Turn-key PCB assembly services in prototype quantities or low-volume to mid-volume production runs

Fractal antenna constructions

Among the usual antennas used in today’s data transfer, there are also different type of antennas used. First publications about electrodynamic characteristics of fractal structures were published in the 1980s, but the first practical approach appeared after 10 years. Dr. Nathan Cohen professor of Boston university designed, engineered and patented many practical fractal antenna solutions and founded “Fractal Antenna Systems” in 1995.

As Nathan states in the center of Boston, there were forbidden to use external antennas in the city so he managed to hide antenna within the design of amateur radio station. He took aluminum foil and made antenna as decoration according to Van Koch figure:


This figure builds as follows: first-line (length is z)is cut in 3 even pieces z/3. In the middle, the triangle is formed with same side lengths z/3 and same angles. This way wee gets single element template. Then repeat this process with other segments where sizes diminish 3 times (z/9) then follows again 3 times (z/27) and so on. This way fractal size doesn’t change.

Today fractal antenna technology is in early stages because engineers are doing empirical experiments to find out what geometrical structures give better results. During these experiments, they found out that using ordinary type antenna templates building fractals give better gain coefficient. Like this antenna type:


This type of structure is a so-called recursive tree. Each new iteration multiplies branches by two and lowers resonance frequency. So using iterations it is possible to use the antenna at lower frequencies without increasing antenna size.

Dipole antennas usually have narrow band-about 2.4% around frequency carrier. If 5th iteration is used then this parameter grows up to 3.1%. If the 3D tree is used (when there are 4 branches used instead of 2) then this parameter grows up to 12.7%.

Besides Dipole antennas there are resonant loop antennas used. Loop antennas are build using Koch figures:

loop_fractal antena.PNG

Ordinary frame antennas have low input impedance what makes difficult to connect to the feeder. Fractal loops allow increasing impedance even for frequencies lower resonance and this way effectiveness increases.

Another thing what makes fractal antennas so attractive is that they can be fabricated using PCB making methods. Because of the compact size, they can be put directly on PCB inside like a cell phone.

Additionally to narrowband antennas there one type of antennas – wide band. These are Sierpinski antennas are frequency independent and have several bands of resonance and can be compared to log-periodic and spirals. Frequency independence is a result of retaining similar shape at many scales. Sierpinski fractals don’t require additional space while frequency band grows as it happens with spiral and log-periodic antennas:


Sierpinski fractal antennas can be successfully used in automotive where transparent antennas are stuck to the front window (or other) and can receive multiple bands independently to standard and country.


Another widely used example is cell phones. They are a long time using internal fractal antennas:


This allows using multiple bands like 900MHz, 1800MHz, 1900MHz and so on.

Source: RA-2002-09


  1. Meesage from Jyoti Joshi by email:
    I am student of Karlsruhe University, Germany. Currently I am experimenting on Sierpinski Fractal Antennas for 200 MHz to 900 Mhz range.
    Has anybody tried Sierpinski Fractal in this range ?
    Can you share your experiences, suggestions ?

  2. I am interested in building a fractal antenna which would be omnidirectional with a bandwidth from 27 MHz through to 3 GHz… Has anyone experimented along these lines? If so, can they share their experiences so that we neophytes may learn? Thanks.

  3. can you please provide me with some more material on Fractal Slot Antennas. Actually i am a student of M.Tech at IIT Roorkee and will be doing my thesis on Fractal Slot Antennas.

  4. this is a very good site for info on fractal antennas. 21 different designs were made in a seven month period, and the fra 1a is the best of the best.


  5. Interesting question, Britt… did you ever hear from anyone or learn anything anyhwere else about building an omnidirectional antenna with bandwidth from 27 MHz to 3GHz?

  6. @Churka,

    Where did you see 21 different fractal antenna designs?

  7. Pingback: Grelmar.com » Blog Archive » Maybe a Fractal a day?

Leave a Reply