分数阶双二次型导抗函数的无源综合

Passive Synthesis of Fractional Biquadratic Immittance Function

无源网络综合一直是备受关注的研究课题,近几年,随着分数阶微积分的广泛应用,人们开始研究含有分数阶阶次的策动点函数综合。基于三口纯电阻网络与两个分数阶储能元件的连接,提出了分数阶双二次型导抗函数最少储能元件无源综合方法。推导了其实现的充分必要条件。此外,对于无法用电阻矩阵表示三口电阻网络的情况,通过相应的串并联电路得到其实现条件及对应元件值。当两个分数阶阶次均为1时,所提方法可退化为传统双二次型导抗函数综合,因而具有更广的应用范围,最后,通过数值例子验证了所提方法的准确性。

Passive network synthesis is a research topic which has been a focus one. In recent years,with the wide application of fractional calculus,researchers began to study and analyze the driving-point function synthesis containing fractional order. The passive synthesis method which contains minimal energy storage element for fractional biquadratic immittance function is proposed based on the connection of three-port pure resistive network and two fractional order storage elements. The necessary and sufficient conditions for the realization of the proposed method are deduced. In addition,if the three-port pure resistive network cannot be represented by resistance matrix,the realization condition and corresponding component values can be obtained by relevant series-parallel circuit. When the both orders are equal to1,the proposed method degenerates into traditional biquadratic immittance function synthesis,which indicates it has wider application. At last,the proposed method is verified by numerical examples.