Welcome to the
fractal antenna FAQ. Since fractal antennas (more specifically
fractal element antennas (FEA) are still an exotic and unknown
option to many we believe this FAQ will be helpful. All the
antennas shown are either patented or patent pending. Please
see the home page for patent numbers issued to date.
Q: Do you sell your
antenna design is a big part of what we do, we are not a
‘design house’. Our customers get solutions from us by
delivery of product or by licensing. We do not provide ‘work
for hire’ for antennas. Typically NRE charges are required
for applications, because of the need for custom designs that
work best for the form factor and environment.
Q: Why can’t I
just go to another company or university which works on
fractal antenna designs?
A: Fractal Antenna Systems, Inc.,
provides fractal element antennas—exclusively. As Dr. Steven Best, President of
the IEEE-APS has said publicly: ” Nathan Cohen invented fractal antennas” -- our
founder invented fractal antennas on 1988; published the first fractal antenna
paper; and resolutely reduced the invention(s) to practice, thereby establishing
the priority date on fractal element antennas. Patent filings date back to 1995. Our
patents are free and clear and not in dispute. We invented fractal element antennas,
we control the patents, and we are the exclusive source. For example, in the US,
here are the patents which make it happen:
- USP 7999754 "Fractal counterpoise, groundplane, loads and resonators"
- USP 7973732 "Wide-band Vehicular antenna"
- USP 7830319 "Wideband Antenna Systems for Garments"
- USP 7750856 "Fractal Antennas and Fractal Resonators"
- USP 7705798 "Fractal counterpoise, groundplane, loads and resonators"
- USP 7701396 "Wide-band fractal antenna"
- USP 7659862 " Antenna System for Radio Frequency Identification"
- USP 7456799 "Wideband Vehicular Antenna"
- USP 7345642 "Antenna System for Radio Frequency Identification"
- USP 7256751 "Fractal Antennas and Fractal Resonators"
- USP 7215290 "Fractal counterpoise, groundplane, loads and resonators"
- USP 7190318 "Wide-band fractal antenna"
- USP 7145513 "Tuning fractal antennas and fractal resonators"
- USP 7126537 "Cylindrical conformable antenna on a planar substrate"
- USP 7019695 "Fractal antenna ground counterpoise, ground planes, and loading elements
and microstrip patch antennas with fractal structure"
- USP 6985122 "Antenna System for Radio Frequency Identification"
- USP 6476766 "Fractal antenna ground counterpoise, ground planes, and loading elements
and microstrip patch antennas with fractal structure"
- USP 6452553 "Fractal antennas and fractal resonators"
- USP 6445352 "Cylindrical conformable antenna on a planar substrate"
- USP 6140975 "Fractal antenna ground counterpoise, ground planes, and loading
- USP 6127977 "Microstrip patch antenna with fractal structure"
- USP 6104349 "Tuning fractal antennas and fractal resonators"
Although we do license our technologies we have
not authorized making, using, offering, importing/exporting, and/or sales thru foreign
antenna companies. Kindly check if you have questions regarding sales or another source.
We’d love to hear from you. Universities are not companies—that’s our job. Theirs is
education and research, isn’t it? They certainly have no authority to sell or license you
a design that is covered by others’ patents.
Q: What is a
are 'broken curves'. They are a class of geometry that has
been defined and popularized through the efforts of Benoit
Mandelbrot and many others. They break into two main geometric
types: deterministic; and random (chaotic). Random fractals
are quite familiar and many look like random walks (Brownian
motion); dendrites; or lightning bolts. Deterministic fractals
take a 'motif' or 'generator' and apply it on successive size
scales. Usually fractals are described as being
'self-similar', or 'self-symmetric'.
Q: What is an
iteration and doesn't a fractal have to go on forever to be a
iteration is an application of the motif on a given size
scale. Mathematicians usually refer to fractals as having
n-iterations where n is taken to infinity. In fact, no graphic
or physical representation of a fractal is capable of meeting
this criteria. Physicists, computer scientists, and engineers
have adopted the less constraining--and realistic--
description of fractals as having a finite number of
iterations. Certainly one needs at least two to claim the self
similar aspect of fractals.
Q: Someone said you
have a 'skunk works' lab. Is this true?
conduct research and product development in antennas and
electromagnetics for our customers. We succeed at high risk
projects. Our work defines the state of the art.
We are not affiliated
with the Lockheed-Martin Skunk Works, which is an aviation
Q: If fractal antennas
as so good then why don't I see them in use?
antennas are widely used in applications across many
industries, and military; government and security/public
safety applications. It would be a rare time that you will
'see' our antennas, as they tend to be embedded inside
products or under radomes, for example. Our new Customer
Spotlight series showcases some recent examples where our
product 'wins' easily give the customer the Fractal
Q: Do fractals
have any practical use (irrespective of antennas)?
Fractals have been applied as a descriptor of many physical
structures such as terrain; clouds; vegetables; trees;
anatomical organs; galactic clusters; lightning; and so on.
They have been applied most successfully in engineering as a
means of image compression and image enhancers. Fractal
antennas are the most successful hardware implementation of
is the “FRAGO’ and why is it important?
Fractal Genetic Optimizer is a computer-based optimizing
tool which we use to help identify the best fractal designs
for a given antenna or electronics problem. It uses a genetic
algorithm (see Haupt and Haupt, 1996, Practical Genetic
Algorithms, Wiley) to help find these best designs. At the
core of our proprietary approach is a process using a fractal
coding to compress the genome for a dramatic speedup of the
search process, as well as a PC cluster. We operate anywhere
from 100-1000 times faster than other GA based antenna
optimizers and can investigate at a rate of close to 2 million
antennas a month with a rack of 16 PC’s . FRAGO proves
invaluable as a means to help customize an antenna need, for
example. It is both a methodology and solution which goes
beyond the trial and error needed to explore the huge design
space of fractal geometric shapes. We are the only ones with
FRAGO: we pioneered it (Cohen published the theory
in 1997) and built it. And, we debugged it to make it
Q: What is a
fractal element antenna (FEA)?
A: A FEA
is an antenna (as opposed to an array) which has been shaped
in a fractal fashion. This can either be through bending or
shaping a volume or introducing holes.
Q: How were
elements have been around for a very long time--but were not
discussed as such. The log periodic array element of Isbell
and DuHamel is clearly a fractal. Log periodics have been an
important antenna design class for 50 years. The home TV
antenna is a variation of this idea. Twenty years ago,
Landstorfer and Sacher, using optimization approaches, came up
with randomly bent antenna designs which are clearly random
fractals--but again not discussed as such. In 1988, Dr. Nathan
Cohen built the first bona fide FEA. After years of
building upon a knowledge base of FEA, with very modest
resources, Cohen was ready to report some results. In October 1994,
Cohen first publicly reported his results (at a radio
convention), defining FEA and elaborating on their
characteristics, such as multiband and broadband capabilities;
shrinking of size; and so on. In August, 1995 Cohen published
the very first FEA article. This included modeling and
measurement data on multiband and broadband capabilities;
shrinkage; and so on. An independent corroboration of some FEA
properties by a university group in Spain was submitted only
two months later and published in January 1996. Because
the basic science of FEA
is so easy to demonstrate, it has caught on like wildfire--even
high school students have won science fairs by demonstrating
fractal antennas. At this time there are over 200 articles
published on FEA; major technical and scientific symposia have
sessions on FEA; and over 100 independent research groups,
across the globe, have or are conducting research on FEA. The
science of FEA is now well established (see for example, a discussion
of the corroboration
by a UCLA group) in the mainstream of electromagnetics and
engineering. All this happened in less than a decade from
first discussion to recognition and acceptance—and it
started with the humble bending of a piece of wire.
Q: I am an educator
and would like to know something about the schooling and
background of the inventor. Could you provide a brief
See the attached bio for Nathan Cohen.
Q: What does
fractalizing an antenna do?
benefits depend on the fractal applied, frequency of interest,
and so on. In general the fractal parts produces 'fractal
loading' and makes the antenna smaller for a given frequency
of use. Practical shrinkage of 2-4 times are realizable for
acceptable performance. Surprisingly high performance is
attained. Multiband behavior is manifest at non-harmonic
frequencies, while some bands are broadened. At the higher
frequencies the FEA is extremely and naturally broad band and
can be made frequency independent without a log periodic
geometry. Shrunken, very wideband FEA are possible. Arrays
naturally benefit as well, as the arrangement of elements must
be defined by 'Hohlfeld-Cohen-Rumsey' (HCR) conditions for
frequency invariance. Phasing and polarization control are also
attainable in FEA.
Q: A new article
says that fractals have no benefit compared to
"random" shapes. Could you comment?
The article is an interesting one by Dr. Steven Best, which
appears in the June 2003 AP Magazine. Unfortunately, based on
Dr. Nathan Cohen's assessment, it appears to be based on
several errors of fact and interpretation which render the
conclusions as incorrect. For example, it compares a specific
fractal shape to other fractal shapes and concludes that
fractals perform no better than a crank-line (see
discussion below). In fact, when made very small, all
antennas are mediocre performers, so that comparison may not
be insightful to real antennas To wit: a flea sized antenna
delivers flea-like performance. It doesn't matter what color
is the flea.
fractals outperform other antennas in the 2-4 times size
reduction regime. Smaller than that, such comparisons yield
mediocre or poor antennas of any and all types chosen.
right question to ask is: what is the smallest antenna that
can be made that is closest to the performance requirements of
a conventional one--such as a dipole? Best's article did not
take this approach . Compare the crank-line antenna discussed
below for size to a fractal, for example. Then decide.
Q: Did you guys
invent the fractal capacitor?
Is there some advantage? What is a fractal resonator?
have been discussing fractals as capacitors now for nearly two
decades. Liu’s 1985 paper (Phys Rev.Let.,55,529) clearly
shows a fractal capacitor built from a Cantor set. It sets the
date of relevant prior art.
first looked at fractal capacitors in 1988 and included
commonly known structures such as Koch islands. He found that
near/at DC, and only near/at DC, a fractal structure can
approximate a capacitor and thus there can be bona fide
fractal capacitors. They are a little hard to make for these
applications, and the thickness of the foil or trace material
sets a limit to the practical advantage. Voltage gradients are
also an issue and fractal capacitors are likely to pit easily
over time—not what you want in any powered application!
at RF, the complexity of a fractal structure cannot
be described simply as a ‘C’ in a ‘LC’ or ‘RLC’
circuit. It is an ‘LC’ or ‘RLC’ circuit
and thus is defined as a fractal resonator. We
thus recognized that a fractal capacitor was of limited
interest or viability, but a fractal ‘LC’ circuit was
Cohen first described the idea of a fractal resonator in his
1995 seminal paper. Additional disclosure occurred with the
publication, in 1997, of one of our PCT applications (which is
pending; watch for updates). It is protected by our patents
and covered in patents pending. Our invention of fractal
resonators establishes priority and defines what is now the
Think of a fractal
resonator as a non-radiating, or poorly radiating, fractal
antenna and you’ll get the idea of the possibilities.
Remember, all antennas are themselves RLC circuits.
Q: I understand that fractals have
been used to solve an old problem from Maxwell's Equations.
What is that?
A: In 1999, Fractal's Nathan Cohen published an article solving a basic
problem--what are the requirements to make antennas
frequency invariant. A later article by Robert Hohlfeld
and Nathan Cohen then analytically showed that you need
origin and self symmetry (self similarity) for this to occur
in Maxwell's Equations.
The implications are profound for antenna design, as a
previous but less universal explanation by Victor Rumsey, made
nearly 50 years ago, was shown to not be the total
picture. The necessary and sufficient conditions for frequency
invariance have been dubbed 'HCR Conditions', after the three
contributors to solving this age old problem.
Q: If a FEA
shrinks an antenna, how can it still work well?
A: It is
well known that physical limitations impose severe field
strength restrictions on electrically small antennas. And,
when FEA are chosen to be very small (compared to a
wavelength) they perform poorly--like all such small antennas.
However, at the top side of the electrically small regime (say
shrunk 2-4 times) FEA perform extremely efficiently and
practically exceed other methods of antenna loading, including
Q: What are
some other benefits of FEA?
A: FEA are
self-loading so no antenna parts, such as coils and
capacitors, are needed to make them resonant. In addition they
often do not require any matching circuitry for their
multiband or broadband capabilities. In effect the fractal
design 'does the work', thus lowering the cost and increasing
the reliability compared to other options.
Q: What types
of designs benefit from fractal application?
A: FEA are
an across-the-board option in antenna design and are
applicable to any type of antenna such as: dipoles; monopoles;
helices; patches; and many others.
frequencies and types of FEA are presently available?
specialize at present on 900MHz, PCS, and WLAN
applications. In addition, our line of wideband products have
unique capabilities that are available no where else and we
have antennas that work over moderate and wide bandwidths. We
also have successfully met customer needs from 5 MHz to 20
Q: How can I
decide if FEA meet my application?
first step in the process is to fill out and FAX the Application
Inquiry Form. Please note that we specialize in custom
Q: Do you
provide FEA or are they available from other vendors?
Antenna Systems, Inc., meets the needs of its customers by
providing antenna solutions. We can provide the antenna as a
component (often customized) or license the applicable
technology as needed. Our antenna solutions are not available
from other vendors.
Q: I experimented
with a Hilbert curve fractal antenna and tested it, based on
some claims about uses for mobile and handheld uses. It small
but works very poorly as an antenna. Why?
There are a near
infinite number of possible fractal antennas. While all of
them share certain attributes, such as shrinkage; broad
bandedness at higher resonances; and so on, only a very few
are good or great antennas for a particular application or
frequency. Many researchers have not taken the trouble to
consider the issue at hand: 'what problem is being solved'?
Instead, they often choose a well-known fractal geometric
design and report its RF properties. This served the field
well in its infancy, but not its present maturity. That’s
why we’ve spent over 30 man-years of manual effort and then
optimization-directed searching to find the very best fractal
antennas for desired applications-- with great success.
We are indeed practical: we enjoy solving application
problems. We have resisted publishing fractal antenna taxonomy
as this fails to contribute to the true science of fractal
antennas, and is worthless in exploring practical novelty from
an inventive sense. In other words, it doesn’t benefit our
customers. We do not publish articles at the ‘minimum
publishable unit’. All of our publications have exposed
basic insight into fractal antennas and how they work.
For small sized
antennas, the Hilbert curve doesn’t make the cut. At higher
iterations it has
the unusual attribute of being its own’ Faraday shield’
and is a remarkably poor radiator. Its radiation cancels in
the far field. Peano curves are close behind as poor, small
radiators. A better description might be as ‘fractal
resonators’; see US patent 6452553. You may wish to ask your
citation source why the Hilbert curve was chosen and described
as a useful antenna and pose the question: what was the
problem to be solved?
Q: How is a fractal
antenna better than a meander (crank-line)antenna?
Antennas made of repeating sections are not new. The
first of these ‘meander antennas’ is the ever popular
spring, or a ‘Wheeler helix’, now over 50 years old. It is
a three dimensional version. Two dimensional ones look like
Grecian frescos or rug borders. Antennas engineers refer to
these meanders as ‘crank-line antennas’, or CLA’s.
are uniform , discrete and repeating reactive loads, and can
be replaced as an equivalent circuit by a series of the same
valued reactive component. As such, the benefit is that
the height of the antenna is shortened, juts as with FEA.
But because CLA’s are limited by the repetition of
the same sized geometric pattern, they do not have the chance
to be shaped to best produce the reactive loads needed for
best performance and multiple frequency operation. Basically,
they get by, but have never been shown to be the best in
performance for smaller antennas with multiple band needs.
On the other hand, FEA
are, by definition, easily shaped, just by changing motifs and
iterations. An FEA takes advantage of the freed-up design
space that a CLA cannot possible have, to get the best out of
the least form factor.
Most meander antennas
are off-patent, despite any statements to the contrary. These
off-patent antennas are freely available to any and all firms.
firm sees no impediment to giving customers CLA antennas from
these off-patent inventions—we just haven’t found that
they meet the need, as FEA options do better for their
Below is an off-patent CLA dipole (right) and a fractal dipole
with virtually the same performance and SWR . Note the size
We have tested many
meander antennas, and never found one that solves an
application problem better than the respective FEA solution.
antenna line is one of
many examples of a FEA which beats a meander handily.
Q: I know of
someone who has been warned (by another company) not to use
the term ‘fractal antennas’. Yet your firm uses it freely.
Isn’t this what you do? What gives?
A: We freely
create, make, and sell fractal antennas and describe them as
fractal antennas. The term ‘fractal antennas’ is not
trademarked. Trademarks refer to brands and not to things.
They are adjectives that describe a noun. The term uses
‘fractal’ as an adjective to the noun
‘antennas’, thus ‘fractal antennas’ is not an
adjective by itself—it has no noun to describe. The term
‘fractal antennas’ is a generic one which has long been in
use well before any attempt to claim some trademark aspect
(for example, Nathan Cohen’s seminal 1995 paper on fractal
antennas is: ‘Fractal Antennas: Part 1’), and is not
defensible as a trademark.
We are the holder of the web names www.fractalantennas.com
. We use the term and the domain names without any impediment.
there exists a trademark that uses the term to describe
aerials. This is akin to saying ‘Yellow bananas® bananas’
, by analogy, as
registered by the owner. We do not believe that there is any
problem with the use of ‘Yellow bananas®
bananas’, or ‘wavelet antennas(R) antennas’, or
‘fantastic antennas® antennas’, as examples, and wish the
owners the best with their trademark, as used properly.
However, incorrect use of a trademark by the owner creates
exposure from competitive confusion; and additionally can
force the trademark in jeopardy as a protected mark. The
warning you describe would appear to indicate confusion on the
use and scope of the trademark on the part of that owner.