A ℘-order R-L high-pass filter modeled by local fractional derivative

Abstract

As an important electronic device, filter is applied to all kinds of electronic products. In this paper, a new ℘-order R-L High-pass filter (HPF) modeled by the local fractional derivative (LFD) is proposed for the first time. With the help of the local fractional Laplace transform (LFLT), we obtain the non-differentiable(ND) transfer function, and present the expressions of ND amplitude-frequency characteristic (AFC) and ND phase-frequency characteristics (PFC). The corresponding parameters and properties of the ℘-order R-L HPF are also studied. What’s interesting is that the ℘-order R-L HPF becomesthe ordinary one in the exceptional case at ℘ = 1. The obtained results in this paper reveal the sufficiency of the local fractional derivative for analyzing the circuit systems in fractal space.

Keywords

• Fractal space
• Local fractional derivative
• R-L High-pass filter
• Fractal circuit systems