分数阶LC电路特性探索及应用

Characteristics and Applications of Fractional LC Circuits

研究分数阶串并联LC电路及分数阶LC传输线与传统RC、RL串并联电路及对应传输线之间的联系。基于拉普拉斯变换,给出了分数阶LC串联和并联电路方程的解析解形式;分析了分数阶电容与分数阶电感阶次和为1时分数阶LC电路与传统RC电路的异同;最后提出了分数阶LC电路可能的应用。研究表明传统RC电路仅为分数阶LC电路中极特殊的情形。分数阶电路的应用能够为用户提供更多的设计自由度和选择空间,满足不同场合的不同需求。

The relationship between fractional series/parallel LC circuits with traditional series/parallel RC and RL circuits is explored. At first,the solution of fractional series/parallel LC circuits are obtained by using the Laplace transform technology,then the similarities and differences between fractional LC circuits and traditional RC/LC circuits are emphasized under conditions that the sum of the orders of fractional inductor and capacitor is equal 1. The study shows that fractional LC circuits can provide more design freedoms and more circuits performances to satisfy different demands of users.