design formula for sierpinski gasket

Hello Everyone,
I've been trying to find a thumb rule for designing a sierpinski gasket patch antenna for operation at 4 GHz. I've tried to find this but all the literature tels you about the iterations but not a starting point for the size of the first triangle!!
Any help is appreciated..
Thanks,
Ananth.

How many iterations will your sierpinski gasket have??
Sierpinski gasket is a multiband antenna, do you want its first resonance (omnidirectional radiation pattern) to be at 4 GHz, or do you want 4 GHz to be a higher resonance ( directive pattern) ??

Hey Aaron,
The antenna is to operate between 0.8 to 6 GHz. I mentioned 4 GHz because thats the mid band frequency.
So do you think I should start the design at the lower band and then have iterations? I don't think I'll be able to do more than 2 or 3 iterations but I guess that'll depend on the performance of the antenna.

How does one get the starting dimension of the triangle for a particular frequency of operation?
I know (I think!) how to make the iterations if I have some way of obtaining the basic/first dimension of the triangle to start with. I'm thinking of making this in a patch configuration.

Ananth.

Ananth,
In that case, the Sierpinski gasket's base structure must be designed to resonate at 0.8GHz. The rest of the bands can be obtained by iterations/fractal growth.

There is a design methodology for getting the triangle resonant at 0.8GHz. Refer Antenna texts like Antenna Theory by Balanis, Microstrip Antennas by Girish Kumar et.al.

The first resonance of a 4 iterations sierpinski gasket occurs when the monopole's height is arround 0.15 lambda. This may vary a bit for a 2 o 3 iteration gasket but you should use this value as a starting point and then tune your height until you get what you're looking for.

An initial assessment of the fractal geometry is gotten while using the following equation that permits to determine the resonance frequencies of the antenna :

fn=0.152 c/h. cos(x/2). a exp(n)

Where:
- x = flare angle
- c = speed of light
- h = height of the antenna.
- a = log-period (two in Sierpinski case)
- n = iteration number

Hi Elkimhoc,
I'll try using the formula you've given.
Can you tell me where I can find some more setails like the one you mentioned about fractal antennas?

Ananth.

http://www.tsc.upc.es/fractalcoms/ :D