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ON THE GENERALIZATION OF SECOND-ORDER FILTERS TO THE FRACTIONAL-ORDER DOMAIN

A. G. RADWAN

Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Egypt

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A. S. ELWAKIL

Department of Electrical and Computer Engineering, University of Sharjah, P. O. Box 27272, Emirates

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, and

A. M. SOLIMAN

Department of Electronics and Communications, Faculty of Engineering, Cairo University, Egypt

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https://doi.org/10.1142/S0218126609005125Cited by:212 (Source: Crossref)

Abstract

This work is aimed at generalizing the design of continuous-time second-order filters to the non-integer-order (fractional-order) domain. In particular, we consider here the case where a filter is constructed using two fractional-order capacitors both of the same order α. A fractional-order capacitor is one whose impedance is Z_c = 1/C(jω)^α, C is the capacitance and α (0 < α ≤ 1) is its order. We generalize the design equations for low-pass, high-pass, band-pass, all-pass and notch filters with stability constraints considered. Several practical active filter design examples are then illustrated supported with numerical and PSpice simulations. Further, we show for the first time experimental results using the fractional capacitive probe described in Ref. 1.

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