规则RC分形分抗逼近电路的零极点分布

从电路结构特性与数学表示特征两方面,考察与探讨经典的规则RC分形分抗逼近电路的阻抗函数之零极点解析求解与数值求解理论与方法.首先简要介绍经典分形分抗逼近电路并引入迭代电路、迭代函数、迭代矩阵等新概念.通过特征值分解或Hamilton-Cayley展开,求出迭代矩阵幂而获得某些经典(比如Oldham分形链、Carlson分形格、B型、2h型等)分形分抗的阻抗函数之简洁数学解析表达式.最后给出分抗逼近电路零极点的解析求解法与有效数值求解法及其解结果并进行理论与实践验证.     

一种可变阶次模拟分抗电路的实现方案

在分数阶微积分的工程应用中,一个最重要的步骤是模拟分抗电路的实现,为此采用跨导运算放大器设计了可变阶次分抗电路,并利用有限数量的二端口网络级连,能够在电路设计形式固定的情况下,通过调节跨导运算放大器的控制电流,在一定的范围内改变分抗的运算阶数。模拟结果与理论分析结果相一致,证明该设计方案对于分数阶微积分的实际应用有着一定的工程意义。     

RC models of a constant phase element

The paper describes models of a constant‐phase element consisting of passive R and C components. The models offer any input impedance argument (phase) between ?90° and 0° over a selectable frequency band covering several decades. The design procedure makes it possible to choose values of average phase, phase ripple, frequency bandwidth, and total number of R and C elements. The model can cover three frequency decades with as few as five resistors and five capacitors. The models can be used for practical realization of fractional analog differentiators and integrators, fractional oscillators, chaotic networks or for analog simulation of fractional control systems. Copyright © 2011 John Wiley & Sons, Ltd.     

可变阶次的分抗元件的电路实现

分数阶微积分运算是整数阶微积分运算概念的延伸,它们是分析和处理许多＂非＂问题和现象的有用工具,为了分析和处理许多＂非＂问题和现象,采用有限的惯性和比例微分电路的级联实现分数阶算子（Sv）,并利用Pspice软件对所设计的电路做仿真验证,仿真结果与理论结果（Matlab仿真结果）基本一致,分数阶算子（Sv）的电路实现将为分数阶微积分的工程应用铺平道路。     

Arbitrary-Order Fractance Approximation Circuits With High Order-Stability Characteristic and Wider Approximation Frequency Bandwidth

This paper discusses a novel rational approximation algorithm of arbitrary-order fractances, which has high order-stability characteristic and wider approximation frequency bandwidth. The fractor has been exploited extensively in various scientific domains. The well-known shortcoming of the existing fractance approximation circuits, such as the oscillation phenomena, is still in great need of special research attention. Motivated by this need, a novel algorithm with high order-stability characteristic and wider approximation frequency bandwidth is introduced. In order to better understand the iterating process, the approximation principle of this algorithm is investigated at first. Next, features of the iterating function and frequency-domain characteristics of the impedance function calculated by this algorithm are researched, respectively. Furthermore, approximation performance comparisons have been made between the corresponding circuit and other types of fractance approximation circuits. Finally, a fractance approximation circuit with the impedance function of negative 2/3-order is designed. The high order-stability characteristic and wider approximation frequency bandwidth are fundamental important advantages, which make our proposed algorithm competitive in practical applications.      

1/2阶分数演算的模拟OTA电路实现

为了更有效地进行分抗的电路设计,对信号处理中分数演算的模拟电路实现进行了探讨,给出了分数演算的模拟电路无源实现和有源电路实现方案;推导出求解分抗阻抗的精确递推公式.无源电路中给出了分数阶低通和高通滤波器方案,有源电路采用高带宽电流型跨导运算放大器（OTA）进行设计,满足高频信号分数阶运算的要求;同时进行了理论计算和电路模拟性能分析,分析结果表明两种实现方案均能很好地完成信号的分数演算功能,对于分数演算的理论研究与工程实践有着实际意义.     

现代信号分析与处理中分数阶微积分的五种数值实现算法

研究目的是在计算机上数值实现信号的分数阶微积分。首先,分析比较分数阶微积分常用的3种时域定义,以及其在傅立叶变换域和子波变换域中的两种频域定义;然后,推导比较信号分数阶微分的幂级数数值算法、傅里叶级数数值算法、基于Grümwald-Letnikov定义的数值算法之间的优劣;进而,推导具有较高精度和计算速度的基于子波变换的分数阶微积分快速数值算法;最后,以计算精度为代价进一步提高计算速度,推导基于子波变换和连续内插的快速工程算法。理论推导和实验结果均证明基于子波变换的数值算法具有较高精度和运算速度,其改进的快速工程算法运算速度最高,但精度下降。这两种算法都具有较强的实用价值。