Ultra‐low voltage fractional‐order circuits using current mirrors

Summary Fractional-order blocks, including differentiators, lossy and lossless integrators as well as filters of order 1 + a (0 < a < 1), are presented in this paper. The proposed topologies offer the benefit of ultra low-voltage operation; in addition, reduced circuit complexity is achieved compared to the corresponding companding schemes, which have been already introduced in the literature. The ultra-low voltage operation is performed through the employment of metal oxide semiconductor transistors biased in the subthreshold region. The reduction of circuit complexity is achieved through the utilization of current mirrors as active elements for realizing the required building blocks. The performance of the proposed fractional-order circuits has been evaluated through the Analog Design Environment of the Cadence software and the design kit provided by the Taiwan Semiconductor Manufacturing Company (TSMC) 180 nm complementary metal oxide semiconductor process. Copyright © 2015 John Wiley & Sons, Ltd.

[1]  B. Goswami,et al.  Fabrication of a Fractional Order Capacitor With Desired Specifications: A Study on Process Identification and Characterization , 2011, IEEE Transactions on Electron Devices.

[2]  Ahmed S. Elwakil,et al.  Measurement of Supercapacitor Fractional-Order Model Parameters From Voltage-Excited Step Response , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[3]  Hironori A. Fujii,et al.  H(infinity) optimized wave-absorbing control - Analytical and experimental results , 1993 .

[4]  Juraj Valsa,et al.  Analogue Realization of Fractional-Order Dynamical Systems , 2013, Entropy.

[5]  Ahmed S. Elwakil,et al.  Field programmable analogue array implementation of fractional step filters , 2010, IET Circuits Devices Syst..

[6]  Shantanu Das,et al.  Extending the concept of analog Butterworth filter for fractional order systems , 2012, Signal Process..

[7]  Ahmed S. Elwakil,et al.  First-Order Filters Generalized to the fractional Domain , 2008, J. Circuits Syst. Comput..

[8]  Todd J. Freeborn,et al.  A Survey of Fractional-Order Circuit Models for Biology and Biomedicine , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[9]  Khaled N. Salama,et al.  Microscale electrostatic fractional capacitors using reduced graphene oxide percolated polymer composites , 2013 .

[10]  Maneesha Gupta,et al.  Digital fractional‐order differentiator and integrator models based on first‐order and higher order operators , 2011, Int. J. Circuit Theory Appl..

[11]  Ahmed S. Elwakil,et al.  Towards the realization of fractional step filters , 2010, Proceedings of 2010 IEEE International Symposium on Circuits and Systems.

[12]  Ahmed S Elwakil,et al.  Fractional-order circuits and systems: An emerging interdisciplinary research area , 2010, IEEE Circuits and Systems Magazine.

[13]  Jirí Vlach,et al.  RC models of a constant phase element , 2011, Int. J. Circuit Theory Appl..

[14]  K. Biswas,et al.  Performance study of fractional order integrator using single-component fractional order element , 2011, IET Circuits Devices Syst..

[15]  G. Ablart,et al.  Influence of the electrical parameters on the input impedance of a fractal structure realised on silicon , 2005 .

[16]  Ahmed S. Elwakil,et al.  High-quality factor asymmetric-slope band-pass filters: A fractional-order capacitor approach , 2012, IET Circuits Devices Syst..

[17]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[18]  Ahmed S. Elwakil,et al.  An expression for the voltage response of a current‐excited fractance device based on fractional‐order trigonometric identities , 2012, Int. J. Circuit Theory Appl..

[19]  I. Podlubny,et al.  Analogue Realizations of Fractional-Order Controllers , 2002 .

[20]  M. Ortigueira An introduction to the fractional continuous-time linear systems: the 21st century systems , 2008, IEEE Circuits and Systems Magazine.

[21]  K. Moore,et al.  Discretization schemes for fractional-order differentiators and integrators , 2002 .

[22]  A. G. Radwan,et al.  Resonance and Quality Factor of the $RL_{\alpha} C_{\alpha}$ Fractional Circuit , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[23]  Karabi Biswas,et al.  Realization of a Constant Phase Element and Its Performance Study in a Differentiator Circuit , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[24]  Costas Psychalinos,et al.  Realization of current-mirror filters with large time-constants , 2014 .

[25]  Khaled N. Salama,et al.  Fractional-Order RC and RL Circuits , 2012, Circuits Syst. Signal Process..

[26]  Ahmed S. Elwakil,et al.  On the practical realization of higher-order filters with fractional stepping , 2011, Signal Process..

[27]  Ahmed M. Soliman,et al.  Fractional order filter with two fractional elements of dependant orders , 2012, Microelectron. J..

[28]  Ahmed S. Elwakil,et al.  On the Generalization of Second-Order Filters to the fractional-Order Domain , 2009, J. Circuits Syst. Comput..

[29]  Costas Psychalinos,et al.  1.5-V Complex Filters Using Current Mirrors , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[30]  Ahmed M. Soliman,et al.  Fractional Order Butterworth Filter: Active and Passive Realizations , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[31]  Karabi Biswas,et al.  A Design Example of a Fractional-Order Kerwin–Huelsman–Newcomb Biquad Filter with Two Fractional Capacitors of Different Order , 2013, Circuits Syst. Signal Process..

[32]  Ahmed S. Elwakil,et al.  Extracting the parameters of the double-dispersion Cole bioimpedance model from magnitude response measurements , 2014, Medical & Biological Engineering & Computing.

[33]  Costas Psychalinos,et al.  Ultra-low voltage fractional-order differentiator and integrator topologies: an application for handling noisy ECGs , 2014 .

[34]  C. Halijak,et al.  Approximation of Fractional Capacitors (1/s)^(1/n) by a Regular Newton Process , 1964 .