Circuit models for Sierpinski gasket antennas

TL;DR

This paper introduces two circuit models for Sierpinski gasket antennas, one detailed and one simplified, to analyze electromagnetic behavior and complexity growth with fractal iterations.

Contribution

It presents a lumped-parameter and a 2-port network model for the Sierpinski gasket antenna, highlighting their differences in complexity and applicability.

Findings

The detailed model reveals electromagnetic field patterns within the antenna.

The simplified 'black-box' model's complexity remains constant regardless of fractal iteration.

The black-box model converges to a reciprocal triangular network at the fractal limit.

Abstract

A lumped-parameter impedor-oriented and a 2-port-network-oriented circuit models for the Sierpinski gasket prefractal antenna are presented. With the former, the voltage and current patterns give a detailed understanding of the electromagnetic fields' self-similar distribution throughout the antenna geometry; on the other hand model complexity exponentially increases with the prefractal iteration order. The latter "black-box" model only controls port-oriented global parameters which are the ones commonly used in antennas' circuit models and its complexity is independent of prefractal order. The "black-box" model is also shown to converge, at fractal limit, to a reciprocal triangular network.