What is a fractal antenna?
A fractal antenna uses a self-similar, space-filling geometry such as a Koch curve or Sierpinski gasket to pack a long conductor into a small area or to create multiple self-similar resonances. Popularized by Nathan Cohen in 1995,[1] fractal shapes can lower the resonant frequency of a given footprint, but studies by Best showed that comparable non-fractal bent and meandered wires of similar total length achieve similar performance, and no geometry escapes the Chu limit.[2]
What do fractal geometries offer?
- Size reduction: a Koch monopole resonates lower than a straight monopole of the same height because its conductor length is greater.
- Multiband behavior: the Sierpinski gasket shows log-periodic resonances related to its self-similar scale factor.
- Design freedom in PCB layouts.[1]
What are their limits?
Best compared Koch fractals with meander and helical wires of equal height and wire length and found that resonant frequency, bandwidth and efficiency depend mostly on total wire length and occupied volume, not fractal dimension. The fundamental size–bandwidth–efficiency trade-off remains.[2][3]
Frequently asked questions
Are fractal antennas better than meander lines?
Not inherently; performance tracks occupied volume and conductor length.
Can fractals be wideband?
Some self-similar shapes give multiband rather than continuous wideband response.
Are fractals used commercially?
Yes, in some embedded and multiband antennas, alongside conventional meanders.
See also
References
Online sources accessed October 21, 2026; printed works cited by edition. See all sources.
- “Fractal Antennas: Part 1”. N. Cohen, Communications Quarterly, pp. 7-22. Summer 1995.
- “On the Performance Properties of the Koch Fractal and Other Bent Wire Monopoles”. S. R. Best, IEEE Transactions on Antennas and Propagation, vol. 51, no. 6, pp. 1292-1300. June 2003.
- “A Re-examination of the Fundamental Limits on the Radiation Q of Electrically Small Antennas”. J. S. McLean, IEEE Transactions on Antennas and Propagation, vol. 44, no. 5, pp. 672-676. May 1996.