Theory of impedance networks: the two-point impedance and LC resonances

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Title:	Theory of impedance networks: the two-point impedance and LC resonances
Authors:	曾文哲;Tzeng, Wen-jer;Wu, F. Y.
Contributors:	淡江大學物理學系
Keywords:	Impedance network;complex matrices;resonances
Date:	2006-07-07
Issue Date:	2009-12-31 10:29:23 (UTC+8)
Publisher:	Institute of Physics (IOP)
Abstract:	We present a formulation of the determination of the impedance between any two nodes in an impedance network. An impedance network is described by its Laplacian matrix L which has generally complex matrix elements. We show that by solving the equation Luα = λαu*α with orthonormal vectors ua, the effective impedance between nodes p and q of the network is Zpq = ∑α(uαp − uαq)2/λα, where the summation is over all λα not identically equal to zero and uαp is the pth component of uα. For networks consisting of inductances L and capacitances C, the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of λα. This curious result suggests the possibility of practical applications to resonant circuits. Our formulation is illustrated by explicit examples.
Relation:	Journal of Physics A: Mathematical and General 39(27), pp.8579-8591
DOI:	10.1088/0305-4470/39/27/002
Appears in Collections:	[Graduate Institute & Department of Physics] Journal Article

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