Full Text:   <1997>

Summary:  <219>

CLC number: O441.1; TN711.3

On-line Access: 2023-02-27

Received: 2022-08-27

Revision Accepted: 2022-09-18

Crosschecked: 2023-02-27

Cited: 0

Clicked: 1244

Citations:  Bibtex RefMan EndNote GB/T7714


Xiaoyan LIN


Zhizhong TAN


-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2023 Vol.24 No.2 P.289-298


Unified construction of two n-order circuit networks with diodes

Author(s):  Xiaoyan LIN, Zhizhong TAN

Affiliation(s):  Department of Physics, Nantong University, Nantong 226019, China

Corresponding email(s):   xiaoyanlin02@163.com, tanz@ntu.edu.cn

Key Words:  Complex networks, Equivalent transform, Nonlinear difference equation, Equivalent resistance

Xiaoyan LIN, Zhizhong TAN. Unified construction of two n-order circuit networks with diodes[J]. Frontiers of Information Technology & Electronic Engineering, 2023, 24(2): 289-298.

@article{title="Unified construction of two n-order circuit networks with diodes",
author="Xiaoyan LIN, Zhizhong TAN",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Unified construction of two n-order circuit networks with diodes
%A Xiaoyan LIN
%A Zhizhong TAN
%J Frontiers of Information Technology & Electronic Engineering
%V 24
%N 2
%P 289-298
%@ 2095-9184
%D 2023
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.2200360

T1 - Unified construction of two n-order circuit networks with diodes
A1 - Xiaoyan LIN
A1 - Zhizhong TAN
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 24
IS - 2
SP - 289
EP - 298
%@ 2095-9184
Y1 - 2023
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.2200360

In this paper, two different n-order topological circuit networks are connected by diodes to establish a unified network model, which is a previously unexplored problem. The network model includes not only five resistive elements but also diode devices, so the network contains many different network types. This problem can be solved through three main steps: First, the network is simplified into two different equivalent circuit models. Second, the nonlinear difference equation model is established by applying Kirchhoff’s law. Finally, the two equations with similar structures are processed uniformly, and the general solutions of the nonlinear difference equations are obtained by using the transformation technique. As an example, several interesting specific results are deduced. Our study on the network model has significant value, as it can be applied to relevant interdisciplinary research.




Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Aitchison RE, 1964. Resistance between adjacent points of Liebman mesh. Am J Phys, 32(7):566.

[2]Albert VV, Glazman LI, Jiang L, 2015. Topological properties of linear circuit lattices. Phys Rev Lett, 114(17):173902.

[3]Asad JH, 2013a. Exact evaluation of the resistance in an infinite face-centered cubic network. J Stat Phys, 150(6):1177-1182.

[4]Asad JH, 2013b. Infinite simple 3D cubic network of identical capacitors. Mod Phys Lett B, 27(15):1350112.

[5]Asad JH, Diab AA, Hijjaw RS, et al., 2013. Infinite face-centered-cubic network of identical resistors: application to lattice Green's function. Eur Phys J Plus, 128(1):2.

[6]Atkinson D, van Steenwijk FJ, 1999. Infinite resistive lattices. Am J Phys, 67(6):486-492.

[7]Bianco B, Giordano S, 2003. Electrical characterization of linear and non-linear random networks and mixtures. Int J Circ Theor Appl, 31(2):199-218.

[8]Bianco B, Chiabrera A, Giordano S, 2000. DC-ELF characterization of random mixtures of piecewise nonlinear media. Bioelectromagnetics, 21(2):145-149.

[9]Brayton RK, Moser JK, 1964a. A theory of nonlinear networks. I. Quart Appl Math, 22(1):1-33.

[10]Brayton RK, Moser JK, 1964b. A theory of nonlinear networks. II. Quart Appl Math, 22(2):81-104.

[11]Chen HX, Tan ZZ, 2020. Electrical properties of an n-order network with Y circuits. Phys Scr, 95(8):085204.

[12]Chen HX, Yang L, 2020. Electrical characteristics of n-ladder network with external load. Ind J Phys, 94(6):801-809.

[13]Chen HX, Yang L, Wang MJ, 2019. Electrical characteristics of n-ladder network with internal load. Results Phys, 15:102488.

[14]Chen HX, Li N, Li ZT, et al., 2020. Electrical characteristics of a class of n-order triangular network. Phys A, 540:123167.

[15]Cserti J, 2000. Application of the lattice Green's function for calculating the resistance of an infinite network of resistors. Am J Phys, 68(10):896-906.

[16]Cserti J, Dávid G, Piróth A, 2002. Perturbation of infinite networks of resistors. Am J Phys, 70(2):153-159.

[17]Cserti J, Széchenyi G, David G, 2011. Uniform tiling with electrical resistors. J Phys A Math Theor, 44(21):215201.

[18]Desoer CA, Wu FF, 1974. Nonlinear monotone networks. SIAM J Appl Math, 26(2):315-333.

[19]Doyle PG, Snell JL, 1984. Random Walks and Electric Networks. The Mathematical Association of America, Washington, USA.

[20]Essam JW, Wu FY, 2009. The exact evaluation of the corner-to-corner resistance of an M×N resistor network: asymptotic expansion. J Phys A Math Theor, 42(2):025205.

[21]Essam JW, Tan ZZ, Wu FY, 2014. Resistance between two nodes in general position on an m×n fan network. Phys Rev E, 90(3):032130.

[22]Essam JW, Izmailyan NS, Kenna R, et al., 2015. Comparison of methods to determine point-to-point resistance in nearly rectangular networks with application to a 'hammock' network. Royal Soc Open Sci, 2(4):140420.

[23]Fang XY, Tan ZZ, 2022. Circuit network theory of n-horizontal bridge structure. Sci Rep, 12(1):6158.

[24]Giordano S, 2007. Two-dimensional disordered lattice networks with substrate. Phys A, 375(2):726-740.

[25]Guttmann AJ, 2010. Lattice Green's functions in all dimensions. J Phys A Math Theor, 43(30):305205.

[26]Hijjawi RS, Asad JH, Sakaji AJ, et al., 2008. Infinite simple 3D cubic lattice of identical resistors (two missing bonds). Eur Phys J Appl Phys, 41(2):111-114.

[27]Hum SV, Du BZ, 2017. Equivalent circuit modeling for reflectarrays using Floquet modal expansion. IEEE Trans Antennas Propag, 65(3):1131-1140.

[28]Izmailian NS, Huang MC, 2010. Asymptotic expansion for the resistance between two maximally separated nodes on an M by N resistor network. Phys Rev E, 82(1):011125.

[29]Izmailian NS, Kenna R, Wu FY, 2014. The two-point resistance of a resistor network: a new formulation and application to the cobweb network. J Phys A Math Theor, 47(3):035003.

[30]Kimouche A, Ervasti MM, Drost R, et al., 2015. Ultra-narrow metallic armchair graphene nanoribbons. Nat Commun, 6:10177.

[31]Kirchhoff G, 1847. Ueber die auflösung der gleichungen, auf welche man bei der untersuchung der linearen vertheilung galvanischer ströme geführt wird. Ann Phys Chem, 148(12):497-508(in German).

[32]Redner S, 2001. A Guide to First-Passage Processes. Cambridge University Press, New York, USA.

[33]Stavrinidou E, Gabrielsson R, Gomez E, et al., 2015. Electronic plants. Sci Adv, 1(10):1501136.

[34]Tan ZZ, 2011. Resistance Network Model. Xidian University Press, Xi'an, China(in Chinese).

[35]Tan ZZ, 2015a. Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary. Chin Phys B, 24(2):020503.

[36]Tan ZZ, 2015b. Recursion-transform method for computing resistance of the complex resistor network with three arbitrary boundaries. Phys Rev E, 91(5):052122.

[37]Tan ZZ, 2015c. Recursion-transform method to a non-regular m×n cobweb with an arbitrary longitude. Sci Rep, 5:11266.

[38]Tan ZZ, 2015d. Theory on resistance of m×n cobweb network and its application. Int J Circ Theor Appl, 34(11):1687-1702.

[39]Tan ZZ, 2016. Two-point resistance of an m×n resistor net- work with an arbitrary boundary and its application in RLC network. Chin Phys B, 25(5):050504.

[40]Tan ZZ, 2017. Recursion-transform method and potential formulae of the m×n cobweb and fan networks. Chin Phys B, 26(9):090503.

[41]Tan ZZ, 2022. Resistance theory for two classes of n-periodic networks. Eur Phys J Plus, 137(5):546.

[42]Tan Z, Tan ZZ, 2018. Potential formula of an m×n globe network and its application. Sci Rep, 8:9937.

[43]Tan ZZ, Tan Z, 2020a. Electrical properties of an m×n rectangular network. Phys Scr, 95(3):035226.

[44]Tan ZZ, Tan Z, 2020b. Electrical properties of m×n cylindrical network. Chin Phys B, 29(8):080503.

[45]Tan ZZ, Tan Z, 2020c. The basic principle of m×n resistor networks. Commun Theor Phys, 72(5):055001.

[46]Tan ZZ, Zhang QH, 2015. Formulae of resistance between two corner nodes on a common edge of the m×n rectangular network. Int J Circ Theor Appl, 43(7):944-958.

[47]Tan ZZ, Asad JH, Owaidat MQ, 2017. Resistance formulae of a multipurpose n-step network and its application in LC network. Int J Circ Theor Appl, 45(12):1942-1957.

[48]Tan Z, Tan ZZ, Chen JX, 2018a. Potential formula of the nonregular m×n fan network and its application. Sci Rep, 8(1):5798.

[49]Tan Z, Tan ZZ, Zhou L, 2018b. Electrical properties of an m×n hammock network. Commun Theor Phys, 69(5):610-616.

[50]Tzeng WJ, Wu FY, 2006. Theory of impedance networks: the two-point impedance and LC resonances. J Phys A Math General, 39(27):8579-8591.

[51]Venezian G, 1994. On the resistance between two points on a grid. Am J Phys, 62(11):1000-1004.

[52]Wu FY, 2004. Theory of resistor networks: the two-point resistance. J Phys A Math General, 37(26):6653-6673.

[53]Xu GY, Eleftheriades GV, Hum SV, 2021. Analysis and design of general printed circuit board metagratings with an equivalent circuit model approach. IEEE Trans Antenn Propag, 69(8):4657-4669.

[54]Zhou L, Tan ZZ, Zhan QH, et al., 2017. A fractional-order multifunctional n-step honeycomb RLC circuit network. Front Inform Technol Electron Eng, 18(8):1186-1196.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE