Power dissipation in fractal AC circuits

Abstract

We extend Feynman's analysis of an infinite ladder circuit to fractal circuits, providing examples in which fractal circuits constructed with purely imaginary impedances can have characteristic impedances with positive real part. Using (weak) self-similarity of our fractal structures, we provide algorithms for studying the equilibrium distribution of energy on these circuits. This extends the analysis of self-similar resistance networks introduced by Fukushima, Kigami, Kusuoka, and more recently studied by Strichartz et al.

arXiv commentv2: 16 pages, 8 figures. See also the recent preprint arXiv:1701.08039

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Cited by in corpus (6)

• Complex networks with complex weights
• Power dissipation in fractal Feynman-Sierpinski AC circuits
• High-dimensional dynamics in a single-transistor oscillator containing Feynman-Sierpinski resonators: effect of fractal depth and irregularity
• Effective Impedance over Ordered Fields
• Dynamical processes on metric networks
• Scaling, Fractal Dynamics and Critical Exponents: Application in a non-integer dimensional Ising model