The frequency response of a fractal photolithographic structure

Haba, T. Cisse; Ablart, G.; Camps, Thierry

doi:10.1109/94.598289

Cited by 32 publications

(12 citation statements)

References 6 publications

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“…A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-sized copy of the whole" [29]. Fractals such as the Sierpinski [30], Tree [25,27], Hilbert [6], Koch and Peano [28] structures, when implemented as one of the plates in a capacitor, have been shown to exhibit fractional order electrical impedances. These fractional capacitors (FCs) can be used in the realization of fractional systems without having to use an integer order approximation of the FCs.…”

Section: Resultsmentioning

confidence: 99%

“…While there are currently no commercial fractional capacitors available for the physical implementation of fractional order circuits, there are reported prototype implementations of such devices [6,[25][26][27][28] using fractal shapes. A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-sized copy of the whole" [29].…”

Section: Resultsmentioning

confidence: 99%

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Fractional-step Tow-Thomas biquad filters

Freeborn

Maundy

Elwakil

2012

NOLTA

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Abstract:In this paper we propose the use of fractional capacitors in the Tow-Thomas biquad to realize both fractional lowpass and asymmetric bandpass filters of order 0 < α 1 + α 2 ≤ 2, where α 1 and α 2 are the orders of the fractional capacitors and 0 < α 1,2 ≤ 1. We show how these filters can be designed using an integer-order transfer function approximation of the fractional capacitors. MATLAB and PSPICE simulations of first order fractional-step low and bandpass filters of order 1.1, 1.5, and 1.9 are given as examples. Experimental results of fractional low pass filters of order 1.5 implemented with silicon-fabricated fractional capacitors verify the operation of the fractional Tow-Thomas biquad.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Fractional-step Tow-Thomas biquad filters

Freeborn

Maundy

Elwakil

2012

NOLTA

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“…Many literature have noticed presence of FO operator while studying fractal model (Sapoval et al 1993). In 1997, Haba et al first developed a fractal structure which gives prominent CP zone (Haba 1997). It is a fractal tree in star structure with level 3 of iterations.…”

Section: Realization Of Single Component Foementioning

confidence: 99%

Realization of Fractional Order Elements

et al. 2017

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Fractional order (FO) element (FOE) is the building block for realization of FO systems, an important research domain. However, the realization of FO system is still a challenge. Till date, no FOE or fractor is available in the market. However, many researchers have developed various types of FOE, multi-component and single component, over past 50 years or more. This paper reviews some significant research work, along with their success and limitations, in the field of FOE realization. Also, it discusses the chronological development and a brief comparative study to present an overall idea on current stage of FOE research to the readers.

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“…Obviously, the structure, the composition, and the number of layers yield fractal elements that could exhibit frequency response of complex orders [16,46].…”

Section: The Point Of View Of Reyad El-khazali Real and Complex-ordementioning

confidence: 99%