分数阶T型L_αC_β电路仿真研究

Numerical Simulation of a T-Shaped Fractional L_αC_β Circuit

为了研究分数阶元器件的引入对电路基本特性的影响,选择典型的T型LC电路为研究对象,将其拓展到分数阶领域.通过计算机数值模拟方法,系统地研究了电路参数L,C,特别是新参数分数阶阶次α和β对分数阶T型LαCβ电路的基本特性——阻抗和相位的影响规律.进一步地引入了灵敏度分析的概念,分析了分数阶阶次α和β对阻抗和相位极值的影响.丰富的数值模拟结果不仅形象地展示了分数阶T型LαCβ电路的阻抗和相位随各参数的变化规律,还充分证明了分数阶阶次α和β的引入,极大地增强了电路设计的灵活性和选择性.

In order to study the effect of fractional order components on the characteristics of the basic cir‐cuit ,we focus on a typical T‐shaped fractional LαCβcircuit .With computer numerical simulation we make a systematic study of the influences of circuit parameters L and C ,especially of the new parameter frac‐tional orders αandβ,on impedance and phase ,w hich are basic properties of the T‐shaped fractional LαCβcircuit .Moreover ,we introduce the concept of “sensitivity analysis” to study the influence of the parame‐ter fractional ordersαandβon the maximum and minimum of the impedance and phase .The results of lots of numerical simulations are presented to illustrate how the impedance and phase of the T‐shaped LαCβcir‐cuit change with the changes of various parameters and prove that the introduction of fractional orders αand βgreatly increases the elasticity and selectivity in circuit design .