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Designing constant phase elements of complement order

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Abstract

Once designing analogue fractional-order function blocks, the capacitive and/or inductive fractional-order elements (FOEs), also referred to as constant phase elements, being defined with their fractional order \(\alpha\) (\(0< \alpha < 1\)) are required. Although currently capacitive FOEs are being discussed in the literature, still these passive elements are not readily available in discrete form and mainly do not offer the whole span of \(\alpha\). Therefore, to overcome such an obstacle, we primary propose the transformation of FOEs and their fractional order \(\alpha\) to obtain the complement order \(\beta\), whereas \(\beta =1{-}\alpha\). Following the theory and mathematical description, also other transformation cases on fractional-order element are discussed and analysed in this paper. Using simple impedance converter employing single current conveyor and transconductance amplifier, the theoretical presumptions are verified both by simulations and experimental measurements.

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Acknowledgements

This work was supported by Czech Science Foundation under Grant No. 16-06175S and the National Sustainability Program under Grant LO1401. For the research, infrastructure of the SIX Center was used. This article is based upon work from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology).

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Authors and Affiliations

  1. Brno University of Technology, Technicka 12, 616 00, Brno, Czech Republic

    Jaroslav Koton, David Kubanek, Norbert Herencsar & Jan Dvorak

  2. Physics Department, Electronics Laboratory, University of Patras, Rio Patras, Greece

    Costas Psychalinos

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  1. Jaroslav Koton
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  2. David Kubanek
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  3. Norbert Herencsar
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  4. Jan Dvorak
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  5. Costas Psychalinos
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Correspondence to Jaroslav Koton.

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Koton, J., Kubanek, D., Herencsar, N. et al. Designing constant phase elements of complement order. Analog Integr Circ Sig Process 97, 107–114 (2018). https://doi.org/10.1007/s10470-018-1257-7

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  • DOI: https://doi.org/10.1007/s10470-018-1257-7

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