The project deals with the research on description and design of fractional-order elements, essential for future synthesis of analog systems of fractional (non-integer) order. These researched elements are realized by means of resistive-capacitive layers and for their description and design use theory of circuits with distributed parameters. Software design tool is created that based on the requirements on FOC and parameters of the expected design technology. The validity of mathematical description and the design tool is verified by experimental realization of CMOS FOCs. Using the same principles of multilayer structures description, possible realization of FOCs being implemented on a chip using CMOS technology is also proposed, additionally enabling electronical control of parameters of the designed element. Researching the design and realization of FOCs contributes to the further development in electronics and the design of analog fractional systems.

Keywords
Fractional-order element; CMOS; RC-EDP;R-C-NR;C-R-NC;tunability;

GA23-06070S

English

Jeřábek Jan, doc. Ing., Ph.D. - principal person responsible
Dvořák Jan, Ing., Ph.D. - fellow researcher
Kledrowetz Vilém, doc. Ing., Ph.D. - fellow researcher
Kubánek David, doc. Ing., Ph.D. - fellow researcher
Šeda Pavel, RNDr. Ing., Ph.D. - fellow researcher
Šotner Roman, prof. Ing., Ph.D. - fellow researcher

Department of Telecommunications
- responsible department (29.3.2022 - not assigned)
Department of Telecommunications
- beneficiary (29.3.2022 - not assigned)

DUCKWORTH, C.; ŠOTNER, R.; JEŘÁBEK, J.; FREEBORN, T. Fractional-Order Equivalent Circuit Representation of Sucrose Solutions Electrical Impedance Measured in Bipolar Configuration. In SoutheastCon 2025. USA, Concorde: IEEE, 2025. p. 1487-1493. ISBN: 979-8-3315-0484-7.
Detail

ŠOTNER, R.; BLACK, C.; JEŘÁBEK, J.; FREEBORN, T.; COLBURN, S.; SVOBODA, M. Practical design of variable fractional-order capacitors with a single tuning feature using field effect transistors and variable capacitance diodes. Scientific Reports, 2025, vol. 15, no. 7, p. 1-17. ISSN: 2045-2322.
Detail

ŠOTNER, R.; COLBURN, S.; JEŘÁBEK, J.; POLÁK, L.; FREEBORN, T. Electronically tunable pseudocapacitance for fractional-order (α=0.25) passive element. MEASUREMENT, 2025, vol. 253, no. 1, p. 1-11. ISSN: 1873-412X.
Detail

ALDRIDGE, R.; KUBÁNEK, D.; KOTON, J.; FREEBORN, T. Generalized Approach for Fractional-Order Low-Pass Butterworth Filter Realization with an Inverse Follow the Leader Filter (IFLF) Topology. In Proceedings of IEEE SoutheastCon 2025 Conference. Concord, NC, USA: IEEE, 2025. p. 1596-1602. ISBN: 979-8-3315-0484-7.
Detail

PROKUP, L.; KUBÁNEK, D.; FREEBORN, T. Finite Element Model in LTspice of a Distributed RC-Structure Fractional-Order Capacitor Device. In Proceedings of IEEE SoutheastCon 2025 Conference. Concord, NC, USA: IEEE, 2025. p. 1494-1500. ISBN: 979-8-3315-0484-7.
Detail

MCGOWAN, M.; KUBÁNEK, D.; HERENCSÁR, N.; FREEBORN, T. Transitional Frequencies of Fractional-Order Transitional Transfer Functions Using Butterworth and Sync-Tuned Approximations. In Proceedings of IEEE SoutheastCon 2025 Conference. Concord, NC, USA: IEEE, 2025. p. 1609-1614. ISBN: 979-8-3315-0484-7.
Detail

KUBÁNEK, D.; SHADRIN, A.; ŠEDA, P.; DVOŘÁK, J.; JEŘÁBEK, J.; KLEDROWETZ, V.; CHRISTIE, C.; FREEBORN, T.; USHAKOV, P. Design, synthesis and simulation of fractional-order element using MOS transistors as distributed resistive capacitive devices. Scientific Reports, 2025, vol. 15, no. 4, ISSN: 2045-2322.
Detail

DVOŘÁK, J.; KUBÁNEK, D.; JEŘÁBEK, J.; ŠEDA, P.; ALDRIDGE, R. Design of Fractional-Order Chebyshev Filter with FOE Based on R-C-NR Structure. In ICUMT 2024; 16th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops. 2024. p. 1-6. ISBN: 978-3-8007-6544-7.
Detail

SEMENOV, D.; ŠOTNER, R.; POLÁK, L.; JEŘÁBEK, J.; PETRŽELA, J.; LANGHAMMER, L. Comparison of Analytical and Algorithm-Based Design of Two-Port Using Two Bilinear Sections. IEEE Access, 2024, vol. 12, no. July, p. 105069-105079. ISSN: 2169-3536.
Detail

KERR, R.; JEŘÁBEK, J.; ŠOTNER, R.; FREEBORN, T. Exploring the Effect of Electrode Material on the Electrical Impedance of Liquid Samples. In IEEE SoutheastCon-Proceedings. NEW YORK: IEEE, 2024. p. 1099-1105. ISBN: 979-8-3503-1710-7.
Detail

BLACK, C.; JEŘÁBEK, J.; ŠOTNER, R.; FREEBORN, T. Emulation of Fractional-Order Impedance with α=0.5 using MOSFET Revised RC-Ladder Topology. In IEEE SoutheastCon-Proceedings. NEW YORK: IEEE, 2024. p. 1223-1228. ISBN: 979-8-3503-1710-7.
Detail

CANTRELL, K.; JEŘÁBEK, J.; KOTON, J.; FREEBORN, T. Fractional-Order Immitance Converter (FGIC44) Performance Using Wideband Fractional-Order Element Seeds. In IEEE SoutheastCon-Proceedings. NEW YORK: IEEE, 2024. p. 1216-1222. ISBN: 979-8-3503-1710-7.
Detail

ŠOTNER, R.; JEŘÁBEK, J.; POLÁK, L.; JAIKLA, W.; ANDRIUKAITIS, D. Compact active analog device for novel applications useful for sensing and measurement. MEASUREMENT, Journal of the International Measurement Confederation (IMEKO), 2024, vol. 235, no. August 2024, p. 1-11. ISSN: 0263-2241.
Detail

CHRISTIE, C.; KUBÁNEK, D.; USHAKOV, P. Influence and Algorithmic Suppression of Parasitic Capacitance of the R-C-NR Layer Contacts in Thick-Film Fractional-Order Capacitor. In Proceedings of IEEE SoutheastCon 2024 Conference. Atlanta, GA, USA: IEEE, 2024. p. 1235-1242. ISBN: 979-8-3503-1710-7.
Detail

SLAY, J.; ŠOTNER, R.; FREEBORN, T.; JEŘÁBEK, J.; POLÁK, L.; PETRŽELA, J.; VYPLEL, V. Distinguishing Liquid Solutions With Alcohol Using Electrical Impedance Measurements: Preliminary Study for Food Safety Applications. IEEE SENSORS JOURNAL, 2023, vol. 23, no. 22, p. 26997-27007. ISSN: 1558-1748.
Detail

CHRISTIE, C.; CLEMENTS, T.; HUMPAL, A.; KUBÁNEK, D.; JEŘÁBEK, J.; ŠEDA, P.; DVOŘÁK, J.; USHAKOV, P.; KNYAZEV, I. Design and Examples of Fractional-Order Capacitor Based on C-R-NC Layer Structure. In Proceedings of the 2023 15th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Ghent, Belgium. 2023. p. 91-96. ISBN: 979-8-3503-9328-6.
Detail

Responsibility: Jeřábek Jan, doc. Ing., Ph.D.