2006/01/31 by W. J. Tzeng, F. Y. Wu · 1 citation
Physics and Astronomy · Mathematics · #math-ph #cond-mat.stat-mech #math.MP
paper · pdf · doi:10.1088/0305-4470/39/27/002
published as J. Phys. A: Math. Gen. 39 (2006) 8579-8591 · 21 pages, 3 figures; v4: typesetting corrected; v5: Eq. (63) corrected
arxiv created 2006/07/04 · arxiv updated 2009/12/01
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 ua = lambdaa ua^* with orthonormal vectors ua, the effective impedance between nodes p and q of the network is Z = Suma [ua,p - ua,q]2/lambdaa where the summation is over all lambdaa not identically equal to zero and ua,p is the p-th component of ua. For networks consisting of inductances (L) and capacitances (C), the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of lambdaa. This curious result suggests the possibility of practical applications to resonant circuits. Our formulation is illustrated by explicit examples.