Research On Passive Synthesis Of Fractional Order Circuits With Three Element Orders In Multivariable Domain

Fractional calculus theory has been widely used in chemistry,biology,medicine,materials science,geology,electrical engineering,etc.,and has become a research hotspot.With the development of fractional order circuits and system theory,and its wide application in engineering,the passive realization of fractional order circuits has begun to attract people’s attention.In recent years,fractional order elements have made great progresses in manufacturing,making it possible to directly construct fractional order circuits by using them.Where the passive realization of fractional order networks is crucial.However,the study about passive realization of fractional order networks is still rare and in its infancy.This paper introduces the fractional order gyrator,and improves the definition of multivariable positive-real and multivariable reactance matrix respectively,then extends multivariate domain passivity criterion to the fractional order networks with general fractional order passive coupled inductors.By improving two-variable reactance matrix passive synthesis method,a passive synthesis method of three-variable reactance matrix is proposed,then the extended Darlington synthesis of three-variable immittance function is given.Based on this and variable substitution,a synthesis method of fractional order immittance function with three element orders is proposed.