基于连分式分解的1/2^n阶模拟分抗逼近电路设计

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。

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

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 fractance.The network function of the correponding analog fractance approximation circuit was obtained,and generalized to 1/2n.The circuit structure was constructed by ordinary RC component,and simulated through multisim10.It was proved that the 1/2n order analog fractance approximation circuit has good performance in both amplitude-frequency response and phase-frequency response,and it’s approximation to ideal fractance is effective.