Research On Passive Synthesis Methods Of Immittance For Fractional-Order Four-Element-Kind Circuits

Fractional calculus is widely used and has now become a research hotspot.With the development of the preparation of fractional components,the theory of fractional calculus has also been widely used in the field of electrical engineering.In fact,both capacitance and inductance are of non-integer order.The introduction of fractional-order components poses a new challenge to traditional integer-order circuit synthesis theory,and it is necessary to explore the synthesis of fractional-order circuits.Exploring the passive realization conditions and passive synthesis methods of fractional-order circuits is of great significance to circuit design and device modeling.Research on the synthesis of fractional-order circuits at home and abroad is in its infancy.Due to the complexity of the fractional immittance function,it is not possible to propose a general method for synthesis of fractional circuits,and only different circuit synthesis methods can be adopted for different forms of fractional expressions.The research in this article has important reference value for discussing the passive synthesis method of general fractional impedance function in the future.This thesis mainly studies the passive synthesis method of fractional-order circuits with four-element-kind circuits.Firstly,the synthesis method of the three-variable immittance function is summarized and applied to the passive synthesis of the fractional-order circuit with four-element-kind circuits.Secondly,based on univariate spectral decomposition and bivariate spectral decomposition,two three-variable impedance functions are proposed to be realized as non-reciprocal networks by Darlington synthesis.Finally,through impedance conversion and variable substitution,the impedance function of the fractional four-element-kind circuits circuit is transformed into a three-variable reactance function,and then a passive synthesis method for the fractional four-element-kind circuits is proposed.This method is suitable for passive synthesis of any four-element-kind circuits fractional-order circuit.