The passive synthesis of the fractional-order driving-point immittance functions is of great significance for the modeling and design of fractional-order circuits. This paper studies the synthesis of a class of two-element-order fractional immittance functions based on variable substitution. First, the method of realizing the two-variable immittance functions corresponding to this kind of two-element-order fractional immittance functions is established; second, we perform the inverse substitution of variables to realize the two-element-order fractional immittance network; finally, the synthesis program of this kind of two-element-order fractional immittance functions is proposed, and specific examples are given for simulation verification. This synthesis method overcomes the disadvantages of using a multi-port transformer, and is more conducive to network analysis.

中文翻译：

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一类二元阶分数导抗函数的级联合成

分数阶驱动点导抗函数的无源综合对于分数阶电路的建模和设计具有重要意义。本文研究了基于变量代换的一类二元阶分数导抗函数的合成。首先，建立了这种二元阶分数导纳函数对应的二元导​​纳函数的实现方法；其次，我们进行变量的逆代换，实现了二元阶分数导抗网络；最后，提出了这种二元阶分数导抗函数的综合程序，并给出了具体实例进行仿真验证。这种合成方法克服了使用多端口变压器的缺点，