An approach to improve the performance of fractional-order sinusoidal oscillators

Abstract This paper presents a simple technique to approximate fractance devices (FDs) capable of improving the performance of any fractional-order oscillator. The proposed technique is based on an elementary mathematical tool of impedance equalization, and requires significantly lesser number of passive components than the existing FD approximation schemes. To compare the merit of approximated FDs with the existing R-C ladder based FDs, a well-known fractional-order Wien-bridge oscillator is realized using both FDs one by one; and the corresponding results are compared exhaustively. It is observed that the fractional-order oscillator realized using the proposed FDs gives better performance in terms of phase-noise, figure of merit (FoM), total harmonic distortion (THD), settling time, peak-to-peak voltage, power dissipation, and hardware compactness. Authenticity and accuracy of the proposed design has been verified using PSpice simulation and practical implementation.

[1]  Georges Gielen,et al.  Temperature- and Supply Voltage-Independent Time References for Wireless Sensor Networks , 2014 .

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

[3]  Yanhong Zhou,et al.  A Critical Review: Coupling and Synchronization Analysis Methods of EEG Signal with Mild Cognitive Impairment , 2015, Front. Aging Neurosci..

[4]  B. T. Krishna,et al.  Active and Passive Realization of Fractance Device of Order 1/2 , 2008 .

[5]  B. Achar,et al.  Dynamics of the fractional oscillator , 2001 .

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

[7]  A. Elwakil,et al.  On the stability of linear systems with fractional-order elements , 2009 .

[8]  Dan Kuylenstierna,et al.  Calculation of the Performance of Communication Systems From Measured Oscillator Phase Noise , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Ahmed S. Elwakil,et al.  Experimental demonstration of fractional-order oscillators of orders 2.6 and 2.7 , 2017 .

[10]  Chien-Cheng Tseng,et al.  Design of FIR and IIR fractional order Simpson digital integrators , 2007, Signal Process..

[11]  Fractional Driven Damped Oscillator , 2017, 1706.08596.

[12]  M. Dehghan,et al.  The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique , 2009 .

[13]  A. Demir,et al.  Phase noise in oscillators: a unifying theory and numerical methods for characterization , 2000 .

[14]  Rami Ahmad El-Nabulsi,et al.  Fractional oscillators from non-standard Lagrangians and time-dependent fractional exponent , 2014 .

[15]  A. Abidi,et al.  Noise in relaxation oscillators , 1983 .

[16]  Robert B. Staszewski,et al.  Analysis and Design of a Multi-Core Oscillator for Ultra-Low Phase Noise , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  A. Elwakil,et al.  Design equations for fractional-order sinusoidal oscillators: Four practical circuit examples , 2008 .

[18]  Maneesha Gupta,et al.  Switched Capacitor Realizations of Fractional-Order Differentiators and Integrators Based on an Operator with Improved Performance , 2011 .

[19]  Rami Ahmad El-Nabulsi,et al.  Non-standard fractional Lagrangians , 2013 .

[20]  Saurabh Sinha,et al.  A modified multiphase oscillator with improved phase noise performance , 2017, Microelectron. J..

[21]  Yoshiaki Hirano,et al.  Frequency behavior of self-similar ladder circuits , 2002 .

[22]  Won Sang Chung,et al.  Fractional damped oscillators and fractional forced oscillators , 2013, 1302.2847.

[23]  A. Stanislavsky,et al.  Fractional oscillator. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  R. El-Nabulsi A Generalized Nonlinear Oscillator From Non-Standard Degenerate Lagrangians and Its Consequent Hamiltonian Formalism , 2014 .

[25]  Lobna A. Said,et al.  Three Fractional-Order-Capacitors-Based Oscillators with Controllable Phase and Frequency , 2017, J. Circuits Syst. Comput..

[26]  Richard L. Magin,et al.  On the fractional signals and systems , 2011, Signal Process..

[27]  Ahmed S. Elwakil,et al.  Experimental comparison of integer/fractional-order electrical models of plant , 2017 .

[28]  Ahmed M. Soliman,et al.  Fractional-order multi-phase oscillators design and analysis suitable for higher-order PSK applications , 2016 .

[29]  Shaher Momani,et al.  Solutions of a fractional oscillator by using differential transform method , 2010, Comput. Math. Appl..

[30]  El-nabulsi Ahmad Rami,et al.  A periodic functional approach to the calculus of variations and the problem of time-dependent damped harmonic oscillators , 2011 .

[31]  Kendall E. Atkinson An introduction to numerical analysis , 1978 .

[32]  S. M. Rezaul Hasan,et al.  A CMOS DCO design using delay programmable differential latches and a novel digital control scheme , 2007 .

[33]  B. Achar,et al.  Response characteristics of a fractional oscillator , 2002 .

[34]  Smarajit Ghosh Network theory : analysis and synthesis , 2005 .

[35]  D. Mondal,et al.  Packaging of Single-Component Fractional Order Element , 2013, IEEE Transactions on Device and Materials Reliability.

[36]  Huirem Tarunkumar,et al.  Operational Amplifier-Based Fractional Device of Order s ±0.5 , 2017 .