ANALYSIS OF THE FRACTIONAL-ORDER PARALLEL TANK CIRCUIT

Abstract

A parallel LβCα tank circuit with an α-order capacitor and a β-order inductor is proposed in this paper, where α and β are positive real numbers. The impedance of the parallel LβCα tank circuit, which could perform as a pure real, pure imaginary or short impedance, is discussed in detail, followed by the phase response analysis in α – β plane. The results show that the parallel LβCα tank circuit could act as a constant phase element. The resonance frequency analysis demonstrates that there exists more than one resonance frequency. And the time domain response expression of the proposed LβCα tank circuit is given by applying the inverse Laplace transform. The dual transformation relationship between the series and parallel LβCα tank circuit is summarized at last.