Pseudo-Differential (2 + α)-Order Butterworth Frequency Filter

Ondrej Sladok,Jan Dvorak,David Kubanek,Jaroslav Koton,Costas Psychalinos

doi:10.1109/access.2021.3091544

Ondrej Sladok, Jan Dvorak + Show 3 more

Open Access

https://doi.org/10.1109/access.2021.3091544

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Journal: IEEE Access	Publication Date: Jan 1, 2021
Citations: 13	License type: CC BY 4.0

Affiliation: Brno University of Technology, University of Patras

Abstract

This paper describes the design of analog pseudo-differential fractional frequency filter with the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(2+\alpha)$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0 < \alpha < 1$ </tex-math></inline-formula> . The filter operates in a mixed-transadmittance mode (voltage input, current output) and provides a low-pass frequency response according to Butterworth approximation. General formulas to determine the required transfer function coefficients for desired value of fractional order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> are also introduced. The designed filter provides the beneficial features of fully-differential solutions but with a less complex circuit topology. It is canonical, i.e. it employs a minimum number of passive elements, whereas all are grounded, and current conveyors as active elements. The proposed structure offers high input impedance, high output impedance, and high common-mode rejection ratio. By simple modification, voltage response can also be obtained. The performance of the proposed frequency filter is verified both by simulations and experimental measurements proving the validity of theory and the advantageous features of the filter.

Highlights

W ITHIN the last decades, there is a significantly rising attention being paid to fractional-order (FO) calculus due to its promising utilization in various research areas such as economy and finance [1] – [3], medical and health science [4] – [6], agriculture and food processing [7] – [10], automotive [11] – [13], and in electrical engineering [14] – [43] to design, describe, model and/or control various systems and function blocks
There are generally two approaches to overcome the absence of discrete fractional-order element (FOE), both approximating the behavior of FOE in a specific frequency range and with required accuracy
List of previously unexplained abbreviations used in this table: CFOA: Current Feedback Operational Amplifier, CG-CCDDCC: controlled gain current-controlled differential difference current conveyor, VGA: Variable Gain Amplifier, IOGC-CA: individual output gain controlled current amplifier

Summary

THEORY ON PSEUDO-DIFFERENTIAL FILTERS

(2 + α) BUTTERWORTH APPROXIMATION For the purpose of (2 + α)-order frequency filter design, the following general low-pass transfer function is assumed: H2L+Pα(s) s2+αk. Where 0 < α < 1, and k1, k2, k3, and k4, are the transfer function coefficients that were determined using an optimization algorithm to match the target Butterworth fractional lowpass magnitude response. To determine the transfer function coefficients k1, k2, k3, and k4 in (7) according to Butterworth approximation for specific values of fractional order α, the following interpolation matrix can be used: k1 0.357. The transfer function coefficients should be modified by dividing them by the respective power of ω0 as follows: H2L+Pα,ω0 (s) s2+α k1

PROPOSED PSEUDO-DIFFERENTIAL FRACTIONAL-ORDER FILTER

C2 C3 C4 C5 C6 C7

SIMULATIONS AND EXPERIMENTAL MEASUREMENTS

Findings

CONCLUSION