Publication detail

Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters

KUBÁNEK, D. FREEBORN, T. KOTON, J. DVOŘÁK, J.

Original Title

Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters

English Title

Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters

Type

journal article in Web of Science

Language

en

Original Abstract

In this paper, fractional-order transfer functions to approximate the passband and stopband ripple characteristics of a second-order elliptic lowpass filter are designed and validated. The necessary coefficients for these transfer functions are determined through the application of a least squares fitting process. These fittings are applied to symmetrical and asymmetrical frequency ranges to evaluate how the selected approximated frequency band impacts the determined coefficients using this process and the transfer function magnitude characteristics. MATLAB simulations of (1 + α) order lowpass magnitude responses are given as examples with fractional steps from α = 0.1 to α = 0.9 and compared to the second-order elliptic response. Further, MATLAB simulations of the (1 + α) = 1.25 and 1.75 using all sets of coefficients are given as examples to highlight their differences. Finally, the fractional-order filter responses were validated using both SPICE simulations and experimental results using two operational amplifier topologies realized with approximated fractional-order capacitors for (1 + α) = 1.2 and 1.8 order filters.

English abstract

In this paper, fractional-order transfer functions to approximate the passband and stopband ripple characteristics of a second-order elliptic lowpass filter are designed and validated. The necessary coefficients for these transfer functions are determined through the application of a least squares fitting process. These fittings are applied to symmetrical and asymmetrical frequency ranges to evaluate how the selected approximated frequency band impacts the determined coefficients using this process and the transfer function magnitude characteristics. MATLAB simulations of (1 + α) order lowpass magnitude responses are given as examples with fractional steps from α = 0.1 to α = 0.9 and compared to the second-order elliptic response. Further, MATLAB simulations of the (1 + α) = 1.25 and 1.75 using all sets of coefficients are given as examples to highlight their differences. Finally, the fractional-order filter responses were validated using both SPICE simulations and experimental results using two operational amplifier topologies realized with approximated fractional-order capacitors for (1 + α) = 1.2 and 1.8 order filters.

Keywords

fractional-order filters; fractional calculus; Chebyshev filters; low-pass filters; magnitude responses

Released

13.12.2018

Publisher

MDPI

Location

Basel, Switzerland

Pages from

1

Pages to

17

Pages count

17

URL

Full text in the Digital Library

BibTex


@article{BUT151884,
  author="David {Kubánek} and Todd {Freeborn} and Jaroslav {Koton} and Jan {Dvořák}",
  title="Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters",
  annote="In this paper, fractional-order transfer functions to approximate the passband and
stopband ripple characteristics of a second-order elliptic lowpass filter are designed and validated. The necessary coefficients for these transfer functions are determined through the application of a least squares fitting process. These fittings are applied to symmetrical and asymmetrical frequency ranges to evaluate how the selected approximated frequency band impacts the determined coefficients using this process and the transfer function magnitude characteristics. MATLAB simulations of (1 + α) order lowpass magnitude responses are given as examples with fractional steps from α = 0.1 to α = 0.9 and compared to the second-order elliptic response. Further, MATLAB simulations of the (1 + α) = 1.25 and 1.75 using all sets of coefficients are given as examples to highlight their differences. Finally, the fractional-order filter responses were validated using both SPICE simulations and experimental results using two operational amplifier topologies realized with approximated fractional-order capacitors for (1 + α) = 1.2 and 1.8 order filters.",
  address="MDPI",
  chapter="151884",
  doi="10.3390/app8122603",
  howpublished="online",
  institution="MDPI",
  number="12",
  volume="8",
  year="2018",
  month="december",
  pages="1--17",
  publisher="MDPI",
  type="journal article in Web of Science"
}