The Fractional Sallen-Key Filter Described by Local Fractional Derivative
Kang‐Jia Wang, Hong-Chang Sun, Qin-Chao Cui
Abstract
The local fractional derivative (LFD) has attracted wide attention in the field of engineering application. In this paper, the LFD is used to model the fractional Sallen-Key filter for the first time. The non-differentiable(ND) transfer function is obtained by using the local fractional Laplace transform(LFLT). And the amplitude frequency response is analyzed in detail for different 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">$\varsigma $ </tex-math></inline-formula> . It is found that the fractional Sallen-Key filter becomes the ordinary one in the special case <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varsigma =1$ </tex-math></inline-formula> . The obtained results of this paper show the powerful ability of local fractional calculus in the analysis of complex problems arising in engineering fields.