整数阶电路定理到分数阶电路推广及分析

Generalization and Analysis of the Theorem of Integer-order Circuits to Fractional-order Circuits

近几十年来,对分数阶电路的研究逐渐深入,但对其中电路定理的分析较少,因此针对分数阶电路需要进一步探究其规律,将一些经典的电路定理推广到分数阶电路中,使得在以后的分析过程中能直接使用。在整数阶电路定理的基础上,运用基尔霍夫定律在分数阶电路中证明了叠加定理、替代定理、等效电源定理和互易定理,并进行了应用分析。

In recent decades,the research on fractional-order circuits has been gradually deepened,but there are few analysis of circuit theorems among them.Therefore,it is necessary to further explore its laws for fractional-order circuits,and extend some classic circuit theorems to fractional-order circuits,so that they can be directly used in the subsequent analyses process.Based on integer-order circuit theorems,this paper uses Kirchhoff′s law to prove the superposition theorem,substitution theorem,equivalent power theorem and reciprocity theorem in the fractional-order circuit,and conducts application analysis.