Realization of Fractional-Order Capacitors with Field-Effect Transistors

A novel and efficient approach to realize fractional-order capacitors is investigated in this paper. Meanwhile, a new approach which is more efficient for semiconductor implementation of fractional-order capacitors is proposed. The feasibility of the approach has been verified with the preliminary measured results.




References:
[1] R. Yadav, M. Gupta, "Design of fractional order differentiators and
integrators using indirect discretization scheme," pp. 1-6, India
International Conference on Power Electronics, Jan. 2011.
[2] D. Mondal, K. Biswas, "Performance study of fractional order integrator
using single-component fractional order element," IET Circuits, Devices
& Systems, Vol. 5, No. 4, pp. 334-342, July 2011.
[3] Z. Gao, X. Liao, "Improved Oustaloup approximation of fractional-order
operators using adaptive chaotic particle swarm optimization," Journal of
Systems Engineering and Electronics, Vol. 23, No. 1, pp. 145-153, Feb.
2012.
[4] D. A. Robinson, "Lateral directional fractional order (PI)n control of a
small fixed-wing unmanned aerial vehicles: controller designs and flight
tests," IET Control Theory & Applications, Vol. 5, No. 18, pp.
2156-2167, Dec. 2011.
[5] W. Ahmad, R. El-khazali, A. S. Elwakil, "Fractional-order Wien-bridge
oscillator," IET Electronics Letters, Vol. 37, pp. 1110-1112, 2001
[6] P. Xie, Z. Xu, Q. Zou, "Compensation for the dynamics effect on
nanoscale broadband viscoelasticity measurements using adaptive
filtering approach," IEEE Transactions on Instrumentation and
Measurement, Vol. 60, No. 4, pp. 1155-1162, April 2011.
[7] N. Markris, "Dynamic analysis of viscoelastic-fluid dampers," Journal of
Engineering Mechanics, Vol. 121, No. 10, pp. 1114-1121, 1995.
[8] B. S. Liebst, "Asymptotic approximations for systems incorporating
fractional derivative damping," ASME Journal of Dynamic Systems,
Measurement, and Control Vol. 118, pp. 572-579, 1996.
[9] A. Fenander, "Modal synthesis when modeling damping by use of
fractional derivatives," AIAA Journal, Vol. 34, No. 5, pp. 1051-1058,
1996.
[10] X. Lei, F. Feng, J. Sun, "Optimal damping of EMI filter input
impedance," IEEE Transactions on Industry Applications, Vol. 47, No. 3,
pp.1432-1440, May 2011.
[11] J. P. Clerc, "A. C. response of fractal networks," Le Journal de
Physique-Lettres Vol. 45, No. 19, pp. 913-924, 1984.
[12] S. H. Liu, "Fractal model for the AC response of a rough interface,"
Physical Review Letters Vol. 55, No. 5, pp. 529-532, 1985.
[13] K. Theodore, "Self-AÆne fractal model for a metal-electrolyte interface,"
Physical Review B Vol. 35, No. 10, pp. 5379-5381, 1987.
[14] A. L. Mehaute, Fractal Geometries: Theory and Applications. Penton
Press, 1991.
[15] T. J. Anastasio, "The fractional-order dynamics of brainstem vestibulooculomotor
neurons," Biological Cybernetics, Vol. 72, pp. 69-79, 1994.
[16] A. Oustaloup, "Fractional order sinusoidal oscillators: optimization and
their use in highly linear FM modulation," IEEE Transactions on Circuits
and Systems, Vol. 28, No. 10, pp. 1007-1009, 1981.
[17] I. Podlubny, Fractional Diferential Equations. Academic Press, San
Diego, 1999.
[18] J. A. T. Machado, "Analysis and design of fractional-order digital control
systems," SAMS-Journal Systems Analysis, Modeling, Simulation, Vol.
27, pp. 107-122, 1997.
[19] J. A. T. Machado, "Position/force fractional control of mechanical
manipulators," IEEE International Workshop on Advanced Motion
Control, 1998.
[20] J. R. M. Hosking, "Fractional dierencing," Biometrika, Vol. 68, No. 1, pp.
165-176, 1981.
[21] M. Haldun, "Digital computation of the fractional Fourier transform,"
IEEE Transactions on Signal Processing, Vol. 44, No. 9, pp. 2141-2150,
1996.
[22] S. Roy, "On the realization of a constant-argument immitance or
fractional operator," IEEE Transactions on Circuits and Systems, Vol. 14,
pp. 264-274, 1967.
[23] G. Carlson and C. Halijak, "Approximation of fractional capacitors
(1/s)1/n by a regular Newton process," IEEE Transactions on Circuits and
Systems, Vol. CAS-11, No. 2, pp. 210-213, Mar. 1964.
[24] K. Steiglitz, "An RC impedance approximation to s-1/2," IEEE Trans.
Circuits Syst., Vol. 11, pp. 160-161, 1964.
[25] M. Nakagawa, K. Sorimachi, "Basic characteristics of a fractance
device," IEICE Trans. Fundam. Electron. Commun. Comput. Sci., Vol.
12, pp.1814-1819, 1992.
[26] K. Saito and M. Sugi, "Simulation of power-law relaxations by analog
circuits: fractal distribution of relaxation times and non-integer
exponents," IEICE Trans. Fundam. Electron. Commun. Comput. Sci.,
E76, Vol. 2, pp. 205-209, 1993.
[27] M. Sugi, Y. Hirano, Y. F. Miura and K. Saito, "Simulation of fractal
immittance by analog circuits: An approach to the optimized circuits,"
IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E82, Vol. 8, pp.
1627-1634, 1999.
[28] K. Biswas, S. Sen, and P. Dutta, "Modelling of a capacitive probe in
apolarizable medium," Sens. Actuat. Phys., Vol. 120, pp. 115-122, 2005.
[29] K. Biswas, S. Sen, and P. Dutta, "Realization of a constant phase
elementand its performance study in a differentiator circuits," IEEE
Circuits Syst. II, Exp. Briefs, Vol. 53, No. 8, pp. 802-806, Aug. 2006.
[30] V. P. Popov and T. A. Bickart, "RC transmission line with nonlinear
resistance: large-signal response computation," IEEE Circuits Syst, Exp.
Briefs, Vol. 21, No. 5, pp. 666-671, Sep. 1974.