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2 2014

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Resonance in series fractional order RLβCα circuit

Walczak J., Jakubowska A.

Przegląd Elektrotechniczny

2014

R. 90, nr 4

210--213

The paper describes the results of studies on the phase and magnitude resonance phenomenon in a series RLC circuit with fractional order reactive elements. Formulas for frequency characteristics and resonance conditions have been derived. Simulations of concerned fractional order system have been conducted too.

W artykule opisano wyniki badań zjawiska rezonansu w szeregowym obwodzie RLC z elementami reaktancyjnymi Lβ, Cα ułamkowego rzędu. Wyprowadzono zależności określające charakterystyki częstotliwościowe układu oraz warunki rezonansu fazy i amplitudy. Podano także wyniki badań symulacyjnych rozpatrywanego układu.

Analysis of the parallel resonance circuit with supercapacitor

Walczak J., Jakubowska A.

Poznan University of Technology Academic Journals. Electrical Engineering

2014

No. 77

93--99

The article presents an analysis of phase resonance conditions for the parallel RLCα circuit with supercapacitor. Supercapacitors behaviour somehow differs from classic dielectric capacitors, therefore it is necessary to develop their new mathematical models, using fractional - order differential equations. A simple fractional - order supercapacitor model has been assumed, taking into account its internal equivalent series resistance ESR too. A lossless inductance has also been assumed and relations for equivalent admittance and resonance occurence conditions have been derived in the considered parallel RLCα circuit with supercapacitor. The analysis was conducted for different fractional-order parameter α values. Derived relations have been illustrated by simulation examples. The existence of resonance frequency depends largely on the supercapacitor series resistance value.