任意2×n阶Fan网络的电特性研究
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摘要
采用递推-变换(RT)方法研究了一类2×n阶Fan(扇形)电阻网络的电特性(包括支路电流,任意节点的电压,等效电阻),取得了理论和方法上的创新.文章以支路电流为变量应用基尔霍夫定律建立矩阵方程模型以及边界条件方程模型,通过矩阵变换研究矩阵差分方程的通解与特解,获得了任意2×n阶Fan电阻网络的支路电流公式,导出了2×n阶Fan网络任意节点的电压公式,同时获得了任意2节点间的等效电阻公式,并分析与讨论了结论的特殊情形.
We achieve the innovation in theory and method on the research of the electrical properties(including the branch current, voltage of any node, and equivalent resistance) of an arbitrary 2×n Fan resistor network by the Recursion-Transform(RT) method. In this paper, the matrix equation model and the boundary condition equation model are established by using the branch current as the variable in terms of applying Kirchhoff's law. We study the general solution and special solution of the matrix equation by the matrix transform, thus the branch currents of the 2×n Fan network are obtained, and derived the voltage formula of arbitrary node, at the same time, the equivalent resistance formula between any two nodes is obtained as well. The special situation of the conclusion is analyzed and discussed.
We achieve the innovation in theory and method on the research of the electrical properties(including the branch current, voltage of any node, and equivalent resistance) of an arbitrary 2×n Fan resistor network by the Recursion-Transform(RT) method. In this paper, the matrix equation model and the boundary condition equation model are established by using the branch current as the variable in terms of applying Kirchhoff's law. We study the general solution and special solution of the matrix equation by the matrix transform, thus the branch currents of the 2×n Fan network are obtained, and derived the voltage formula of arbitrary node, at the same time, the equivalent resistance formula between any two nodes is obtained as well. The special situation of the conclusion is analyzed and discussed.
引文
[1] 谭志中. 电阻网络模型[M]. 西安电子科技大学出版社, 2011,12: 1-236.
[2] 谭志中, 基于递推-变换方法计算圆柱面网络的等效电阻及复阻抗[J]. 物理学报, 2017, 66(7): 070501.
[3] Tan Zhi-Zhong, Fang J H. Two-point resistance of a cobweb network with a 2r boundary[J]. Communications in Theoretical Physics,2015, 63 (1): 36-44.
[4] Tan Zhi-Zhong. Two-Point Resistance of a Non-Regular Cylindrical Network with a Zero Resistor Axis and Two Arbitrary Boundaries[J]. Communications in Theoretical,Physics, 2017,67 (3): 280-288.
[5] Tan Zhi-Zhong. Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary[J]. Chinese Physics B, 2015, 24 (2): 020503.
[6] Tan Zhi-Zhong. Two-point resistance of an m×n resistor network with an arbitrary boundary and its application in RLC network[J]. Chinese Physics B, 2016, 25 (5): 050504.
[7] Tan Zhi-Zhong,Recursion-transform method and potential formulae of the m×n cobweb and fan networks[J]. Chinese Physics B. 2017, 26 (9): 090503.
[8] 彭政, 王红萍. 电渗析装置中布水槽/集水槽热效应[J]. 武汉大学学报( 理学版), 2015, 61(5): 470-476.
[9] 胡鉴耿, 金可勇, 金水玉,等. 双极膜技术在海岛反渗透海水淡化中水质调整的应用[J].水处理技术, 2014,40 (11) : 99-102.
[10] 陆建隆, 谭志中. 关于梯形网络等效电阻的普适研究[J].大学物理, 2001,20(10):26-28
[11] 李建新, 刘栓江. N级梯形电阻网络的研究[J].大学物理,2003, 22 (7):20-21
[12] 周蒨, 谭志中. n阶网络任意2节点的等效电阻公式[J]. 大学物理, 2017, 36 (3):20-24
[13] 谭志中. 内嵌交叉电阻的N阶多功能电阻网络的等效电阻研究[J]. 南通大学学报(自然科学版),2016, 15(2): 48-54.
[14] 谭志中. 多功能n阶蜂巢型电阻网络的等效电阻公式 [J]. 首都师范大学学报(自然科学版), 2016, 37(6): 29-36.
[15] 谭志中, 陆建隆, 吴国祥, 三端梯形网络等效电阻的普适研究[J]. 河北师范大学学报(自然科学版)2004,28(3):258-262
[16] 曹秀华, 谭志中, 李颂. 构建等效模型研究2×N阶网络的等效电阻[J].大学物理, 2008, 27 (3): 25-29.
[17] 刘松山.基于对称性研究 2×n 阶梯形电阻网络等效电阻[J].大学物理,2015,34 (1): 26-29.
[18] 谭志中, 罗礼进.2×n阶网络等效电阻的再研究[J].南通大学学报(自然科学版), 2010,9(1):86-89.
[19] 李颂, 谭志中, 曹秀华. 2×n阶网络侧端等效电阻的另一个公式[J].物理与工程, 2007. 17(4):36-39.
[20] 谭志中, 罗礼进.加强型2×n阶电阻网络的两个普适公式[J].杭州师大学报(自然科学版), 2010,9(1):37-42.
[21] 李建新, 李保刚.2×n阶梯形电阻网络等效电阻研究[J].大学物理, 2012,31 (6): 21-24.
[22] 谭志中, 方靖淮. 2×n阶LC蛛网网络的等效复阻抗研究[J]. 南通大学学报(自然科学版), 2016, 15(1): 49-57.
[23] 谭志中,吴鹏,罗小廉,孔泽霖. 一类任意n阶Fan 网络的电特性研究[J]. 大学物理, 2018, 37(8):24-28.
[2] 谭志中, 基于递推-变换方法计算圆柱面网络的等效电阻及复阻抗[J]. 物理学报, 2017, 66(7): 070501.
[3] Tan Zhi-Zhong, Fang J H. Two-point resistance of a cobweb network with a 2r boundary[J]. Communications in Theoretical Physics,2015, 63 (1): 36-44.
[4] Tan Zhi-Zhong. Two-Point Resistance of a Non-Regular Cylindrical Network with a Zero Resistor Axis and Two Arbitrary Boundaries[J]. Communications in Theoretical,Physics, 2017,67 (3): 280-288.
[5] Tan Zhi-Zhong. Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary[J]. Chinese Physics B, 2015, 24 (2): 020503.
[6] Tan Zhi-Zhong. Two-point resistance of an m×n resistor network with an arbitrary boundary and its application in RLC network[J]. Chinese Physics B, 2016, 25 (5): 050504.
[7] Tan Zhi-Zhong,Recursion-transform method and potential formulae of the m×n cobweb and fan networks[J]. Chinese Physics B. 2017, 26 (9): 090503.
[8] 彭政, 王红萍. 电渗析装置中布水槽/集水槽热效应[J]. 武汉大学学报( 理学版), 2015, 61(5): 470-476.
[9] 胡鉴耿, 金可勇, 金水玉,等. 双极膜技术在海岛反渗透海水淡化中水质调整的应用[J].水处理技术, 2014,40 (11) : 99-102.
[10] 陆建隆, 谭志中. 关于梯形网络等效电阻的普适研究[J].大学物理, 2001,20(10):26-28
[11] 李建新, 刘栓江. N级梯形电阻网络的研究[J].大学物理,2003, 22 (7):20-21
[12] 周蒨, 谭志中. n阶网络任意2节点的等效电阻公式[J]. 大学物理, 2017, 36 (3):20-24
[13] 谭志中. 内嵌交叉电阻的N阶多功能电阻网络的等效电阻研究[J]. 南通大学学报(自然科学版),2016, 15(2): 48-54.
[14] 谭志中. 多功能n阶蜂巢型电阻网络的等效电阻公式 [J]. 首都师范大学学报(自然科学版), 2016, 37(6): 29-36.
[15] 谭志中, 陆建隆, 吴国祥, 三端梯形网络等效电阻的普适研究[J]. 河北师范大学学报(自然科学版)2004,28(3):258-262
[16] 曹秀华, 谭志中, 李颂. 构建等效模型研究2×N阶网络的等效电阻[J].大学物理, 2008, 27 (3): 25-29.
[17] 刘松山.基于对称性研究 2×n 阶梯形电阻网络等效电阻[J].大学物理,2015,34 (1): 26-29.
[18] 谭志中, 罗礼进.2×n阶网络等效电阻的再研究[J].南通大学学报(自然科学版), 2010,9(1):86-89.
[19] 李颂, 谭志中, 曹秀华. 2×n阶网络侧端等效电阻的另一个公式[J].物理与工程, 2007. 17(4):36-39.
[20] 谭志中, 罗礼进.加强型2×n阶电阻网络的两个普适公式[J].杭州师大学报(自然科学版), 2010,9(1):37-42.
[21] 李建新, 李保刚.2×n阶梯形电阻网络等效电阻研究[J].大学物理, 2012,31 (6): 21-24.
[22] 谭志中, 方靖淮. 2×n阶LC蛛网网络的等效复阻抗研究[J]. 南通大学学报(自然科学版), 2016, 15(1): 49-57.
[23] 谭志中,吴鹏,罗小廉,孔泽霖. 一类任意n阶Fan 网络的电特性研究[J]. 大学物理, 2018, 37(8):24-28.