一类2×n阶K形电阻网络的等效电阻研究A STUDY ON THE EQUIVALENT RESISTANCE OF A CLASS OF 2×N ORDER K-SHAPED RESISTOR NETWORKS
谭震
摘要(Abstract)：
电路结构通常复杂多样,不少电路网络问题充满了挑战性。文章分析探索了一类多参数2×n阶K形电阻网络模型,采用创造性思维与严密的计算导出了一个等效电阻解析式。文章所采用的研究方法包括三种:一是建立电路网络的三个等效模型,二是建立递推差分方程,三是采用变量代换技术求解差分方程。文章讨论了等效电阻的一些特殊情形,并且将特殊情形的结论与其他相关结果进行了比较与验证。本文的研究工作对促进教学与科研协同发展具有积极意义,对培养大学生的科学探究能力与创造性思维能力具有较好的指导意义。
关键词(KeyWords)： K形网络;等效模型;变量代换;差分方程;等效电阻
基金项目(Foundation): 南通大学引进人才启动资金项目(编号：135424630060);; 2025年南通市自然科学青年项目(编号：JC2024046);; 教育部产学合作协同育人项目(编号：2504210044; 250403492210637)
作者(Author): 谭震
DOI: 10.27024/j.wlygc.2025.07.21.01
参考文献(References)：
- [1] 谭志中.电阻网络模型[M].西安：西安电子科技大学出版社，2011,12:3-70.TAN Z Z.Resistance network model[M].Xi'an:Xidian University Press,2011,12:3-70.(in Chinese)
- [2] WU F Y.Theory of resistor networks:the two-point resistance[J].Journal of Physics A:Math.Gen.2004,37:6653-6673.
- [3] TAN Z Z,ASAD J H,Owaidat M Q.Resistance formulae of a multipurpose n-step network and its application in LC network[J].International Journal of Circuit Theory and Applications,2017,45:1942-1957.
- [4] TAN Z Z,TAN Z.The basic principle of m×n resistor networks[J].Communications in Theoretical Physics,2020,72:055001.
- [5] TAN Z Z.Recursion-transform method and potential formulae of the m×n cobweb and fan networks[J].Chinese Physics B 2017,26(9):090503.
- [6] TAN Z,TAN Z Z,ASAD J H,et al.Electrical characteristics of the 2×n and ×n circuit network[J].Physica Scripta,2019,94:055203.
- [7] ZHOU L,TAN Z Z,ZHANG Q H.A fractional-order multifunctional n-step honeycomb RLC circuit network[J].Front Inform Technol Electron Eng,2017;18(8):1186-1196.
- [8] LUO X L,TAN Z Z.Fractional circuit network theory with n-V-structure[J].Physica Scripta 2023;98(4):045224.
- [9] 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.LI J X,LIU S J.Research on N-step trapezoidal resistor network[J].College Physics,2003,22 (7):20-21.(in Chinese)
- [10] 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.TANG H,TAN Z Z.Research on the equivalent resistance of any node in an n-order network[J].College Physics,2012,31 (11):18-22.(in Chinese)
- [11] 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.TAN Z Z,YANG J H.The equivalent resistance formula for a class of n-order triangular networks containing complex resistors[J].College Physics,2015,34 (6):24-35.(in Chinese)
- [12] 刘雅慧，陈芸，檀钰，等.含反馈电路的n 阶电阻网络的新理论[J].大学物理，2024,43(6):63-67.LIU Y H,CHEN Y,TAN Y,et al.A new theory of n-order resistor network with feedback circuits[J].College Physics,2024,43(6):63-67.(in Chinese)
- [13] 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.PENG Z,WANG H P.Thermal Effect of the Feed/Drain Channels in Electro-Dialyzer[J].Journal of Wuhan University (Science Edition),2015,61(5):470-476.(in Chinese)
- [14] 胡小阳.双极膜电渗析装置电路特性及热效应机制研究[D].武汉：武汉大学，2019.HU X Y.Study on Circuit Characteristics and Thermal Effect Mechanism of Bipolar Membrane Electrodialysis Device[D].Wuhan:Wuhan University,2019.(in Chinese)
- [15] 谭志中，余清怡，王一骁.任意2×n阶Fan网络的电特性研究[J].大学物理，2019,38(3):14-19,31.TAN Z Z,YU Q Y,WANG Y X.Study on the electrical characteristics of any 2×n Fan network[J].College Physics,2019,38(3):14-19,31.(in Chinese)
- [16] 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.LIU S S.Research on the equivalent resistance of 2×n order ladder resistance network based on the symmetry[J].College Physics,2015,34 (1):26-29.(in Chinese)
- [17] ZHOU S,WANG Z X,ZHAO Y Q,et al.Electrical properties of a generalized 2×n resistor network[J].Communications in Theoretical Physics,2023,75:075701.
- [18] CHEN J Q,JI W Y,TAN Z Z.Electrical properties of a 2×n non-regular hammock network[J].Indian Journal of Physics,2024,98(8):2851-2860.
- [19] TAN Z Z,WANG X.Electrical characteristics of a fractional order 3×n Fan network[J].Commun.Theor.Phys.2024,76:045701.