Research On Simulation And Calculation Of Fractional Order Circuits

With the development of the theory of fractional calculus,the fractional calculus theory has been widely applied in the field of electrical engineering,such as the establishment and research of models of transformer windings,transmission line,cable line and super capacitor.These models not only reduced the models' complexity,but also improved the accuracy of simulation.The research on the fractional order models in the field of electrical engineering is based on the theory of fractional order circuits.So the fractional order circuit elements,the properties of fractional order circuits and their simulations have important significance for the development of electrical engineering.The classical circuit elements can be described by the electromagnetic field knowledge.As an extension of the classical electromagnetic field,the fractional electromagnetic field can also be used to explain the fractional circuit elements.The fractional Maxwell equation is expanded by Taylor series and then fractional elements are described by the combination of some order electric field,magnetic field,and the fractional electromagnetic wave impedance.The existence of fractional order elements is proved by the fractional electromagnetic knowledge.The study of the properties of fractional order circuits is the basis for the development of fractional order circuit theory.A lot of new concepts have been generated in the classical circuit due to the fractional calculus has been introduced into the classical circuit theory.According to the related research of fractional order circuits,this paper systematically summarizes the properties of fractional order RL_?C_? circuits and presente the oscillation condition of fractional order circuits.This paper lays the foundation for the development of fractional order circuits.The research of the properties of fractional order circuits is related to simulation.The L1 interpolation approximation method is selected to establish the discrete adjoint models of fractional order elements in this paper.Based on MATLAB,a general program for analysis of fractional order circuits is written by the sparse tabular method.The correctness of these models and the program are verified by simulation.The models and the program of the fractional order circuits can be used as an auxiliary tool for the analysis of fractional order circ uits and make up for the shortcomings of the existing software which cannot simulate the fractional order circuits.