Optimal Modelling of (1 + <i>α</i>) Order Butterworth Filter under the CFE Framework
This paper presents the optimal rational approximation of (1+<i>α</i>) order Butterworth filter, where α ∊ (0,1) under the continued fraction expansion framework, by employing a new cost function. Two simple techniques based on the constrained optimization and the optimal pole-zero place...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/4/4/55 |
| _version_ | 1797545799519830016 |
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| author | Shibendu Mahata Rajib Kar Durbadal Mandal |
| author_facet | Shibendu Mahata Rajib Kar Durbadal Mandal |
| author_sort | Shibendu Mahata |
| collection | DOAJ |
| description | This paper presents the optimal rational approximation of (1+<i>α</i>) order Butterworth filter, where α ∊ (0,1) under the continued fraction expansion framework, by employing a new cost function. Two simple techniques based on the constrained optimization and the optimal pole-zero placements are proposed to model the magnitude-frequency response of the fractional-order lowpass Butterworth filter (FOLBF). The third-order FOLBF approximants achieve good agreement to the ideal characteristic for six decades of design bandwidth. Circuit realization using the current feedback operational amplifier is presented, and the modelling efficacy is validated in the OrCAD PSPICE platform. |
| first_indexed | 2024-03-10T14:20:10Z |
| format | Article |
| id | doaj.art-282a2565672e40ad9a44f8a59dc27e20 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T14:20:10Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-282a2565672e40ad9a44f8a59dc27e202023-11-20T23:24:45ZengMDPI AGFractal and Fractional2504-31102020-12-01445510.3390/fractalfract4040055Optimal Modelling of (1 + <i>α</i>) Order Butterworth Filter under the CFE FrameworkShibendu Mahata0Rajib Kar1Durbadal Mandal2Department of Electronics and Communication Engineering, National Institute of Technology Durgapur, M.G. Avenue, Durgapur 713209, IndiaDepartment of Electronics and Communication Engineering, National Institute of Technology Durgapur, M.G. Avenue, Durgapur 713209, IndiaDepartment of Electronics and Communication Engineering, National Institute of Technology Durgapur, M.G. Avenue, Durgapur 713209, IndiaThis paper presents the optimal rational approximation of (1+<i>α</i>) order Butterworth filter, where α ∊ (0,1) under the continued fraction expansion framework, by employing a new cost function. Two simple techniques based on the constrained optimization and the optimal pole-zero placements are proposed to model the magnitude-frequency response of the fractional-order lowpass Butterworth filter (FOLBF). The third-order FOLBF approximants achieve good agreement to the ideal characteristic for six decades of design bandwidth. Circuit realization using the current feedback operational amplifier is presented, and the modelling efficacy is validated in the OrCAD PSPICE platform.https://www.mdpi.com/2504-3110/4/4/55biquadratic approximationButterworth filtercontinued fraction expansioncurrent feedback operational amplifierfractional-order filter designoptimization |
| spellingShingle | Shibendu Mahata Rajib Kar Durbadal Mandal Optimal Modelling of (1 + <i>α</i>) Order Butterworth Filter under the CFE Framework Fractal and Fractional biquadratic approximation Butterworth filter continued fraction expansion current feedback operational amplifier fractional-order filter design optimization |
| title | Optimal Modelling of (1 + <i>α</i>) Order Butterworth Filter under the CFE Framework |
| title_full | Optimal Modelling of (1 + <i>α</i>) Order Butterworth Filter under the CFE Framework |
| title_fullStr | Optimal Modelling of (1 + <i>α</i>) Order Butterworth Filter under the CFE Framework |
| title_full_unstemmed | Optimal Modelling of (1 + <i>α</i>) Order Butterworth Filter under the CFE Framework |
| title_short | Optimal Modelling of (1 + <i>α</i>) Order Butterworth Filter under the CFE Framework |
| title_sort | optimal modelling of 1 i α i order butterworth filter under the cfe framework |
| topic | biquadratic approximation Butterworth filter continued fraction expansion current feedback operational amplifier fractional-order filter design optimization |
| url | https://www.mdpi.com/2504-3110/4/4/55 |
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