Series-, Parallel-, and Inter-Connection of Solid-State Arbitrary Fractional-Order Capacitors: Theoretical Study and Experimental Verification
Series-, Parallel-, and Inter-Connection of Solid-State Arbitrary Fractional-Order Capacitors: Theoretical Study and Experimental Verification
Abstract
In the paper, general analytical formulas are introduced for the determination of equivalent impedance, magnitude, and phase, i.e. order, for n arbitrary fractional-order capacitors (FoCs) connected in series, parallel, and their interconnection. The approach presented helps to evaluate these relevant quantities in the fractional domain since the order of each element has a significant effect on the impedance of each FoC and their equivalent capacitance cannot be considered. Three types of solid-state fractional-order passive capacitors of different orders, using ferroelectric polymer and reduced Graphene Oxide-percolated P(VDF-TrFE-CFE) composite structures, are fabricated and characterized. Using an impedance analyzer, the behavior of the devices was found to be stable in the frequency range 0.2MHz–20MHz, with a phase angle deviation of ±4 degrees. Multiple numerical and experimental case studies are given, in particular for two and three connected FoCs. The fundamental issues of the measurement units of the FoCs connected in series and parallel are derived. A MATLAB open access source code is given in Appendix for easy calculation of the equivalent FoC magnitude and phase. The experimental results are in good agreement with the theoretical assumptions. In the paper, general analytical formulas are introduced for the determination of equivalent impedance, magnitude, and phase, i.e. order, for n arbitrary fractional-order capacitors (FoCs) connected in series, parallel, and their interconnection. The approach presented helps to evaluate these relevant quantities in the fractional domain since the order of each element has a significant effect on the impedance of each FoC and their equivalent capacitance cannot be considered. Three types of solid-state fractional-order passive capacitors of different orders, using ferroelectric polymer and reduced Graphene Oxide-percolated P(VDF-TrFE-CFE) composite structures, are fabricated and characterized. Using an impedance analyzer, the behavior of the devices was found to be stable in the frequency range 0.2MHz–20MHz, with a phase angle deviation of ±4 degrees. Multiple numerical and experimental case studies are given, in particular for two and three connected FoCs. The fundamental issues of the measurement units of the FoCs connected in series and parallel are derived. A MATLAB open access source code is given in Appendix for easy calculation of the equivalent FoC magnitude and phase. The experimental results are in good agreement with the theoretical assumptions.
Keywords
Arbitrary-order FoC, FoC, fractional calculus, fractional-order capacitor, interconnection, MATLAB open access source code, parallel connection, series connection, solid-state device, Arbitrary-order FoC, FoC, fractional calculus, fractional-order capacitor, interconnection, MATLAB open access source code, parallel connection, series connection, solid-state devicePersistent identifier
http://hdl.handle.net/11012/70924Document type
Peer reviewedDocument version
Final PDFSource
IEEE Access. 2018, vol. 6, issue 1, p. 10933-10943.http://ieeexplore.ieee.org/document/8302886/
Collections
- oddělení-REL-SIX [4]
- Ústav telekomunikací [314]
- Ústav radioelektroniky [179]
- oddělení-TKO-SIX [25]
Citace PRO
Except where otherwise noted, this item's license is described as Creative Commons Attribution 3.0 Unported
Related items
Showing items related by title, author, creator and subject.
-
Analog Implementation of Fractional-Order Elements and Their Applications
Kartci, Aslihan (2019-06-24)With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received ... -
Analogová implementace prvků neceločíselného řádu a jejich aplikace
Kartci, AslihanS pokroky v teorii počtu neceločíselného řádu a také s rozšířením inženýrských aplikací systémů neceločíselného řádu byla značná pozornost věnována analogové implementaci integrátorů a derivátorů neceločíselného řádu. Je ... -
Analog Implementation of Fractional-Order Elements and Their Applications
Kartci, Aslihan (2019-06-24)With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received ...