In this work, a new fractional-order sinusoidal oscillator is proposed. The proposed oscillator consists of one fractional-order all-pass filter and one fractional-order lossless integrator blocks. In order to emulate fractional-order capacitors, three different approximation methods the R – C pair, Matsuda and Oustaloup are employed and the results are compared. Three sinusoidal voltage signals with different phases that are controlled by fractional orders are provided by the proposed oscillator topology that is not possible for the classical integer-order case. Grounded passive components are used in the introduced oscillator circuit. Additionally, the output voltage signals are available at the low impedance terminal W of AD844ANs. Moreover, the time constant of the fractional-order all-pass filter can be adjusted accurately by means of second resistor R _x in the all-pass filter section. In addition to the simulation results, the proposed fractional oscillator is also implemented to verify the oscillator circuit experimentally. For the case of fractional orders α = 1 and β = 0.5, the measurement results are 10.3 kHz, 43.22° and 67.99°, respectively, while the desired values are 10 kHz, 45° and 67.36°, respectively.

中文翻译：

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分数阶正弦振荡器的设计与实现

在这项工作中，提出了一种新的分数阶正弦振荡器。所提出的振荡器由一个分数阶全通滤波器和一个分数阶无损积分器模块组成。为了模拟分数阶电容器，可以采用三种不同的近似方法[R – C对，采用松田和Oustaloup进行比较。所提出的振荡器拓扑提供了由分数阶控制的具有不同相位的三个正弦电压信号，这对于经典整数阶情况是不可能的。引入的振荡器电路中使用了接地的无源元件。此外，输出电压信号在低阻抗端子上可用w ^AD844AN的数量。此外，可以通过第二电阻器精确调整分数阶全通滤波器的时间常数[R _x在全通滤波器部分。除仿真结果外，所提出的分数振荡器还用于实现实验电路的验证。对于小数订单α = 1并且 β = 0.5时，测量结果分别为10.3 kHz，43.22°和67.99°，而所需值分别为10 kHz，45°和67.36°。