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arXiv · 1507.05682

Fractal AC circuits and propagating waves on fractals

Eric Akkermans·Joe P. Chen·Gerald Dunne·Luke G. Rogers·Alexander Teplyaev
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Abstract

We extend Feynman's analysis of the infinite ladder AC circuit to fractal AC circuits. We show that the characteristic impedances can have positive real part even though all the individual impedances inside the circuit are purely imaginary. This provides a physical setting for analyzing wave propagation of signals on fractals, by analogy with the Telegrapher's Equation, and generalizes the real resistance metric on a fractal, which provides a measure of distance on a fractal, to complex impedances.

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Eric Akkermans, Joe P. Chen, Gerald Dunne, Luke G. Rogers, Alexander Teplyaev. 2015-07-21. Fractal AC circuits and propagating waves on fractals. https://doi.org/10.1142/9789811215537_0018

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