Research On Passive Synthesis Method Of Fractional-Order Circuits Based On Impedance Scaling

In recent years,research on fractional calculus theory has developed rapidly.At present,fractional calculus has been successfully applied in many disciplines such as electrochemistry,biochemistry,physics,material mechanics,biomedicine,economic and so on.In the field of electrical engineering,many devices and systems are fractional in nature.Studying the properties of fractional-order(FO)circuits and passive synthesis methods of FO circuits can further develop and improve circuit theory,and the studies have important theoretical significance and practical value for the advanced modeling of electrical equipment.Due to the appearance of FO elements,the oscillation properties of FO circuits and integer-order circuits are different.This paper analyzes the osci llation conditions of FO two-element-kind circuits.Sufficient conditions for oscillation of FO twoelement-kind circuit are given by using complex frequency domain analysis.The traditional circuit synthesis theory has been perfected by the exploration of many scholars,but the introduction of FO elements has brought new challenges to circuit synthesis.In the traditional circuit synthesis theory,the synthesis of two-element-kind circuits(RC,RL,LC circuits)is the basis of the circuit synthesis theory,and the three-element-kind circuit composed of RLC is the most common implementation circuit.In this paper,the impedance scaling is applied in the synthesis of FO circuits.With the existing achievements in the traditional circuit synthesis theory,the passive synthesis methods of the FO two-element-kind circuit and the FO three-element-kind circuit are given.The proposed methods are applicable to passive synthesis of any FO two-element-kind circuits and FO threeelement-kind circuits,where the order of each element is a real number between 0-1.