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Open AccessArticle

Integer-and Fractional-Order Integral and Derivative Two-Port Summations: Practical Design Considerations

1
SIX Research Center, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 616 00 Brno, Czech Republic
2
Department of Electronics Engineering, Faculty of Electrical and Electronics Engineering, Kaunas University of Technology, Studentu st. 48-209, LT-51367 Kaunas, Lithuania
*
Author to whom correspondence should be addressed.
Appl. Sci. 2020, 10(1), 54; https://doi.org/10.3390/app10010054
Received: 14 November 2019 / Revised: 9 December 2019 / Accepted: 12 December 2019 / Published: 19 December 2019
This paper targets on the design and analysis of specific types of transfer functions obtained by the summing operation of integer-order and fractional-order two-port responses. Various operations provided by fractional-order, two-terminal devices have been studied recently. However, this topic needs to be further studied, and the topologies need to be analyzed in order to extend the state of the art. The studied topology utilizes the passive solution of a constant-phase element (with order equal to 0.5) implemented by parallel resistor–capacitor circuit (RC) sections operating as a fractional-order two-port. The integer-order part is implemented by operational amplifier-based lossless integrators and differentiators in branches with electronically adjustable gain, useful for time constant tuning. Four possible cases of the fractional-order and integer-order two-port interconnections are analyzed analytically, by PSpice simulations and also experimentally in the frequency range between 10 Hz and 1 MHz. Standard discrete active components are used in this design for laboratory verification. Practical recommendations for construction and also particular solutions overcoming possible issues with instability and DC offsets are also given. Experimental and simulated results are in good agreement with theory. View Full-Text
Keywords: constant phase element; differentiator; electronic adjusting; fractional-order element; integrator; summing of responses; two-port transfer; variable gain amplifier constant phase element; differentiator; electronic adjusting; fractional-order element; integrator; summing of responses; two-port transfer; variable gain amplifier
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Sotner, R.; Domansky, O.; Jerabek, J.; Herencsar, N.; Petrzela, J.; Andriukaitis, D. Integer-and Fractional-Order Integral and Derivative Two-Port Summations: Practical Design Considerations. Appl. Sci. 2020, 10, 54.

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