Publication detail

(1+α) Fractional-order transfer functions to approximate low-pass magnitude responses with arbitrary quality factor

KUBÁNEK, D. FREEBORN, T.

Original Title

(1+α) Fractional-order transfer functions to approximate low-pass magnitude responses with arbitrary quality factor

English Title

(1+α) Fractional-order transfer functions to approximate low-pass magnitude responses with arbitrary quality factor

Type

journal article in Web of Science

Language

en

Original Abstract

The coefficients of three fractional-order low-pass transfer functions are presented to aid in the design of these filters based on their arbitrary quality factors. These coefficients are found by minimizing the error between these fractional-order transfer functions and the second-order transfer function using numerical least squares optimization. Coefficients and design equations are presented for fractional-orders between one and two. Stability of the transfer functions with the presented coefficients is examined and possibilities of characteristic frequency shifting are shown. The results are verified by PSpice simulation of a conveyor-based low-pass filter with fractional order of 1.5 and quality factor Q = 5.

English abstract

The coefficients of three fractional-order low-pass transfer functions are presented to aid in the design of these filters based on their arbitrary quality factors. These coefficients are found by minimizing the error between these fractional-order transfer functions and the second-order transfer function using numerical least squares optimization. Coefficients and design equations are presented for fractional-orders between one and two. Stability of the transfer functions with the presented coefficients is examined and possibilities of characteristic frequency shifting are shown. The results are verified by PSpice simulation of a conveyor-based low-pass filter with fractional order of 1.5 and quality factor Q = 5.

Keywords

Fractional-order filter; Analog filter; Fractional-order transfer function; Fractional calculus

Released

29.04.2017

Publisher

ELSEVIER GMBH, URBAN & FISCHER VERLAG

Location

Germany

Pages from

1

Pages to

10

Pages count

10

URL

BibTex


@article{BUT137071,
  author="David {Kubánek} and Todd {Freeborn}",
  title="(1+α) Fractional-order transfer functions to approximate low-pass magnitude responses with arbitrary quality factor",
  annote="The coefficients of three fractional-order low-pass transfer functions are presented to aid in the design of these filters based on their arbitrary quality factors. These coefficients are found by minimizing the error between these fractional-order transfer functions and the second-order transfer function using numerical least squares optimization. Coefficients and design equations are presented for fractional-orders between one and two. Stability of the transfer functions with the presented coefficients is examined and possibilities of characteristic frequency shifting are shown. The results are verified by PSpice simulation of a conveyor-based low-pass filter with fractional order of 1.5 and quality factor Q = 5.",
  address="ELSEVIER GMBH, URBAN & FISCHER VERLAG",
  chapter="137071",
  doi="10.1016/j.aeue.2017.04.031",
  howpublished="online",
  institution="ELSEVIER GMBH, URBAN & FISCHER VERLAG",
  number=", IF: 0.786",
  volume="2017 (78)",
  year="2017",
  month="april",
  pages="1--10",
  publisher="ELSEVIER GMBH, URBAN & FISCHER VERLAG",
  type="journal article in Web of Science"
}