Semary Mourad S, Fouda Mohammed E, Hassan Hany N, Radwan Ahmed G
Department of Basic Engineering Sciences, Faculty of Engineering, Benha University, Benha 13518, Egypt.
Engineering Mathematics and Physics Dept., Cairo University, Giza 12613, Egypt.
J Adv Res. 2019 Feb 21;18:147-159. doi: 10.1016/j.jare.2019.02.004. eCollection 2019 Jul.
In this paper, a new realization of the fractional capacitor (FC) using passive symmetric networks is proposed. A general analysis of the symmetric network that is independent of the internal impedance composition is introduced. Three different internal impedances are utilized in the network to realize the required response of the FC. These three cases are based on either a series RC circuit, integer Cole-impedance circuit, or both. The network size and the values of the passive elements are optimized using the minimax and least optimization techniques. The proposed realizations are compared with well-known realizations achieving a reasonable performance with a phase error of approximately . Since the target of this emulator circuit is the use of off-the-shelf components, Monte Carlo simulations with tolerance in the utilized elements are presented. In addition, experimental measurements of the proposed capacitors are preformed, therein showing comparable results with the simulations. The proposed realizations can be used to emulate the FC for experimental verifications of new fractional-order circuits and systems. The functionality of the proposed realizations is verified using two oscillator examples: a fractional-order Wien oscillator and a relaxation oscillator.
本文提出了一种利用无源对称网络实现分数阶电容器（FC）的新方法。介绍了一种与内部阻抗组成无关的对称网络的通用分析方法。网络中使用了三种不同的内部阻抗来实现FC所需的响应。这三种情况分别基于串联RC电路、整数阶科尔阻抗电路或两者兼而有之。使用极小极大和最小二乘法优化技术对网络规模和无源元件的值进行了优化。将所提出的实现方法与具有合理性能且相位误差约为……的知名实现方法进行了比较。由于该仿真器电路的目标是使用现成的元件，因此给出了对所使用元件具有……容差的蒙特卡罗模拟。此外，还对所提出的电容器进行了实验测量，结果表明与模拟结果具有可比性。所提出的实现方法可用于模拟FC，以对新的分数阶电路和系统进行实验验证。利用两个振荡器示例：分数阶维恩振荡器和张弛振荡器，验证了所提出实现方法的功能。
