Mechanisms of chaos generation in an atypical single-transistor oscillator
Mechanisms of chaos generation in an atypical single-transistor oscillator
复制标题
非典型单晶体管振荡器的混沌产生机制
DOI：
10.1016/j.chaos.2022.111878
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Frasca Mattia
中科院分区：
文献类型：
--
作者：
Minati Ludovico;Innocenti Giacomo;Mijatovic Gorana;Ito Hiroyuki;Frasca Mattia
本文研究了一种新的电子混沌发生器，它的基本电路拓扑结构不是由规范振荡器产生的。它包括一个双极结型晶体管、一个电阻、两个电感和一个电容。虽然其显着的生成潜力已被注意到，其运作原理至今仍不清楚。在这里，我们系统地研究它们。首先，说明了与组件值有关的可用行为的多样性。以电阻值为主要控制参数，一个周期加倍的路线混沌是显而易见的。其次，电路被视为一个弛张振荡器激励阻尼谐振器，这反过来又扰乱它通过影响其复位，并引入了一个近似，大大简化了非线性项。结果表明，混沌的出现，因为这两个方面的动态之间的相互作用，即，在参数设置之间的极端，其中一个或另一个占主导地位。第三，推导出Lur 'e形式，将电路表示为线性传递函数旁边的非线性反馈块。它的波特图进一步阐明了每个组件在形成宽带振荡动力学频谱中的作用。最后，尝试应用谐波平衡法预测系统的行为，虽然有几个因素阻碍了这一点，给出了振荡幅度，频率和失真的部分近似。除了说明这个特定的电路的动态丰富性，可能普遍有效性的几个考虑因素。
A recently-introduced autonomous electronic chaos generator which has an elementary circuit topology not intentionally derived from canonical oscillators is considered. It comprises a bipolar junction transistor, a resistor, two inductors and one capacitor. Though its notable generative potential has been remarked, its functioning principles have thus far remained unclear. Here, we investigate them systematically. First, the diversity of available behaviours in relation to the component values is illustrated. Taking the resistor value as the primary control parameter, a period-doubling route to chaos is evident. Second, the circuit is viewed as a relaxation oscillator exciting a damped resonator which in turn perturbs it via influencing its reset, and an approximation which considerably simplifies the non-linear term is introduced. It is shown that chaos arises because of the reciprocal interaction between these two aspects of the dynamics, namely, at parameter settings in between the extremes for which one or the other dominates. Third, the Lur’e form is derived, representing the circuit as a non-linear feedback block alongside a linear transfer function. Its Bode plots further clarify the role of each component in shaping the frequency spectrum of the broadband oscillatory dynamics. Finally, an attempt is made to apply the harmonic balance method towards predicting the system behavior; while several factors hinder this, partial approximations for the oscillation amplitude, frequency and distortion are given. Besides illustrating the dynamical richness characterizing this particular circuit, several considerations of possibly general validity are offered.