Basic Characteristics of a Fractance Device

Masahiro NAKAGAWA  Kazuyuki SORIMACHI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E75-A   No.12   pp.1814-1819
Publication Date: 1992/12/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Phenomena and Analysis
fractance,  fractional integration,  fractional differentiation,  

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In this work we propose a recursive electric circuit which has a fractal structure composed of resistances and capacitors. It is first confirmed in practice that such a device, which is referred as fractance, possesses a novel characteristics between the constituent elements, or the resistance and the capacitance. That is, the absolute value of the impedance shows such a characteristics as |Z|ω-1/2, whereas the phase angle does such a constant phase property as θ=-π/4 independent of the frequency. As an application of the presently proposed fractance device, we constructed a fractional integral circuit as well as a fractional differential circuit, and confirmed that the observed output wave forms agree well with those derived from a computer simulation.