Fractional-order transfer function - Doing a better choice

Fractional-order transfer function - Doing a better choice

Paper in proceedings (conference paper)

In this paper we analyze fractional-order transfer function and its possible variant forms, each of (2+α)-order and being suitable for low-pass filter design. Using the Butterworth approximation, we show that all variant forms; three in this case; of such transfer functions basically always result in the required magnitude response, but are characteristic with other behavior from the viewpoint of phase response and mainly the group delay. Hence, we show that the presence of fractional order α in fractional-order filter design does not provide just another degree of freedom regarding fine setting the slope of magnitude response in the stop-band. Dealing with fractional order, the possibility to assume and later select from variant forms of transfer function can be seen as another degree of freedom. We show that depending on selecting the specific form from the set of possible transfer functions we may observe different performance in the other analyzed parameters of the filter. This feature gives us the possibility to select such fractional transfer function that primarily follows the approximation type from the viewpoint of magnitude response but also may provide better performance regarding other frequency filter parameter.

In this paper we analyze fractional-order transfer function and its possible variant forms, each of (2+α)-order and being suitable for low-pass filter design. Using the Butterworth approximation, we show that all variant forms; three in this case; of such transfer functions basically always result in the required magnitude response, but are characteristic with other behavior from the viewpoint of phase response and mainly the group delay. Hence, we show that the presence of fractional order α in fractional-order filter design does not provide just another degree of freedom regarding fine setting the slope of magnitude response in the stop-band. Dealing with fractional order, the possibility to assume and later select from variant forms of transfer function can be seen as another degree of freedom. We show that depending on selecting the specific form from the set of possible transfer functions we may observe different performance in the other analyzed parameters of the filter. This feature gives us the possibility to select such fractional transfer function that primarily follows the approximation type from the viewpoint of magnitude response but also may provide better performance regarding other frequency filter parameter.

Capacitor; Differentiators; Low Pass Filters

Capacitor; Differentiators; Low Pass Filters

KOTON, J.; KUBÁNEK, D.

2024

27.02.2023

American Institute of Physics Inc.

9780735444119

AIP Conference Proceedings

2605

020011-1

020011-8

7

https://pubs.aip.org/aip/acp/article/2605/1/020011/2876024/Fractional-order-transfer-function-Doing-a-better