内接一任意负载的n阶T形网络的电特性
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摘要
研究复杂电阻网络的电特性一直是一个比较困难的问题,本文采用电压参数建立递推模型的方法研究了一类复杂的n阶T形网络的电特性(节点电压,支路电流,等效电阻),该网络不仅有一个负载内接在任意节点上而且该网络含有一个任意右边界电阻.文章首先采用网络分析建立关于电压的差分方程模型,然后根据约束条件建立边界条件方程模型,由此导出差分方程程的通解与特解,进而得到任意节点的电压公式以及支路电流和等效电阻.文章所得公式具有多功能和普适性,包含了多种特殊情形的结果.
The electrical characteristics of complex resistor networks are always sophisticated theses to deal with.Using the voltage parameter to construct a recursion model,this paper studies electrical characteristics,including the node voltage,branch current and equivalent resistor etc.,a type of the complex n-order ladder shaped resistor network,which has an external load on an arbitrary node and a random resistor on the right boundary.By means of the network analysis,this paper establishes the difference equation model of the voltage,and the equation model of the boundary compatible with the constraint conditions.After then,explicit expressions of the common solution and the particular solution are derived,from which the formulae of voltages of arbitrary nodes,branch currents,and the equivalent resistors are also obtained.All the formulae obtained here have multi-functions and universality,and many special cases.
The electrical characteristics of complex resistor networks are always sophisticated theses to deal with.Using the voltage parameter to construct a recursion model,this paper studies electrical characteristics,including the node voltage,branch current and equivalent resistor etc.,a type of the complex n-order ladder shaped resistor network,which has an external load on an arbitrary node and a random resistor on the right boundary.By means of the network analysis,this paper establishes the difference equation model of the voltage,and the equation model of the boundary compatible with the constraint conditions.After then,explicit expressions of the common solution and the particular solution are derived,from which the formulae of voltages of arbitrary nodes,branch currents,and the equivalent resistors are also obtained.All the formulae obtained here have multi-functions and universality,and many special cases.
引文
[1] 谭志中.电阻网络模型[M].西安:西安电子科技大学出版社,2011.
[2] 谭志中,张庆华.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] Cserti J.Application of the lattice Greens function for calculating the resistance of an infinite network of resistors[J].American Journal of Physics,2000,68:896-906.
[4] Tan Zhi-Zhong.Recursion-transform method for computing resistance of the complex resistor network with three arbitrary boundaries[J].Physical Review E,2015,91 (5):052122.
[5] Tan Zhi-Zhong.Recursion-Transform method to a non-regular m×n cobweb with an arbitrary longitude[J].Scientific Reports,2015,5:11266.
[6] Tan Zhi-Zhong,Essam J W,Wu F Y.Two-point resistance of a resistor network embedded on a globe[J].Physical Review E,2014,90 (1):012130.
[7] Tan Zhi-Zhong.Two-Point Resistance of a Non-Regular Cylindrical Network with a Zero Resistor Axis and Two Arbitrary Boundaries[J].Commun Theor Phys,2017,67 (3):280-288.
[8] 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.
[9] 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.
[10] Tan Zhen,Tan Zhi-Zhong,Chen Jianxin.Potential formula of the nonregular m×n fan network and its application[J].Scientific Reports.2018,8:5798.
[11] 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
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[15] 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(1):49-57.
[16] 谭志中,吴鹏,罗小廉,等.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,张庆华.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] Cserti J.Application of the lattice Greens function for calculating the resistance of an infinite network of resistors[J].American Journal of Physics,2000,68:896-906.
[4] Tan Zhi-Zhong.Recursion-transform method for computing resistance of the complex resistor network with three arbitrary boundaries[J].Physical Review E,2015,91 (5):052122.
[5] Tan Zhi-Zhong.Recursion-Transform method to a non-regular m×n cobweb with an arbitrary longitude[J].Scientific Reports,2015,5:11266.
[6] Tan Zhi-Zhong,Essam J W,Wu F Y.Two-point resistance of a resistor network embedded on a globe[J].Physical Review E,2014,90 (1):012130.
[7] Tan Zhi-Zhong.Two-Point Resistance of a Non-Regular Cylindrical Network with a Zero Resistor Axis and Two Arbitrary Boundaries[J].Commun Theor Phys,2017,67 (3):280-288.
[8] 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.
[9] 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.
[10] Tan Zhen,Tan Zhi-Zhong,Chen Jianxin.Potential formula of the nonregular m×n fan network and its application[J].Scientific Reports.2018,8:5798.
[11] 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
[12] 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
[13] 汤华,谭志中.n阶网络任意节点的等效电阻的研究[J].大学物理,2012,31 (11):18-22
[14] 谭志中,杨建华.一类含有复杂电阻的n阶三角形网络的等效电阻公式[J].大学物理,2015,34 (6):24-35.
[15] 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(1):49-57.
[16] 谭志中,吴鹏,罗小廉,等.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.