分数阶RL_βC_α电路特性研究

Study on Characteristics of Fractional-order RL_βC_α Circuit

为探究RLC电路在分数阶下的新特性与新规律,将分数阶电感与电容引入RLC电路。基于分数阶电容与电感定义,推导出分数阶RLC电路阻抗表达式的一般情况;给出纯虚阻抗的满足条件,分析分数阶阶次等系统参数对纯虚阻抗的影响规律;给出分数阶RLC电路短路状态的一般规律与满足条件,推导出短路频率与短路电阻的规律表达式;推导出分数阶RLC电路纯实阻抗电路状态的满足电路频率;给出分数阶RLC电路设计优化举例。研究结果表明,由于分数阶阶次引入,RLC电路设计将展现更多自由度与灵活性。

Aiming to study the new fundamentals and laws of the RLC circuit under the fractional order,fractional inductance and capacitance are introduced into RLC circuit. The general case of impedance expression of the fractional-order RLC circuit is systematically derived based on the definitions of fractional inductance and capacitance. First,the satisfaction conditions are given for pure virtual impedance to analyze influence law of system parameter such as fractional order on pure virtual impedance. Second,the general laws and satisfaction conditions of the RLC short circuit are obtained,which induces the regular expression of the short circuit frequency and short circuit resistance. The circuit frequency of pure impedance circuit state of the fractional-order RLC circuit is derived. Finally,some examples of circuit design optimization of the RLC circuit are made. The results of the research show that the designs of the RLC circuit have more freedom and flexibility owing to the introduction of the fractional orders.