分形分抗逼近电路零极点的数值求解与验证

Numerical solution and verification of zero-pole for some fractal fractance approximation circuits

摘要:

随着分抗逼近电路理论的高速发展，如何求解分抗电路的零极点是研究的重点问题之一。利用常规友矩阵求解分抗逼近电路的零极点，出现虚根而得不到正确的解。为了解决这个问题，基于分抗逼近电路的迭代电路和迭代矩阵，利用矩阵实验室(MATLAB)中的"solve"和"roots"函数实现分抗逼近电路归一化零极点的数值求解，并比较两者的精确度和运算速度。对求得的解进行直接验证和间接验证。仿真结果表明，该方法实现了分抗逼近电路零极点的准确求解，对于分抗逼近电路的分析具有指导性意义。

Abstract:

With the development of the theory of fractance approximation circuits，one of the hot topics is how to solve the zero-pole of the circuits. The precise solution cannot be obtained by companion matrix. To solve the problem, based on the iterative circuit and iterative matrix，numerical solution of normalized zero-pole of fractance approximation circuit is achieved by two functions，“solve”and “roots”，in Matrix Laboratory(MATLAB). The accuracy and speed of these two operations are compared. Then the zero-pole is verified by direct ways and indirect ways. The simulation results indicate that the accurate solution is obtained. The solution of zero-pole shows a guiding significance on analyzing the fractance approximation circuits.