任意阶高运算恒定性分抗逼近电路--标度格型级联双口网络  

Arbitrary-order high-operation constant fractance approximation circuit--lattice cascaded two-port network

作　　者：张月荣 袁晓[1] Zhang Yue-Rong;Yuan Xiao(College of Electronics and Information Engineering,Sichuan University,Chengdu 610065,China)

机构地区：[1]四川大学电子信息学院,成都610065

出　　处：《物理学报》2021年第4期349-359,共11页Acta Physica Sinica

摘　　要：标度拓展经典负半阶分抗逼近电路,可实现具有任意分数阶微积算子运算功能的分抗逼近电路,但牺牲了运算恒定性.从电路网络的角度分析具有恒定运算性能的负半阶Carlson分形格分抗逼近电路.根据标度分形格分抗逼近电路的等效无源双口网络,探讨该双口网络右侧端口的运算有效性,设计具有高运算恒定性的任意阶标度分形格分抗逼近电路.结合负实零极点对基元系统的零极点分布及其局域化特性,阐述具有任意实数阶微积算子运算功能的标度分形格分抗逼近电路运算振荡现象的物理本质,并从理论上分析有效抑制频域运算振荡现象的方法.结合对称阻容T型节电路优化理论及方法,对任意阶对称格型级联双口网络的频域逼近性能进行优化,获得具有高逼近效益的任意阶标度分形格分抗逼近电路.具有低振荡幅度的任意阶对称格型级联双口网络为高运算恒定性的分抗逼近电路设计及应用提供了一种新方法及思路.Fractional calculus is widely used in the analysis and description of various nonlinear and non-integer dimensional physical phenomena and processes in nature,and it gradually becomes a research hotspot.The order value of fractional-order system is more flexible,and fractional-order system is more accurate for analysis of non-integer dimensional physical phenomena and processes.In recent years,various negative half-order fractance approximation circuits and rational approximation algorithms for negative half-order fractional operators have been proposed and aroused people's research interest.The scaling extension of classic negative half-order fractance approximation circuits can facilitate the design of fractance approximation circuits with arbitrary-order fractional operators,but the operational constancy is sacrificed.The typical arbitrary-order fractance approximation circuits have operational oscillating phenomena in frequency domain,both the orderfrequency characteristic curves and the phase-frequency characteristic curves have obvious oscillating waveforms.The operational oscillating phenomena will inevitably affect the fractional operator operational performance of the fractance approximation circuits,and result in errors in physical application.In this paper,the negative half-order Carlson fractal-lattice fractance approximation circuit with constant operational performance is analyzed from perspective of circuit network,the symmetry for equivalent two-port network of Carlson fractal-lattice fractance approximate circuit is analyzed.The equivalent two-port network of scaling fractal-lattice fractance approximation circuit is explored,Operational validity for the right port of scaling lattice cascaded two-port network is studied.A symmetrical lattice cascaded passive two-port network after scaling extension is designed through cascade of the ports on both sides of two-port network,and an arbitraryorder scaling fractal-lattice fractance approximation circuit with high-operation constancy is designed.By stu

关 键 词：分数微积分 标度拓展 分数阶元件 运算恒定性 

分 类 号：TN710[电子电信—电路与系统]