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"
}