The passive synthesis method of circuits has important applications to the modeling of electrical equipment. Aiming at the passive synthesis problem of RLαCβ fractional-order component circuits, the article introduces its multivariable domain synthesis method. Through variable substitution, the frequency domain circuit driving point impedance function is transformed into the multivariable domain; the Foster synthesis method and Cauer synthesis method of the multivariable domain are further deduced, and the circuit model corresponding to the synthesis method is given. Finally, the feasibility of the comprehensive method theory proposed in the article is verified through simulation and analysis of examples. The proposed synthesis method overcomes the shortcomings of the previous synthesis method using multi-port transformers, and has important application value for fractional-order circuit modeling of electrical equipment.
