基于连分式分解的1/2~n阶模拟分抗逼近电路设计

Design of 1/2n Order Analog Fractance Approximation Circuit Based on Continued Fractions Decomposition

应用连分式理论设计1/2n阶模拟分抗逼近电路。基于分数阶微积分理论,推导理想模拟分抗的网络函数。对1/2阶理想分抗的网络函数进行连分式分解,得到相应模拟分抗逼近电路的网络函数,并将其推广到1/2n阶。采用无源RC器件设计电路的具体结构,并通过multisim10仿真。实验结果证明,由连分式分解理论设计的1/2n阶分抗逼近电路具有良好的幅频响应和相频响应,能有效地逼近理想分抗。

Continued fraction theory was applied to design the 1/2n order analog fractance approximation circuit. Based on the fractional calculus theory, the network function of ideal fractance was derived. Continued fraction decomposition was applied to the network function of 1/2 order ideal fractanee. The network function of the correponding analog fractanee approximation circuit was obtained, and generalized to 1/2n. The circuit structure was constructed by ordinary RC component, and simulated through muhisim10. It was proved that the 1/2n order analog fraetance approximation circuit has good performance in both amplitude-frequency response and phase-frequency response, and it＇ s approximation to ideal fractance is effective.