Fractal Antennas
"Considering how many fools can calculate, it is surprising that
it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks.
"Some calculustricks are quite easy, Some are enormously difficult. The fools who write the textbooks of
advanced mathematics  and they are the most clever fools  seldom take the trouble to show you how easy the easy
calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going
about it in the most difficult way.
"Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present
to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool
can do, another can."
Silvanus P. Thompson, F.R.S.
this.fool's website of foolish fractals :
These pages are devoted to the analysis of those forms known as Fractals. The list of designs
to the left cover topics reviewed by myself in the rec.radio.amateur.antenna newsgroup. The designs are those presented
to the newsgroup through web site http://www.seanet.com/~rwclark/kb7qhc in the Feb.mar. period of 1997. This work
was moved to this present location in 1998. The next significant overhaul came in the summer of 1999 when all designs
were reevaluated in the Constant Wire and Constant Height surveys.
Introduction
Constant Wire survey
Constant Fractal survey
Constant Height survey
Constant Band survey
Wide Band survey
Constant Height Paired Fractals
Introduction
The goal of this work is to observe how fractal antennas might exhibit characteristics that are
correlated to their form. To anticipate a question: "does a koch quadratic
have more gain than a triadic?" The
correlation inferred in this question is between the fractal iteration or form and the field distortions. This
setup question simplifies too much as there are a multitude of variables and constants that make simple answers
to simple questions rare. In light of these impediments, the methods employed in these studies are designed to
reduce variables and share constants. Through these methods, a number of tests in survey form were performed. Their
purpose successfully achieved the goal where the data displays separable characteristics. This is demonstrated
in the presentation of the "special wire equation" for any 2 iteration regular fractal.
There is no attempt to prequalify any of the designs except by the most fundamental relationship
of fractal form, wavelength and length of wire. The height of an antenna or amount of wire consumed in the construction
of any particular design was chosen to be an easily scalable and resolvable value. The designs here in these pages
generally have a value of 16, 32, or 64 meters. Now this value may be an expression of the height of a design,
or the amount of wire consumed (the length of wire in the bends and turns). Through these constraints in size,
come reduction in variables.
The designs in this site are vertical for the greater majority with minor attention given to
dipoles and loops. Another note, there is no attempt here to model against "real" conditions. All models
are tested in as neartoperfect circumstances as may be accomplished on a computer. There were several reasons
for this choice and economy was high amongst them. By employing a perfect environment, the computations went much
faster. Another consideration was that all work here was committed to the single goal of finding separable characteristics
of fractals. The employment of a perfect environment presents no problems with that goal and also serves the requirements
to reduce variables and share constants.
Other antennas offered singly as buttons to the left are amusing, interesting, useful, but not
particularly insightful.
Constant Wire survey
The "constant wire" design is a survey of drive point impedance variation across a family of fractals, over a frequency
range. The purpose of this testing is to reveal how fractal forms are differentiable through the resonant frequency
for a constant length of wire. Increasing complexity in the underlying form shortens the antenna's height. In this
page I derive what I call the fractal form's "ordering factor." By displaying all data (through all these
pages) in the order derived on this page, the data's shape reveals each fractal form occupies a region distinct
from the data of another fractal form. The data reveals the shift of the resonance
is positively correlated to the number of elements in the fractal form. This is also
illustrated in the Constant Band
survey.
Two lengths are used in these surveys: 16 meters and 64 meters of wire consumed. Derived from
these investigations are the "special wire equations" or mathematical formulas for determining
the amount of wire consumed by any second iteration regular fractal. This
portion of the page is still under construction.
Constant Fractal survey
This test looks at the variability of a fractal over iterations. Current under
construction and it shows it by missing labels and links to some data.
Constant Height survey
The purpose of the "constant
height" design is to look at fractal structures that use more wire than the monopole
reference. The characteristic of interest here is with lobe gain.
There are two tables listing radiation characteristics for 16 Meter 2nd iteration designs. Compared
to a simple monopole, the Fractals as a class offer more tunable opportunities. The proof of the is found with
the Koch Quadratic providing a SWR null near or within every Amateur Band from 160M to 6M.
Constant Band survey
The intent behind this survey was to test for the possibility of distinguishing features at the first resonance. The key distinction found was that for a constant volume of wire in any fractal form, the first resonance
changed, generally higher than a monopole cut with the same amount of wire. When the data is sorted by frequency,
there is a clear trend where degree of complexity correlates to degree of resonance shift from the monopole standard.
Wide Band survey
This data reveals how fractals can become nearly flat matches over considerable stretches of frequency.
Constant Height Paired Fractals
This design is a whim where I combine two Koch Triadic forms in parallel. The twist
though is that one branch is 1st iteration, and the other is 2nd iteration. I use an uncharacteristic 64 meters
of wire in this experiment so the frequencies range in the 4 to 5 MHz range. Must be seen to be appreciated.
Insofar as whims go, this had an unanticipated consequence of demonstrating a folded
monopole characteristic in the drive point Z.
