequency range).

119 Chapter 4 – New Microstrip Filter Design

QFfil06

S 0 11 S 21

-10

-20 [dB] 21

-30 and S and 11 S -40

-50

-60 0.7 0.75 0.8 0.85 0.9 0.95 Frequency [GHz]

Figure 4.31. Quasi-fractal filter response in tuning configuration of Fig. 4.26d.

QFfil07

S 0 11 S 21

-10

-20 [dB] 21

-30 and S and 11 S -40

-50

-60 0.7 0.75 0.8 0.85 0.9 0.95 Frequency [GHz]

Figure 4.32. Quasi-fractal filter response in tuning configuration of Fig. 4.26e.

120 Chapter 4 – New Microstrip Filter Design

4.3. Filters with Cross-Coupled Resonators

Many band-pass filters, such as the edge coupled band-pass filter in Fig. 4.3, or all the filters illustrated in Fig. 2.8 allow only positive couplings between cascaded resonators. Beside this type of coupling, the filters with cross-coupled resonators permit negative couplings between non-cascaded resonators. The presence of negative couplings allows the realization of the generalized Chebyshev response introduced in Section 2.3 by equations (2.33) and (2.34). The presence of transmission zeros in the stop-band, such as the zero at Ω0 = 1.23 in Fig. 2.7, is caused by negative couplings.

Figure 4.33. Equivalent circuit of a four-pole band-pass filter with cross- coupled resonators.

Let us consider the equivalent circuit of a four-pole band-pass filter with cross- coupled resonators shown in Fig. 4.33. The same notations as in Section 2.3 are used for the circuit elements. As shown in Fig. 4.33, the equivalent circuit of each non-ideal microstrip resonator includes a conductance Gi, (i=1,2), in parallel to the Ci and Li components. Consequently, the model based on the equivalent circuit of Fig. 4.33 includes also the effects due to the finite unloaded quality factors Qu of the microstrip resonators. Let us denote the ratio between the filter bandwidth and the central frequency by the fractional bandwidth (FBW). Let g0, g1, g2 be the elements of the low-pass prototype of the filter shown in Fig. 4.33 and J1 and J2 are the admitance inverters parameters. Then, the positive coupling coefficients between the resonators are: FBW 12 MM 34 == , (4.28) gg 21

121 Chapter 4 – New Microstrip Filter Design

FBW ⋅ J 2 and M 23 = . (4.29) g2 The negative coupling is given by

FBW ⋅ J1 M 14 = . (4.30) g1 The knowledge of the coupling coefficients is required by the band-pass filter synthesis.

4.3.1. Design of HTS Filter with Cross-Coupled Loop Resonators

Besides the improved filter response, filters with cross-coupled resonators provide a smaller size than for conventional filters. HTS four pole filter with cross coupled resonators was designed for GSM / GPRS base stations up-link channel. The filter can easily fit on a common 2 inches diameter substrate, shown in Fig. 4.34. This is much smaller than the edge coupled filter in Fig. 4.3, which requires a 4 inches substrate.

Figure 4.34. Layout on a 2 inch diameter LaAlO3 substrate of a proposed 4 pole band-pass filter to be used for GSM up-link channel.

The filter sections are actually bent half wavelength resonators. Along the open loop, the electric field varies from minimum in the middle to maximum at the ends; on the contrary, the magnetic field is minimum at the ends and maximum at the middle of

122 Chapter 4 – New Microstrip Filter Design the loop. Therefore, resonators 2 and 3 are magnetically coupled. The couplings between resonator 1 and 2, and between 3 and 4 are partially electric and partially magnetic. Finally, the coupling between resonator 1 and 4 is of electric nature. The couplings between resonators 1-2 and 3-4 are positive, and the coupling between 1 and 4 is negative to allow a quasi-elliptic response, with transmission poles each side the frequency bandwidth as illustrated by the simulated filter response shown in Fig. 4.35.

4-pole square-loop cross-coupled filter 0

-10

-20

-30 [dB]

11 -40 ,S 21

S -50

-60

-70

-80 0.75 0.8 0.85 0.9 0.95 1 1.05 Frequency [GHz] Figure 4.35. Simulated response of the cross-coupled filter shown in Fig. 4.34.

4.3.2. Stubs Effect on Half-Wavelength Resonators and Stepped Impedance Resonators

In this section, the miniaturisation of the microstrip filters with cross coupled resonators is discussed. At mobile communications frequencies, such as for GSM / GPRS 900 MHz bandwidth, the large wavelength causes inconvenient large size of the transmission lines filters. Our aim is to design size reduced microstrip resonators, by modifying the half wavelength resonators. The new resonators require no lumped capacitors, inductors, nor short circuit elements, such as via holes, therefore they are easy to implement in HTS technology.

123 Chapter 4 – New Microstrip Filter Design

Let us consider a segment of an ideal loss-less transmission line of characteristic impedance yc, propagation constant β and length l0. If the segment is capacitively coupled at end 1, and end 2 open circuited, then l0 = 0.5 λο init, where λο init is the wavelength at the initial resonance frequency f0 init. The resonator size reduction while keeping the resonance frequency unchanged is equivalent to the decrease of the resonance frequency and having the size unchanged. The resonance frequency of this linear resonator can be reduced by adding parallel stubs, as is shown in Fig. 4.36. Firstly, let us consider the stubs have equal characteristic impedance yc..

Figure 4.36. Model of a linear resonator with added stubs.

a) Simple linear resonator with the resonance frequency f0 init and the wavelength

at resonance λ0 init; b) Linear resonator with added stubs with the resonance

frequency f0 and the wavelength at resonance λ0.

The input impedance at port 1 in Fig. 4.36b is given by

tan()β 2 + ()(tan ()1 + ()ββ lll 3 []+ 2 )()tantan2tan (1 )+ tan(βββ lll 3 ) in = yjy c , (4.31) + ()()()()2 3 []1 ()tantantantan1 1 + tan ()βββββ lllll 3 −1 when

()()1 tantan 2 + ()()2 ββββ llll 3 ≠ 1tantan . (4.32)

124 Chapter 4 – New Microstrip Filter Design

1.1

l1 = 0.16 1 0 init 0 l = 0.18

/ f 1 0 0.9 l1 = 0.22

0.8

0.7

l1 = 0.125 0.6

Resonance frequency f frequency Resonance l1 = 0.1 0.5 l = 0.06 1 l1 = 0.02 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Distance l / λ 3 0 init

Figure 4.37. The resonance frequency versus the length of the stubs for l1=0.02, 0.10, 0.125, 0.16, 0.18, 0.22 (Dimensions normalized to λ0 init).

2.8 l = 0.125 l1 = 0.02 1 2.6 l = 0.1 l1 = 0.06 1 2.4 0 l1 = 0.16 / f 1 2.2

2 Ratio f

1.8

1.6 l = 0.18 1 l = 0.22 1.4 1

1.2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Distance l / λ 3 0 init

Figure 4.38. Ratio between the spurious mode frequency f1 to fundamental resonance frequency f0 versus the length of the stubs for l1=0.02, 0.10, 0.125,

0.16, 0.18, 0.22. (Dimensions normalized to λ0 init).

125 Chapter 4 – New Microstrip Filter Design

The resonance frequencies are given by yin = 0. When only the fundamental mode is investigated, the model can be simplified considering only first half of the structure with a short circuit at point O in the symmetry plane. However, we will consider the entire resonator, since the first higher resonance f1 is also investigated.

The stubs’ addition results in the reduction of the resonance frequency from f0 init to f0. The variation of the ratio ff 00 init as function of dimensions l1 and l3 is depicted in Fig. 4.37. It can be seen that the stubs effect is large when stubs are close to the ands 1 and 2 of the linear resonator, and decreases as the stubs are approaching the symmetry point O.

The resonator first higher resonance f1 often determines the filter spurious pass- band. For the initial simple linear resonator, f1 init = 2f0 init. The variation of the ratio f1 /f0 with dimensions l1 and l3 depicted in Fig. 4.38 presents regions where the ratio f1 /f0 is greater than the value 2, which corresponds to the simple linear resonator.

The variation of the ratio f1 /f0 with dimensions l1 and l3 shows that it is possible to move the higher resonance away from the fundamental resonance. This effect can be used to enhance the spurious stop-band.

Figure 4.39. Size comparison between (a) half wavelength resonator with stubs bent towards outside, (b) simple half wavelength open loop, (c) resonator proposed in [22].

126 Chapter 4 – New Microstrip Filter Design

It might be useful to apply the same transmission line theory to provide a simplified model of the resonator proposed in [22]. The square resonator [22] shown in Fig. 4.39c is basically described as two hair pin resonators joined back to back. This resonator can also be roughly described by the model in Fig. 4.36, after the stubs of lengths l1 and l3 are added in such a way to from the square resonator in Fig. 4.39a. If a small gap ∆ between the ends 1 and 2 is considered with ∆ = 0.0018λ0 init, then l1 = 0.16365λ0 init, l2 = 0.17270 λ0 init. As the result of the stubs, the resonance frequency f0 reduces to f0 = 0.7872 f0 init. This reduction in resonance frequency allows the reduction of all the lengths l0, l1, l2 and l3 by the factor f0 / f0 init to come back to the initial resonance frequency f0 init. However, even after resizing, the resonator shown in Fig. 4.39a occupies a larger surface than a simple half wavelength loop shown in Fig. 4.39b. In conclusion, when a compact size is aimed, the added parallel stubs should be folded in a different way than is shown in Fig. 4.39a. Therefore, the configuration illustrated in Fig. 4.39 is not a good start for size optimization. Later, it will be shown that better results can be obtained when the stubs of length l3 are folded inside the main loop composed by the transmission line segments of lengths l1, l2 and again l1. Before approaching the practical aspects of the stubs folding, a discussion on the addition of parallel stubs to a stepped impedance resonator (SIR) is required. The stepped impedance resonators [23] are characterized by small sizes and spurious responses at frequency values more than twice the fundamental frequency. In the following, how to improve the SIR characteristics by addition of parallel stubs will be discussed. Let us consider a SIR with the admittance ratio S, and S>1 as shown in

Fig. 4.40b. Two uniform stubs of characteristic admittance S1 yc are added symmetrically on both sides of point O, at point M and N, as shown in Fig. 4.40c. S1 is the ratio of the stub admittance and yc. The transmission lines are regarded as loss-less and non-dispersive in this model. The same propagation constant β is considered for sections with different admittance. In addition, the discontinuities along the transmission line such as step impedance, T-connections, the open end effects will be neglected in the initial model. It is already known [23], that the maximum reduction of resonance frequency is obtained when the section with the high admittance Syc has the length equal with the half of the length of the section with low admittance yc. This

127 Chapter 4 – New Microstrip Filter Design condition applied to the SIR in Fig. 4.40 leads to l4=l5. For the model presented in Fig. 4.40 two stubs have been symmetrically added at points M and N.

Figure 4.40. Model of a SIR resonator with stubs.

a) Simple linear resonator with the resonance frequency f0 init and the wavelength

at resonance λ0 init; b) Simple stepped-impedance (SIR) resonator; c) Stepped

impedance resonator with added stubs with the resonance frequency f0 and the

wavelength at resonance λ0.

For the fundamental mode analysis, the symmetry point O in Fig. 4.40c may be considered as short-circuited. The resonance frequency f0 of the fundamental mode is

β 0 f = v , where veff is the effective propagation velocity along the line, and β0 is the 0 2π eff propagation constant at resonance. The cancellation of the input impedance at port 1 leads to the following equations in β

[]1 tan()3 − ()ββ 2 []− ()()4 tantan1cot ββ llSllS 6 (4.33a) tan()β 6 ++ ()β lSl 4 = ,0tan when ≥ ll 41 ,

128 Chapter 4 – New Microstrip Filter Design and []+ ()()tancot ββ []tan()β + tan ()β lSlSllS 5 16 3 1 (4.33b) + []tan()6 − cot ()ββ llSS 5 = ,0 when < ll 41 .

The case l1 > l4 holds when the stub of length l3 in Fig. 4.40 is connected to the

SIR segment with lower yc characteristic admittance. In the case l1 < l4, the stub is connected to the SIR segment with higher S1 yc characteristic admittance. The solution

β0 of (4.33) gives the resonance frequency f0 of the fundamental mode. As shown in

Fig. 4.41, the frequency f0 decreases with the increase of the stub length l3 and increases with the increase of the distance l1, which gives the stub position. Dimensions are normalized to λ0 init, which is the wavelength corresponding to the resonance frequency f0 init=900 MHz of the simple linear resonator shown in Fig. 4.40a. The frequency f0 also decreases with the increase of S, as shown in Fig. 4.42. The analysis of the first higher order resonating mode provides information about the filter spurious pass-band. For the first higher mode analysis, the symmetry point O can be considered as open-circuited. The frequency f1 of the first spurious mode can be obtained from the solutions of the following equations

[]1 tan()3 + ()ββ 2 []− ()()4 tantan1tan ββ llSllS 6 (4.34a) tan()β 6 ++ ()β lSl 4 = ,0tan when ≥ ll 41 , and

[]− ()()5 tantan ββ []16 tan()β 3 + tan ()β lSlSllS 1 (4.34b) + []tan()6 + tan ()ββ llSS 5 = ,0 when < ll 41 .

Similar to the model described in Fig. 4.36, the stubs addition can lead to the increase of the f1 /f0 ratio. The case of the simple stepped-impedance resonator

(SIR) corresponds to the values l3 = 0 in Figs. 4.43-4.44. The variation of the f1 /f0 ratio shown in Figs. 4.43-4.44 presents regions above the values for the simple SIR. The ratio f1 / f0 between the spurious mode frequency and the fundamental frequency reaches its maximum when l1=l3=λ0 init / 4. However, when l1 approaches 0.25 λ0 init, the increase of l1 leads to the decrease of the ratio f1 / f0. In other words, the addition of long stubs close to the symmetry point O may result in a narrow isolation band of the resonator, since the resonator first spurious frequency f1 may approach the fundamental mode frequency f0.

129 Chapter 4 – New Microstrip Filter Design

S = 2 0.8

0.75

0 init 0 l1 = 0.24

/ f 0.7 0 l1 = 0.20 0.65 l = 0.02 1 l = 0.16 l = 0.04 1 0.6 1 l1= 0.08 l = 0.12 0.55 1 l1= 0.14

Resonance frequency f 0.5

0.45 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Distance l / λ 3 0 init

Figure 4.41. The resonance frequency reduction (f0 / f0 init ) versus stubs length l3 and stubs position l1, for admittance ratio S=2. (Dimensions are normalized to

λ0 init).

λ l1=0.13 0 init 0.9 S = 1.5 0.85 S = 2 0 init 0.8 S = 2.5 / f 0 S = 3 0.75 S = 3.5 0.7 S = 4 0.65

0.6

Resonance frequency f 0.55

0.5

0.45 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Distance l / λ 3 0 init

Figure 4.42. The resonance frequency reduction (f0 / f0 init ) versus stubs length l3, and admittance ratio S, when the stub position is l1 = 0.13 λ0 init. (Dimensions are normalized to λ0 init).

130 Chapter 4 – New Microstrip Filter Design

S = 2 3 l = 0.12 1 l1 = 0.08 2.8 l1 = 0.04 2.6 l1 = 0.02 2.4 0 / f

1 2.2

2 Ratio f 1.8 l = 0.14 1.6 1 l1 = 0.16 1.4 l1 = 0.20 1.2 l1 = 0.24 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Distance l / λ 3 0 init

Figure 4.43. The variation of spurious frequency f1 versus stub length l3 and position l1, for admittance ratio S=2. (Dimensions are normalized to λ0 init).

λ l1=0.13 0 init 3.8 S = 4 3.6 S = 3.5 S = 3 3.4 S = 2.5 3.2

0 S = 2

/ f 3 1 S = 1.5 2.8

Ratio f 2.6

2.4

2.2

1.8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Distance l / λ 3 0 init

Figure 4.44. The variation of spurious frequency f1 versus stub length l3 and admittance ratio S, when the same stub position is l1 = 0.13 λ0 init. (Dimensions are normalized to λ0 init).

131 Chapter 4 – New Microstrip Filter Design

The conclusion drawn from this transmission line model is that, for the maximum size reduction, S and l3 must be as big as possible and l4=l5. However, for the practical design of microstrip resonators, the preferred solution will compromise between these conditions, the practical geometrical requirements, and the realistic effect of the microstrip discontinuities. Furthermore, for the practical designs, non-uniform stubs rather than uniform stubs will be preferred. The non-uniform stubs give more design options to control the resonance frequency, spurious responses and other parameters of the resonators.

4.3.3. Novel Microstrip Resonators

Novel compact size microstrip resonators have been developed on the basis of the considerations presented in the previous section. The newly designed microstrip resonators consist of folded SIR resonators with four added stubs as for type I resonator shown in Fig. 4.45c, or with two added stubs as for compact resonators ranging from type II shown in Fig. 4.45d to type X shown in Fig. 4.45l. Square open-loop microstrip resonators (Fig. 4.45a) have already been proposed for canonical filters [24]. However, for lower frequency bands of mobile communications systems such as for GSM 900 MHz band, the size reduction is a major requirement, and therefore filters with more compact resonators are needed. These new resonators have been designed on Rogers substrate 0.635 mm thick and having 10.8 ±0.25 dielectric constant. The characteristic impedance of the microstrip line, which forms the main loop was

Z 0 Z C Ω== ,34 Zwhere 0 50 Ω= . (4.35) yc

The normalized admittance yc is the same as in the model illustrated in Fig. 4.40. The added stubs are non-uniform. They consist of microstrip sections with characteristic impedances ranging from 12 Ω to 50 Ω. The low impedance lines allow a good power handling, which makes the resonators attractive to HTS planar technology. Using the notations of Fig. 4.40, the resonators of type I, II, IV, VIII, IX, and X correspond to the case l1 > l4 and the resonators of type III, V, VI, and VII correspond to the case l1 < l4.

132 Chapter 4 – New Microstrip Filter Design

Figure 4.45. Size comparison of resonators for 900 MHz; a) simple half- wavelength loop resonator; b) square-loop stepped-impedance resonator; c) compact resonator, type I; d) compact resonator, type II; e) compact resonator, type III; f) compact resonator, type IV; g) compact resonator, type V; h) compact resonator, type VI; i) compact resonator, type VII; j) compact resonator, type VIII; k) compact resonator, type IX; l) compact resonator, type X; m) miniaturized hairpin resonator resonating with 986 MHz resonance frequency.

133 Chapter 4 – New Microstrip Filter Design

Table 2.1. Characteristics of the newly designed compact resonators

Type of Geometry Occupied area (compared to Measure unloaded

Resonator simple wavelength resonator) quality factor (Qu) Type I Fig. 4.45c 51 % 135 Type II Fig. 4.45d 40 % 152.5 Type III Fig. 4.45e 40 % 154 Type IV Fig. 4.45f 32 % 120 Type V Fig. 4.45g 32 % 132.2 Type VI Fig. 4.45h 32 % 141.2 Type VII Fig. 4.45i 32 % --- Type VIII Fig. 4.45j 32 % --- Type IX Fig. 4.45k 32 % --- Type X Fig. 4.45l 32 % ---

The final design of the new compact resonators was performed by using the 3-D FDTD method developed for planar circuits, which was described in Chapter 3. The FDTD method allowed the accurate analysis of filters and resonators of complex shapes. The characteristics of the newly designed compact resonators are listed in Tab. 2.1. In order to characterize these resonators, each resonator was capacitively coupled through a 1.5 mm coupling gap. While the fundamental frequency was found to be approximately the same for all resonators, f0=900 MHz, the spurious frequency f1 was found to be 2116 MHz, 2073 MHz and 1972 MHz for the resonators of type I, III, and VII respectively. These values of f1 correspond to an improvement in the isolation band of the resonators, when compared with the simple half wavelength resonator with f1 @ 1800 MHz. The resonator coupling analysis was performed by using the 3-D FDTD method. The final filter design requires the coupling coefficients between the resonators and with the external circuit. The variation of the coupling coefficients between type I and type II resonators versus resonator position is illustrated in Fig. 4.46, Fig. 4.47 and Fig. 4.48 for the electric, magnetic and mixed coupling, respectively. The variation of the external quality factor Qext versus the input line position is shown in Figs. 4.49-4.50.

134 Chapter 4 – New Microstrip Filter Design

0.016

0.014

0.012

0.01

0.008

Coupling coeficient Coupling 0.006 (a) (b) 0.004

0.002

0 0 0.5 1 1.5 2 2.5 Coupling gap s [mm]

Figure 4.46. Variation of the electric coupling coefficient versus coupling gap s for (a) type II resonators (continuous line), and (b) type I resonators (dashed line) [20]. In set, the electric coupling for type II resonators is shown.

0.08

0.07

0.06

0.05

0.04

Coupling coeficient Coupling 0.03 (a) (b) 0.02

0.01

0 0 0.5 1 1.5 2 2.5 3 3.5 4 Coupling gap s [mm]

Figure 4.47. Variation of the magnetic coupling coefficient versus the coupling gap s for (a) type II resonators (continuous line), and (b) type I resonators (dashed line) [20]. In set, the magnetic coupling for type II resonators is shown.

135 Chapter 4 – New Microstrip Filter Design

0.045

0.04

0.035

0.03

0.025

0.02 Coupling coeficient Coupling

0.015 (a) 0.01 (b)

0.005

0 0 0.5 1 1.5 2 2.5 3 3.5 Coupling gap s [mm]

Figure 4.48. Variation of the mixed coupling coefficient with the coupling gap s for (a) type II resonators (continuous line), and (b) type I resonator (dashed line) [20], for the missalignment t=0, i.e. for aligned resonators. In set, the mixed coupling for type II resonators is shown.

100

80 (a)

ext (b) 70

30 External factor quality Q 20

0 0 0.5 1 1.5 2 2.5 3 Input line position d [mm]

Figure 4.49. Variation of the external quality factor Qext versus the input line position d for (a) type II resonators (continuous line), and (b) type I resonators (dashed line) [20]. In set, the external coupling to a type II resonator is shown.

136 Chapter 4 – New Microstrip Filter Design

30 ext 25

(a) External factor quality Q 10 (b)

0 0 1 2 3 4 5 6 Input line position d [mm]

Figure 4.50. Variation of the external quality factor Qext with the input line position d for (a) type II resonators (continuous line), and (b) type I resonators (dashed line) [20]. Inset, the external coupling to a type II resonator is shown.

4.3.4. Filters with Novel Microstrip Resonators Coupled in Cascade

Before approaching the filters with cross-coupled resonators, let us analyze the case of filters with cascaded novel compact resonators. Once the dependence of inter- resonators coupling coefficients on the resonators positions and spacing is acquired, one can proceed with the multi-pole filter design. The filters were designed using a Finite-Difference Time-Domain (FDTD) software presented in Chapter 3. The experimental investigation was performed using a Computer Aided Measurements (CAM) system including a HP 8757C network analyzer. Two-pole filters have been designed using type I new compact resonators. The filter layout is presented in the insert of Fig. 4.51. The resonators are mixed coupled, that is they are coupled partially magnetic and partially electric. The inter-resonators coupling constant was k = 0.034. The predicted transmission zero at 1155 MHz is out

137 Chapter 4 – New Microstrip Filter Design of the finite dynamic range of the instrument. The measured response follows closely the response simulated by using the FDTD method. The measured 3 dB bandwidth is 59 MHz, that is about 5% fraction bandwidth. The insertion loss is less than 1.6 dB and the return loss is better than 15 dB.

-10

-20 [dB] 11 -30

-40 -50 [dB] and S and [dB] 21

S -60 -70

500 700 900 1100 1300

Frequency [MHz] Figure 4.51 Response of the two-pole filter with type I resonators [18].

Simulated S21 Measured S21 Simulated S11 Measured S 11 .

Another configuration with two-pole filter using type II resonators is illustrated in Fig. 4.52. In this case, the type II resonators are coupled magnetically. The two-pole filter shown in Fig. 4.52 has 1.3 dB in-band insertion loss. The response predicted by using the FDTD method follows closely the measured response except for a region situated at lower frequencies.

138 Chapter 4 – New Microstrip Filter Design

Two pole filter response

-10

-20 [dB] 21

-30 andS

11 S meas

S 21 S sim -40 21 S meas 11 S sim 11 -50

-60 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Frequency [GHz]

Figure 4.52. The response of the two-pole filter with type II resonators.

Two-pole filters designed with type V type resonators are shown in the insert of Fig. 4.53. For both a) and b) configurations, the coupling coefficient and the external quality factor are the same. Nevertheless, due to the asymmetric positions of the input/output coupling lines, the response of filter in configuration a) exhibits two transmission zeros on both sides of the pass-band, compared to only one transmission zero for filter in configuration b). The second transmission null makes a sharper response at lower frequencies resulting in a greater filter rejection. The FDTD simulated response follows closely the measured response. However, since the actual FDTD model does not take into account any losses, the in-band insertion loss is underestimated.

139 Chapter 4 – New Microstrip Filter Design

Two-pole filter

-10

| (dB) -20 11

-30 | and |S

21 -40 |S

-50

-60

200 400 600 800 1000 1200 Frequency (MHz)

Fig. 4.53. Two-pole filter response using type V resonators shown in Fig. 4.45g. The solid line and the dashed line represent the measured and simulated response, respectively, for the structure shown in the a) insert. The dotted line represents the simulated response of the filter shown in the insert b) [19].

The feasibility of microstrip filters using type VI resonators was demonstrated by the three-pole compact filter shown in Fig. 4.54. The resonators are coupled in cascade. The large coupling gap between resonators caused increased radiation losses and increased insertion loss as shown in Fig. 4.55.

Fig. 4.54. Three-pole filter using type VI new resonators coupled in cascade [21].

140 Chapter 4 – New Microstrip Filter Design

Three-pole filter

-10 S meas 21 S calc 21

(dB) -20 21

-30 and S 11 S -40

-50

-60 200 400 600 800 1000 1200 1400 Frequency (MHz)

Fig. 4.55. Response of the three-pole filter presented in Fig. 4.54. Comparison between measured response and response calculated by using the FDTD method [21].

4.3.5. Filters with Cross-Coupled Novel Microstrip Resonators

The filters with cross-coupled resonators allow the control of the transmission zeros on both sides of the filter pass-band. The cross-coupling improves the filter skirt sharpness because the two transmission zeros on both sides of the pass-band. For a desired filter response, a set of coupling coefficients and external quality factors are established using (4.28-4.30). The spacing between the resonators is given from the curves coupling coefficients versus coupling gaps. The input/output line position is given by the required external quality factor Qext. A quasi-elliptic four-pole filter inserted in Fig. 4.56 was designed in order to obtain a higher selectivity. Type I resonators were used for the filter design. The filter was synthesized using the approximate method in [25]. The coupling matrix is

141 Chapter 4 – New Microstrip Filter Design

 − 0036.000173.00   00148.000173.0  M =   . (4.36)  0173.000148.00    − 00173.000036.0 

Moreover, the external quality factor is Qe=44.5.

-10 [dB]

11 -20

-30 [dB] and S and [dB]

21 -40 S

-50

750 800 850 900 950 1000 1050

Frequency [MHz] Figure 4.56. Response of the four-pole filter with type I resonators [18].

Simulated S21 Measured S21 Simulated S11

Measured S11

The coupling gaps between the resonators corresponding to the above coupling constants together with the positions of the input and output lines had to be adjusted to the FDTD grid. The measured response in Fig. 4.56 presents a sharp skirt of 2.4 dB/MHz next to pass-band. Good selectivity was achieved with a 20 dB rejection bandwidth of 36 MHz. The central frequency is fC=910 MHz and the filter 3 dB bandwidth is 20 MHz, that is about 2% fraction bandwidth. The closest spurious

142 Chapter 4 – New Microstrip Filter Design bandwidth with the insertion loss 14 dB is present at 2116 MHz = 2.32 fC. This enlargement of stop-bandwidth occurs due to the SIR and stubs effects discussed in Section 4.3.2. Filters have been developed also by using type II resonators [21]. The four-pole filter shown in the insert of Fig. 4.57, has 4 dB insertion loss and 49 MHz 3 dB bandwidth. The filter is centered at 899 MHz. The measured S11 has two dips at 879.1 MHz and 913.6 MHz. The measured response in Fig. 4.57 is compared versus the response calculated from the narrow-band theory simulation of the model in Fig. 4.33.

Four pole filter response

|S | meas -10 21 |S | sim 21 |S | meas 11 | (dB) -20 |S | sim 21 11

-30 | and |S and | 11 |S -40

-50

-60 0.2 0.4 0.6 0.8 1 1.2 1.4 Frequency (GHz)

Figure 4.57. The response of the four-pole filter with cross-coupled type II resonators [19].

The coupling matrix is  − 0074.000448.00   00356.000448.0  M =   . (4.37)  0448.000356.00    − 00448.000074.0 

143 Chapter 4 – New Microstrip Filter Design

The external quality factor is Qext= 16.19. In order to achieve this Qext the coupling lines were connected to the vertical edges rather than to the horizontal edges as for filter in Fig. 4.56. The measured and calculated responses can be compared in Fig. 4.57. For the calculated response the narrow-band model of the filter was considered. The narrow-band model shown in Fig. 4.33 takes into account the unloaded quality factor of the resonators. The calculated response by using this model underestimates by 0.6 dB the in-band insertion loss. The differences between the out-of-band responses are caused mainly due to the narrow-band nature of the considered simulation model.

Fig. 4.58. Four-pole filter using cross-coupled type III compact resonators [21].

A four-pole filter design using type III novel compact resonators was designed . Similar to the four-pole filter design presented in Fig. 4.56-4.57. The coupling matrix is

 − 0081.000360.00   00259.000360.0  M =   . (4.38)  0360.000259.00    − 00360.000081.0 

The external quality factor is Qext= 17.86.

144 Chapter 4 – New Microstrip Filter Design

Four-pole filter response

-10 S measured 21 S FDTD 21 -20 S narrow band model (dB) 21

21 S measured 11 -30 and S

-4011 S

-50

-60 500 600 700 800 900 1000 1100 Frequency (MHz)

Fig. 4.59. Response of the four-pole filter [21] presented in Fig. 4.58. Comparison between measured response, response calculated by using the FDTD method, and response calculated by using the narrow band model depicted in Fig. 4.33.

A higher out of band rejection can be achieved by adding two more resonators to the four-pole cross-coupled filter shown in Fig. 4 58. The wide-band response of the six-pole filter using type III resonators is illustrated in Fig. 4.60. The coupling matrix for this filter is

 0342.00 0000     01917.000342.0 − 00078.00   01917.00 0245.00 00  = (4.39) M6    0245.000 01917.00 0   − 01917.000078.00 0342.00     00342.00000 

The external quality factor for the six-pole filter is Qe= 19.69.

145 Chapter 4 – New Microstrip Filter Design

Six-pole filter

-10

-20

| (dB) -30 21 |S -40

-50

-60

0 500 100 150 200 250 Frequency (MHz)

Fig. 4.60. Wide band response of the six-pole filter [19], designed with improved out-of-band rejection, using type III resonators shown in Fig. 4.45e.

The proposed filter [18-21] design needs no via holes and is fully compatible with the microstrip or stripline High Temperature Superconducting (HTS) technology. The low impedance lines are well fitted with the power handling requirements on HTS devices. The HTS technology can substantially increase the unloaded quality factors of the resonators allowing the design of high-selective multi-pole filters with very small in- band insertion loss.

146 Chapter 4 – New Microstrip Filter Design

4.4. The Influence of the Resonators' Unloaded Quality Factor Qu on the Filter Response

In many cases the microwave filter design is based on idealized low-pass prototypes with loss-less elements. However, the practical response of a filter often depends on the resonators characteristics. The model of cross-coupled filter shown in Fig.4.33 includes the resonators' losses in the conductances G1 and G2. The unloaded quality factor of QU resonator is ω C Q = (4.40) U G The simulated response of a 4% fractional bandwidth filter with cross-coupled resonators having identical finite quality factors is presented in Fig. 4.61. The reflection dips become less evident and the in-band insertion loss increases when Qu decreases. The effect of a small quality factor become more evident for a filter with a narrower filter s shown in Fig. 4.56. It can be seen that, for Qu=100, the minimum insertion loss can be as big as 13 dB for 1% fractional bandwidth filter, compared with only 4 dB for filter with 4% fractional bandwidth. The simulation results clearly show the requirement of designing with very high quality factors when selective multipole narrowband filters are desired. This conclusion emphasises the importance of HTS planar technology which can provide very high quality factor thin film resonators.

147 Chapter 4 – New Microstrip Filter Design

FBW = 4% 0

-5 Qu = 2000

-10 Qu = 700

Qu = 200 (dB)

21 -15 Qu = 100 -20 and S S11 11

S -25

-30

Qu = 100 -35 S21 Qu = 200

Qu = 700

Magnitude of -40 Qu = 2000 850 860 870 880 890 900 910 920 930 940 950 Frequency (MHz)

Figure 4.61. Four pole filter 4% fractional bandwidth response having resonators with Qu=2000, 700.200,100.

FBW = 1 % 0

-5 Qu = 2000 -10 Qu = 700

-15 Qu = 200 Qu = 100 [dB] [dB] 11

S Qu = 200 -20 Qu = 100 S11 and 21

S -25 S21 Qu = 700

-30 Qu = 2000

-35 Magnitude of of Magnitude -40

-45 850 860 870 880 890 900 910 920 930 940 950 Frequency [MHz]

Figure 4.62. Four pole 1% fractional bandwidth filter response having resonators with Qu=2000, 700.200,100.

148 Chapter 4 – New Microstrip Filter Design

4.5. Chapter Summary

Several low-pass and band-pass microstrip filters have been designed and tested. Most of the filters have been designed to match the specifications for GSM / GPRS cellular standards. However, an edge coupled filter was designed for the Australian L mobile satellite system for 1.265 GHz. Dual mode filters (DMF) can offer a solution when a narrow band is desired. Open loop and patch DMF are investigated and DMF for GSM / GPRS bands are designed. A novel quasi-fractal resonator is developed in order to reduce the square DMF patch size. Filters with cross-coupled resonators are investigated due to their ability to show generalized Chebyshev (or quasi-elliptic) response. Filters with cross-coupled open half-wavelength loops are designed. For mobile communications bands, the simply half-wavelength resonators are inconveniently long, therefore novel type of resonators are developed. Original theoretical principles of size reducing for these resonators are presented. The newly developed filters take up to 32% of the surface of a simple square half-wavelength resonator, both being designed for 900 MHz. The coupling coefficients of the novel resonators, function of their relative positions are obtained using the 3D-FDTD method. The external quality factor function of the input / output line positions are obtained in the same way. On the basis of the coupling coefficients, microstrip filters with novel cross- coupled resonators have been developed. The filters exhibit sharp skirt due to the attenuation zeros on both sides of the pass-band. The design of the new type of filters does not require any short-circuit via holes or lumped elements, therefore it can be easily extended to HTS technology. The dependence of the filter response on the unloaded quality factor of the resonators is investigated at the end of the chapter. It is concluded that HTS resonators with high quality factors represent a solution for the design of narrowband, multi-pole, selective filters with low insertion loss.

149 Chapter 4 – New Microstrip Filter Design

References

[1] M. G. Banciu, R. Ramer, “ FDTD Method for Mobile Communicationss Filters”, Progress In Electromagnetics Research Symposium, PIERS 2000, Cambridge, Massachusetts, USA July 2000 [2] E. H. Fooks, R. A. Zakarevicius, “Microwave Engineering using Microstrip Circuits”, Prentice Hall, 1989 [3] R. R. Mansour, S. Ye., S. Peik, V. Dokas, B. Fitzpatrik, “Quasi Dual-Mode Resonators”, Digest of IEEE Microwave Theory and Techniques Symposium, 2000, pp. 183-185 [4] A. Cassinese, F. Palomba, G. Pica, A. Andreone, G. Panariello, “Dual mode cross-slotted filters realized with superconducting films”, Applied Physics Letters, vol. 77, pp. 4407-4409, December 2000 [5] A. Cassinese, A. Andreone, M. Cirillo, F. Palomba, G. Panariello, G. Pica, R. Russo, F. Schettino, and R. Vaglio, “Superconducting Planar Filters Using Dual- Mode Cross-Slotted Square Resonators”, Journal of Superconductivity incorporating Novel Magnetism, vol. 14, pp. 131-137, 2000 [6] S. J. Fiedziuszko, J. A. Curtis, S. C. Holme, R. S. Kwok, “Low Loss Multiplexers with Planar Dual Mode HTS Resonators”, IEEE Trans. on Microwave Theory and Tech., 1996, vol. MTT-44, (7), 1248-1257 [7] M. G. Banciu, R. Ramer, “Design of Microstrip Dual Mode Filters Using Finite- Difference Time-Domain Method”, Proceedings of the Asia-Pacific Microwave Conference – APMC 2000, December 2000, Sydney, vol. 1, pp. 975-978 [8] A. C. Kundu, I. Awai, T. Kajitani, "Attenuation pole frequency control of a dual- mode circular microstrip ring resonator", 29th European Microwave Conference 99. Incorporating MIOP '99. Conference Proceedings. Microwave Eng. Eur. Part vol.2, 1999, pp.329-32 vol.2. London, UK. [9] I. Awai, “General Theory of a Circular Dual-Mode Resonator and filter”, IEICE Trans. Electron., vol. E81-C, November 1998, pp.1757-1763 [10] A. C. Kundu, I. Awai, “Control of Attenuation Pole Frequency of a Dual-Mode Microstrip Ring Resonator Bandpass Filter“, IEEE Transactions on Microwave Theory and Techniques, vol. 49, 2001, pp. 1113-1117

150 Chapter 4 – New Microstrip Filter Design

[11] A. C. Kundu, I. Awai, “Effect of External Circuit Susceptance Upon Dual- Mode Coupling of a Bandpass Filter”, IEEE Microwave and Guided Wave Letters, vol. 10, 2000, pp. 457 – 459 [12] U. Karacaoglu, I. D. Robertson, M. Guglielmi, “A Dual-Mode Microstrip Ring Resonator Filter with Active Devices for Loss Compensation”, 1993 IEEE MTT-S Digest, pp. 189-192 [13] J.-S. Hong, M. J. Lancaster, “Couplings of Microstrip Square Open-Loop Resonators for Cross-Coupled Planar Microwave Filters”, IEEE Transactions on Microwave Theory and Techniques, vol. 44, 1996, 2099-2109 [14] L. Zhu, P.-M. Wecowski, K. Wu, “New Planar Dual-Mode Filter Using Cross- Slotted Patch Resonators for Simultaneous Size and Loss Reduction”, IEEE Trans. on Microwave Theory and Tech., vol. MTT-47, (5), 650-654, 1999 [15] L. Zhu, K. Wu, “A Joint Field/Circuit Design Model of Line-to-Ring Coupling Structures and Its Application to the Design of Microstrip Dual-Mode Filters and Ring Resonator Circuits”, IEEE Trans. on Microwave Theory and Tech., vol. MTT-47, (10), 1938-1948, 1999 [16] F. S. Thomson, R. R. Mansour, S. Ye, W. Jolley, “Current Density and Power Handling of High-Temperature Superconductive Thin Film Resonators and Filters”, IEEE Transactions on Applied Superconductivity, 1998, Vol.8, (2), 84- 93 [17] R. R. Mansour, B. Jolley, S. Ye, F. S. Thomson, V. Dokas, “On the Power Handling Capability of High Temperature Superconductive Filters”, IEEE Trans. on Microwave Theory and Techniques, vol. 44, 1996, pp. 1322-1338 [18] M. G. Banciu, R. Ramer, A. Ioachim, “Microstrip Filters Using New Compact Resonators”, Electronics Letters, vol. 38, 2002, pp. 228-229 [19] M. G. Banciu, R. Ramer, A. Ioachim, “Compact Microstrip Resonators for 900 MHz Frequency Band”, to appear in the IEEE Microwave and Wireless Components Letters, May 2003 [20] M. G. Banciu, A. Ioachim, R. Ramer, “New Microstrip Resonators and Filters for GSM / GPRS”, Proceedings of the 25th Edition of the International Semiconductor Conference, CAS 2002, (IEEE Romania Section), Sinaia, Romania, 2002, vol. 1, pp. 41-44

151 Chapter 4 – New Microstrip Filter Design

[21] M. G. Banciu, A. Ioachim, R. Ramer, “New Microstrip Filters for GSM / GPRS”, to appear in the Proceedings of the EMFC 2002 (former ICMF), (IEE Slovakia Section), Bratislava 2002 [22] M. Reppel, H. Chaloupka, S. Kolesov, “Novel Approach for Narrowband Superconducting Filters”, Digest of IEEE Microwave Theory and Techniques Symposium, vol. 4, 1999, pp. 1563-1566 [23] M. Sagawa, M. Makimoto, S. Yamashita, “Geometrical Structures and Fundamental Characteristics of Microwave Stepped-Impedance Resonators”, IEEE Transactions on Microwave Theory and Techniques, MTT-45, 1997, pp. 1078-1085 [24] J.S. Hong, and M.J. Lancaster, "Canonical Microstrip Filter Using Square Open- Loop Resonators", Electronics Letters, vol. 31, 1995, pp. 2020-2022 [25] R. Levy, “Synthesis of General Asymmetric Singly- and Doubly Terminated Cross-Coupled Filters”, IEEE Transactions on Microwave Theory and Techniques, vol. 42, 1994, pp. 2468-2471

Acronyms and Abbreviations in Chapter 4

BPF Band Pass Filter DMF Dual Mode Filter DMR Dual Mode Resonator FBW Fractional Bandwidth FDTD Finite Difference Time Domain Method GSM Global System for Mobile communications GPRS General Packet Radio Service HPF High Pass Filter HTS High Temperature Superconductors LPF Low-Pass Filter NH-PML Non-Homogeneous Perfectly Matched Layer Q-factor Quality Factor VNA Vector Network Analyzer

152 Chapter 5- High Temperature Superconducting Microwave Devices

C H A P T E R 5 High Temperature Superconducting Microwave Devices

High Temperature Superconductors (HTS) are more and more present in RF and microwave applications [1-3]. HTS thin film technology can be used for high Q resonators and very selective multi-pole filters with very low insertion-loss. In order to prove the HTS devices feasibility for RF and microwave applications, HTS microstrip resonators and HTS antennas have been investigated experimentally. The work described in this Chapter is limited to a few preliminary studies. This is due to the lack of further funding.

5.1. HTS Thin Film Fabrication

We prepared off-axis thin films by using single target RF magnetron sputtering [4,6].

The superconducting. YBa2Cu3O7-δ thin films were deposited on Lanthanum Aluminate

(LaAlO3) and on Yttria Stabilized Zirconia (YSZ) substrates. Both “in situ” and “ex situ” methods have been used. “In situ” method was used for deposition on both sides of the substrates. Standard ceramic technique was used to produce the target. The raw materials were ground and calcined at 900°C for 12 h. Sintering was carried out in oxygen at 930°C for 20h. The target size was 50 mm in diameter and 4 mm thick. When the “in situ” method was used, the substrates were glued on a heated stainless steel piece by using silver paste The actual substrate temperature was measured using a Chromel-Alumel thermocouple. The substrate was heated during the deposition. The sputtering gas was a mixture of 50%Ar and 50%O2 at 20 Pa sputtering pressure. The sputtering power was 40 W and the deposition rate was 100 nm/h. The typical film thickness was in the range of 250-300 nm. Following the deposition, the films were annealed in the sputtering chamber at 750°C in pure oxygen atmosphere at a pressure of 29 Pa. Next, the films were cooled at a rate of 1°C/min, again in pure

153 Chapter 5- High Temperature Superconducting Microwave Devices oxygen atmosphere. When the temperature was decreased to 450°C, the oxygen pressure was increased to 104Pa. The films were additionally kept for 1h at 450°C. Finally the films were cooled at a rate of 100°C/h down to room temperature. When using the ex-situ method, the deposition was carried out at room temperature and followed by post annealing. The post annealing was achieved in a gas o flow consisting of a mixture of N2 and 29 Pa O2 for 3.5 h at 750 C. Next, the films were cooled from 750°C to 450°C at a rate of 3°C/min, in pure oxygen atmosphere at a pressure increasing from 29 Pa to 104 Pa at a rate of 100 Pa/min. The films were further kept at 450°C for 1h in order to provide them with the necessary amount of oxygen required by stoichiometry. The films were next cooled at a rate of 100C°/h back to room temperature. The temperature dependence of resistivity shows that the YBCO thin films grown by in situ method have a metallic behaviour in the natural state and that the critical temperature is Tc = 92 K with an onset temperature Tco = 90 K. The YBCO films grown by the “ex situ” method have Tc = 92 K and Tco = 89 K. The measured 6 2 critical current density Jc was 4x10 A/cm .

Figure 5.1. X-Ray diffraction patterns for YBCO thin films [7].

X-ray diffraction patterns in Fig. 5.1, showed a single 123 phase thin films and a good orthorhombic structure characteristic of the superconducting materials, when

154 Chapter 5- High Temperature Superconducting Microwave Devices grown “in situ”. The SEM images reveal glossy surfaces and lamellar grains of the “in situ” films.

5.2. YBCO Microstrip Ring Resonator

Microstrip resonators were manufactured in order to prove the quality of the HTS thin films and asses the feasibility of manufacture of HTS microwave devices patterning facilities. Microstrip resonators were patterned. The linear resonator and the ring resonator are shown in Fig. 5.2, left and right respectively. In this case, the YBCO “off axis” thin films were deposited on Yttria Sabilized Zrconia substrates.

Figure 5.2. Microstrip ring and linear resonators patterned of YBa2Cu3O7-δ thin film deposited on Yttria Stabilized Zirconia.

The mean diameter of the ring resonator (Fig. 5.2) was 9.0 mm. We used microstrip lines of 0.64 mm width, and 25.7 Ω characteristic impedance. Technical difficulties encountered with the fabrication of narrow microstrip lines on high dielectric constant substrates were avoided by using such wide lines. However, the impedance mismatches increased reflection loss and insertion loss. Microwave measurements have been performed on the ring microstrip resonator. The package was mounted inside a closed cycle cooler. Transmission characteristics

(S21) versus frequency are presented in Figs. 5.3-5.6 for different temperatures.

155 Chapter 5- High Temperature Superconducting Microwave Devices

Figure 5.3. Measured S21 versus frequency for a HTS ring resonator at temperature 40 K.

Figure 5.4. Measured S21 versus frequency for a HTS ring resonator at temperature 50 K.

156 Chapter 5- High Temperature Superconducting Microwave Devices

Figure 5.5. Measured S21 versus frequency for a HTS ring resonator at temperature 65 K.

Figure 5.6. Measured S21 versus frequency for a HTS ring resonator at temperature 70 K.

157 Chapter 5- High Temperature Superconducting Microwave Devices

The resonance is clearly shown above the noise for all the measuring temperatures taken, T=40 K, 54 K, 65 K and 70 K. The measurements also indicate the way the quality factor decreases from 272 to 60 as the temperature increases from 40 K to 70 K. The variation of unloaded quality factor Qu function of temperature is presented in Fig. 5.7.

Fig58.m 300

250 Qu

200 actor f y it 150

oaded qual oaded 100 Unl

0 0 10 20 30 40 50 60 70 80 90 100 Tem perature T(K)

Figure 5.7. The variation of unloaded quality factor Qu versus temperature T (K) for ring microstrip resonator.

For the same temperature interval the peak insertion loss increases from 21.27 dB to 30.47 dB. The resonance frequency has also a small negative trend with the temperature increase. It decreases from 3.132 GHz at 40 K to 3.015 GHz at 70K. The variation of the resonance frequency with temperature is shown in Fig. 5.8. An interesting feature of the resonance curves in Figs. 5.3-5.5, where there are 330 MHz / div, is the presence of second resonance peak at about 70 MHz below than the main peak. The symmetric coupling cannot generate this peak-splitting. The second resonance peak can be caused by the anisotropic nature of the single crystal substrate. The anisotropy can cause a sort of dual mode effect similar to the dual mode effects observed on loop resonators when non-symmetrically coupled [10].

158 Chapter 5- High Temperature Superconducting Microwave Devices

Fig59.m 3.25

3.2

3.15 GHz] [ 3.1

3.05 equency fr

3 R ezonant 2.95

2.9

2.85 0 10 20 30 40 50 60 70 80 90 100 Tem perature T(K)

Figure 5.8. Resonance frequency f0 versus temperature T (K).

The absolute value of the quality factor was affected by the use of a silver paint ground plane instead of an HTS ground plane. Due to its very good mechanical properties, silver paste was also used for binding the input/output HTS thin film lines to the external connectors. However, the limited conductivity of the silver paste increased both insertion loss and reflection loss.

5.3. HTS Slot Coupled Antenna

5.3.1. Design and Fabrication

Electrically small (sub-wavelength) antennas with radiation resistances comparable to or smaller than the element ohmic resistances, dissipate a significant amount of power in loads other than free space. The power loss can be made smaller by reducing the element resistance. The reduced surface resistance RS of HTS has the potential to lower RF and microwave insertion loss by many dB’s. Electrically and physically small antenna arrays in a superconducting state can be used to obtain a radiation pattern of good directivity with high radiation efficiency.

159 Chapter 5- High Temperature Superconducting Microwave Devices

Figure 5.9. The slot coupled microstrip HTS antenna geometry.

The microstrip high temperature superconducting antenna (Fig. 5.9) consists of a circular radiating patch. The feeding uses a slot coupled method. A rectangular aperture having the width wa and the length la is patterned in the ground plane of the microstrip antenna. The feeding line is patterned on another dielectric substrate, perpendicularly on the slot. The feed line and the aperture are separated by another dielectric substrate such that the line characteristics would be those of a stripline.

5.3.2. Measurements

For measuring the high superconducting antenna, a vacuum chamber for a two-stage closed-cycle helium gas refrigerator is needed. The high-density polyethylene radome should be designed for minimum effect on the antenna field. Preliminary deign tests were performed on three microstrip antennas realised in the same slot coupled feeding method on two different dielectric substrates. The dielectric constants were 2.55 and 6 respectively and for two different frequencies. The complex reflection coefficients were measured for both antennas.

160 Chapter 5- High Temperature Superconducting Microwave Devices

-2

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-6

-8 Relative MagnitudeRelative (dB) -10

-12 -150 -100 -50 0 50 100 150 200 Angle Theta (Degrees)

Figure 5.10. Relative magnitude (dB) versus angle (degrees) for the microstrip antenna fabricated on 2.55 dielectric constant substrate at 1.42 GHz. a) continuous line - E plane, b) dashed line - H plane.

-2

-4

-6

-8

-10 Relative MagnitudeRelative (dB)

-12

-14 -150 -100 -50 0 50 100 150 Angle Theta (Degrees)

Figure 5.11. Relative magnitude (dB) versus angle (degrees) for the microstrip antenna fabricated on 6 dielectric constant substrate at 1.42 GHz, a) continuous line - E plane, b) dashed line - H plane, c) dotted line - H plane (connector in the LHS).

161 Chapter 5- High Temperature Superconducting Microwave Devices

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Relative MagnitudeRelative (dB) -20

-25 -150 -100 -50 0 50 100 150 Angle Theta (Degrees)

Figure 5.12. The radiation pattern versus angle (degrees) of the microstrip antenna on 6 dielectric constant substrate at the frequency 7.5 GHz. a) continuous line - E plane, b) dashed line - H plane.

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-15 Relative MagnitudeRelative (dB)

-20

-25 -150 -100 -50 0 50 100 150 Angle Theta (Degrees)

Figure 5.13. The radiation pattern of the microstrip antenna on 6 dielectric substrate for three frequencies 7.5 GHz (continuous line), 7.7 GHz (dashed line) and 8 GHz (dotted line).

162 Chapter 5- High Temperature Superconducting Microwave Devices

The antennas' patterns are presented in Figs. 5.10-13. All figures show as expected [9], a pattern in H plane wider than in E plane.

Fig. 5.10 shows the pattern of the antenna designed on εr = 2.55 dielectric constant substrate, at frequency 1.42 GHz. Fig. 5.11 presents the pattern of the second antenna at 1.42 GHz. This antenna was designed on a substrate with εr = 6 dielectric constant.

The same εr = 6 dielectric constant substrate was used also for the third antenna designed for 7.5 GHz. The measured pattern of this antenna is shown in Fig. 5.12. The frequency dependence is presented in Fig. 5.13. The pattern is plotted for three frequencies 7.5, 7.7 and 8.0 GHz. It can be noticed that the antenna pattern becomes wider when the working frequency and/or the dielectric constant of the substrate are increased.

5.4. Chapter Summary

The results of experimental investigation of HTS thin film microwave resonators and antennas are presented in this chapter. YBCO thin films have been deposited on LAO and YSZ substrates. The TC and JC measurements together with X-rays diffraction patterns and SEM images confirm the high quality of deposited films. The measurements on HTS microstrip resonators confirm the good thin film characteristics at microwave frequencies. In spite of the later rapid evolution of the technological research for HTS thin film deposition, the developed HTS microstrip resonators constitute an important step towards the realization of multi-pole, low-loss selective filters. This makes HTS technology very attractive for an increasingly crowded radio frequency spectrum. In Section 5.3, the design and fabrication preamble of a microstrip HTS antenna is presented. A slot coupled feeding was chosen as a promising configuration for microstrip antenna arrays. Preliminary measurements on disk slot coupled antennas designed on different substrates and for different frequencies are presented. HTS antennas were manufactured on YBCO thin films and the antenna design is presented.

163 Chapter 5- High Temperature Superconducting Microwave Devices

References

[1] M. J. Lancaster, “Passive Microwave Applications of High-Temperature Superconductors”, Cambridge University Press, 1997 [2] Z.-Y. Shen, “High Temperature Superconducting Microwave Circuits”, Artech, Boston, 1994 [3] M. Hein, “High Temperature-Superconductor Thin Films at Microwave Frequencies”, Springer, Berlin Heidelberg, 1999 [4] R. Ramer, M. G. Banciu, C. Constantin, G. J. Russell, T. B. Vu “Superconducting Thin Films for Microwave Resonators”, Proceedings of the Asia Pacific Microwave Conference, APMC ’97, December 2-5 1997, pp. 121-123 [5] M. G. Banciu, M. S. Pham, R. Ramer, T. B. Vu, “Preliminary Design and Fabrication of Microstrip HTS Antenna”, Proceedings of the 3rd Asia-Pacific Conference on Communications, APCC’97, December 7-10, 1997, pp. 902-905 [6] R. Ramer, M. G. Banciu, “High Temperature Superconducting Thin Films for Microwave Devices”, Proceedings of the XV-th International Conference on Microwave Ferrites, Rokosowo, Poland, September 2000, pp. 120-123 [7] R. Ramer, M. G. Banciu, E. Dimitriu, M. S. Pham, T. B. Vu, “Design and Fabrication Preamble of a Microstrip HTS Antenna”, Industrial Ceramics, vol. 21, no. 2, ISSN 1127-7588, pp. 111-113 [8] H. How, R. G. Seed, C. Vittoria, D. B. Chrisey, J. S. Horwitz, C. Carosella, V.

Folen, “Microwave Characteristics of High TC Superconducting Coplanar Waveguide Resonator”, IEEE Transactions on Microwave Theory and Techniques, vol. 40, 1992, pp. 1668-1673 [9] J. R. James, P. S. Hall, “Handbook of Microstrip Antennas”, Peter Peregrinus, London, 1989 [10] I. Wolff, “Microstrip Bandpass Filter Using Degenerate Modes of a Microstrip Ring Resonator”, Electron. Lett.,1972, Vol.8, (12), 302-303

164 Chapter 5- High Temperature Superconducting Microwave Devices

Acronyms and Abbreviations in Chapter 5

GSM Global System for Mobile communications GPRS General Packet Radio Service HTS High Temperature Superconductors IM Inter-Modulation IMP IM Products

LAO LaAlO3 (Lanthanum Aluminate) SEM Scanning Electron Microscopy

TBCCO Tl2Ba2Ca2Cu3Ox

Tl-2212 Tl2Ba2CaCu2O8

Y-123 YBa2Cu3O7-δ

YBCO YBa2Cu3O7-δ YSZ Yttria Stabilized Zirconia

165 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

C H A P T E R 6 Low Noise RF Electronics for GSM / GPRS Smart Antenna

6.1. Introduction

It was pointed out in Section 2.5, that smart antenna can dramatically improve the signal to interference plus noise ratio (SINR), offering enhanced immunity to multipath fading and reduction of co-channel interference (CCI). The goal of the research described in this chapter was noise minimization, gain uniformity and coherence of the signals provided by different array elements of the smart antenna. The research was carried on at University of New South Wales in the frame of the “Smart Antenna for GSM” project, which was sponsored by the Australian Government, Telstra, Texas Instruments Australia, Argus Technologies and University of New South Wales. As it was shown in Section 2.1, the new GPRS standard shares with GSM physical resources and many properties of the physical transmission layer. Hence, the results obtained in this GSM project can easily be transferred to GPRS.

(a) (b)

Figure 6.1. The GSM / GPRS 900 smart antenna (a) front view; (b) rear view.

166 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

The GSM 900 smart antenna was composed by 2 linear antenna arrays arranged in a T shape. Each linear array was formed by 8 microstrip square patch antennas illustrated in Fig. 6.1a. The research goal was to obtain a good SNR, therefore the RF receiver electronics was positioned right on the back of the microstrip antenna patches [1], as shown in Fig. 6.1b. For each antenna element in the array, there were two feed points implementing polarization diversity. The second feed point was also used for calibration [2]. In addition, the IF and RF sections were enclosed in separate metallic boxes for adequate electromagnetic interference (EMI) isolation.

Figure 6.2. Connection of the sixteen receivers.

Signals from RF and IF local oscillators (LOs) were supplied to all the receivers, as depicted in Fig. 6.2. The power divider networks for local oscillators signals can be noticed on the back of the antenna in Fig. 6.1b. The receivers’ outputs were provided by 50 Ω coaxial cables to analog to digital converters, physically situated together with the digital signal processing (DSP) circuitry. To avoid any spurious noise coupling the DC power was supplied separately for each receiver. The gain of each receiver was controlled using the voltage gain control (VGC).

6.2. Development of GSM 900 Receivers

The GSM 900 receiver design consisted of two stage down-conversion, to allow sufficient noise rejection. The first stage was based on TQ9203, which included two low

167 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna noise amplifiers (LNA) and a Gilbert cell mixer [3]. The RF2612 was used in the second down-conversion stage. The GSM 900 receiver was designed on the basis of the evaluation results. Several evaluation boards, were manufactured to test the main components used for the design. Layouts of some of the evaluation boards are presented in Fig. 6.3. Other evaluation boards are discussed in Appendix 4. The evaluation boards for TQ9203 (Fig. 6.3a) and for RF2612 (Fig. 6.3c) were designed to allow measurements on both the LNAs stage and on the mixer stage.

(a) (b)

Figure 6.3. Layouts of the evaluation boards a) TQ9203 evaluation board, b) SAW filter (B4632) evaluation board, c) RF2612 evaluation board.

(c)

The designed cumulative gain and the cumulative noise figure are presented by the receiver level block diagram in Fig. 6.4. The GSM 900 receiver schematics is shown in Fig. 6.5.

168 Chapter 6–LowNoiseRFElectronicsforGSM/GPRSSmart Antenn

Figure 6.4. Level diagram for GSM 900 Receiver. 169 a

Chapter 6–LowNoiseRFElectronicsforGSM/GPRSSmart Antenn 170 a

Figure 6.5. GSM 900 receiver schematics. Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

The signals coming from the two antenna feed points (RF INPUT 1 and RF INPUT 2 in Fig. 6.5) were fed into the RF inputs LNA IN0 and LNA IN1 of the TQ9203 down-converter. However, the noise reduction research goal required the isolation of the receiver band from the out-of-band interferences, especially from the transmission (downlink) signals, which could saturate the LNAs. This preliminary band selection was performed by preselect SAW filters. The characteristics of the uplink RF SAW filter used for the array receivers, together with the downlink SAW filter used for a mobile station (MS) receiver are illustrated in Figs. 6.6-6.7.

(a) (b)

Figure 6.6. S21 magnitude of the preselect SAW filter for GSM / GPRS 900, a) for downlink, b) for uplink.

The in-band insertion loss of the preselect filters (1.93 dB for the downlink filter in Fig. 6.6a and 1.55 dB for the uplink filter) played an important role in receiver cumulative noise figure as shown in receivers plan (Fig. 6.4). When the group delay definition (2.27) was applied to the SAW filters phase characteristics depicted in Fig. 6.7, average values of 2.4 µs for downlink filter and 2.5 µs filter were obtained. These values were four orders of magnitudes larger than the propagation time along a simple microstrip line, as such in the SAW filter evaluation board illustrated in Fig. 6.3b.

171 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

(a) (b)

Figure 6.7. S21 phase of the preselect SAW filter for GSM / GPRS 900. a) for downlink, b) for uplink.

An important aspect of the receiver RF section was the control of antenna diversity. This control required the LNA characterization, as one of the two LNAs was selected at a time. The difference between the output signal levels, when a certain LNA was selected or not, is called off-isolation. When the TTL signal on pin 5 (SELECT) of the TQ9203 was low then LNA IN0 was selected; when was high, then the LNA IN1 was selected. The “off-isolation” behavior was demonstrated by the Smith chart plots in Fig. 6.8 and by the magnitude plots in Fig. 6.9.

(a) (b)

Figure 6.8. Smith chart plots of the LNA S21 parameters demonstrating the “off- isolation”, (a) LNA 0, (b) LNA 1.

172 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

(a) (b)

Figure 6.9. LNA S21 parameters demonstrating the “off-isolation” (a) LNA0 on and LNA1 off, (b) LNA1 on and LNA0 off.

The RF signal left the LNA through pin 9 and was filtered again by the third RF SAW (B4632) image filter before entering in mixer section. The matching requirements between the output of the image filter and the mixer input required the presence of a shunt inductor of 12 nH on pin 11 (MIXER IN). The RF local oscillator input on pin number 1 (LO in) could be tuned by modifying slightly the position of a 12 nH inductor on pin no 13 (LO tune) as shown in Appendix 4. The mixer output, i.e. pin 14 of TQ9203, was high impedance , but DC voltage needed to be provided on this pin. Therefore, a suitable output matching achieved the DC rejection also. Both TQ9203 LNAs were matched for the minimum noise figure. The constant noise figure circles shown in Fig. 6.8 are described by the equation 2 4R Γ−Γ optsn FF min += (6.1) 2 2  Γ− 11 Γ+  s  opt where ΓS is a complex number representing the reflection coefficient looking from device input towards the source and F is the noise factor defined in Section 2.4. The

Γopt is the particular value of ΓS, when the minimum value was obtained. Fig. 6.10 shows that the noise behavior of microwave devices can be fully characterized by four parameters: the minimum noise factor Fmin, the noise resistance Rn illustrating the radius of the noise circles and the magnitude and phase of Γopt showing the position of the minimum noise factor point on the Smith chart.

173 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

Figure 6.10. Constant noise figure circles for LNAs of TQ9203.

The values of noise parameters depended on frequency [4-5] and the only Γopt o data available was at 881 MHz, opt ,7.0 opt =Γ∠=Γ 31 . However a good noise matching could be performed using a simple LC matching network as shown in Appendix 4. The receiver was controlled in a range of 80 dB by the two AD603 voltage gain amplifiers. The capacitor C3 assured the DC blocking between the mixer output of the RF down-converter and pin 3 (VIN) of the first AD603. The gain of each AD603 could be varied in the range –10 dB to +30 dB in a maximum 90 MHz bandwidth. The gain was controlled by the voltage between the pins 1 (GPOS) and 2 (GNEG). The whole gain range was covered by varying this control voltage in the range –0.5V to +0.5V. The SAW IF filter X6962 with the central frequency at 70 MHz was situated between the two gain controlled amplifiers (GCA). This filter had a 3 dB pass bandwidth of 6.3 MHz and a 30 dB bandwidth of 8.2 MHz. However, the second section of the RF2612 IF down-converter could not provide a gain control solution as reliable as AD603. This occurred because the

174 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

RF2612 is a narrowband device with low input P1dB of 35 mVpp. Fig. 6.11 clearly shows the intermodulation (IM) effects on this device. For input power in the range -90 dBm to –50 dBm, the saturation occurs practically at the same gain settings.

Figure 6.11. Intermodulation effects on the second section of RF2612.

An extra gain was also provided at baseband frequency. Again, the emphasis was on the reduction of noise and intermodulation effects. For that reason, IM products and gain measurements were performed on three devices EL2075C, CLC450 and CLC426. The power of the 2nd harmonic of the output signal is compared in Fig. 6.12 for three input powers –15dBm (Fig. 6.12a), -20 dBm (Fig. 6.12b) and –50 dBm (Fig. 6.12c). The 3rd harmonic of the output signal was analyzed also for three input power –15 dBm (Fig. 6.13a), -20 dBm (Fig. 6.13b) and –50 dBm (Fig. 6.13c). Finally, the gain was also compared in Fig 6.14 for the 8 MHz bandwidth for the three values of the input powers mentioned above.

175 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

The harmonics power and gain measurements presented in Figs. 6.12-6.14 showed that EL2075C was the best choice over CLC450 or CLC426 providing better gain for low IM products. The choice of the device with low intermodulation products corresponded to the general research goal of noise reduction.

(a) (b)

Figure 6.12. Output Power of the 2nd harmonics (dBc) versus frequency (MHz), a) input power Pin = -15 dBm, b) input power Pin = -20 dBm, c) input power Pin = -50 dBm.

(c)

176 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

(a) (b)

Figure 6.13. Output power of the 3nd harmonics (dBc) versus frequency (MHz), a) input power Pin = -15 dBm, b) input power Pin = -20 dBm, c) input power Pin = -50 dBm.

(c)

(a) (b)

Figure 6.14. Gain (dB) versus frequency (MHz), a) input power Pin = -15 dBm, b) input power Pin = -20 dBm, c) input power Pin = -50 dBm.

(c)

177 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

The baseband frequency signal was processed through a low pass LC filter for suppressing any interference frequency, especially the IF LO, outside the baseband bandwidth. The IF LO was suppressed by at least –40 dBc. The final layout of the GSM / GPRS 900 RF receiver is presented in Fig 6.15a. The receiver picture is presented in Fig. 6.15b. The same layout was used for both the upload and download receivers, the main difference consisted in the bandwidth of the preselect filters.

(a) (b)

Figure 6.15. GSM receiver a) layout, b) picture.

The worst measured SNR was 25 dB. Spurious noise reduction was among the research goals, therefore an important attention was paid to understand and avoid the EMI. As a result of this research, the separation between the RF and IF stages in two shielded boxes was decided. The picture of the receiver circuit in Fig. 6.15b shows the RF and IF power dividers also. To avoid the noise coupling along the DC paths, a design with separated paths for power supply was chosen not only for the receivers in the array but also for the IC’s in the receiver. In conclusion, low noise GSM / GPRS 900 receivers were achieved on the basis of original designs and investigations of noise reduction techniques.

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6.3. Design of DCS 1800 Receiver

A DCS 1800 receiver was developed on the same principles as the GSM 900 receiver with two downconversion stages. However, the receiver RF section was modified for the new uplink frequency bandwidth given in Section 2.1 by (2.8b) and (2.8a). The block diagram of the DCS 1800 receiver is illustrated in Fig. 6.16. The first downconversion stage is using a RF Micro-devices monolithic integrated receiver front-end for PCS applications (RF9936). The RF9936 PCS low noise amplifier / mixer contains all of the required components to implement the RF functions of the receiver front-end except for the passive filtering and LO generation. It contains two LNA’s (low noise amplifiers), a double-balanced Gilbert cell mixer, a balanced IF output, a LO isolation buffer amplifier, and a LO output buffer amplifier providing the buffered LO signal as an output.

Figure 6.16. Functional block diagram for DCS 1800 Receiver.

The receiver was designed on the basis of the investigations of RF9936 using the evaluation board depicted in Fig. .6.17. On this board, one can easily distinguish the image filter inserted between the output of the LNA section and the mixer RF input. This design and measured response of this microstrip filter is discussed in Section 4.1. DC bias should be applied to the IF output (pins 15 and 16 of RF9936). This pin has high impedance (open collector). Special matching techniques need to be applied as for the IF output of the TQ9203 in GSM900 receiver.

179 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

Figure 6.17. Evaluation board of the RF9936 (not to scale).

The layout of the DCS 1800 receiver, illustrated in Fig. 6.18 is designed for an IF section using RF2612. Nevertheless, taking into account the narrow-band limitation of RF2612, an improved version of the receiver designed has an IF section identical to the GSM 900 IF section depicted in Fig. 6.4-6.5. In this version, two AD603 chips are used instead RF2612.

Figure 6.18. Layout of the DCS1800 receiver (not to scale).

180 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

6.4. Design of GSM 900 / DCS 1800 Transmitter

A RF transmitter was developed to test the electronics for GSM / GPRS Smart Antenna. The transmitter was aimed to function for both frequency bands GSM 900 and DCS 1800. For testing, no high output power was demanded. Two versions of the transmitter were investigated. The first version was developed on the basis of RF2422 2.5 GHz Direct Quadrature Modulator. The block schematics of this transmitter is depicted in Fig. 6.19. The RF2301 was used to amplify the output RF signal.

Figure 6.19. Block schematics of the first version of the GSM 900 / DCS 1800 transmitter.

The RF2422 device was tested using a phase shifter to supply I and Q signals with a good accuracy in amplitude and phase. The layout of the first version of the GSM 900 / DCS 1800 transmitter is depicted in Fig. 6.20. The RF2422 was a single side band upconvertor. However, the evaluation showed that a good carrier suppression and side-band suppression were very hard to be achieved with this component. This could be proved by the actual output from of RF2422 presented in Fig. 6.21a.

181 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

Figure 6.20. Layout of the first version of the GSM 900 / DCS 1800 transmitter (not to scale).

The measured carrier suppression for the Micro-Dvices TUF-5SM mixer was better than 25 dB as shown in Fig. 6.21b. On the basis of this result, the second version of the transmitter was designed and developed. This version contains two upconversion stages as depicted in the schematics in Fig. 6.22.

Figure 6.21. Spectrum analysis of the output signal (10dB / div), a) from RF2422, b) from the Micro-Dvices TUF-5SM mixer.

182 Chapter 6–LowNoiseRFElectronicsforGSM/GPRSSmart Antenn 183 a

Figure 6.22. Schematics of GSM-900 / DCS-1800 transmitter (second version). Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

6.5. Testing the RF Electronics for GSM / GPRS Smart Antenna

The RF electronics developed for GSM / GPRS Smart Antenna was tested using HP 8922S “GSM MS Service Test Set” and a normal GSM mobile telephone. Since the test set provided no auxiliary input, which could be used for DCS 1800, a measurement setup shown in Fig. 6.23, using a MACOM FR11-0003 circulator (1805-1890 MHz ), and dielectric filters LARK ENG SSD1747 (1747 MHz) and SSD1842 (1842 MHz) was prepared. The Bit Error Rate (BER) was found in the limits of the GSM specifications.

Figure 6.23. Measurement Setup for DCS1800 Receiver –Transmitter.

The RF electronics for GSM / GPRS Smart Antenna [1] was developed to provide adequate signals for further digital processing. The spatial filtering was processed in the baseband. The array main beam was first steered towards the desired mobile phone as in Fig. 6.24. The array pattern was then modified to minimize the influence of other interference sources. The horizontal linear array played an important role in beamforming in the azimuth plane differentiating easily the users transmitting from different locations of the cell. In addition, beamforming in the elevation plane was required especially by the multipath propagation in crowded urban environment. Following the spatial filtering, the digital signal was filtered in time using the constant modulus algorithm (CM) [2].

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-5

-10

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Relative C/I (dB) -20

-25

-30 0 20 40 60 80 100 120 140 160 180

Azimuth angle θ (in degrees)

Figure 6.24. Antenna pattern with the main Figure 6.25. Normalized CIR for punctual beam steered toward the user's DOA sources (dotted line) and sources with (at θ = 45o and φ = 60o in this case) [1]. angular spread of 10o (solid line) [1].

6.6. Chapter Summary

This chapter describes the research work on RF electronics for GSM / GPRS smart antenna. A smart antenna based on adaptive beam-forming and space-time equalization can provide a greater immunity to the multipath fading together with the enhancement of the SINR. The research goal was noise minimization, gain uniformity and coherence of the signals provided by different array elements. Special techniques were investigated to reduce the receivers’ noise and the effects of intermodulation. A special attention was given to the matching of the low noise amplifiers inputs for the minimum noise figure in the presence of mismatches [4, 5]. The IF and the baseband sections were also optimized for lower IM products. For the transmitter, a solution with higher carrier isolation and sideband was preferred. The layout effect on some parameters was also taken into account. It was experimentally proven, that some parameters of the RF down converters, such as the off-isolation or the LO buffer tuning frequency, were very sensitive to the layout. Furthermore, an appropriate out-of-band isolation of the IF SAW filters could be

185 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna obtained only if suitable design techniques were applied to eliminate the spurious cross- couplings between filter ports. Low noise receivers for GSM 900 uplink, GSM 900 downlink and for DCS 1800 frequency bands were achieved. A transmitter for both frequency bands was developed in order to test the system parameters. Sixteen uplink GSM receivers, developed on noise minimization basis, provided gain uniformity and adequate output signals in order to allow digital processing of the baseband signals, required by the spatial and time filtering.

References

[1] M. G. Banciu, P. Rapajic, R. Ramer, “RF Electronics for GSM/GPRS Smart Antenna”, Proceedings of the 25th Edition of the International Semiconductor Conference, CAS 2002, (IEEE Romania Section), Sinaia, Romania, 2002, vol. 1, pp. 45-48 [2] B. Xu, T. B. Vu, G. Jonas, “Implementation of a Smart Antenna Using TMS320C80 DSPs for Mobile Communications”, Proceedings of ICSP’ 98, 355-358 [3] Thomas H. Lee, “The Design of CMOS Radio-Frequency Integrated Circuits”, Cambridge University Press, Cambridge, UK, 1998 [4] M.G. Banciu, “A Measurement Method to Determine the Noise Parameters of Microwave Transistors”, Technische Universiteit Eindhoven, Report EEA-477, August 1993 [5] M.G. Banciu, J.J.M. Kwaspen, H. C. Heyker, “Correction for Mismatches in Measuring Low Noise Microwave Transistors”, Proceedings of the Annual Conference on Semiconductors, CAS’94, Sinaia, Romania, 1994, vol. 2, pp. 379-382

186 Chapter 6 – Low Noise RF Electronics for GSM / GPRS Smart Antenna

Acronyms and Abbreviations in Chapter 6

1G, 2G, 2.5G, 3G First, second, intermediate, third generation of standards in mobile communication AF Array Factor BS Basestation CCI Co-channel Interference DOA Direction of Arrival DR Dielectric Resonator DSP Digital Signal Processsor FDTD Finite Difference Time Domain Method EMI Electromagnetic Interference GSM Global System for Mobile communications GPRS General Packet Radio Service HTS High Temperature Superconductors IF Intermediate Frequency IL Insertion Loss IM product Intermodulation product LMS Least Mean Square LNA Low Noise Amplifier LO Local Oscillator MRC Maximal Ratio Combiner MSE Mean Square Error NF Noise Figure PLL Phase Locked Loops REF Range Extension Factor SAW Surface Acoustic Wave SINR Signal to Interference and Noise Ratio SNR Signal to Noise Ratio VGA Voltage Gain Amplifier VGC Voltage Gain Control

187 Chapter 7 – Conclusions and Future Trends

C H A P T E R 7 Conclusions and Future Trends

7.1. Conclusions

Interference has a notable impact on capacity and quality of service of mobile communications systems. The expansion of the wireless market brings an increase in interference problems and effective techniques for interference suppression are required. On that account, several RF and microwave design techniques applicable to GSM and GPRS basestations in order to mitigate the interference effects were investigated and proposed. Compact microstrip filters for GSM / GPRS basestations were developed for better spectrum utilization. One purpose of the preselect receiver filters is to isolate the uplink frequencies from downlink transmitted power, which could desensitize the low noise amplifiers. Another purpose of these filters is to separate the desired frequencies and reject the out of band interference. It was shown that the newly developed dual mode filters allow narrow pass- bands for their compact size. Meander loop and squared patch dual mode resonators have been investigated. A novel quasi-fractal dual mode resonator was developed in order to reduce the squared DMF patch size. Each dual mode resonator contributes with two poles to the filter response. Therefore, compact filters with narrowband responses have been designed using just a few resonators. Original theoretical principles of size reducing of planar resonators were established. This gives a solution to the miniaturization of distributed parameters devices working for 900 MHz, i.e. for long wavelengths. The novel compact microstrip resonators take up to 32% of the surface of a simple square half-wavelength resonator, both being designed for 900 MHz. New compact planar filters using cross-coupled novel resonators demonstrated a quasi-elliptic response with two controllable transmission nulls on both sides of the pass-band.

188 Chapter 7 – Conclusions and Future Trends

The newly developed filters are simple to realize. They do not require via holes or additional lumped components. The microstrip structures can be inexpensively manufactured by simple lithographic techniques and allow an easy integration with other planar circuits. Therefore, the new filters are very attractive for low-cost mobile communications circuits. Furthermore, the novel filter designs can be easily extended to the planar HTS technology. The investigation of novel resonators and filters required the development of a new 3-D microstrip finite difference time domain (FDTD) technique. A non- homogeneous perfectly matched layer (NH-PML) was developed in order to achieve higher accuracy of the FDTD simulations. The non-homogenous PML drastically minimizes the spurious reflections at the computation domain border. The source geometry was optimized for a minimum generated numerical charge. The FDTD method was validated by measurements, literature data and, for simple cases, output of commercial software. A signal estimation technique based on the ARMA algorithm was developed to decrease the FDTD computation time. The number of iteration could be reduced up to five times by using the newly developed signal estimation technique. A novel design procedure using Neural Networks was developed to reduce the number of FDTD simulations during the device optimization. The total design time was reduced twofold. The ARMA signal estimation technique was firstly utilized to reduce the computation time for each FDTD run. Secondly, the number of FDTD simulations was decreased using the device model provided by a neural network with the ARMA coefficients at the output. The trained network was then incorporated in an optimization procedure for microstrip filter design. In order to prove the use of the HTS thin films for RF and microwave devices, YBCO thin film resonators have been investigated. The full two-port microwave measurements confirmed the high quality of deposited films. Furthermore, preliminary designs and measurements for a slotted coupled HTS antenna are also presented. The HTS planar technology can provide very high Q-factor resonators, required by the design of narrowband multipole filters with increased selectivity and very low insertion loss. However, the research on microwave HTS devices was limited to a few preliminary studies, due to the lack of further funding. Noise minimization techniques have been investigated for RF electronics for GSM / GPRS smart antenna. The adaptive antenna represents an attractive solution for

189 Chapter 7 – Conclusions and Future Trends the mitigation of the co-channel interference and multipath effects. Low noise receivers for GSM 900 uplink, GSM 900 downlink and for DCS 1800 frequency bands have been achieved. A transmitter for both frequency bands was developed in order to test the system parameters. Sixteen uplink GSM receivers, developed on noise minimization basis, provided gain uniformity and adequate output signals in order to allow digital processing of the baseband signals, required by the spatial and time filtering.

7.2. Proposed Further Research

The future mobile communications standards will require better coverage and improved quality of service for a crowded spectrum. Very low-loss, selective preselect filters will considerably reduce the out-of-band interference. A solution to this issue can be provided by HTS filters. The FDTD method can be used in order to extend the novel resonators and filters designs to HTS planar technology. Designing on high dielectric constant substrates will imply a finer discretization grid. Therefore, a larger computer memory and a longer computation time for each iteration will be required by the FDTD simulations. In addition, the chosen time step will be smaller in order to satisfy the stability criterion Courant-Friedrichs-Levy. Therefore, a greater number of FDTD iterations will be required for a given total simulation time. Under these circumstances, the signal estimation techniques need to be effectively applied in order to decrease the required computation time for every FDTD analysis to the minimum. The total number of FDTD simulations required by a resonator or filter design will be reduced by using artificial neural networks. In this way, the design efficiency will be considerably increased. The manufacturing and testing of an HTS filter will permit to gain a more accurate image on the benefits of the HTS planar technology for mobile communications [1]. As a result of experimental investigations, the best option with the highest third-order intercept point will be selected from the newly proposed resonators designs.

190 Chapter 7 – Conclusions and Future Trends

The GaAs LNAs can provide a reduced noise figure at cryogenic temperatures. A cryogenic receiver obtained by integrating commercially available LNA with an HTS filters is likely to present an enhanced selectivity and sensitivity for future base stations. At the mobile station (MS) side, the implementation of HTS filters and smart antennas with elements spaced at a half wavelength in order to reduce the effect of interferences will be less convenient due to the size and weight requirements. New technologies based on large number of sensors [2] connected to software radios would permit radio links at high data rates [3]. Miniaturized preselect filters designed on high dielectric constant substrates [4] will allow a better rejection of the out-of-band interference at MS side.

References

[1] R. Ramer, personal communication [2] V. M. Hietal, G. A. Vawter, W. J. Meyer, S. H. Krawitz, “Phased-array antenna control by a monolithic photonic integrated circuit”, in Selected Papers on Photonic Control Systems for Phased Array Antennas, N. A. Riza, editor, SPIE Optical Engineering Press, Bellingham, WA, 1997, pp. 130-135 [3] P. Rapajic, personal communication, 2001 [4] A. Ioachim, M. I. Toacsan, G. Stoica, R. Coca, F. Vasiliu, G. Banciu,

191 Appendices

A P P E N D I C E S

Appendix 1. The Hata model and the COST model

For carrier frequency fc expressed in MHz, taking values between 150 and 1500, Hata interpolated the Okumura’s graphical data presenting formulas for the median path loss L50 expressed in dB [1]. In urban areas

50 ()urbanL += fc − log82.13log16.2655.69 − (hah rete ) ()−+ te loglog55.69.44 dh . (A1) 30 te ≤≤ 1;200 re ≤≤ 10mhmmhm where d is the transmitter-receiver separation distance expressed in km, hte, hre are the BS and MS effective antenna heights respectively expressed in meters. For a large city the MS antenna correction factor is given in dB by:

()ha = (h )2 − 1.154.1log29.8 ffor ≤ 300 re re c . (A2) 2 ()ha re = (hre )− 97.475.11log2.3 ffor c ≥ 300 For a small and medium city

()(ha re c )hf re −−⋅= ( fc − 8.0log56.17.0log1.1 ). (A3) In a suburban areas 2   fc  = 5050 ()urbanLL − log2   − 4.5 . (A4)   28  In open rural areas 2 = 5050 ()urbanLL − ()log78.4 fc + fc − 94.40log33.18 . (A5)

The Hata model was extended to the range 1500 fc ≤≤ 2000 by the European Co-operative for Scientific and Technical research (EURO-COST). The COST-231 model gives for the path loss

192 Appendices

50 ()urbanL += fc − log82.13log9.333.46 hte ()(ha re −+− te )loglog55.69.44 + Cdh M 1 ≤≤ 20kmdkm (A6) M = dBC for0 medium sized city and suburban areas M = dBC for3 metropolitan centres ()hahh rerete the,, modelHatatheinassame The formula (2.5) simplifies the reality, assuming an isotropic propagation loss. However, the radio range or coverage of each base station is an irregular pattern that depends on local radio propagation. The standard deviation from the Hata and COST models is usually 6-8 dB [1], but increases with the number of points in a confined area, the size of the area, and the number of different areas where the measured data is collected. Coverage depends on the required SNR and the margin to attain a satisfactory grade of service. The mobile unit usually transmits less power than the base station, therefore the radio range is usually limited by the lower powered transmitters of the reverse link. Hence, in order to improve the link, the base station receiver that should be improved.

Appendix 2. Elements of Global System for Mobile Communications (GSM)

The GSM system architecture is illustrated in Fig. A.1. There are three major subsystems, namely, the radio subsystem (or the Base Station Subsystem (BSS) [2]), the Network and Switching Subsystem (NSS) and the Operation Support Subsystem (OSS). The BSS functions are the radio channel management, transmission functions, radio link control and quality assessment and preparation for handover. The NSS is in direct contact with BSS and manages the MS connection and communication to other MS or to relevant networks. A service provider uses OSS to control MS, BSS and NSS. The radio subsystem consists mainly of the Mobile Station (MS), the Base Transceiver Station (BTS) and the Base Station Controller (BSC). Several transmitters are situated in each cell. One BTS is fitted with a number of TX/RX pairs or receiver modules. A BSC controls several BTS.

193 Appendices

An important component of BTS is the Transcoder Rate Adapter Unit (TRAU), which carries out speech encoding and decoding and rate adaptation in case of data transmission. There are three major interfaces, the interface between MSC and BSC, the A-bis interface between BSC and BTS, and an Um interface between the BTS and MS. The A interface uses an SS7 protocol named the Signaling Correction Control Part (SCCP). Fig. A.1. shows also the other interfaces. The NSS functions are switching and echo control, database functions and mobility functions. The Mobile Switching Center (MSC) performs switching and echo control. MSC also updates subscribers’ position and manages resources required by the handoff and mobility procedures for all the users in a certain area called MSC area.

Figure A.1. GSM System Architecture showing the interfaces between different components.

The Home Location Register (HLR) stores subscriber and mobile information such as the International Mobile Subscriber Information (IMSI). The Visitor Location

194 Appendices

Register (VLR) stores subscriber data to allow routing of the incoming calls to a particular mobile. The VLR can be linked to more MSCs and dynamically stores subscriber information, such as location area or IMSI of all the visiting MSs. The MSC informs VLR if a roaming MS has entered in an MSC area. The VLR finds the mobile’s HLR and generates the Mobile Subscriber Roaming Number (MSRN), which is used to route incoming calls to the MS and which is sent also to MS’s HLR. The GSM security functions are performed by the Operation and Maintenance Subsystem (OMSS). The AUthentication Center (AUC) is the OMSS component, which determines whether the MS will be granted service or not. The AUC handles the authentication and encryption keys for every single subscriber in the HLR and VLR. Another component, the Equipment Identity Register (EIR) maintains a list of legitimate, defective and fraudulent MSs. Every MS contains user-specific data on a Subscriber Identity Module (SIM). The SIM card contains, among other data, the IMSI and the cipher key used for encrypting the bit stream to assure the communications privacy. The Operational and Maintenance Center (OMC) represents a functional entity through which the service provider monitors and controls the system. The OMC provides a single point for the maintenance personnel to control the entire system. One OMC can serve multiple MSCs. The logical channels in GSM can be mainly divided in Control Channels (CCHs) and Traffic Channels (TCHs). TCHs carry speech or data and CCHs are used by the system for management and maintenance tasks. CCHs can be classified into broadcast channel (BCH), common control channel (CCCH), dedicated control channel (DCCH) and associated control channel (ACCH). The logical channels are used on the downlink only, uplink only or in both directions as shown in Table A.1 GSM system use Gaussian Minimum Shift Keying (GMSK) modulation [2]. The choice of the Gaussian premodulation filter bandwidth of 0.3 with relation to the channel rate of 270.8 kbps data rate is a compromise between the bit error rate (BER) and out of band interference. A too narrow filter increases intersymbol interference (ISI) and reduces the signal power.

195 Appendices

Table A.1. GSM logical channels.

Channel type Logical Channel – short description Transmitt. Direction TCH TCH/FS Traffic channel/full-rate speech MSÅÆBS TCH/HS Traffic channel/half rate speech MSÅÆBS TCH/F9.6 Traffic channel for data at full rates MSÅÆBS / 4.8 / 2.4 9.6, 4.8, 2.4 kbps TCH/H4.8 Traffic channel for data at half rates MSÅÆBS / 2.4 CCH BCH BCCH Broadcast control channel MS Å BS - informs MS about specific system parameters FCCH Frequency-correction channel MS Å BS - provides MS with the frequency reference SCH Synchronization channel MS Å BS CCCH RACH Random access channel – used by MS Æ BS MS to request a channel PCH Paging channel – used by BS to call MS Å BS MS AGCH Access grant channel MS Å BS DCCH SDCCH Standalone dedicated control MSÅÆBS channel – for transfer of signaling Information SACCH Slow associated control channel – MSÅÆBS Always used in association with a TCH or SDCCH; exits on its own FACCH Fast associated control channel MSÅÆBS - as SDCCH replaces a TCH CBCH Cell broadcast channel MS Å BS - similar to BCCH with some additional parameters

196 Appendices

Beside the voice service, GSM provides fax service, short message service (SMS) (160 characters or 140 bits), and data service with 9600 bps maximum rate, allowing access to modems in Public Switched Telephone Network (PSTN). However, there is a need to enhance the requirements of the standard for bursty traffic accommodation with high data rates.

Appendix 3. General Packet Radio Service (GPRS)

The services provided by GPRS [3-5] can be point-to-point (PTP) or point-to-multipoint (PTM). The point-to-point services can be classified into point-to point connectionless network service (PTP-CLNS) and point-to-point connection oriented network service (PTP-CONS). The point-to-multipoint (PTM) services can be PTM multicast and IP multicast or PTM group calls [3]. Under GPRS there are three classes of mobile terminals. Class A terminals support simultaneous circuit switched and packet switched traffic. Class B terminals support either circuit switched and packet switched traffic and a terminal in class C can be attached either as a circuit switched or packet switched terminal. Besides the packet switched resource allocation, another key feature of GPRS is the flexible channel allocation. GPRS is not restricted to only one time slot as GSM, and can use up to all eight time slots. The uplink and downlink channels can be reserved separately. The interworking between GPRS network with GSM network allow GPRS and GSM to use the same time slots alternatively. One user engaged in an active data transfer can suspend operation should he/she wish to make or to receive a call. Depending on the data operation being performed, the data transaction may be resumed. This is not possible for other packet switched data networks such as the North American Cellular Digital Packet Data (CDPD) system. The GPRS system architecture illustrated in Fig. A.2. shows that GPRS adds new elements to GSM network presented in Fig. A.1. The GPRS Support Node (GSN) is a new logical node, which supports by definition the packet routing and transfer. The Serving GPRS Support Node (SGSN) is actually a packet data switch that routes data packets to appropriate mobile stations. SGSN connects to BSS and is the same hierarchical level as a MSC. SGSN keeps track

197 Appendices of individual MS’s locations and performs security functions and access control. Practically the NSS in GPRS means SGSN and GGSN.

Figure A.2. GPRS system architecture.

The Gateway GPRS Support Node (GGSN) provides interworking with external packet switched networks. GGSN connects to SGSNs via an IP-based GPRS backbone network. GGSN contains information for attached GPRS users. GGSN controls dynamic Packet Data Protocol (PDP) address assignment. GGSN requests subscriber’s location information from the HLR when necessary. SGSN and GGSN may be co- located or reside in different physical nodes. The GPRS Tunneling Protocol (GTP) [4] tunnels user data and signaling between two GSN in the GPRS backbone network by adding routing information. For the packet data routing, SGSN encapsulates the incoming packets and routes them to the appropriate GGSN. GGSN forwards the packets to the correct Packet Data Network (PDN). Inside PDN specific routing procedures are applied to send the packets to the corresponding host. For packets coming to MS the process is reversed. The GPRS Register (GR) is part of the GSM location register. It contains all GPRS user related data needed by the SGSN to perform the routing and data transfer functionality such as routing information maps and the International Mobile Subscriber Identity (IMSI).

198 Appendices

The packet data routing is illustrated in Fig. A.3. For packets sent by the MS, SGSN encapsulates the incoming packets and routes them to the appropriate GGSN. GGSN forwards the packets to the correct packet data network (PDN). Inside PDN specific routing procedures are applied to send the packets to the corresponding host.

MS BTS MS BTS BSC BSC Source Destina- Inter PLMN tion IP BG SGSN-S backbone SGSN-D Intra BG PLMN IP Intra backbone PLMN IP GGSN-D backbone GGSN-S Packet Data Visited PLMN Network Home Peer Host PLMN Firewall Router

Figure A.3. Simplified routing example.

The protocol architecture covers the signaling plane and the transmission plane. On signaling plane protocols that support the transmission of user information and realize GPRS associated functions such as connection control, routing, mobility management, etc. are specified.

On the signaling plane, an important role is played by the signaling GS interface between the MSC and SGSN. This interface is based on enhancements to the GSM MSC and enables efficient coordination of GPRS and non-GPRS (GSM or IS-136) services and functionality which includes non-GPRS paging, location updates, alerts, IMSI detaches, etc. The transmission plane is represented by the protocols for user information transmission and by associated control procedures, like flow control and error handling. The GPRS transmission plane protocol architecture is illustrated in Fig. A.4. The first layer is the physical layer, which provides the connection over which bitstreams flow. On this layer, data unit framing and data coding occur together with

199 Appendices detection and corrections of physical medium transmission errors. The physical layer is split in RF sublayer (RFL), which covers modulation and demodulation of the physical waveforms, and the physical sublayer (PLL) which provides services for information transfer over the physical layer. The PLL sublayer is accountable for detecting physical link congestion, for interleaving one radio block over four bursts in consecutives TDMA frames, and for forward error correction (FEC) in transmitted codewords.

Figure A.4. The GPRS protocol architecture on transmission plane.

On data link layer (DLL), data are transferred over a single communications link without intermediate nodes and the frames’ flow is controlled in order to avoid overloads. At the air interface Um data layer can be split between the Radio Link Control (RLC) / Medium Access Control (MAC) sublayers and the Logical Link Control (LLC) sublayer. The RLC/MAC sublayer encompasses efficient multiplexing of data and signaling information defining procedures to allow multiple users to share a common physical medium which may consists of more radio channels. The collisions minimization is achieved by MAC sublayer, which is derived from a slotted reservation ALOHA protocol. The backward error corrections (BEC) using automatic repeat request (ARQ) is performed by the RLC sublayer.

200 Appendices

The logical link between MS and SGSN is provided by the highest data link sublayer, that is the Logical Link Control (LLC) sublayer, designed to be as independent of RLC/MAC as possible. The Base Station System GPRS Protocol (BSSGP) is a specific GPRS layer and replaces the GSM Transmission Capabilities Application Part (TCAP), which is the top layer of SS7. BSSGP handles communications, flow control, load balancing, etc. The SubNetwork Dependent Convergence Protocol (SNDCP) is a protocol layer between MS and SGSN. SNDCP maps network level attributes onto the underlying LLC. It is responsible for multiplexing network layer messages onto a single virtual connection, for compression functionalities and for ciphering. In GPRS, the GSM logical channels became packet channels. The TCH evolved under GPRS to packet data channel (PDCH) and the CCH became packet control channel (PCCH). The air interface protocol is based on the Master Slave Dynamic Rate Access (MSDRA) protocol [3]. The master-slave concept implies that at least one PDCH accommodates a packet common control channel (PCCCH) and the other packet channels are for data only. The mobility management has the function to inform the GPRS network about the MS’s location. During the attach procedure the subscription of a normal user is stored, copied from HLR to VLR. After being attached, the mobile’s location is tracked by the network. The GPRS routing area (RA) updates are similar to the GSM location area (LA) updates. The routing area (RA) is always a subset of location area (LA). GPRS itself evolved towards Enhanced GPRS (EGPRS), which together with the Enhanced Circuit-Switched Data (ECSD) are the components of Enhanced Data for GSM Evolution (EDGE) [6-8]. EDGE is based on nine Modulation and Coding Schemes (MCSs) [7,8] and allows higher peak data rate such as 384 kbps for pedestrian (microcell) and low speed vehicular (macrocell) environment, 144 kbps for high speed vehicular or 2 Mbps indoor using wide-band 1.6MHz carrier. The EDGE provides 3G option of the TDMA systems [7].

201 Appendices

Appendix 4. Evaluation of the RF electronics for GSM/GPRS Smart Antenna

The optimal design of the transmitter and receivers for Smart Antenna was the result of several investigations on components and circuits. The initial design of the GSM900 receivers included two TQ9122 chips as additional LNAs. They were inserted between the preselector SAW filters and the LNAs inputs of TQ9203 to provide extra gain in the RF section. The S parameters of TQ9122 were measured using the board in Fig. A.5a.

The plot of the TQ9122 S21 trace in the Smith chart is depicted in Fig. A.5b.

(b) (a)

Figure A.5. TQ9122 (a) evaluation board and (b) S21 trace in the Smith chart.

The variation of the TQ9122 gain versus frequency is illustrated in Fig. A.6. The gain slowly decreased with frequency in the desired uplink and downlink GSM bands. The saturation effect appeared for input power levels around –5 dBm. Finally, the 80 dB overall gain of the GSM 900 receiver could be obtained without using the TQ9122 low noise amplifier. Therefore, this device was not used in the receiver final design.

202 Appendices

(a) (b)

Figure A.6. Gain versus frequency measurements for TQ9122 LNA

(a) Pin = -5 dBm and Pin = -20 dBm, (b) Pin = -15 dBm.

Either the TQ9122 was used or not, matching the LNA input for optimum noise figure was very important for a low receiver noise figure. A narrowband matching to a given impedance (50 Ω in this case) can be realized with two discrete components only. The matching possibilities with two inductors, two capacitors or with one inductor and one capacitor are presented in Fig. A.8.

Figure A.7. Tuning possibilities of the LNA input port using only two lumped components.

203 Appendices

In the Smith chart, only the dashed regions can be matched with the specified LC circuit. Therefore, to match TQ9203 for the minimum noise as in Fig. 6.10, either the configurations in Fig. A.8c or in Fig. A.8e could be used.

Figure A.8. Tuning of the local oscillator input port for the TQ9203.

The TQ9203 required the tuning of the input port of the RF local oscillator signal in the mixer section. This tuning was performed with a shunt inductor. The inductance value required fine adjustments. For this, two configurations depicted in Fig. A.8 were possible. In the final design, the LO in tuning was performed by adjusting the inductor position as illustrated in Fig. A.8. Evaluation boards alternative to those presented in Chapter 6 are illustrated in Fig. A.9. The RF2612 evaluation board shown in Fig. A.9a allowed the investigation on the RF2612 gain controlled amplifier section. The input signal in the amplifier was low –pass filtered. The TQ9203 evaluation board (Fig. A.9b) allowed investigations on tuning of the IF signal and local oscillator output by adjusting the inductor position. Fig. A.9c illustrates the evaluation board of the RF9957 “CDMA/FM receive AGC and demodulator”. The RF9957 chip was used as an alternative to the RF2612 for the IF section of the GSM 900 and DCS 1800 receivers. A version of the GSM 900 receiver was investigated using the evaluation board in Fig. A.9d. An improved version including additional AD603 chips was finally preferred due to the saturation effects occurred at the RF2612 gained controlled amplifier section.

204 Appendices

(a) (b)

Figure A.9. Layouts of the evaluation boards for (a) RF2612, (b) TQ9203, (c) RF9957, (d) version of the GSM 900 receiver, (not to scale).

(b) (a)

Figure A.10. TQ9122 (a) Evaluation boards for (a) TQ9122, (b) RF SAW filter(not to scale).

205 Appendices

A special measurement setup was requested by the testing of the DC S1800 transmitter-receiver chain. The board used by the measurement setup is shown in Fig. A.10a. The ground patches for narrowband dielectric filters and the signs for positioning the three-port circulator can be easily noticed. The board depicted in Fig. A.10b, which was also shown in Fig. 6.3b, was used for RF filter evaluation. Surface Acoustic Wave (SAW) filters have been used for out of band rejection. The functioning of this type of filters is based on the acoustic wave propagation in a crystal [9], discovered by Lord Rayleigh. About 90% of the wave energy is confined in only one wavelength of the surface. Hence, this wave is called surface acoustic wave. The surface acoustic wave is not dispersive and has a velocity of typically 3000 m/s, therefore 105 times slower than an electromagnetic wave. The most frequent crystals used for SAW filter fabrication are lithium niobate

LiNbO3, sapphire Al2O3, piezoelectric thin film ZnO, lithium tantalate, etc. The filtering effect is obtained by the propagation of the surface acoustic wave between a pair of interdigital electrode transducers (IDT’s). The response of a SAW filter has no poles. At DC the response is always zero, therefore SAW filters cannot be used as low pass filters. The number of zeros can be as large as the number of electrodes, typically several hundreds [9]. The 1% or better accuracy of the contribution of each electrode to the filter response allows designs of compact SAW filters with flat pass-band, sharp skirts and very good out-of-band rejection. Several filters have been tested for the optimal solution. Attention was paid to the insertion loss. Insertion Loss of the preselect filter has a great influence on the receiver’s noise figure. Another parameter for the filter selection was the phase linearity. Some of the measured data on RF SAW filters are presented in Chapter 6. The pass-band ripple for the RF SAW filters is presented in Fig. A.11a for the downlink and in Fig. A.11b for the uplink. The wide scope amplitude response in Fig. A.12a shows good out-of-band rejection loss. Very small deviation between the group delays for different RF channels was required by a normal functioning GSM system. The S21 phase characteristics shown in Fig. A.12b suggest the large group delay of the filter caused by the propagation speed of the surface wave, which is much smaller than the electromagnetic waves propagation speed for the respective dielectric material.

206 Appendices

(a) (b)

Figure A.11. Pass band ripple of the SAW filter for GSM 900, (a) downlink, (b) uplink.

(a) (b)

Figure A.12. Wide scope filter response (a) S21 mgnitude, (b) S21 phase.

The same board was used for the evaluation of the MBF 9323 SAW filter. The in-band reflection response is given in Fig. A.13a for S11 parameter and in Fig. A13b for VSWR.

207 Appendices

(a) (b)

Figure A.13 Reflection measurements on MBF 9323 SAW filter,

(a) S11 versus frequency, (b) VSWR versus frequency.

Figure A.14. Transmission measurements on IF SAW filter centered at 36.12 MHz.

208 Appendices

The intermediate frequency of the receiver was designed depending on the IF SAW filter central frequency. This filter was strongly required to reject the RF mixer intermodulation products, to attenuate the strong RF local oscillator signal, etc. Fig. A.14 illustrates the response of an SAW IF filter. Without any matching, the SAW filter presents an insertion loss of 34.6 dB at the central frequency of 36.12 MHz. The final design choice was X6961, a SAW filter with 70 MHz central frequency. Matching sections allow considerable reduction of the insertion loss. X6961 provides also a very good out-of –band rejection loss, if the layout is carefully designed to avoid the cross- couplings.

References

[1] T. S. Rappaport, “Wireless Communications – Principles and Practice”, Prentice Hall, Upper Saddle River, NJ, 1999 [2] J. D. Gibson, “The Communications Handbook”, CRC Press and IEEE Press, Boca Raton, FL, 1997 [3] Götz Brasche and Bernard Walke, “Concepts, Sevices, and Protocols of the New GSM Phase 2+ General Packet Radio Sevice”, IEEE Communications Magazine, August 1997, pp. 94-104, 1997 [4] Jian Cai and David. J. Goodman, “General Packet Radio Service in GSM”, IEEE Communications Magazine, October 1997, pp. 122-131, 1997 [5] K. Balachandran, R. Ejzak, e.a., “GPRS-136: High-Rate Packet Data Service for North American TDMA Digital Cellular Systems”, IEEE Personal Communications, June 1999, pp. 34-47 [6] A. Furuskär, D. Bladsjö, e.a., “System Performance of the EDGE Concept for Enhanced Data Rates in GSM and TDMA/136”, in Proc. IEEE VTC’ 98 [7] S. Nanda, K. Balachandran, S. Kumar, “Adaptation Techniques in Wireless Packet Data Services”, IEEE Communications Magazine, vol. 38, 2000, pp. 54-64 [8] A. Mashhour, “Understanding Offset 8-PSK Modulation for GSM EDGE”, Microwave Journal, 1999, pp. 78-88

209 Appendices

[9] D. P. Morgan, “Surface-Wave Devices for Signal Processing”, Elsevier, Amsterdam, 1991

Acronyms and Abbreviations in Appendices

1G, 2G, 2.5G, 3G First, second, intermediate, third generation of cellular standards AGCH Access Grant Channel AMPS Advanced Mobile Phone Service ARQ Automatic Repeat Request AUC Authentication Register BCH Broadcast Channel BCCH Broadcast Control Channel BEC Backward Error Corrections BER Bit Error Rate BS Base Station BSC Base Station Controller BSS Base Stations System BSSGP Base Station Subsystem GPRS Protocol BTS Base Transceiver Station CBCH Cell Broadcast Channel CCH Control Channel CCCH Common Control Channel CDPD Cellular Digital Packet Data CLNS Connectionless Network Service CONS Connection Oriented Network Service COST (European) Co-operative for Scientific and Technical research DCCH Dedicated Control Channel DCS-1800 Digital Cellular System in 1800 MHz bandwidth DLL Data Link Layer ECSD Enhanced Circuit-Switched Data EDGE Enhanced Data Rates for GSM Evolution EGPRS Enhanced GPRS EIR Equipment Identity Register ETSI European Telecommunications Standards Institute FACCH Fast Associated Control Channel FCCH Frequency Correction Channel

210 Appendices

FDD Frequency Division Duplexing FDMA Frequency-Division Multiple Acces FEC Forward Error Corrections GGSN Gateway GPRS Support Node GPRS General Packet Radio Service GR GPRS Register GMSK Gaussian Minimum Shift Keying GSM Global System for Mobile Communications GSN GPRS Support Node GTP GPRS Tunneling Protocol HLR Home Location Register IMEI International Mobile Equipment Identity IMSI International Mobile Subscriber Information (Identification) IPv4 Internet Protocol version 4 ISI Inter-Symbol Interference ITU-T International Telecommunications Union – Telecommunications Standardization Sector LA Location Area LLC Logical Link Control LEOS Low Earth Orbiting Satellites LoS Line of Sight MAC Medium Access Control MAHO Mobile Assisted Handover MIP Mobile Internet Protocol MS Mobile Station MCS Modulation and Coding Scheme MSC Mobile Switching Center MSDRA Master-Slave Dynamic Rate Access MSRN Mobile Subscriber Roaming Number NLoS Non Line of Sight NMC Network Management Centre NSS Network and Switching Subsytem OMC Operational and Maintenance Center OMSS Operation and Maintenance Subsystem OSS Operation Support Subsytem PCCH Packet Control Channel PCCCH Packet Common Control Channel

211 Appendices

PCH Paging Channel PDCH Packet Data Channel PDN Packet Data Network PDP Packet Data Protocol PLL Physical sublayer PLMN Public Land Mobile Network PMR Professional (or Private) Mobile Radio PSTN Public Switched Telephone Network PTP Point To Point PTM Point to Multipoint QoS Quality of Service RA Routing Area RACH Random Access Channel RFL RF sublayer RLC Radio Link Control TCH Traffic Channel TDD Time Division Duplexing TETRA Trans European TRunked Radio TRAU Transcoder Rate Adapter Unit TS Time Slot SACCH Slow Associated Control Channel SCH Synchronization Channel SCCP Signaling Correction Control Part SDCCH Standalone Dedicated Control Channel SGSN Serving GPRS Support Node SIM Subscriber Identity Module SMS Short Message Service SNDCP SubNetwork Dependent Convergence Protocol SS7 Signaling System no. 7 TCAP Transmission Capabilities Application TRAU Transcoder Rate Adapter Unit

Um GSM (or GPRS) air interface VLR Visitors Location Register WLAN Wireless Local Area Network

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