Passive Synthesis of Immittance for Fractional-Order Three-Element-Kind Circuit

As an interdisciplinary research area, fractional circuits and systems have attracted extensive attention of scholars and researchers for their superior performance and potential applications. The passive realization of the fractional-order (FO) immittance function plays an important role in fractional circuits' theory, which is useful in fractional circuit design and modeling. This paper deals with the passive synthesis of FO three-element-kind circuits. First, the method is given for judging the immittance functions of FO three-element-kind circuits. Then, by making use of impedance scaling and variable substitution, the synthesis method of such an FO immittance function is proposed, which is based on the bivariate reactance synthesis method. Finally, a procedure is proposed to realize such immittance functions using the three-element-kind circuit. And several examples are given to illustrate the proposed method.