Abstract
This paper introduces the generalization of the classical Transitional Butterworth-Butterworth Filter (TBBF) to the Fractional-Order (FO) domain. Stable rational approximants of the FO-TBBF are optimally realized. Several design examples demonstrate the robustness and modeling efficacy of the proposed method. Practical circuit implementation using the current feedback operational amplifier employed as an active element is presented. Experimental results endorse good agreement (R2= 0.999968) with the theoretical magnitude-frequency characteristic.
Highlights
INTRODUCTIONT HE modeling techniques and realization of classical (integer-order) analog filters are well-established
T HE modeling techniques and realization of classical analog filters are well-established
This paper introduces the generalization of the classical Transitional ButterworthButterworth Filter (TBBF) to the Fractional-Order (FO) domain
Summary
T HE modeling techniques and realization of classical (integer-order) analog filters are well-established. The theoretical concept of fractional calculus, which deals with the generalization of the classical definitions of differentiation and integration, has been applied to achieve a more precise attenuation behavior of analog filters [5] This is possible due to the generalization of the classical Laplacian operator s to the Fractional-Order (FO) form sα, where α ∈ (0, 1), which causes additional degrees of freedom in system modeling. The sα operator forms the basic building block of the FO transfer functions, which can lead to generalizations of classical Butterworth filter [9], oscillators [10], and resonators [11] Both active and passive elements have been employed to realize the FO impedances [12], [13]. Mahata et al.: A Fractional-Order Transitional Butterworth-Butterworth Filter and Its Experimental Validation
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