The Study of Sierpinski Fractal Antennas for Detecting Various Object

Forms

OURAHMOUN ABBES

Institute of optics and precision mechanics

Ferhat Abbas Setif1, university

SÉTIF, ALGERIA

Abstract: - In this work leverages fractal patch antenna benefits to create a sensor detecting object variations

(cube, cylinder, and sphere). CST software empowers precise complex system simulations. The antenna

effectively controls and detects changes in these objects. Resonance frequency proves highly sensitive to their

variation, yielding impressive performance. A significant contribution to artificial intelligence.

Key-Words: Fractal forms, sensor, antenna, CST Microwave Studio, artificial intelligence.

Received: June 16, 2022. Revised: July 15, 2023. Accepted: August 17, 2023. Published: October 2, 2023.

1 Introduction

In this study, we harness the advantages of

fractal patch antennas to design a sensor capable

of detecting variations in objects such as cubes,

cylinders, and spheres. We employ CST

software for accurate simulations of complex

systems. The triangles Sierpinski carpet antenna,

composed of triangles, effectively manages and

identifies alterations in these objects. The

resonance frequency exhibits remarkable

sensitivity to these variations, resulting in

impressive performance.This research represents

a significant contribution to the field of artificial

intelligence. This work highlights the innovative

application of the Triangles Sierpinski fractal

antenna in controlling and detecting changes in

object shapes, presenting a substantial

contribution to the field of artificial intelligence.

The antenna's unique design and capabilities

make it a valuable tool for enhancing object

recognition and manipulation within AI systems,

offering promising opportunities for

advancements in various AI applications.

2 Introduction

The term "fractal" was coined by B. Mandelbrot,

derived from the Latin word "fractus," meaning

irregular or broken. It was introduced to describe

a novel set of objects that went beyond the

traditional definitions of squares, circles, or

triangles within Euclidean geometry. While

Euclidean geometry worked well for well-

defined shapes, it fell short when it came to

describing everyday elements such as clouds,

blood vessels, and irregular coastlines.

Visionaries like W. Sierpinski, N. Von Koch, D.

Hilbert, and H. Minkowski further enriched the

field of fractal geometry. Their contributions

sparked the interest of antenna engineers in

exploring these geometries for potential antenna

applications.

Fractal geometries have indeed had a profound

impact on the field of antennas and have been

applied in various telecommunications

applications. Here are some key ways in which

fractal geometries have influenced antenna

design and performance [1-6].

One intriguing application of fractal antennas,

particularly those based on Sierpinski carpet

iterations, is for the control and detection of

various objects such as cubes, cylinders, and

spheres.

The primary objective of your work is to design

antennas based on the fractal Sierpinski carpet

and utilize these antennas to detect changes in

the shapes of various objects.

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Indeed, the choice of simulation software for

antenna design depends on various factors,

including antenna geometry, size, materials, and

specific design aspects that need analysis. Let's

take a closer look at the simulation tools you

mentioned and their typical applications:

CST is a high-performance 3D electromagnetic

(EM) analysis software solution dedicated to the

design, analysis, and optimization of

electromagnetic components and systems. CST

enables us to perform complex system

simulations with unparalleled accuracy. It is a

powerful tool for simulating a wide range of

electromagnetic phenomena, making it valuable

for various applications in the fields of antennas,

microwave circuits, RF systems, and more.

3 Simulation of a Sierpinsky carpet

antenna

Our antennas consist of a copper ground (ground

plane), patch and line microstrip (microstrip),

with an FR4 dielectric substrate(see figure.1).

We can calculate the width of the microstrip line

by the following relation:

   

󰇛

 󰇜   

(1)

With

L: width of the microstrip line

h: height of the dielectric

t : thickness of the line

Z0: Impedance = 50 Ohm

: Dielectric constant (dielectric constant of

FR4 = 4.3)

Figure.1 Presentation of characteristic

necessary to calculate the width of a line

microstrip

The base of a Sierpinski carpet is a square patch,

the dimensions we used for the patch are 30x30

mm with a thickness of 0.035mm, a substrate of

60x60mm and a thickness of 1.56mm, for the

ground plane we used the dimensions 60x60mm

and the thickness 0.035mm as shown in Figure.2

For the first iteration and second iteration (see

Figure.3 and Figure.4). An equivalent circuit is

proposed for the triangles Sierpinski carpet as

shown in Figure.5, we removed a square of

10x10mm from the center, the result obtained is

presented in figure.6 and figure .7.

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Figure.2 Simulation of a square patch by CST

Figure.3 Triangles Sierpinski carpet iteration 1

by CST

Figure.4 .Triangles Sierpinski carpet iteration 2

by CST

Figure. 5. Equivalent circuit model of triangles

Sierpinski carpet iteration 2

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Figure .6 Parameter S11 of the 1st iteration

triangles Sierpinsky carpet

Figure .7 Parameter S11 of the 2nd iteration

triangles Sierpinsky carpet

Figure .8 Comparative analysis between the

parameter S11 of the 1st iteration and the 2nd

triangles Sierpinsky carpet.

According to the curve of the parameter S11

presented in figure .6 and figure .7 , we notice

that the Sierpinsky carpet antenna of iteration 1

has a frequency band minimum 2.1GHz and

maximum 9.6GHz.

Figure .8 presents the parameters S11 of the 1st

iteration and the 2nd iteration of the triangles

Sierpinsky carpet antenna simulated by CST,

according to the curves we notice that there is a

small difference in the frequency domain

between the two iterations.

We will use three different shapes (cube,

cylinder, and sphere) in glass, the dimensions are

presented in the following table:

Form

Diameter/dimension

Height

Cube

25 mm

Cylinder

25 mm

Sphere

25 mm

detection by Sierpinsky carpet

We conduct a comparative study between

triangles Sierpinsky carpet and Sierpinsky it2

carpet for object detection sensor

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Figure .9 object detection by Triangles

Sierpinsky carpet

Figure .10 S11 simulation result for 2nd

iteration of the triangles Sierpinsky carpet

antenna

Figure .11 Zoomed of S11 simulation result for

the Triangles Sierpinsky carpet for fr =6.1 GHz

to 7.8 GHz

Figure .12 and Figure .13 present the curves of

parameter S11 of carpet antenna Sierpinsky it2

carpet and the different objects according to the

frequency, according to the two figures, it is

clearly noticed that there is a change and a

difference between the four curves, then we can

say that our fractal is well detected the change of

the objects.

Figure .12 object detection by Sierpinsky it2

carpet

Figure .13 S11 simulation result for the 2nd

Iteration

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Figure .14 Zoomed of S11 simulation result for

the 2nd Iteration for fr =6.1 GHz to 7.8 GHz

The curves figure .10 and figure .13, present the

result of CST simulation of detections of the

various objects, it is noted that the curves S11

according to the frequency of each object

compared with the Sierpinsky antenna. the

Triangles Sierpinski fractal antenna has emerged

as a remarkable technology in its capacity to

effectively control and detect changes in object

forms. This achievement holds great promise for

making significant contributions to the field of

artificial intelligence.

4 Conclusion

In the article, we delved into the simulation aspect of

fractal antennas using CST software, focusing on

simulating a fractal antenna based on the Sierpinski

carpet. The outcomes yielded positive results; all

antennas successfully detected changes in the

objects. However, the triangles Sierpinski carpet

antenna stood out with notably clearer results

compared to the other antennas. This distinction

became evident due to a significant difference

observed among the four curves generated by this

particular antenna. The antenna's ability to precisely

monitor and respond to alterations in object shapes is

poised to revolutionize various applications within

AI, from object recognition to robotics and beyond.

As we continue to explore and harness the potential

of this antenna, we anticipate exciting developments

that will drive forward the capabilities and

sophistication of artificial intelligence systems,

ultimately ushering in a new era of innovation and

practicality in this dynamic field.

Acknowledgement:

The authors express their thanks to Dr. A.

Mansoul, Development Centre of Advanced

Technologies (CDTA), Algiers

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The author contributed in the present research, at all

stages from the formulation of the problem to the

final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The author has no conflict of interest to declare that

is relevant to the content of this article.

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(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

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