Design of CMOS Analog Integrated Fractional-Order Circuits (eBook)

Georgia Tsirimokou   received B.Sc. degree in Physics and M.Sc. degree in Electronics and Communications from the University of Patras, Greece, in 2011 and 2013, respectively. She is currently a PhD candidate working with the analog Integrated Circuits Design group of the Electronics Laboratory, Department of Physics, University of Patras, Greece. Her main research interests are focused on the design of ultra-low voltage analog signal processing blocks, including fractional-order filters as well as circuits for biomedical applications.Costas Psychalinos   received his B.Sc. and Ph.D. degrees in Physics and Electronics from the University of Patras, Greece, in 1986 and 1991, respectively. From 1993 to 1995, he worked as Post-Doctoral Researcher in the VLSI Design Laboratory, University of Patras. From 1996 to 2000, he was an Adjunct Lecturer in the Department of Computer Engineering and Informatics, University of Patras. From 2000 to 2004 he served as Assistant Professor in the Electronics Laboratory, Department of Physics, Aristotle University of Thessaloniki, Greece. From 2004 he serves as faculty member in the Electronics Laboratory, Department of Physics, University of Patras, Greece and, currently, he is full Professor. His research area is in the continuous and discrete-time analog filtering, including fractional-order filters, companding filters, current amplifier filters, CCII and CFOA filters, and sampled-data filters, and in the development of ultra-low voltage building blocks for biomedical applications. He serves as Area Editor of the International Journal of Electronics and Communications (AEU) Journal, and Associate Editor of the Circuits Systems and Signal Processing Journal. He is member of the Editorial Board of the Analog Integrated Circuits and Signal Processing Journal, and Microelectronics Journal. He is also an IEEE Senior Member. Ahmed Elwakil   was born in Cairo, Egypt. He received the B.Sc. and M.Sc. degrees from the Department of Electronics and Communications at Cairo University, Cairo, Egypt and the Ph.D. degree from the Department of Electrical and Electronic Engineering, National University of Ireland, University College Dublin.  His research interests are primarily in the areas of Circuit Theory, Nonlinear Dynamics, Chaos Theory, as well as Fractional-Order Circuits and Systems with diverse applications ranging from the modeling of oscillatory networks and nonlinear electronic circuits to energy devices and bio-materials. He is the author and co-author of over 185 publications in these areas. He has served as a reviewer, review committee member and organizing committee member for many conferences including ISCAS, NOLTA, ICECS, ECCTD, ICM, NDES and ISSPA and currently serves as an Associate Editor for the Int. J. of Circuit Theory and Applications (Wiley) and was a past Editor of this journal. He is also an Associate Editor of the Int. J. Bifurcation & Chaos, (World Scientific) and the Journal of Nonlinear Theory and its Applications (NOLTA), published by the Institute of Electronics, Information and Communication Engineers of Japan (IEICE-Japan) and was a past Associate Editor for the J. of Dynamics of Continuous, Discrete and Impulsive Systems: Series-B, published by the American Institute of Mathematical Sciences (AIMS) and is currently on the Editorial Board of the IEEE J. Emerging and Selected Topics in Circuits and Systems. Prof. Elwakil has been a member of the IEEE Technical Committee on Nonlinear Circuits and Systems (TCNCAS) since 2003 and was a Lead Guest Editor for the IEEE J. of Emerging and Selected Topics in Circuits & Systems, special issue on fractional-order circuits and systems (Sep. 2013) and a Guest Editor for a special issue on Chaos-Fractals Theories and Applications published in the J. of Mathematical Problems in Engineering, 2014. He is also the guest editor for a special issue on Fractional-Order Circuits (June 2016) in the J. Circuits Systems & Signal Processing (Springer). He received the Egyptian Government first class medal for achievements in Engineering Sciences in 2003, 2009 and 2015 respectively and was a visiting Professor/Researcher at Istanbul Technical University (Istanbul, Turkey), University of Calgary (Alberta, Canada), Queens University (Belfast, UK), Technical University of Denmark (Lyngby, Denmark), Ohio State University (Columbus, Ohio), University College Cork (Cork, Ireland), King Abdullah University of Science and Technology (KAUST, Saudi Arabia) and Nile University (Cairo, Egypt). He is currently an Adjunct Prof. in the Nano-electronics Integrated Systems Center at Nile University, Egypt.  

Preface 5
Contents 7
About the Authors 10
Chapter 1: Introduction 12
1.1 Fractional Calculus 12
1.2 Literature Overview 17
1.3 Book Objectives 19
References 21
Chapter 2: Procedure for Designing Fractional-Order Filters 24
2.1 Introduction 24
2.2 Fractional-Order Generalized Filters (Order ?) 25
2.2.1 Fractional-Order Differentiator 25
2.2.2 Fractional-Order Integrator 26
2.3 Fractional-Order Generalized Filters (Order ?) 27
2.3.1 Fractional-Order Low-Pass Filter (FLPF) 28
2.3.2 Fractional-Order High-Pass Filter (FHPF) 28
2.3.3 Fractional-Order Band-Pass Filter (FBPF) 29
2.3.4 Fractional-Order All-Pass Filter (FAPF) 30
2.3.5 Design Equations for Generalized Filters of Order ? 31
2.4 Fractional-Order Generalized Filters (Order 1+?) 33
2.4.1 Fractional-Order Low-Pass Filter (FLPF) 33
2.4.2 Fractional-Order High-Pass Filter (FHPF) 35
2.4.3 Fractional-Order Band-Pass Filter (FBPF) 36
2.4.4 Fractional-Order Band-Stop Filter (FBSF) 37
2.4.5 Design Equations for Generalized Filters of Order 1+? 37
2.5 Fractional-Order Generalized Filters (Order ?+beta) 39
2.5.1 Fractional-Order Low-Pass Filter (FLPF) 40
2.5.2 Fractional-Order High-Pass Filter (FHPF) 41
2.5.3 Fractional-Order Band-Pass Filter (FBPF) 41
2.5.4 Fractional-Order Band-Stop Filter (FBSF) 42
2.5.5 Design Equations for Generalized Filters of Order ?+beta 43
2.6 Fractional-Order Filters of Order n+? 46
2.6.1 Design Equations for Generalized Filters of Order n+? 47
2.7 Summary 49
References 50
Chapter 3: Current-Mode Fractional-Order Filters 51
3.1 Introduction 51
3.2 Basic Building Blocks 51
3.3 Fractional-Order Filters with Large Time-Constant 56
3.4 Simulation and Comparison Results 59
3.4.1 First-Order Filter Using Current Mirrors with Large Time-Constants 59
3.4.2 Fractional-Order Circuits Using Current Mirrors with Large Time-Constants 60
3.5 Summary 63
References 64
Chapter 4: Voltage-Mode Fractional-Order Filters 65
4.1 Introduction 65
4.2 Basic Building Blocks 65
4.3 Fractional-Order Generalized Filters 66
4.4 Simulation Results 68
4.5 Summary 72
References 72
Chapter 5: Emulation of Fractional-Order Capacitors (CPEs) and Inductors (FOIs) 74
5.1 Introduction 74
5.2 Proposed Emulation Scheme for Voltage Exited CPE and FOI 75
5.3 Proposed Emulation Scheme for Current Excited CPE and FOI 80
5.4 Chip Fabrication and Experimental Results 81
5.4.1 Effects of Variation of the External Capacitors of the Chip 83
5.4.2 Effects of Variation of the Bias Current of the Chip 83
5.4.3 Effects of Variation of both the Bias Current (Io) and External Capacitors (Cext) of the Chip 83
5.5 Fractional-Order Resonators Using Emulated CPEs and FOIs 89
5.6 Summary 93
References 94
Chapter 6: Applications of Fractional-Order Circuits 96
6.1 Introduction 96
6.2 A Preprocessing Stage Suitable for Implementation of the Pan-Tompkins Algorithm 97
6.3 A fully Tunable Implementation of the Cole-Cole Model 105
6.4 Simple Non-impedance-Based Measuring Technique for Supercapacitors 109
6.5 Design and Evaluation of a Fractional-Order Oscillator 114
References 120
Chapter 7: Conclusions and Motivation for Future Work 122
7.1 Conclusions 122
7.2 Motivation for Future Work 123