A very simple Z shaped dipole, the Fractal of it, and 5 dB Gain

Generally folks who have done radio stuff for a while know you can take your basic dipole of two straight wires and bend those wires in various ways while still getting an OK antenna out of it.

This takes all sorts of forms. Inverted V. “Bent Dipole” where you just sort of droop the ends. all sorts of shapes have been given specific names. Yet this one was new to me. The Z shaped dipole.

The paper, linked below, most likely is very clearly saying in what direction to bend the arms to make the Z but they assume there is some standard axis for X Y and Z relative to ground. A standard, if I ever knew it 50 years ago when more serious about this stuff, I’ve long ago forgotten. For the basic antenna, the ‘feed’ is in the middle of the Z and the two wires are bent about the middle. My impression was that the Z is in the front to back plane, but others will need to sort that out. It might work just as well if the ends are in the up-down or right-left, though perhaps with some change of polarization. Here’s the link to the paper:


2.1 Antenna Structure

This antenna is made of a Z-shaped thin wire and is fed symmetrically as shown in Figure 1. The antenna is located in the
xz–plane. The fractal first, second and third iterations of Z-shaped dipole antenna are depicted in figures 2, 3 and 4. Each iteration is formed by replacing the half of the free arm of Z-shape by another Z-shape. All of these antennas have the same wire length (202 cm) and a radius of 0.1 cm. The MoM with one-volt delta gap source is applied to theses antennas. The previous antennas occupy different spaces as shown in the figures and table 1. The antenna performance properties are obtained using commercial software (NEC-WIN Pro V.1.6)

It would be nice if they had labeled their graphs. ( I remember my high school algebra teacher giving us great grief for any graph with unlabeled axis. )

The paper then goes on to look at fractal derivations. For those, some of the main central wire, and the end segment is itself bent into another Z for a first order fractal. Then again for a 2nd order and so on to 3rd order. This image is the first step:

Z dipole and first fractal

Z dipole and first fractal

Two things about this got my attention. First off, it is just a wire. Nothing really fancy going on here with cutting slots or making flag shaped pennants or needing to hold circular shapes.

Second, when I read the gain figures I was a bit surprised. I am used to the idea of a dipole being basically a ‘no gain’ vs a reference standard dipole, even if bent. Here’s the chart of gain (from Table 4, 7th page #145):

Antenna     400 MHz     900 MHz     1900 MHz
Z Dipole     4.4 dB      4.1 dB       10 dB  (Honest, I read it twice.  10)
1st Iter     3   dB      7.5 dB       2.0 dB
2nd Iter     5.1 dB      4.9 dB       5.5 dB
3rd Iter     4.8 dB      4.53 dB      3.9 dB

All I can figure is that the long wire is acting off the ends as a long wire multiple wavelength for that 1900 MHz one, or maybe their reference is not a ‘standard dipole’.

By the time you are at the 3rd Iteration, the antenna fits in a 40 cm by 51 cm box. Now the TV range I’m trying to pick up runs about that 400 to 900 range, so something in this size or double ought to work. Call it a meter by 80 cm. Given that the 2nd iteration is a bit more gain and still fits in a 45 x 50 cm box, it is likely the one I’d use.

For two bent wires and nothing else. Makes a fella go “Hmmmm….”

From the previous figures we notice that the fractal ZDA has superior performance over the linear dipole. The linear dipole is resonant antenna but fractal ZDAs show broad characteristics. The fractal ZDA has superior current distribution at the linear dipole. The main difference between these two antennas is the polarization where the linear dipole is linearly polarized antenna [1,2] but fractal Z-shaped dipole antenna is elliptically polarized antenna.

Remember that a circularly polarized antenna is an elliptically polarized one that is radially equal…

The two handednesses have opposite circular polarization, so a dipole of one each would pick up both circular polarizations along with horizontal and vertical linear polarizations. Equally out front and back.

Now that’s an interesting antenna… especially since shifts of polarization at UHF from reflections is one of the most annoying kinds of ‘fade’ and ‘flutter’ to deal with. Go ahead and shift, or rotate, or whatever, this antenna just won’t give a damn…

FWIW, if I’m reading the graphs correctly, down in the 400 MHz range the standing wave ratios et. al. are a bit more peaky, then smooth out at the higher frequencies. This implies a (still small…) double size one would be even better at multiband. This one looks to have been designed for the peak at lower frequencies to be usable at that frequency, then pick up the upper bands as near harmonic and broader band segments. As I’m not interested in 1900 MHz, I’d look to make the thing larger to put the base at about 200 MHz and then 400 to 800 in that nice upper range.

The other interesting potential this raises is testing some “Z Dipole” log periodic layouts… but that would take math involving logs and this is a weekend ;-)

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About E.M.Smith

A technical managerial sort interested in things from Stonehenge to computer science. My present "hot buttons' are the mythology of Climate Change and ancient metrology; but things change...
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16 Responses to A very simple Z shaped dipole, the Fractal of it, and 5 dB Gain

  1. Larry Ledwick says:

    Hmmm interesting.

    The first Z form should behave very similar to a base fed inverted L over a ground plane.

    Inverted L is sometimes used for short wave frequencies where vertical height is limited. For example go up as high as you can then horizontal (between two trees for example)


    Inverted L antenna short video

  2. jim2 says:

    Here’s a copy of the paper with no sign-up:


  3. jim2 says:

    The copper-tape hoverman alone wouldn’t pull in the distant stations, ~60 mi. So, I pointed the one with a reflector to the distant stations and the copper-tape one to the local stations, ~15 mi. Each antenna has a 300:75 ohm transformer, each fed into a splitter (combiner). Now can get both sets of stations. I’m going to play with the separation distance between them. I have about 15 feet to play with. I’m happy with the result so far.

  4. jim2 says:

    Next up for me is a hoverman with infinite balun, just for fun.

  5. jim2 says:

    Also, could you use one of the Z-fractals and its twin as a dipole?

  6. E.M.Smith says:

    The Z fractal IS a dipole… Feed is in the middle and there are two ‘wings’ out from it as the ends of the dipole… or perhaps you are saying the thing I pondered… having an L form on one side of the feed point and an R on the other..?..

    It ought to also be possible to put an L and an R together as a stacked dipole array… spacing about like any dipole array I’d expect…

    Oh, and thanks for adding the ‘no sign up’ link. I’d not noticed the one I put in needed a sign up as it displays the whole thing anyway…

  7. Eric Fithian says:

    Now, all I need is to make up a set of these as Rectennae, and run my equipment off the 8 Megawatts of local Digital TV signals in the local Denver area….

  8. jim2 says:

    Yes, I was thinking of the L-R configuration.

  9. jim2 says:

    With the reflector hov. pointing N, and the non-reflector one pointing S, 3-4 ft apart, one station’s signal completely dropped out even though it was very strong before. It came back on. Was it a plane, truck on a highway, what? Anyway, put them back to back so the non-reflector one “borrowed” the reflector of the other, better but still got occasional pixelation.

    So, aligned them so the elements are co-planer. So one is plain hoverman with reflector, the other made of copper tape with upper and lower detached elements but no reflector, with the reflector one pointed to most distant stations. Now getting max number of channels and so far all are strong. This should prevent one antenna getting main signal and another one getting a spurious reflection.

    Will see how this works out.

  10. Larry Ledwick says:

    In that first configuration, you might have had perfect signal cancellation for that one station with one antenna being exactly 180 degrees out of phase with the other. If so might be able to fix that configuration by playing with the spacing between the antennas if the current setup has issues you have not seen yet.

  11. E.M.Smith says:


    Sounds like a good arrangement!


    Well, only if you can get more than 0.2 VDC in the antenna… for that you need a pretty strong beam. (Very few semiconductors have a diode voltage below 0.2 gap… so that’s the minimum before you can actually rectify anything… Germanium is most widely available with low band gap.)

  12. Nathan says:

    This patented antenna is restricted for commercial purposes, but as the inventor I have authorized the patent holder to allow experimentation for private use. Kindly appreciate that there has been a tremendous amount of derivative and unattributed work on fractal antennas that all goes back to my efforts and IP over many years. Thank you.–Nathan Cohen

  13. E.M.Smith says:


    Thank you for your creation and permission to explore it.

    Do note that patents grant exclusive commercial use, but do not restrict personal research or experimentation of a non commercial nature. That is why patents are published and must be sufficient for those “skilled in the art” to reproduce them.

    That said, we’re just technical hobbyists here, not commercial folks, and mostly interested in climate science issues at that (though I’m interested in computers too) so you have nothing to fear from us playing with bent wire in our attics.

    Also note that the source publication is cited in the article as attribution.

    Again, thank you for your work in creating this design.

  14. E.M.Smith says:

    Hmmmm the pdf of the paper says it is written by Mustafa H. Abu Nasr and cites other papers but not Nathan. So, from the fractal antenna wiki:

    Log periodic antennas and fractals

    The first fractal “antennas” were, in fact, fractal “arrays”, with fractal arrangements of antenna elements, and not recognized initially as having self-similarity as their attribute. Log-periodic antennas are arrays, around since the 1950s (invented by Isbell and DuHamel), that are such fractal arrays. They are a common form used in TV antennas, and are arrow-head in shape.

    Fractal element antennas and performance

    Antenna elements (as opposed to antenna arrays) made from self-similar shapes were first created by Nathan Cohen then a professor at Boston University, starting in 1988.

    Cohen’s efforts with a variety of fractal antenna designs were first published in 1995 (thus the first scientific publication on fractal antennas), and a number of patents have been issued from the 1995 filing priority of invention. Most allusions to fractal antennas make reference to these “fractal element antennas”.

    So there’s a generic attribution.

    I note in passing that 1995 is 22 years ago, so patents from then ought to be expired and more expiring going forward. Each year, more designs will be in the public domain and the general concept of self similar antennae have been public even longer.

    Do you have a citation for a patent on the Z fractal and when it expires?

  15. Larry Ledwick says:

    I would guess this is the patent he is referring to.

    List of his patent applications:

  16. Larry Ledwick says:

    A FAQ on his work and the antennas.

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