新型任意阶分抗逼近电路及新型标度方程

New arbitrary order fractance approximation circuits and new scaling equations

摘要:

介绍并研究一类具有物理可实现性的描述分数算子有理迭代过程的非正则标度方程，提出几种新型分抗逼近电路，并用广义非正则标度方程描述。推广出基于未知参量m,n的一类非正则标度方程，并研究其描述的分数算子有理迭代过程的特性。置换已知分抗逼近电路中元件位置获得4种新的分抗逼近电路，并用相应的广义非正则标度方程描述。研究表明，广义非正则标度方程具有不同的近似解。最后，介绍广义非正则标度方程描述的阻抗函数代数迭代过程的优化方法，基于新型分抗逼近电路，提出几种具有高运算恒定性的任意阶标度分形分抗逼近电路设计方案。设计分数阶微电路仿真实验，验证新型分抗逼近电路的运算性能。

Abstract:

A kind of irregular scaling equations with physical feasibility is introduced and studied to describe the rational iterative process of fractional-order operators. Several new Frantance Approximation Circuits(FACs) are put forward and described by generalized irregular scaling equations. A class of irregular scaling equations based on the unknown parameters m,n is extended, and the characteristics of the rational iterative processes of the fractional order operators described by this type of equation are studied. Four new FACs are obtained by replacing the position of the components of the known FACs, and described by the corresponding generalized irregular scaling equations. Research shows that generalized irregular scaling equations have different approach solutions. Finally, the optimization methods for the algebraic iterative processes of impedance functions described by generalized irregular scaling equations are introduced. Based on the new FACs, several design schemes of arbitrary-order scaling fractal FACs with high operational constancy are proposed. A simulation experiment of fractional-order differential circuit is designed to verify the operational performance of the new FACs.