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Non-Foster Circuit Design and Stability Analysis for Wideband

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Non-Foster Circuit Design and Stability Analysis for Wideband Non-Foster Circuit Design and Stability Analysis for Wideband Antenna Applications DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Aseim M. N. Elfrgani, M.S., B. S. Graduate Program in Electrical and Computer Engineering The Ohio State University 2015 Dissertation Committee: Professor Roberto G. Rojas, Adviser Professor Patrick Roblin Professor Fernando L. Teixeira @ Copyright by Aseim M. N. Elfrgani 2015 ABSTRACT In recent years, there has been a great interest in wide-band small antennas for wireless communication in both ground and airborne applications. Electrically small antennas; however, are narrow bandwidth since they exhibit high a quality factor (Q). Therefore, matching networks are required to improve their input impedance and radiation characteristics. Unfortunately, due to gain-bandwidth restrictions, wideband matching cannot be achieved using passive networks unless a high order matching network is used. Fortunately, the so-called non-Foster circuits (NFCs) employ active networks to bypass the well-known gain-bandwidth restrictions derived by Bode-Fano. Although NFCs can be very useful in numerous microwave and antenna applications, they are difficult to design because they are potentially instable. Consequently, an accurate and efficient systematic stability assessment is necessary during the design process to predict any undesired behavior. In this dissertation, the design, stability, and measurement of two non-Foster matching networks for two different small monopole antennas, a non-Foster circuit embedded within half loop antenna, a combination of Foster and non-Foster matching network for small monopole antenna are presented. A third circuit; namely, a non-Foster coupling network for a two-element monopole array is also presented for phase enhancement applications. It all examples, the NFCs substantially improve the antenna’s performance over a wide frequency band. ii First, the stability properties of NFCs are discussed with a time-domain technique that computes the largest Lyapunov exponent for time series signals. In case of instability, it is shown how the circuit can be stabilized with different controllers. The proposed stability approach has been successfully applied to a negative capacitor to match a 3" electrically small monopole receiver antenna. Measured results verified that the system is stable and the non-Foster matching networks improve both the antenna gain and the signal to noise ratio (SNR). Second, an efficient way to improve the performance of an electrically small antenna by embedding a non-Foster circuit (NFC) within the antenna structure is presented. This technique is based on the theory of Characteristic Modes (CMs). The antenna, loaded with a non-Foster circuit, shows remarkable improvement in gain and SNR. Furthermore, by loading the antenna the omnidirectional pattern is maintained up to a higher frequency by delaying the onset of higher order current modes. Third, to the best of our knowledge, this is the first time a complete systematic stability analysis of non-Foster systems is introduced. The method was applied to two non-Foster matching networks; namely, a series connection of a negative capacitor- inductor and a combination of Foster and non-Foster circuits for use with a small monopole antenna. Measured results show that the non-Foster matching networks improve both the antenna gain and the SNR for the largest frequency band reported in the literature. Lastly, a stable system consisting of a non-Foster coupling circuit is introduced to amplify the output phase difference of an array of two coupled monopole antennas over a iii wide frequency band. Measured data of the output phase response of the NFC-two- element biomimetic antenna array (BMAA) shows that it has much wider 3-dB bandwidth in comparison with the passive case. The NFC improves the normalized available output power of the BMAA compared to the case when passive coupling networks are used. iv Dedication This document is dedicated to my family. v Acknowledgments I would like to express my sincere gratitude to my advisor, Professor Roberto G. Rojas for his guidance and support during my years at The Ohio State University. I would also like to thank Professor Fernando L. Teixeira and Professor Patrick Roblin for their time and effort to serve on my dissertation committee. I would also like to thank all my friends at the ElectroScience Laboratory (ESL) for their helpful discussion and support during my doctoral studies, especially Ezdeen Elghannai, Anas Abumansaar, Renaud Mousanda, Chuan-Chang (Ethan) Liu, and Abdul- Maalik. I would like to acknowledge my country Libya for the financial support throughout my PhD study in the United State of America through the Libyan-North American scholarship. My sincerest thanks to my parents and siblings for their extraordinary support and encouragement throughout my life in its various phases. I sincerely thank my wife for her personal support and great patience during my study and at all times. vi Vita 2003 ............................................................B.S. in Electrical and Electronics Engineer- ing, Garyounis University, Libya 2008 ............................................................M.S. in Electrical and Electronics Engineer- ing, Garyounis University, Libya 2013 ............................................................M.S. in Electrical and Computer Engineeri- ng, The Ohio State University, Columbus, Ohio 2010-2014 .....................................................Graduate Student, Electrical and Computer Engineering, The Ohio State University 2014-Present ................................................Graduate Teaching Associate, Electrical and Computer Engineering, The Ohio State Uni- versity Publications 1) Aseim Elfrgani, and Ahmed Elbarsha, “Sample Rate Converter from CD to DAT Using Truncated Lagrange Interpolation,” 4th International Colloquium on Signal Processing & Its Applications (CSPA), March 2008, Kuala Lumpur, Malaysia. 2) Aseim. M. Elfrgani, Roberto. G. Rojas, “Comparison of Negative Impedance Inverters and Converters in the Design of Non-Foster Reactive Elements,” IEEE Int. Symp. Ant. & propag. and USNC-URSI National Radio Science Meeting (NRSM), July. 8-12, 2012, Chicago, IL. 3) Aseim. M. Elfrgani, Roberto. G. Rojas, “Compensation Networks to Improve Performance of Non-Foster Circuit,” USNC-URSI National Radio Science Meeting (NRSM), Jan. 9-12, 2013, Boulder, CO. vii 4) Roberto G. Rojas, Aseim Elfrgani and Ezdeen Elghannai, “Distributed Impedance matching with Foster and Non-Foster Elements,” Antenna and propagation (EuCAP), Proceeding of 7th Conference, April 08-12, 2013, Gothenburg, Sweden. 5) Aseim M. Elfrgani, Renoud Moussounda and Roberto G. Rojas, “Time-domain Stability Analysis/Design of Negative Impedance Inverters and Converters,” IEEE/MTT-S International Microwave Symposium, June 2-7, 2013, Seattle, WA. 6) Aseim. M. Elfrgani, Roberto. G. Rojas, “Loop-Type Electrically Small Antenna Loaded with Non-Foster Circuit,” USNC-URSI National Radio Science Meeting (NRSM), Jan. 8-11, 2014, Boulder, CO. 7) Aseim. M. Elfrgani, Roberto. G. Rojas, “Non-Foster Circuit Embedded Within Electrically Small Antenna,” IEEE Int. Symp. Ant. & propag. AP-S/ URSI, July 6-11, 2014, Memphis, TN. 8) Aseim. M. Elfrgani, Roberto. G. Rojas, “Stabilizing Non-Foster-Based Tuning Circuits For Electrically Small Antennas,” IEEE Int. Symp. Ant. & propag. AP-S/ URSI, July 6-11, 2014, Memphis, TN. (Honorable mention). 9) Aseim. M. Elfrgani, Roberto. G. Rojas,“Signal to Noise Ratio of Electrically Small Antennas Impedance Matched using Non-Foster Circuits,” AMTA 36th Annual Meeting & Symposium, Oct 12-17, 2014, Tucson, AZ. 10) Aseim. M. Elfrgani, Roberto. G. Rojas,“Stability of Non-Foster Circuits for Broadband Impedance Matching of Electrically Small Antennas,” IEEE Radio Wireless Symposium (RWS), Jan 25-28, 2015, San-Diego, CA. ( Finalist ) 11) Aseim. M. Elfrgani, Roberto. G. Rojas, "Successful Realization of Non-Foster Circuits for Wide-Band Antenna Applications," IEEE/MTT-S International Microwave Symposium 2015, May17-22, Phoenix, AZ. 12) Aseim M. Elfrgani, Renoud Moussounda and Roberto G. Rojas, “Stability Assessment of Non-Foster Circuits based on Time-Domain Method,” IET Microwaves, Antennas & Propagation. Under review 2015. viii 13) Aseim. M. Elfrgani, Roberto. G. Rojas, “Broadband Biomimetic Antenna Arrays using Non-Foster Networks,” IEEE Microwave and Wireless Components Letters. To be submitted May 2015. 14) Aseim. M. Elfrgani, Roberto. G. Rojas, “Non-Foster Circuit Loading Network For An Electrically Small Antenna Using Theory of Characteristic Modes,” IEEE Antennas and Wireless Propagation Letters. To be submitted May 2015 Fields of Study Major Field: Electrical and Computer Engineering Studies in: Electromagnetic RF Circuits ix TABLE OF CONTENTS Abstract……………………………………………………………………………… ii Dedication…………………………………………………………………………… vi Acknowledgments…………………………………………………………………… vii Vita………………………………………………………………………………….. viii List of Tables………………………………………………………………………... xi List of Figures………………………………………………………………………. xv CHAPTER PAGE 1 Introduction…………………………………………………………………. 1 1.1 Motivation and Approach…………………………………………….... 1 1.2 Background and Review 4 1.2.1 Electrically Small Antennas…………………………………….. 4 1.2.2 Gain-Bandwidth Limitation of Losses Passive Matching Networks……………………………………………………….... 6 1.2.3 Foster and Non-Foster Reactive Impedances…………………...
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