On models of fractal networks

Abstract

SUMMARYA couple of iterative models for the theoretical study of fractal networks whose topologies are generated via iterated function systems is presented: a lumped-parameter impedor-oriented one and a two-portnetwork-oriented one. With the former, the voltage and current patterns give a detailed understanding of the electromagnetic fields' self-similar distribution throughout the network; on the other hand, model complexity exponentially increases with the prefractal iteration order. The latter 'black-box' model only controls port-oriented global parameters that are the ones commonly used in the integration of different electronic systems, and its complexity is independent of prefractal order. Sierpinski gasket and carpet topologies are reported as examples.

Symmetrical two‐port networks: An eigenspace perspective

“…This is always possible exactly for transimpedance and transadmittance functions, and for less than a multiplicative constant in the case of voltage or current ratios. The use of symmetrical networks for circuit synthesis has been exploited by several authors [4][5][6][7][8][9]. In this letter, the canonical unbalanced realizations of symmetrical two-port networks are derived using the eigendecomposition of the open-circuit impedance matrix Z.…”