Report on Fractal Antennas.

Abstract The objective of this project is to characterize a planar fractal antenna. To accomplish this, a micro strip patch antenna is designed at the operating frequency of 2.4 GHz. A microstrip Sierpinski carpet fractal antenna having the same physical dimensions is then numerically modeled, the results of the two antennas are compared and fabrication of fractal antenna small size Sierpinski carpet for WLAN application.

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CONTENTS Chapter 1: Introduction 1.1Overview 1.2Motivation 1.3Outline

4 4 4

Chapter2: problem statement

2.1 The goals of this project are as follows 2.2 The approach to completing the abovementioned goals is as follows

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Chapter3: Literature Review

3.1.1 Microstrip Antenna 3.1.2 .Rectangular microstrip patch antenna 3.1.3. Feeding Techniques 3.2 Fractals 3.2.1 Why Fractal Antennas? 3.2.2 Iterated Function Systems 3.2.3 Type of fractal antennas 3.3. Advantages and disadvantages of using fractal antenna

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Chapter 4: Preliminary Results 4.1 Microstrip Antenna Calculations 4.2 Design of the Microstrip Patch Antenna 4.3 Results 4.4 Design of fractal antenna 4.4.1 First iteration of Sierpinski carpet fractal antenna 4.4.2 Second iteration of microstrip Sierpinski carpet fractal antenna

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Chapter 5: Conclusions and plans for next semester References

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List of figures Fig3.1: Different shapes of microstrip antenna Fig 3.2 Rectangular microstrip patch antenna Fig 3.3: Top and side view of the probe feed Fig3.4: Top view for line feed Fig 3.5 Block diagram of the Iterated Function System (IFS) Figure 3.6: Koch Curve Figure 3.7: Sierpinski gasket Fig3.8: Sierpinski carpet iterative constriction Figure 4.1: Microstrip patch geometry Figure 4.2: The return Loss (Ґ Vs Frequency) Figure 4.3 Geometry of square microstrip patch in IE3D Figure 4.4: The return Loss (Ґ Vs Frequency) Figure 4.5: Geometry of the first iteration of Sierpinski carpet fractal antenna Figure 4.6: The return Loss (Ґ Vs Frequency) Figure 4.7: Geometry of the second iteration of Sierpinski carpet fractal antenna Fig 4.8: The return Loss (Ґ Vs Frequency)

Tables

Table4.1 Design parameter value Table 4.2 Basic parameter for IE3D

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Chapter 1: Problem statement

1.1 The goals of this project are as follows: (i) (ii)

To gain familiarity with the design, fabrication and experimental characterization of microstrip patch antennas. To design a fractal antenna and compare its characteristics with a microstrip patch antenna.

1.2 The approach to completing the abovementioned goals is as follows: i) ii) iii) iv) v) vi) vii) viii) ix)

Literature review for microstrip and fractal antennas. This is presented in the next chapter. Gaining a working knowledge of the computational electromagnetics software (CEM). Designing a microstrip patch antenna. Numerical modeling of microstrip antenna using CEM software. Numerical modeling of a fractal antenna using CEM software. Comparison of the numerical results for the microstrip patch and fractal antenna. Fabrication of antennas. Experimental characterization of antennas. Comparison of the numerical model and experimental results.

1.3 problem statement: The purpose of this project is to design fractal antennas,The designs of small size Sierpinski carpet Monopole antenna are undertaken to achieve this goal.

1.4 Solution overview: Since using fractals as an approach to antenna design is a relatively new development in the field of antenna research, the Sierpinski carpet microstrip antenna were Selected for this project. They are simple to design and their radiation properties are far better documented in research literature than those of other types of fractals Before undertaking the design of both antennas, it is prudent to establish general design plan and to determine the constraints imposed on that plan. The design plan includes the following phases:

1. Theoretical development: rough calculations of antenna parameters as wells develop a general idea of the physical implementation of the antenna. 2. Numerical simulation: perform software simulations in order to verify the theoretical design and adjust any parameters to predict the desired antenna performance. 4

3. Physical implementation: undertake physical construction of the antennas based on simulationconfirmed parameters. 4. Experimental testing: measure antenna performance is measured and compare with the simulated results.

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Chapter 2: Introduction

1.1 Overview In the current world of wireless communications, there has been an increasing need for more compact and portable communications systems, just as the size of circuitry has evolved to transceivers on a single chip, there is also a need to evolve antenna designs to reduce size. The goal of this project is to characterize a fractal antenna. Fractal antenna engineering is a relatively recent development [1], and is an active area of research, as small size and multiband property of fractals make them an attractive candidates for wireless communications [1]. In this report a microstrip patch operating at 2.4 GHz is designed. A Sierpinski carpet fractal antenna of the same physical dimension is numerically modeled and the results of antennas are compared.

1.2 Motivation Antennas are an integral part of any communication system, and the purpose of this project is to acquire experience in antenna design. To achieve this goal, the most commonly used antenna, i.e., the microstrip antenna is first designed and analyzed. This is followed by the design of a fractal antenna.

1.3 Outline of the Report: Problem statement is given in Chapter 1. A research literature review on microstrip patch and fractal antenna is given in Chapter 2. Chapter 4 describes the design and numerical modeling of microstrip patch and fractal antenna.

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3.1.1 Microstrip Antenna: Microstrip antenna is one of the types of antennas classified as a printed antenna or planar antenna. Small size, low production costs, ease and inexpensiveness of fabrication, mechanically robustness, compatibility with MMIC designs and conformability on the curved surfaces are the advantages that make microstrip antennas to be extensively used in the telecommunication industry [2]. But despite these advantages there are some disadvantages, including narrow bandwidth, low efficiency and low gain. The dimensions of the patch are usually in the range from and the dielectric constant of the substrate εr is usually in the range from 2.2 to 12. The most common designs use relatively thick substrates with lower εr because they provide better efficiency and larger bandwidth. There are many shapes for microstrip antenna for example square, rectangular and circular, as shown in the Figure 3.1.

Fig3.1: Different shapes of microstrip antenna 3.1.2 .Rectangular microstrip patch antenna: The rectangular microstrip or patch antenna as shown in the Figure 3.2 is most commonly used and attention is restricted to this shape in this project. The patch is a highly conducting metal placed at a height h above the ground plane. The height h is normally 0.003 0 to 0.05 0 here 0 is the free space wavelength. The length L of the patch antenna is normally from 0.333 0 < L < 0.5 0 and the thickness t of the metallic patch is much less than the operating wavelength.

Fig 3.2 Rectangular microstrip patch antenna

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3.1.3. Feeding Techniques: There are many type of feeds for microstrip antenna, the commonly used ones are as follows: i) Coaxial probe feed ii) Microstrip line feed iii) Aperture coupling iv) Proximity coupling and Here only coaxial feed and microstrip line feed will be described. Coaxial probe feed: This method is well known for a number of advantages, including ease of fabrication, low spurious radiation and a strong feature is that it has the flexibility to place the feed anywhere inside the patch in order to match the input impedance, as shown Figure 3.3. However there are disadvantages for this method as it is difficult to model accurately and has narrow bandwidth between 2-5%. Patch probe feed

substrate ground plane

Fig .Top view of probe fe

probe feed

Fig 3.3: Top and side view of the probe feed Microstrip line feed: This type is easy to fabricate, simple to match by controlling the inset position and relatively simple to model. The feed is etched on the same side as the metallic patch as shown in the Figure 3.4. Line feed

Fig3.4: Top view for line feed

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3.2 Fractals “A fractal is a shape made of parts similar to the whole in some way” B. B. Mandelbrot [3]

Madelbrot defined fractals as a rough and fragmented geometrical shape, which can be subdivided into parts each of which is a reduced copy of the whole [3,4]. Therefore the basic property of a fractal shape is self-similarity and structure at all scales. A strict mathematical definition of a fractal is an object whose Hausdorff-Besicovitch dimension strictly exceeds its topological dimension [4]. 3.2.1 Why Fractal Antennas? The relationship of the physical size of the antenna to its operating wavelength is a fundamental parameter in antenna design. The physical size of an antenna is generally half or quarter of its operating free space wavelength, and the range of frequencies over which the antenna operate satisfactorily is normally 10-40% of this center wavelength. This range of frequencies is generally called the bandwidth of the antenna. Making the dimensions of the antenna much smaller than its operating wavelength will reduce its radiation resistance, efficiency and bandwidth. Recent work [5] has shown that fractal geometry due to its self similarity property can overcome this limitation of antenna size and its operating wavelength, that is, fractal antennas can be much smaller size than the operating wavelength without seriously affecting the other antenna parameters. Also antennas based on fractal geometry display multiband behavior, not easily available in conventional antenna design. In summary, the compact size of the fractal antenna (relative to its operating wavelength) and its multiband behavior makes its very useful in current telecommunication industry. 3.2.2 Iterated Function Systems: [6] One way to generate fractals is through an iterative process. The fractal generation begins with generator shape and a feedback process as shown in the Figure 3.5.

Fig 3.5 Block diagram of the Iterated Function System (IFS)

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3.2.3 Type of fractal antennas: Koch curve: The Koch fractal curve is one of the most well known fractal shapes. It consists of repeated application of the IFS. The Koch curve is shown in Figure 3.6. Each iteration adds length to the total curve which results in a total length that is 4/3 the length of Koch curve and is given by: ( ) Here k is the iteration stage.

Figure 3.6: Koch Curve

Sierpinski gasket: The Sierpinski gasket or triangle is generated by using triangle as the basic function shape. The Sierpinski Gasket fractal is generated by the IFS method and Figure 3.7 shows the step generation of Sierpinski gasket

Figure 3.7: Sierpinski gasket Sierpinski carpet: The Sierpinski carpet is shown in Figure 3.8, it uses a square instead of the triangle as the basic function shape.

Fig3.8: Sierpinski carpet iterative constriction

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3.3. Advantages and disadvantages of using fractal antenna Advantages of fractal antenna technology are: i) Minimize the size ii) Increase the bandwidth iii) Good input impedance matching iv) Wideband/multiband (use one antenna instead of many) v) Frequency independent, i.e., a consistent performance over a large frequency range Disadvantage of fractal antenna technology are: i) Complexity in modeling the antenna ii) The benefit begin to diminish after first few iterations

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Chapter 4: Design and Results In this chapter will show the design and result for microstrip and fractal antenna Sierpinski carpet.

4.1 Microstrip Antenna Calculations: Given relative permittivity εr, height of the substrate (see Figure 3.2) and the operating frequency the design of the microstrip patch proceeds as follows [2]. Finding the width of the patch: W=

√ε

(4.1)

Here c is speed of light and

is the resonant frequency

Finding the effective dielectric constant: (4.2) √

Taking into account the fringing effect: The fringing fields along the width of the structure are taken as radiating slots and the patch antenna is electrically seen to be a bit larger than its physical size. ( (

)(

) )(

(4.3)

)

Calculating the effective length of the patch (4.4) √

Calculating the actual length of the patch (4.5) 4.2 Design of the Microstrip Patch Antenna: Design Parameters εr

Dielectric Constant of the Substrate Height of the dielectric substrate Operating frequency

2.2 1.588mm 2.4 GHz

Table 4.1: design parameters value Step 1: Calculation of Width (W): From Eq. (4.1), W = 49.4mm Step 2: Calculation of Effective dielectric constant( Using Eq. (4.2), Step 3: Calculation of effective length: 12

)

From Eq. (4.4), Leff= 43.0298 mm Step 4 : Calculation of the length extension(ΔL ) From Eq. (4.3), ΔL =.83711mm Step 5 :Calculation of the length of the patch (L): Using Eq. (4.5), L = 41.3558mm This calculations are also checked using the online microstrip calculator [7] 4.3 Results: The numerical modeling of the microstrip patch is done using computational electromagnetic software. The software which is used for this project is known as IE3D [8], and it is a method of moments based software. The parameters of the micro strip patch which are used for this modeling with this software given in Table 4.2. Parameter used in IE3D : Parameter

Value

Dielectric Constant of the Substrate

2.2

Center Frequency

2.4GHz

Loss tangent

0.0009

Width of the patch Length of the Path Height

49.4mm 41.4mm 1.588mm

Table 4.2: Basic parameter for IE3D The microstrip patch is fed through probe feed, and the geometry of the microstrip patch in IE3D is shown in Figure 4.1 which also shows the location of the probe feed.

Figure 4.1: Microstrip patch geometry

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Figure 4.2 shows the return loss for this design, it may be noted that the location of the probe feed is varied to get the maximum value of the return loss. The value of return loss for different feed locations and for GHz is shown in the Table 4.2.From the Figure 4.2 it may also be noted that the maximum return loss is not exactly at the design frequency of 2.4 GHz, the reasons for this is the approximate value of εr available for the substrate as well as the loss tangent of the substrate which is not used in the design calculations.

Figure 4.2: The return Loss (Ґ Vs Frequency) Figure 4.3 shows the geometry of the patch when its width is equal to its length, again in this case the location of probe feed is varied to get the maximum return loss, while Figure 4.4 shows the return loss versus frequency. Again the antenna appears to be resonant at the design frequency.

Figure 4.3 Geometry of square microstrip patch in IE3D 14

0 -5 -10 -15 -20

No.1

-25 -30 -35 -40 2.1

2.2

2.3

2.4

2.5

2.6

2.7

Figure 4.4: The return Loss (Ґ Vs Frequency)

4.4 Design of fractal antenna 4.4.1 First iteration of Sierpinski carpet fractal antenna The design of the microstrip Sierpinski carpet fractal antenna follows the approach of ref. [9]. First a microstrip patch at the required operating frequency is designed, as done in the previous section. Then the first iteration of the Sierpinski carpet fractal antenna proceeds by dividing the microstrip patch into nine equal squares and removing the center square. This is shown in Figure 4.5 in IE3D simulation window. Since the length of the microstrip patch is L0 = 41.4 mm as noted in the previous section, the length of the side of the square is L1 = 13.7 mm here L1 is called the scale factor for length. Figure 4.5 also shows the location of the probe feed. The probe feed location is adjusted so as to connect to the metallic portion of the patch.Figure 4.6 shows the results from IE3D simulations, as may be noted that the antenna has a magnitude of return loss greater 20 dB at the frequencies approximately 8.2 and 12 GHz, thus it isdisplaying multiband behavior, but there also a shift from the initial design frequency.

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Figure 4.5: Geometry of the first iteration of Sierpinski carpet fractal antenna

5 0 -5 -10 No.1

-15 -20 -25 -30 0

2

4

6

8

10

12

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Figure 4.6: The return Loss (Ґ Vs Frequency)

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4.4.2 Second iteration of microstrip Sierpinski carpet fractal antenna In the second iteration of microstrip Sierpinski carpet fractal antenna, each of the eight remaining square is divided into nine equal squares,and the center square is removed, this is shown in figure 4.7. The scale factor for length in this case is L2 = 4.6 mm. Figure 4.8 shows the results for this iteration, as may be noted that the antenna displays the multiband behavior at the frequencies of 3.8, 9.6 and 12.1 GHz.

Figure 4.7: Geometry of the second iteration of Sierpinski carpet fractal antenna

5 0 -5 -10

No.1

-15 -20 -25 0

2

4

6

8

10

12

Fig 4.8: The return Loss (Ґ Vs Frequency) 17

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4.4.3 First iteration of Sierpinski carpet fractal antenna (small size) Small size prop feed: In fig 4.9 the value of W=42.4mm and the value of L=35.3mm , W/L=83.25 % the return loss around 2.4 GHz .

Fig 4.9 Geometry of the second iteration of Sierpinski carpet fractal antenna (small size)

Fig 4.10: The return Loss (Ґ Vs Frequency) 18

4.4.3 second iteration of Sierpinski carpet fractal antenna (small size) In this project want to reduce size and get same result ,at Fig4.11 will reduce the value of W to 41.69mm and reduce the value of L to 34.6 mm at W/L =82.45% to get the the return loss around 2.4 GHz.

Fig 4.11 Geometry of the third iteration of Sierpinski carpet fractal antenna (small size)

Fig 4.12: The return Loss (Ґ Vs Frequency) 19

Chapter 5 : Analysis

Chapter 6: Conclusions and plans for next semester:

The following are the tentative steps to be taken next semester for completion of this project. i)

ii) iii)

Numerical simulations to be done to observe the behavior of return loss on the probe feed location. This will be done for the microstrip patch and microstrip Sierpinski carpet fractal antenna. Numerical simulations to be done for the third iteration of the Sierpinski carpet fractal antenna. To complete the remaining tasks as noted in problem statement.

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References [1] D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research”, IEEE Antennas and Propagation Magazine, vol. 45, pp. 38-57, Feb., 2003. [2] C.Balanis, “Antenna Theory- Analysis and Design”, Third Edition , John Wiley &Sons Ltd,2005. [3] D. L. Jaggard et. al, “Fractal Electrodynamics: Surfaces and Superlattices” in “Frontiers in Electromagnetics”, R. Mittra et. al editors [4] X. Yang et. al, “Fractal antenna elements and arrays”, Applied Microwave and Wireless [5] C. Puente et. al, “Fractal Shaped Antennas” in “Frontiers in Electromagnetics”, R. Mittra et. al editors [6] Philip Wang Sing Tang, “Fractal Antennas”, PhD dissertation, University of Central Florida, 2002. [7] http://www.emtalk.com. [8] IE3D 10.0, Zeland Software Inc., Fremont, CA. [9] Noorsaliza bt Abdullah, “Microstrip Sierpinski carpet antenna design”, MS thesis, Universiti Teknologi Malaysia, Malaysia 2005.

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