Simulation of fractal immittance by analog circuits: An approach to the optimized circuits

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E82-A, Issue 8, 1999, Pages 1627-1635

  Sugi, Michio ^a   Hirano, Yoshiaki ^a   Miura, Yasuhiro F ^a   Saito, Kazuhiro ^a  

^a TOIN UNIVERSITY OF YOKOHAMA   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CAPACITANCE; COMPUTER SIMULATION; CORRELATION METHODS; ELECTRIC RESISTANCE; FRACTALS; MATHEMATICAL MODELS;

FRACTAL IMMITTANCE;

LINEAR INTEGRATED CIRCUITS;

EID: 0032596298     PISSN: 09168508     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. M. Pollak and T.H. Geballe, "Low-frequency conductivity due to hopping processes in silicon," Phys. Rev., vol.122, pp.1742-1753, 1961.
2. A.K. Jonscher, Dielectric Relaxations in Solids, Chelsea Dielectric Press, 1983.
3. J.R. Macdonald, "Linear relaxation: Distributions, thermal activation, structure, and ambiguity," J. Appl. Phys., vol.62, pp.R51-R62, 1987.
4. M. Sugi and K. Saito, "Power-law conductivity -Its interpretation and application," Oyo Butsuri, vol.64, pp.226231, 1995.
5. M. Pollak, "On the frequency dependence of conductivity in amorphous solids," Phil. Mag., vol.23, pp.519-542, 1971.
6. G. A. Niklassen, "Fractal aspects of the dielectric response of charge carriers in disordered materials," J. Appl. Phys., vol.62, pp.Rl-R14, 1987.
7. H. Takayasu, ed., Fractal Science, Asakura Shoten, 1987. [8] H. Scher, M.F. Shlesinger, and J.T. Bendler, "Time-scale invariance in transport and relaxation," Physics Today, January 1991, pp.2G-34, 1991.
8. M. Riesz, "L'intégrale de Riemann-Liouville et le problème de Cauchy," Acta Mathematica, vol.81, pp.1-223, 1949.
9. K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, 1974.
10. K. Yoshida, Operational Calculus: A Theory of Hyperfunctions, Springer-Verlag, 1984.
11. K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, 1993.
12. K. Saito and M. Sugi, "Fractal time response of molecular assemblies and possible applications," Extended Abstracts of 10th Symposium on Future Electron Devices, (Tokyo), pp.107-110, 1991.
13. M. Sugi and K. Saito, "Non-integer exponents in electronic circuits: F-matrix representation of the power-law conductivity," IEICE Trans. Fundamentals, vol.E75-A, no.G, pp.720-725, June 1992.
14. M. Sugi and K. Saito, "Power-law conductivity as circuit element," Bul. Electrotech. Lab., vol.56, pp.785-801, 1992.
15. K. Saito and M. Sugi, "Simulation of power-law relaxations by analog circuits: Fractal distribution of relaxation times and non-integer exponents," IEICE Trans. Fundamentals, V01.E76-A, no.2, pp.204-209, Feb. 1993.
16. M. Sugi and K. Saito, "Non-integer exponents in electronic circuits II: Memory effects in the fractal immittance," IEICE Trans. Fundamentals, vol.E77-A, no.4, pp.688-697, April 1994.
17. M. Nakagawa and K. Sorimachi, "Basic characteristics of a fractance device," IEICE Trans. Fundamentals, vol.E75-A, no.12, pp.1814-1819, Dec. 1992.
18. M. Sugi and K. Saito, "The fractal device -A novel circuit element based on organized molecular films," Thin Solid Films, vol.284-285, pp.879-881, 1996.
19. M. Sugi, Y. Hirano, H. Chiba, J. Kawata, and K. Saito, "Fractal immittance of molecular assemblies -A prospect of its applications," Mol. Cryst. Liq. Cryst., vol.290, pp.157-162, 1997.
20. Y. Hirano, K. Omata, J. Ishizaki, J. Kawata, Y. F. Miura, and M. Sugi, "Power-law conductivity in merocyanine LB films," Thin Solid Films, vols.327-329, pp.387-390, 1998.
21. E.A. Guillemin, The Mathematics of Circuit Analysis, John Wiley & Sons, 1949.
22. E.A. Guillemin, Introductory Circuit Theory, John Wiley fc Sons, 1953.
23. S. Kai, S. Higaki, M. Igasaki, and H. Furukawa, "1/f noise, long-normal distribution, and cascade process in electrical networks," Phys. Rev. A, vol.35, pp.374-379, 1987.
24. A.K. Jonscher, "The universal dielectric responses," Proc. 1990 CEIDP, IEEE Dielectric and Electrical Insulation Society, pp.23-40, 1990. :