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Formulae of resistance between two corner nodes on a common edge of the m × n rectangular network
Author(s) -
Tan ZhiZhong,
Zhang QingHua
Publication year - 2015
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.1988
Subject(s) - resistor , tridiagonal matrix , trigonometry , transformation (genetics) , mathematics , trigonometric functions , matrix (chemical analysis) , topology (electrical circuits) , function (biology) , enhanced data rates for gsm evolution , diagonal , electrical impedance , transformation matrix , mathematical analysis , algorithm , computer science , combinatorics , physics , telecommunications , geometry , eigenvalues and eigenvectors , engineering , electrical engineering , materials science , voltage , chemistry , composite material , biology , biochemistry , quantum mechanics , evolutionary biology , gene , kinematics , classical mechanics
Summary This paper deals with the equivalent resistance for the m × n resistor network in both finite and infinite cases. Firstly, we build a difference equation driven by a tridiagonal matrix to model the network; then by performing the diagonalizing transformation on the driving matrix, and using the auxiliary function tz( x , n ), we derive two formulae of the equivalent resistance between two corner nodes on a common edge of the network. By comparing two different formulae, we also obtain a new trigonometric identity here. Our framework can be effectively applied in complex impedance networks. As in applications in the LC network, we find that our formulation leads to the occurrence of resonances at frequencies associated with ( n + 1) ϕ t = kπ . This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits. At the end of the paper, two other formulae of an m × n resistor network are proposed. Copyright © 2014 John Wiley & Sons, Ltd.