分形塔分抗逼近电路——标度拓展与优化设计原理

Fractal-pyramid fractance approximation circuit—scaling extension and optimization design principle

摘要:

分析B型分形塔分抗逼近电路的特征，结合标度拓展获得具有任意实数阶微积算子的分抗逼近电路—标度分形塔分抗逼近电路，并用非正则双重标度方程进行描述. 运用典型的数值求解算法分析频域特征及运算特征，对比不同初始阻抗值对零极点分布及频域曲线的影响. 结合运算特征曲线与标度特征参量的不同取值情形，理论分析标度分形塔分抗逼近电路的优化原理并给出具体优化方法. 对比分析标度分形塔分抗优化前后的逼近性能，定量分析运算振荡现象. 介绍标度分形塔分抗的实际电路设计方案并给出实例，使用电阻电容与有源器件将该分抗的运算阶由-1<μ<0推广为0<|μ|<2. 标度分形塔分抗逼近电路及其优化电路为分抗的构造与应用提供新思路.

Abstract:

Analyze the characteristics of B-type fractal-pyramid fractance approximation circuit, which has only negative half-order operational performance. According to scalingextension theory, a fractance approximation circuit with arbitrary real-order calculus operator is obtained——a scaling fractal-pyramid fractance approximation circuit, which then can be described by anirregular double scaling equation. The operational performance and approximation performance of this fractance approximation circuit is analyzed. The typical numerical solution algorithmsare used to analyze the frequency-domain characteristics and operational characteristics, the effects of different initial impedance values on the pole-zero distributions and frequency-domain curves are compared. By combining the operational characteristic curves and thedifferent values of scalingfeature parameters, the optimization principle of the scaling fractalpyramid fractance approximation circuit is theoretically analyzed and a specific optimization method is given. The approximation performance before and after the optimization of the scaling fractal-pyramid fractance approximation circuit is comparatively analyzed, and the operational oscillation phenomenon isquantitatively analyze.The actual circuit design scheme of the scaling fractal-pyramid fractance approximation circuit is introduced and an example is given. Resistors,capacitors, and active devices are used to generalize the operational order of this fractance from-1<μ<0 to 0<|μ|<2. Scalingfractal-pyramid fractance approximation circuit and its optimized circuit provide new ideas for the construction and application of fractance.