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# Sierpinski gasket fractal dimension design.

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#### ananth

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.

#### aaron412

##### Member level 2
fractal dimension sierpinski

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) ??

#### ananth

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.

#### arunkumar

##### Junior Member level 2
Ananth,
The antenna is to operate between 0.8 to 6 GHz.

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.

How does one get the starting dimension of the triangle for a particular frequency of operation?
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.

#### aaron412

##### Member level 2
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.

#### elkimhoc

##### Member level 3
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

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

:idea:

Nitin16

### Nitin16

Points: 2

#### ananth

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.

Nitin16

Points: 2