Analysis And Passive Synthesis Of Circuits With Fractional-Order Coupling Inductance

In recent years,fractional-order circuit models have been widely used in many engineering fields,such as the design of fractional-order filters,the establishment of circuit models for fuel cells and biological tissues,etc.Introducing fractional calculus into the circuit can not only describe the memory characteristics of some components better,but also provide more freedom for the design of the circuit.Compared with active circuit models,passive circuit models are more stable and less prone to oscillations,so the study of passive synthesis method is significant.At present,the passive synthesis method of fractional-order circuits is still being explored,and the complex fractional-order circuits are mainly systematically synthesized by multi-port transformers and gyroscopes,and the fractional-order coupling inductors have not been fully used.Fractional-order coupling inductance used in circuit synthesis can not only replace multi-port transformers and make the circuit more concise,but also synthesize some non-reciprocal circuits by virtue of the fact that the fractional-order coupling inductance can still be non-reciprocal in the case of passivity,thus bringing more design space for circuit synthesis.In this thesis,passive condition of fractional order multi-port coupling inductance is studied,the T-type equivalent circuit containing controlled source of fractional order coupling inductance and fractional tightly coupling inductance equivalent circuit is given,the sensitivity analysis method including fractional coupling inductance is given,the characteristics of two-port network containing fractional coupling inductance are studied.A sufficient and necessary condition for passive synthesis of the impedance function of RLαCβ circuit in the W domain is presented,and then a general method for synthesis of this kind of impedance function with fractional coupling inductance is proposed.methods for synthesizing two special types of impedance functions with fractional-order coupled inductors are presented.All the methods are verified by examples,and the theory of passive synthesis of fractional circuits is further enriched.