Analysis and Passive Synthesis of Immittance for Fractional-Order Two-Element-Kind Circuit

Fractional circuits have attracted an extensive attention of scholars and researchers for their superior performance and potential applications. The passive realization of the fractional-order immittance function plays an important role in fractional circuits theory, which is useful in fractional circuits design and modeling. This paper deals with the analysis and passive synthesis of fractional two-element-kind network. Firstly, the time-domain response of fractional two-element-kind network is analyzed based on its immittance function expressions, and the response shows oscillation only in fractional $$ L_{\beta } C_{\alpha } $$LβCα circuits. Then, necessary and sufficient conditions to realize the fractional-order immittance functions by a passive network with only two kinds of elements are obtained in view of impedance scaling. A procedure is also proposed to realize such immittance functions using two-element-kind network. Finally, three examples are given to illustrate the proposed method.

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