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Theory on resistance of m × n cobweb network and its application
Author(s) -
Tan ZhiZhong
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.2035
Subject(s) - tridiagonal matrix , resistor , rlc circuit , inductance , mathematics , network analysis , matrix (chemical analysis) , impedance parameters , electrical impedance , transformation (genetics) , gyrator , equivalent series resistance , capacitance , topology (electrical circuits) , capacitor , electrical engineering , physics , combinatorics , engineering , eigenvalues and eigenvectors , quantum mechanics , materials science , voltage , biochemistry , chemistry , electrode , composite material , gene
Summary A basic theorem of equivalent resistance between two arbitrary nodes in an m × n cobweb network in both finite and infinite conditions is discovered, and two conjectures on the equivalent resistance are proved in terms of the basic theorem. We built a tridiagonal matrix equation by means of network analysis and made a diagonalization method of matrix transformation and work out its explicit expressions. The new formulae obtained here can be effectively applied in complex impedance network, especially the formulation leads to the occurrence of resonances and a series of novel results in RLC (denote resistor, inductance and capacitance) network. These curious results suggest the possibility of practical applications to resonant circuits. Copyright © 2014 John Wiley & Sons, Ltd.