Modeling the single tuned passive harmonic filter based on the fractional calculus

In this paper, the fractional characteristics of capacitor and inductor are considered, and the single tuned passive harmonic filter is modeled and analyzed based on the fractional calculus. The fractional-order mathematical model of the single tuned passive harmonic filter is given. The difference between the integer model and the fractional model is revealed. In the fractional model the resonant frequency and the impedance of the filter when resonant are both related to the parameter L, C and the fractional order of the capacitor and the inductor.