标度分形分抗逼近电路的零极点分布规律
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摘要
针对标度分形分抗逼近电路的结构特点与数学特征,求解并整理了典型标度分形分抗逼近电路对应的非正则标度方程,利用传输矩阵算法并借助矩阵实验室(Matlab)精确求解其零极点的值,发现并验证了零极点的值在电路节数中间段具有线性的分布规律,列出并整理零极点线性分布公式.求解并整理了典型分形分抗逼近电路对应的非正则标度方程.
For the structural and mathematical features of some scaling fractal fractance approximation circuits,the irregular scaling equations of the typical scaling circuits have been solved and trimmed. Accurate zero-pole values are computed by using the transmission matrix algorithm and the matrix labority. It is found and verified the linear distribution rule for the zer-pole value which locates in the middle of the circuit section. Not only the linear distribution formula of zeros and poles are given, but also the irregular scaling equations corresponding to the typical scaling fractal fractance approximation circuits have been solved and sorted.
For the structural and mathematical features of some scaling fractal fractance approximation circuits,the irregular scaling equations of the typical scaling circuits have been solved and trimmed. Accurate zero-pole values are computed by using the transmission matrix algorithm and the matrix labority. It is found and verified the linear distribution rule for the zer-pole value which locates in the middle of the circuit section. Not only the linear distribution formula of zeros and poles are given, but also the irregular scaling equations corresponding to the typical scaling fractal fractance approximation circuits have been solved and sorted.
引文
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[25] Kaplan T, Gray L J. Effect of disorder on a fractal model for the ac response of a rough interface [J]. Phys Rev B, 1985, 55: 529.
[2] Pu Y F, Yuan X, Yu B. Analog circuit implementation of fractional-order memristor:Arbitrary-order Lattice Scaling fracmemristor [J]. IEEE Trans CASI, 2018, 65: 2903.
[3] Morrison R. RC constant-argument driving-point admit tances [J].IEEE Trans Circuit Theory, 1959, 9: 310.
[4] Hill R M, Dissado L A, Nigmatullin R R. Invariant behavior classes for the response of simple fractal circuits [J].J Phys Condens Matter, 1991, 3: 9773.
[5] Carlson G E. Simulation of the fractional derivative operator[square root of] s and the fractional integral operator 1 [divided by the square root of] s[D].Manhattan: KansasState University, 1960.
[6] 袁晓.分抗逼近电路之数学原理 [M]. 北京: 科学出版社, 2015.
[7] Oldham K B. Semiintegral electroanalysis Analog implementation [J]. Anal Chem, 1973, 45: 39.
[8] Grenness M,Oldham K B. Semiintegral electronalaysis theory and verification [J]. Anal Chem, 1972, 44: 1121.
[9] Goto M, Oldham K B. Semiintegral electroanalysis. Shapes of neopolarograms [J]. Anal Chem, 1973, 45: 2043.
[10] Oldham K B, Zoski C G. Analogue instrumentation for processing polarographic data [J]. J Electronanal Chem, 1983, 157: 27.
[11] 袁子, 袁晓. 规则RC分形分抗逼近电路的零极点分布 [J]. 电子学报, 2017, 45: 2511.
[12] 余波, 何秋燕, 袁晓, 等. 分抗的F特征逼近性能分析原理与应用 [J]. 四川大学学报:自然科学版, 2018, 55: 301.
[13] 袁晓, 冯国英. 粗糙界面电极的电路建模与Liu-Kaplan标度方程 [C]. 2015年中国电子学会电路与系统分会第二十六届学术年会论文集. 长沙: 中国电子学会, 2015.
[14] 袁晓, 冯国英. Oldham分形链分抗类与新型Liu-Kaplan标度方程 [C]. 2015年中国电子学会电路与系统分会第二十六届学术年会论文集. 长沙: 中国电子学会, 2015.
[15] 何秋燕, 袁晓. Carlson迭代与任意分数微积分算子的有理逼近 [J]. 物理学报, 2016, 65: 25.
[16] He Q Y, Yu B,Yuan X. Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order [J]. Chin Phys B, 2017, 26: 040202.
[17] Roy S D,Shnoi B A. Distributed and lumped RC realization of a constant argument impedence [J]. J Franklin Inst, 1966, 282: 318.
[18] Dutta R S C. On the realization of a constant-argument immittance of fracrionaloperator [J]. IEEE Trans Circuit Theory, 1967, 14: 264.
[19] Roy S D. Constant argument immittance realization by a distributed RC network [J]. IEEE Trans CAS, 1974, 21: 655.
[20] Liu S H. Fractal aspects of the ac response of rough interface [J].Phys Rev Lett, 1985, 55: 529.
[21] 余波, 何秋燕, 袁晓. 任意阶标度分形格分抗与非正则格型标度方程 [J]. 物理学报, 2018, 67: 070202.
[22] 易舟, 袁晓, 陶磊, 等. Oldham RC链分抗逼近电路零极点精确求解 [J].四川大学学报:自然科学版, 2015, 52: 1255.
[23] 易舟, 袁晓. 分形分抗逼近电路零极点的数值求解与验证 [J]. 太赫兹科学与电子信息学报, 2017, 15: 98.
[24] 何秋燕. 标度分型格分抗 [D]. 成都: 四川大学, 2017.
[25] Kaplan T, Gray L J. Effect of disorder on a fractal model for the ac response of a rough interface [J]. Phys Rev B, 1985, 55: 529.