Time and frequency responses of non-integer order RLC circuits

Köksal M. E.

AIMS MATHEMATICS, vol.4, no.1, pp.64-78, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.3934/math.2019.1.64
  • Journal Name: AIMS MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.64-78
  • Keywords: fractional calculus, electrical filters, RLC circuits, frequency response, step response, Mittag-Leffler function, SYNCHRONIZATION
  • Ondokuz Mayıs University Affiliated: Yes

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 0 < gamma <= 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.