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

Applied Sciences

Todd J. Freeborn¹  Jaroslav Koton²  Jan Dvorak²  David Kubanek² 

[1] Department of Electrical and Computer Engineering, The University of Alabama, Tuscaloosa, AL 35487, USA;Department of Telecommunications, Brno University of Technology, Technicka 12, 616 00 Brno, Czech Republic;

关键词: fractional-order filters;    fractional calculus;    Chebyshev filters;    low-pass filters;    magnitude responses;   

DOI  :  10.3390/app8122603

来源: DOAJ

【 摘 要 】

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 $(1+\alpha )$ order lowpass magnitude responses are given as examples with fractional steps from $\alpha =0.1$ to $\alpha =0.9$ and compared to the second-order elliptic response. Further, MATLAB simulations of the $(1+\alpha )=1.25$ 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 $(1+\alpha )=1.2$ and $1.8$ order filters.

【 授权许可】

Unknown