Fractional-order oscillators
Fractional-order oscillators
复制标题
分数阶振荡器
DOI：
10.1049/pbcs032e_ch3
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
A. Elwakil
中科院分区：
文献类型：
--
作者：
A. Radwan;B. Maundy;A. Elwakil
分数阶微积分是研究非整数阶微分和积分的数学分支。分数阶微积分最近发现了它的工程应用，特别是电子电路与有前途的结果表明，在硅上制造分数阶电容器的可行性。分数阶电容器是一种有损耗的非理想电容器，其阻抗由Zc =（1/jωC）α给出，其中C是伪电容，α是伪电容的阶数（0 < α ≤ 1）。当这些分数阶电容器在振荡器（正弦或弛豫）电路中使用时，该振荡器被称为分数阶振荡器，并由非整数阶微分方程描述。因此，可以获得1.5阶或2.6阶的振荡器。虽然整数阶振荡器的振荡频率与其RC时间常数有关，但分数阶振荡器的振荡频率也与α有关。这增加了更多的设计自由度，即使在大RC时间常数的情况下也能实现极高或极低的振荡频率。本章旨在回顾分数阶振荡器的设计理论，并给出几个设计实例。实验结果也显示。
Fractional-order calculus is the branch of mathematics which deals with non-integerorder differentiation and integration. Fractional calculus has recently found its way to engineering applications; particularly electronic circuits with promising results showing the feasibility of fabricating fractional-order capacitors on silicon. Fractionalorder capacitors are lossy non-deal capacitors with an impedance given by Zc = (1/jωC)α, where C is the pseudo-capacitance and α is its order (0 < α ≤ 1). When these fractional-order capacitors are employed within an oscillator (sinusoidal or relaxation) circuit, this oscillator is called a fractional-order oscillator and is described by non-integer-order differential equations. Therefore, an oscillator of order 1.5 or 2.6 is possible to obtain. While the oscillation frequency in integer-order oscillators is related to their RC time constants, fractional-order oscillators have their oscillation frequencies also related to α. This adds more design freedom and enables extremely high or extremely low oscillation frequencies even with large RC time constants. This chapter aims at reviewing the theory of designing fractional-order oscillators accompanied by several design examples. Experimental results are also shown.