Time and frequency responses of non-integer order RLC circuits

Mehmet Emir Koksal; Mehmet Emir Koksal

doi:10.3934/Math.2019.1.64

AIMS Mathematics

2019, Volume 4, Issue 1: 64-78. doi: 10.3934/Math.2019.1.64

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Research article Special Issues

Time and frequency responses of non-integer order RLC circuits

Mehmet Emir Koksal ^,

Department of Mathematics, Ondokuz Mayis University, 55139 Atakum Samsun, Turkey

Received: 02 October 2018 Accepted: 26 December 2018 Published: 08 January 2019

By introducing an auxiliary parameter, the dynamic of RLC electrical circuits of non-integer order is described by a fractional order differential equation. The order of derivative in the component models is assumed to be zhongwenzy \lt \gamma\leq 1$. The time and frequency domain characteristics of the circuit is investigated, and it is shown that three different filter characteristics of low-pass, high-pass and band-pass filters are obtained. The filter parameters are determined analytically, and the results are verified numerically.
- fractional calculus,
- electrical filters,
- RLC circuits,
- frequency response,
- step response,
- Mittag-Leffler function
Citation: Mehmet Emir Koksal. Time and frequency responses of non-integer order RLC circuits[J]. AIMS Mathematics, 2019, 4(1): 64-78. doi: 10.3934/Math.2019.1.64

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Abstract

By introducing an auxiliary parameter, the dynamic of RLC electrical circuits of non-integer order is described by a fractional order differential equation. The order of derivative in the component models is assumed to be zhongwenzy \lt \gamma\leq 1$. The time and frequency domain characteristics of the circuit is investigated, and it is shown that three different filter characteristics of low-pass, high-pass and band-pass filters are obtained. The filter parameters are determined analytically, and the results are verified numerically.

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