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

W. J. Tzeng·F. Y. Wu
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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 L u_a = lambda_a u_a^* with orthonormal vectors u_a, the effective impedance between nodes p and q of the network is Z = Sum_a [u_{a,p} - u_{a,q}]^2/lambda_a where the summation is over all lambda_a not identically equal to zero and u_{a,p} is the p-th component of u_a. For networks consisting of inductances (L) and capacitances (C), the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of lambda_a. This curious result suggests the possibility of practical applications to resonant circuits. Our formulation is illustrated by explicit examples.

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BibTeXRIS

W. J. Tzeng, F. Y. Wu. 2006-07-04. Theory of impedance networks: The two-point impedance and LC resonances. https://doi.org/10.1088/0305-4470/39/27/002

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