Research On Synthesis Method Of Fractional Immittance Function With Two Element Orders In W Domain

Fractional calculus theory has become a research hotspot in recent years and has been widely used in mathematics,physics,chemistry,economics,medicine,meteorology,electrical engineering and other fields.With the widespread application of fractional-order circuit theory in engineering and the continuous improvement of the production process of fractional-order circuit components,it has been found that studying the properties of fractional-order circuits and the passive implementation of fractional-order networks is of great significance for the promotion of refined simulation modeling of electrical equipment.The s-W transform is a new method proposed in recent years to solve the synthesis problem of fractional order networks.It transforms the rational element fractional order impulse function into an integer order impulse function of W domain.At the same time,in the traditional circuit synthesis theory,reactance synthesis is the basis of conductance synthesis.Based on this,this paper will study the definition and properties of the fractional order reactance function,and propose two types of typical circuit structures of dual-element fractional order reactance network W domain passive implementation method.By generalizing the Darlington synthesis method to the W domain,the W domain synthesis method of the dual-element fractional order immittance function is given.Passive synthesis method in W domain.