二项展开法实现分数阶模拟分抗电路

提出一种通过二项展开式设计任意阶模拟分抗电路的新方法.首先讨论了二项式的收敛条件,并结合收敛域的计算公式,明确指出使用二项展开法所得到的分抗电路的逼近带范围.然后利用电路元件进行电路综合,从而实现能够完成分数阶运算的模拟电路.最后对该电路进行仿真,证明了二项展开法在实际应用中的有效性,对于模拟分抗电路的设计和分数演算的理论研究具有十分重要的意义.

Implementation of fractional-order analog fractance circuit using binomial expansion

A new method in design of arbitrary order analog fractance circuit based on binomial expansion is presented. Firstly, convergence condition of a binomial is discussed, and along with the calculating formula of region of convergence, the matching band of fractance circuit attained by binomial expansion method is indicated definitely. Secondly, circuit elements were used in circuit synthesis, so analog circuit that is capable of realizing fractional order calculus is implemented. Lastly, simulation was carried out, the results verified the efficiency of binomial expansion method in practical applications, therefore it is of great importance in design of analog fractance circuit and theoretical research of fractional calculus.