Characteristic of the equivalent impedance for an <italic style="font-style: italic">m</italic>×<italic style="font-style: italic">n</italic> RLC network with an arbitrary boundary

TAN Zhi-zhong; ZHU Hong; ASAD Jihad H.; XU Chen; TANG Hua

doi:10.1631/FITEE.1700037

Your Location：

Home >

Browse articles >

Characteristic of the equivalent impedance for an m×n RLC network with an arbitrary boundary

Regular Papers | Updated：2022-06-06

- Characteristic of the equivalent impedance for an m×n RLC network with an arbitrary boundary
- 含有任意边界的m×n阶RLC网络的等效复阻抗特性
- Frontiers of Information Technology & Electronic Engineering Vol. 18, Issue 12, Pages: 2070-2081(2017)
- Affiliations：
  
  Department of Physics, Nantong University, Nantong 226019, China
  College of Science, Changzhou Institute of Technology, Changzhou 213002, China
  Department of Physics, Palestine Technical University, Tulkarm P.O. Box 7, Palestine
  School of Electronics and Information, Nantong University, Nantong 226019, China
  Department of Physics, Yunhe Teachers College, Pizhou 221300, China
- Author bio：
  
  Zhi-zhong TAN, E-mail: tanz@ntu.edu.cn
  [ "Hong ZHU, E-mail:zh7404@sina.com" ]
  [ "Jihad H. ASAD, E-mail:jasad@ptuk.edu.ps" ]
  [ "Chen XU, E-mail:xuchen@ntu.edu.cn" ]
- Funds：
- DOI：10.1631/FITEE.1700037
  CLC： O441.1;TN711.3
- Received：12 January 2017，
  
  Revised：2017-12-17，
  
  Published：2017-12
- Accepted：
Scan QR Code
TAN Zhi-zhong, ZHU Hong, ASAD Jihad H., et al. Characteristic of the equivalent impedance for an m×n RLC network with an arbitrary boundary[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(12): 2070-2081.
DOI：

TAN Zhi-zhong, ZHU Hong, ASAD Jihad H., et al. Characteristic of the equivalent impedance for an m×n RLC network with an arbitrary boundary[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(12): 2070-2081. DOI： 10.1631/FITEE.1700037.

摘要

现阶段，精确地计算拓扑网络中任意两节点间等效电阻的技术已经取得较大进展，特别是利用递推-变换（recursion-transform

RT）方法确定含有任意边界的非规则

电阻网络的一般等效电阻公式。然而，等效阻抗具有不同于等效电阻的性质，复杂阻抗网络的研究比电阻网络研究困难得多。基于电阻公式，本文研究了含有任意阻抗边界的非规则

阶RLC网络的等效复阻抗问题，并发现等效复阻抗的振荡特性和谐振特性。在RLC网络中，当边界阻抗取得一系列特殊值时，复阻抗公式与外部交流电产生共振。结果表明，该公式可以应用到谐振电路中。

Abstract

Considerable progress has been made recently in the development of techniques to determine exactly two-point resistances in networks of various topologies. In particular

a general resistance formula of a non-regular

resistor network with an arbitrary boundary is determined by the recursion-transform (RT) method. However

research on the complex impedance network is more difficult than that on the resistor network

and it is a problem worthy of study since the equivalent impedance has many different properties from equivalent resistance. In this study

the equivalent impedance of a non-regular

RLC network with an arbitrary boundary is studied based on the resistance formula

and the oscillation characteristics and resonance properties of the equivalent impedance are discovered. In the RLC network

it is found that our formula leads to the occurrence of resonances at the boundary condition holding a series of specific values with an external alternating current source. This curious result suggests the possibility of practical applications of our formula to resonant circuits.

关键词

Keywords

references

J.H. Asad . Exact evaluation of the resistance in an infinite face-centered cubic network . J. Stat. Phys. , 2013a . 150 ( 6 ): 1177 - 1182 . DOI: 10.1007/s10955-013-0716-x http://doi.org/10.1007/s10955-013-0716-x .

J.H. Asad . Infinite simple 3D cubic network of identical capacitors . Mod. Phys. Lett. B , 2013b . 27 ( 15 ): 1350112 DOI: 10.1142/S0217984913501121 http://doi.org/10.1142/S0217984913501121 .

J.H. Asad , A.A. Diab , R.S. Hijjawi , 等 . Infinite face-centered-cubic network of identical resistors: application to lattice Green's function . Eur. Phys. J. Plus , 2013 . 128 2 DOI: 10.1140/epjp/i2013-13002-8 http://doi.org/10.1140/epjp/i2013-13002-8 .

A. Bao , H.S. Tao , H.D. Liu , 等 . Quantum magnetic phase transition in square-octagon lattice . Sci. Rep. , 2014 . 4 6918 DOI: 10.1038/srep06918 http://doi.org/10.1038/srep06918 .

A. Baule , R. Mari , L. Bo , 等 . Mean-field theory of random close packings of axisymmetric particles . Nat. Commun. , 2013 . 4 2194 DOI: 10.1038/ncomms3194 http://doi.org/10.1038/ncomms3194 .

B. Bianco , S. Giordano . Electrical characterization of linear and non-linear random networks and mixtures . Int. J. Circ. Theory Appl. , 2003 . 31 ( 2 ): 199 - 218 . DOI: 10.1002/cta.217 http://doi.org/10.1002/cta.217 .

N. Chair . Exact two-point resistance, and the simple random walk on the complete graph minus N edges . Ann. Phys. , 2012 . 327 ( 12 ): 3116 - 3129 . DOI: 10.1016/j.aop.2012.09.002 http://doi.org/10.1016/j.aop.2012.09.002 .

N. Chair . The effective resistance of the N -cycle graph with four nearest neighbors . J. Stat. Phys. , 2014a . 154 ( 4 ): 1177 - 1190 . DOI: 10.1007/s10955-014-0916-z http://doi.org/10.1007/s10955-014-0916-z .

N. Chair . Trigonometrical sums connected with the chiral Potts model, Verlinde dimension formula, two-dimensional resistor network, and number theory . Ann. Phys. , 2014b . 341 56 - 76 . DOI: 10.1016/j.aop.2013.11.012 http://doi.org/10.1016/j.aop.2013.11.012 .

R.V. Chamberlin . Mean-field cluster model for the critical behaviour of ferromagnets . Nature , 2000 . 408 337 - 339 . DOI: 10.1038/35042534 http://doi.org/10.1038/35042534 .

R. Chitra , G. Kotliar . Dynamical mean-field theory and electronic structure calculations . Phys. Rev. B , 2000 . 62 12715 DOI: 10.1103/PhysRevB.62.12715 http://doi.org/10.1103/PhysRevB.62.12715 .

J. Cserti . Application of the lattice Green's function for calculating the resistance of an infinite network of resistors . Am. J. Phys. , 2000 . 68 ( 10 ): 896 - 906 . DOI: 10.1119/1.1285881 http://doi.org/10.1119/1.1285881 .

J.W. Essam , Z.Z. Tan , F.Y. Wu . Resistance between two nodes in general position on an m × n fan network . Phys. Rev. E , 2014 . 90 ( 3 ): 032130 DOI: 10.1103/PhysRevE.90.032130 http://doi.org/10.1103/PhysRevE.90.032130 .

J.W. Essam , N.S. Izmailyan , R. Kenna , 等 . Comparison of methods to determine point-to-point resistance in nearly rectangular networks with application to a 'hammock' network . R. Soc. Open Sci. , 2015 . 2 140420 DOI: 10.1098/rsos.140420 http://doi.org/10.1098/rsos.140420 .

J. Gabelli , ve Fè , . G , J.M. Berroir , 等 . Violation of Kirchhoff's laws for a coherent RC circuit . Science , 2006 . 313 ( 5786 ): 499 - 502 . DOI: 10.1126/science.1126940 http://doi.org/10.1126/science.1126940 .

A. Georges , G. Kotliar , W. Krauth , 等 . Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions . Rev. Mod. Phys. , 1996 . 68 ( 1 ): 13 - 125 . DOI: 10.1103/RevModPhys.68.13 http://doi.org/10.1103/RevModPhys.68.13 .

S. Giordano . Disordered lattice networks: general theory and simulations . Int. J. Circ. Theory Appl. , 2005 . 33 ( 6 ): 519 - 540 . DOI: 10.1002/cta.335 http://doi.org/10.1002/cta.335 .

K. Haule . Quantum Monte Carlo impurity solver for cluster dynamical mean-field theory and electronic structure calculations with adjustable cluster base . Phys. Rev. B , 2007 . 75 ( 15 ): 155113 DOI: 10.1103/PhysRevB.75.155113 http://doi.org/10.1103/PhysRevB.75.155113 .

N.S. Izmailian , M.C. Huang . Asymptotic expansion for the resistance between two maximum separated nodes on an M by N resistor network . Phys. Rev. E , 2010 . 82 ( 1 ): 011125 DOI: 10.1103/PhysRevE.82.011125 http://doi.org/10.1103/PhysRevE.82.011125 .

N.S. Izmailian , R. Kenna . A generalised formulation of the Laplacian approach to resistor networks . J. Stat. Mech. Theory Exp. , 2014 . 2014 ( 9 ): 09016 DOI: 10.1088/1742-5468/2014/09/P09016 http://doi.org/10.1088/1742-5468/2014/09/P09016 .

N.S. Izmailian , R. Kenna , F.Y. Wu . The two-point resistance of a resistor network: a new formulation and application to the cobweb network . J. Phys. A , 2014 . 47 ( 3 ): 035003 DOI: 10.1088/1751-8113/47/3/035003 http://doi.org/10.1088/1751-8113/47/3/035003 .

G. Kirchhoff . Ueber die Aufl sung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Str me geführt wird . Ann. Phys. , 1847 . 148 ( 12 ): 497 - 508 . DOI: 10.1002/andp.18471481202 http://doi.org/10.1002/andp.18471481202 .

S. Kirkpatrick . Percolation and conduction . Rev. Mod. Phys. , 1973 . 45 ( 4 ): 574 - 588 . DOI: 10.1103/RevModPhys.45.574 http://doi.org/10.1103/RevModPhys.45.574 .

D.J. Klein , M. Randić . Resistance distance . J. Math. Chem. , 1993 . 12 ( 1 ): 81 - 95 . DOI: 10.1007/BF01164627 http://doi.org/10.1007/BF01164627 .

Z.Z. Tan . Resistance Network Moder , Xi'an, China , : Xidian University Press 2011 . p.28 - 146 . .

Z.Z. Tan . Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary . Chin. Phys. B , 2015a . 24 ( 2 ): 020503 DOI: 10.1088/1674-1056/24/2/020503 http://doi.org/10.1088/1674-1056/24/2/020503 .

Z.Z. Tan . Recursion-transform method for computing resistance of the complex resistor network with three arbitrary boundaries . Phys. Rev. E , 2015b . 91 ( 5 ): 052122 DOI: 10.1103/PhysRevE.91.052122 http://doi.org/10.1103/PhysRevE.91.052122 .

Z.Z. Tan . Recursion-transform method to a non-regular m × n cobweb with an arbitrary longitude . Sci. Rep. , 2015c . 5 11266 DOI: 10.1038/srep11266 http://doi.org/10.1038/srep11266 .

Z.Z. Tan . Two-point resistance of a non-regular cylindrical network with a zero resistor axis and two arbitrary boundaries . Commun. Theor. Phys. , 2017 . 67 ( 3 ): 280 - 288 . DOI: 10.1088/0253-6102/67/3/280 http://doi.org/10.1088/0253-6102/67/3/280 .

Z.Z. Tan , J.H. Fang . Two-point resistance of a cobweb network with a 2r boundary . Commun. Theor. Phys. , 2015 . 63 ( 1 ): 36 - 44 . DOI: 10.1088/0253-6102/63/1/07 http://doi.org/10.1088/0253-6102/63/1/07 .

Z.Z. Tan , Q.H. Zhang . Formulae of resistance between two corner nodes on a common edge of the m × n rectangular network . Int. J. Circ. Theory Appl. , 2015 . 43 ( 7 ): 944 - 958 . DOI: 10.1002/cta.1988 http://doi.org/10.1002/cta.1988 .

Z.Z. Tan , Q.H. Zhang . Calculation of the equivalent resistance and impedance of the cylindrical network based on recursion-transform method . Acta Phys. Sin. , 2017 . 66 ( 7 ): 070501 DOI: 10.7498/aps.66.070501 http://doi.org/10.7498/aps.66.070501 .

Z.Z. Tan , L. Zhou , J.H. Yang . The equivalent resistance of a 3× n cobweb network and its conjecture of an m × n cobweb network . J. Phys. A , 2013 . 46 195202 DOI: 10.1088/1751-8113/46/19/195202 http://doi.org/10.1088/1751-8113/46/19/195202 .

Z.Z. Tan , J.W. Essam , F.Y. Wu . Two-point resistance of a resistor network embedded on a globe . Phys. Rev. E , 2014 . 90 ( 1 ): 012130 DOI: 10.1103/PhysRevE.90.012130 http://doi.org/10.1103/PhysRevE.90.012130 .

W.J. Tzeng , F.Y. Wu . Theory of impedance networks: the two-point impedance and LC resonances . J. Phys. A: Math. Gen. , 2006 . 39 ( 27 ): 8579 - 8591 . DOI: 10.1088/0305-4470/39/27/002 http://doi.org/10.1088/0305-4470/39/27/002 .

C.B. Whan , C.J. Lobb . Complex dynamical behavior in RCL shunted Josephson tunnel junctions . Phys. Rev. E , 1996 . 53 ( 1 ): 405 - 413 . DOI: 10.1103/PhysRevE.53.405 http://doi.org/10.1103/PhysRevE.53.405 .

F.Y. Wu . Theory of resistor networks: the two-point resistance . J. Phys. A , 2004 . 37 ( 26 ): 6653 - 6673 . DOI: 10.1088/0305-4470/37/26/004 http://doi.org/10.1088/0305-4470/37/26/004 .

W.J. Xiao , I. Gutman . Resistance distance and Laplacian spectrum . Theor. Chem. Acc. , 2003 . 110 ( 4 ): 284 - 289 . DOI: 10.1007/s00214-003-0460-4 http://doi.org/10.1007/s00214-003-0460-4 .

L. Zhou , Z.Z. Tan , Q.H. Zhang . A fractional-order multifunctional n-step honeycomb RLC circuit network . Front. Inform. Technol. Electron. Eng. , 2017 . 18 ( 8 ): 1186 - 1196 . DOI: 10.1631/FITEE.1601560 http://doi.org/10.1631/FITEE.1601560 .

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

Chat

Address：Zhejiang University Press, 148 Tianmushan Road, Hangzhou, China Postal code：310028
Tel：+86-571-88273162 Email：fitee@zju.edu.cn
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰

Characteristic of the equivalent impedance for an m×n RLC network with an arbitrary boundary

DOI：10.1631/FITEE.1700037

摘要

Abstract

关键词

Keywords

references