Master's Thesis Report

Multiband Fractal Antenna for Radio Frequency
Identification Systems
Master of Science Thesis
SULTAN AHMED
Department of Microtechnology and Nanoscience, MC2
Micro and Nanosystems group
Bionano Systems Laboratory
CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden, 2009

Multiband Fractal Antenna for
Radio Frequency Identification Systems
1
Abstract
A multiband fractal antenna was designed for the application to radio frequency identification
where the focus was on Minkowski based fractal geometry.
According to the aim of this research the discussion starts with the different types of fractal
antenna and a review of the previous researches done for Minkowski based fractal antenna.
The self similar property of fractal and its geometries whose dimension are not limited to only
length and width or radius for circular shape gives the opportunity to minimize the size of the
antenna as well as to configure the antenna to operate at various frequency bands. These
properties are very important for RFID tags where the small size, planar geometries, multi band
operation and low cost are essential [1].
The design of the antenna first started as a loop antenna and for both 2nd
and 3rd
order of
Minkowski shape has analysed and then the loop antenna was changed to a microstrip patch
antenna for its ease of fabrication thus offering low cost. For patch antenna both 2nd
and 3rd
order were also investigated and finally the 2nd
order has chosen and optimized for 2.45 and 5.8
GHz (frequency band for RFID). The optimized 2nd
order antenna offers a gain of almost 4 dB
with efficiency more than 50% for both frequency bands where the dimension of antenna is
less than 3cm*3cm. The antenna has designed on a Rogers Duroid (εr=2.213) substrate so it’s
possible to make even smaller size of antenna with different substrate where the value of
permittivity, εr is higher than 2.213.

2
List of acronyms
µm micrometer
ADS Advanced Design System
cm centimeter
GHz Gigahertz
HF High Frequency
HPBW Half Power Beam Width
MHz Megahertz
MW Microwave
RFID Radio Frequency Identification
UHF Ultra High Frequency

3
Contents
1. Introduction 4
1.1 Aim of the thesis 4
1.2 Methodology 4
2. Background theory 5
2.1 Introduction to Fractals 5
2.2 Classification of Fractals: 6
2.3 Regular Fractal Geometries 6
2.3.1 Sierpinski Gasket 6
2.3.2 Koch Snowflake 7
2.3.3 Minkowski Island 8
2.4 Microstrip Antennas 9
2.5 RFID and Frequency Band for RFID 10
3. Simulation and Result 11
3.1 Previous research 11
3.2 Second order Minkowski Fractal as a Loop Antenna 13
3.3 Third order Minkowski Fractal as a Loop Antenna 15
3.4 Second order Minkowski Fractal as a Patch Antenna 17
3.5 Third order Minkowski Fractal as a Patch Antenna 20
3.6 Multi Band Response 22
3.7 Asymmetric Minkowski Fractal Antenna 26
4. Discussion and Conclusions 31
Appendix 33
References 35
Acknowledgement 36

4
Chapter 1
Introduction
Nowadays miniaturization is a general trend in communication systems to accommodate the
entire component in a single device. As a result, there is an increasing demand for small
multiband antennas that are also low-cost and robust. An area of research that can fulfill such
needs is the study of fractal geometries with different iteration and different substrates that
constitute single antenna elements.
In this research, the design and analysis of a fractal microstrip patch antenna based on
Minkowski Island, is presented. A fractal is a rough geometric shape that can be split into parts;
and each of it is approximately a reduced-size copy of the whole. Because of their similar
appearance at level of magnification, fractals are often considered to be infinitely complex [2].
Fractals are found everywhere for example, in natural objects like clouds, mountains ranges,
lightning bolts, coastlines, snow flakes, etc.
A fractal can be generated from a “mother” geometrical shape, like a triangle or rectangle,
through a series of iterations and a microstrip patch antenna consists of a conducting radiator
patch printed onto a grounded substrate. The radiator patch needs to be efficient radiators and
thus exhibit acceptable characteristics in terms of frequency response, radiation pattern,
directivity, gain and efficiency.
The objective here is to investigate and analyze the design of fractal microstrip patch antenna
for RFID tags. To accomplish the objective, the Agilent Advanced Design System (ADS) software
package is used.
1.1 Aim of Thesis
The primary goal of the research is to design a multiband antenna based on Minkowski fractal
geometry for RFID tags with maintaining small size and high gain and efficiency.
1.2 Methodology:
As there is no exact formula to find out a proper geometry (like a rectangular or circular patch)
to get a response in specific band, a trial and error method was applied to fulfill the aim of the
project. In this project Minkowski based fractal geometries were studied both as a loop and
patch antenna for their different iteration and then mainly second iteration for a patch
configuration was investigated deeply to get multiband response at 2.45 and 5.8 GHz.

5
Chapter 2
Background Information
This Chapter provides background information regarding the fractal structure, benefits of using
fractals as antennas and the operation of microstrip patch antenna. The materials generally
used to fabricate patch antennas are discussed. A brief description about RFID has also
presented.
2. 1 Introduction to fractals
The term fractal, meaning broken or irregular fragments, was originally used by Mandelbrot to
describe a family of complex shapes that possess an inherent self-similarity or self-affinity in
their geometrical structure. The original inspiration for the development of fractal geometry
came largely from an indepth study of the patterns of nature. Fractals are abundant in nature,
with a few examples of natural fractals being snowflakes, ferns, trees, coastlines, mountain
ranges and even galaxies [3].
There are several qualities which are common to fractals. The first is self-similarity and
structure at all scales and for example, a coastline shows a similar structure (i.e. a rough curve)
when viewed either from hundreds of miles above the earth or from the surface as someone
would see it while walking along the coast. On the other hand, non-fractal Euclidean shapes,
such as a sphere of a given size, would look like a point when seen from the distance, a sphere
when seen by someone larger that the object, and a plane when seen by someone many times
smaller than the object. This statement can be summarized in the fact that fractals show a
similar structure at any scale. This is referred to as self-similarity, a feature that may range from
exact self-similarity (if the shape under study is magnified, the resulting shape looks like an
exact copy of the original one) to statistical similarity (zooming in on the fractal results in a
subset that has similar features, but still is not an exact copy of the original geometry). As
opposed to Euclidean structures, which can be defined in terms of analytical expressions and
described with an integral dimension n, fractal geometries are rather generated by means of
recursive or iterative methods, and are described by non-integral dimensions.

6
2. 2 Classification of Fractals:
Fractals can be classified into two main groups [4]:
 Regular fractals which are generated from scaled-down and rotated copies of
themselves. The exact structure of regular fractals is repeated within each small fraction
of the whole, i.e. they are exactly self-similar such as the Koch snowflake, the Minkowski
and Sierpinski gaskets.
 Random fractals which are not exactly self-similar, but each small part of a random
fractal has the same statistical properties as the whole. Random fractals are particularly
useful in describing the properties of many natural objects. Trees, mountain landscapes
and leaves can be generated using random fractals.
2. 3 Regular fractal Antenna Geometries
2.3.1 Sierpinski gasket
One of the most recognizable fractal geometry is known as the Sierpinski gasket. Figure-2.1
illustrates the first four stages in the construction of the Sierpinski gasket fractal. The
construction of Sierpinski gasket fractal starts with an equilateral triangle shown in black as
stage-1 of figure-2.1. The next step in the construction process is to remove the central triangle
whose vertices are located at the midpoints of the sides of the original stage-1 triangle, which
leads to the geometry shown in stage 2 of figure-2.1. This process is then repeated for the three
remaining black triangles of stage-2, with the result shown in stage-3 of figure-2.1. The same
procedure is applied to construct stage-4 from stage-3. The Sierpinski gasket fractal is
generated by carrying out this iterative process an infinite number of times. It follows from this
definition that the Sierpinski gasket is an example of a self-similar fractal; i.e., it is composed
from small but exact copies of itself [5].
Stage 1 Stage 2 Stage 3 Stage 4
Figure 2.1: The first four stages in the generation of a Sierpinski gasket fractal

7
2.3.2 Koch snowflake
This fractal also starts out as an equilateral triangle in the plane, as depicted by the solid black
triangle in stage 1 of figure-2.2. However, unlike the Sierpinski gasket, which was formed by
systematically removing smaller and smaller triangles from the original structure, the Koch
snowflake is constructed by adding smaller and smaller triangles to the structure in an iterative
fashion [6]. The first four stages in the iterative process of constructing the Koch snowflake are
illustrated in figure-2.2.
Stage 1 Stage 2 Stage 3 Stage 4
Figure 2.2: The first four stages in the generation of a Koch fractal snowflake

8
2.3.3 Minkowski Island
The fractal referred to as the “Minkowski Island” is obtained by applying an iterative process to a
square. The square shown in figure-2.3(2) called initiator, which is the basic geometry used as a
starting point for the generation of the fractal. The first iteration, shown in figure-2.3(3), is drawn
by replacing each of the four sides of the square (initiator) by the generator shown in figure-2.3(1).
In the next iteration, the generator is scaled down to fit each segment of first iteration and the
process may be repeated as many times as needed [7, 8]. Figure-2.4 shows second iteration.
1 2 3
Figure 2.3: Generation of a Minkowski fractal patch: (a) generator, (b) initiator, (c) first iteration
.
The generator consists of a total of five segments defined by three parameters a, b, and h. For a
first iteration, “a” is set equal to the length of the initiator i.e. length of the square; the width of
the indentation, “b”, is given as a fraction of “a” and, finally, the height of the indentation, h, is
also fraction of “a”.
Figure 2.4: Second iteration for Minkowski Island
4
h
b
a

9
In this project, regular fractals, specifically based on the “Minkowski Island”, were used to
generate the geometry for the metallic patch of the microstrip antenna. The reason of using
“Minkowski Island” is the quite good result of previous research [13] on the same geometry
2. 4 Microstrip antennas
A microstrip antenna in its simplest form consists of a sandwich of two parallel conducting
layers separated by a single thin dielectric substrate. The lower conductor functions as a ground
plane and the upper conductor functions as radiator. A microstrip patch antenna in its simplest
form is shown in figure-2.5.
Figure 2.5: Microstrip antenna (single element with an arbitrary shape)
The metallic patch, usually made of copper or gold, can take any shape, although regular
geometries allow for easier design and performance prediction through analytical methods.
Therefore, the basic configurations that have been used in practice include regular shapes such
as squares, rectangles, disks, triangles, thin strips (dipoles), ellipses, and circular rings. Other
configurations used for special applications include pentagons, H-shaped, U-shaped, L-shaped
and T-shaped patches. In this research, “Minkowski island” fractal series have been studied to
design the patch.
Microstrip antennas radiate primarily because of the electrical fields between the patch edge
and the ground plane and the fields extend the outer periphery of the patch to some degree [9]
as shown in figure-2.6. The bending of the field largely depends on the dielectric constant of the
substrate and thickness of the substrate as patch is on the air, dielectric constant of 1. The
thickness of the conducting patch, t, must be many times smaller than the free-space
wavelength, λ0, and that of the substrate, h, is usually in the range 0.003λ0 ≤ h ≤ 0.05λ0 [10]. The
dielectric constant of the substrate is usually εr ≤ 12 [10]
Substrate
(εr)
(GP)
Groundplane
h

10
Figure 2.6: Operation of Microstrip antenna
2. 5 RFID and Frequency bands for RFID
Radio frequency identification (RFID) is a system that transmits the identity (in the form of a
unique serial number) of an object or person wirelessly, using radio waves. Thus, in a sense
RFID can be understood to be similar to the bar code systems. However, the amount of data
and reading ranges are much higher and also, reading is possible without visual contact [11]. A
basic RFID system consist of a radioscanner unit, called reader, and a set of remote
transponders, denoted as tags, which include an antenna and a microchip transmitter with
internal read/write memory [12]. The antenna in a tag is a conductive element that permits the
tag to exchange data with the reader.
There are two kinds of RFID systems i) near field (HF) and ii) far field (UHF and MW) [11]. In this
research MW RFID is considered and the frequency band for UHF and MW RFID is shown in
figure-2.7
Figure- 2.7: Frequency band allocation for UHF RFID
5.5 6.00.5 1.0 1.5 2.0 2.5 3.0 4.0 4.5 5.0
0
3.5
UHF &
MW
RFID
f, GHz
868 MHz 5.8 GHz2.45 GHz
(2.4-2.483 GHz) (5.725-5.875GHz)(860-930 MHz)
h
Groundplane
(GP)
Patch
Substrate
(εr)
t
fringing field
a

11
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.40.8 2.6
-20
-15
-10
-5
-25
0
Frequency
Mag.[dB]
S11
Chapter 3
Simulation and Result
3.1 Previous Research
Previous research at the Micro and Nanosystems group in this area was done in a master’s
thesis by Hashem Rahimi [13] describing the procedure to get multiband response especially at
868 MHz and 2.45 GHz. The research was mainly on the second iteration of the Minkowski
Island working as a loop antenna. The design and the response are shown in figure-1. In this
research first, the same design has been investigated but with smaller dimension and
furthermore next iteration i.e. third iteration has also been designed to examine the behaviour
of that iteration.
Figure3.1: second order Minkowski fractal and its response in terms of S11
The dimension of the design is 2.7cm*3.1 cm with Duroid substrate and differential port. The
substrate permittivity was 2.212 and thickness was 1.575mm. Copper was used as metal with
thickness of 25 um. The port impedance was 10-j31 ohms for 2.45 GHz and 12-j152 ohms for
868 MHz

12
Radiation pattern for the above design at 2.465 GHz is shown in figure-3.2
Figure 3.2: Radiation Pattern of fig-3.1 for frequency 2.45 GHz
From the above two figure we see that the frequency response is same as desired but the gain
is like -21 dB and efficiency is almost 0%.
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-2
1E-3
5E-2
THETA
Mag.[V]
Etheta EphiGain Directivity
-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
Efficiency
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-8
1E-7
1E-6
1E-9
4E-6
THETA
Mag.[W/sterad]
Radiated Pow er
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-30
-20
-10
0
-50
10
THETA
Mag.[dB]

13
1 2 3 4 50 6
-6
-4
-2
-8
0
Frequency
Mag.[dB]
m2
S11
m2
freq=
dB(second_loop_mom..S(1,1))=-6.565
5.778GHz
3.2 Second order Minkowski Fractal as a Loop Antenna
The first case under study was to design the fractal for second order as a loop antenna. In the
previous research (section-3.1) the fractal dimension was 27mm*31mm and the designed
frequencies were 868 MHz and 2.45 GHz. For RFID application there is one more frequency
band at 5.8GHz (figure-2.7), in the here, presented research the designed frequency has chosen
mainly to 5.8 GHz along with tries to get multiband response in combination with 2.45 GHz. As
the dimension decreases with the increase of frequency and also as there are no exact formula
to calculate the geometry of fractal antenna, at first the dimension was assumed to
10mm*10mm with the width of the indentation, ‘b’ as 0.3 of initiator, ‘a’ and height, ‘h’ as 0.3a
(figure-2.3a), and the design was drawn with polygons. The used substrate was duroid where
the substrate permittivity is 2.212 with loss tangent of 0.0012 and thickness of 0.1575 mm.
Copper has used as layout metal and differential port has used with impedance of 50 ohm.
With assumed dimension (10mm*10mm) the response was not exactly at 5.8 GHz so the
dimension was scaled down to 9.06mm*9.85mm to get response at 5.8 GHz. The width of line
is 0.058 mm and the designed second order Minkowski fractal using polygon and its response in
terms of s11 is shown in figure-3.3 along with the radiation pattern for the frequency of 5.778
GHz in figure-3.4.
Figure 3.3: second order Minkowski fractal using polygon and its response in terms of s11

14
Figure 3.4: Radiation pattern of second order Minkowski fractal (fig-3.3) for 5.778 GHz
From the above two figure we see that the frequency response is well enough but the gain is
like -25 dB and efficiency is almost 0% i.e. conducting loop is not working well as a radiator.
Gain Directivity
-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
Efficiency
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-10
1E-9
1E-8
1E-7
1E-11
8E-7
THETA
Mag.[W/sterad]
Radiated Pow er
Etheta Ephi
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-3
1E-2
1E-4
3E-2
THETA
Mag.[V]
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-30
-20
-10
0
-50
10
THETA
Mag.[dB]

15
1 2 3 4 50 6
-30
-20
-10
-40
0
Frequency
Mag.[dB]
S11
3.3 Third order Minkowski Fractal as a Loop Antenna
The response of second order Minkowski fractal in terms of S11 was good enough but in terms
of gain and efficiency it was really poor so one more iteration i.e. third iteration was done with
maintaining all other parameter the same as before. The third order Minkowski fractal and its
response in terms of S11 have shown in figure-3.5 and the radiation pattern for 5.8 GHz has
shown in figure- 3.6. The dimension of the design is 9.25mm*9.98mm where the width of line is
0.02mm.
Figure 3.5: the third order Minkowski fractal and its response in terms of S11

16
Figure 3.6: Radiation pattern of third order Minkowski fractal (fig-3.5) for 5.8 GHz
In terms of S11, the response of the designed third order Minkowski fractal was perfect by
getting the multiband response at desired frequency band both at 2.45 GHz and 5.8 GHz but in
terms of gain (-16.687 dB) and efficiency (0.432%) there was no mentionable improvement with
compare to the designed second order Minkowski fractal. Use of the substrate might be a
reason for being a poor radiator as a loop antenna, which doesn’t require any kind of substrate
and oscillating electric field is tapping into the substrate and becoming poor as an antenna.
Gain Directivity
m1
THETA=
real(Efficiency)=0.432
16.000
-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
m1
m1
THETA=
16.000
Efficiency
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-8
1E-7
1E-6
1E-5
1E-9
7E-5
THETA
Mag.[W/sterad]
Radiated Pow er
Etheta Ephi
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-2
1E-1
1E-3
3E-1
THETA
Mag.[V]
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-20
0
-60
20
THETA
Mag.[dB]
m2
m2
THETA=
10*log10(real(Gain))=-16.687
-1.000

17
1 2 3 4 5 60 7
-10
-5
-15
0
Frequency
Mag.[dB]
m1
S11
m1
freq=
dB(minkowski354_1_good1_report_mom_a..S(1,1))=-13.265
5.718GHz
3.4 Second order Minkowski Fractal as a Patch Antenna
As gain and efficiency are important factors of any antenna and in the designed loop antenna,
for both 2nd
and 3rd
iteration, the gain and efficiency was not so promising the designed loop
antenna is then filled with copper to convert the loop into metal patch. The loop has converted
to patch as the design principle of the loop antenna was same as patch antenna i.e. the metal
loop was placed onto a grounded substrate. The designed second order patch antenna has
shown in fig-3.7 along with response in terms of S11.
Figure 3.7: second order patch antenna.
The substrate of designed second order microstrip patch antenna was Duroid with substrate
thickness=0.5 mm, permittivity=2.213 and loss tangent=0.0012 and copper has used as patch
metal with a thickness of 25μm. In this case the port was defined as a single port with port
impedance of 50 ohm. The radiation pattern for 5.725 GHz is shown in fig-3.8.

18
Figure 3.8: radiation pattern of second order patch (fig-3.7) for frequency 5.725 GHz
By changing the design from loop antenna to patch antenna there was improvement both in
gain and radiation efficiency clearly shown by fig-3.8. Gain and radiation efficiency for the
designed patch antenna according to fig-3.8 was -2dB and 15% respectively.
Now as radiation efficiency largely depends on the substrate permittivity and thickness [14],
and maximum efficiency is achievable for substrate thickness of about 0.02λ0. For simulating
the design at 5.8 GHz, substrate thus should have thickness of 1.03 mm. So the designed patch
antenna (fig-3.7) was simulated with substrate thickness of 1.03 mm with scaled down of the
dimension. The design along with its frequency response and antenna impedance is shown in
fig-3.9 where the dimension of the antenna is 10.6mm*10.6mm, here port was defined also as
a single port with port impedance of 50 ohm. Radiation pattern for 5.804 GHz is shown in fig-
3.10.
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-30
-20
-10
0
-50
10
THETA
Mag.[dB] Gain Directivity
-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
Efficiency Radiated Pow er
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-2
1E-1
1E-3
4E-1
THETA
Mag.[V]
Etheta Ephi
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-7
1E-6
1E-5
1E-4
1E-8
2E-4
THETA
Mag.[W/sterad]

19
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-30
-20
-10
0
-50
10
THETA
Mag.[dB]
m1
m1
THETA=
10*log10(real(Gain))=4.416
0.000
Gain Directivity
-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
Efficiency
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-7
1E-6
1E-5
1E-4
1E-8
3E-4
THETA
Mag.[W/sterad]
Radiated Power
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-2
1E-1
1E-3
5E-1
THETA
Mag.[V]
Etheta Ephi
Figure 3.9: second order patch with substrate thickness of 1.03mm along with its response in terms of
S11 and antenna impedance
Figure 3.10: radiation pattern of second order patch antenna (fig-3.9) for frequency of 5.804GHz
With modified design the radiation efficiency is 53% with gain of 4.416 dB and the polarization
of the antenna is linear. The designed antenna is now working well for the frequency of 5.8 GHz
in the simulation frequency range of 0 to 6 GHz.
1 2 3 4 50 6
-4
-3
-2
-1
-5
0
Frequency
Mag.[dB]
m1
S11
m1
freq=
dB(thick2_mom..S(1,1))=-4.471
5.804GHz

20
1 2 3 4 50 6
-25
-20
-15
-10
-5
-30
0
Frequency
Mag.[dB]
m1
S11
m1
freq=
dB(third_iteration114_report_mom_a..S(1,1))=-25.422
5.807GHz
3.5 Third order Minkowski Fractal as a Patch Antenna
To observe the response and also to get multi-band response, third order Minkowski fractal
was designed as a Patch Antenna. The third order Minkowski fractal along with its frequency
response and antenna impedance is shown in figure-3.11 and the radiation pattern for 5.8 GHz
is shown in figure- 3.12. The dimension of the design is 8.9mm*9.4mm, the substrate thickness
was 0.9 mm and patch thickness was 20μm.
Figure 3.11: the third order Minkowski fractal along with its response in terms of S11 and antenna
impedance
8.9 mm
9.4 mm

21
Figure 3.12: radiation pattern of second order patch antenna (fig-3.11) for frequency of 5.804GHz
Gain and efficiency for third order is -3.91dB and 8% respectively. Though dimension becomes
smaller with the increase of order (from second to third) but gain becomes low with
maintaining all other parameter same as second order, so further optimization has done only
with second order.
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-20
0
-60
20
THETA
Mag.[dB]
m3
m3
THETA=
10*log10(real(Gain))=-3.913
1.000
Gain Directivity
m1
THETA=
63.000
-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
m1
m1
THETA=
63.000
Efficiency Radiated Pow er
Etheta Ephi
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-2
1E-1
1E-3
3E-1
THETA
Mag.[V]
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-8
1E-7
1E-6
1E-5
1E-9
9E-5
THETA
Mag.[W/sterad]

22
1 2 3 4 5 60 7
-5
-4
-3
-2
-1
-6
0
Frequency
Mag.[dB]
m1
m2
S11
m1
freq=
dB(changed6_2_12_mom_a..S(1,1))=-3.614
2.432GHz
m2
freq=
dB(changed6_2_12_mom_a..S(1,1))=-4.827
5.833GHz
3.6 Multi Band Response of Second order Patch
Multi-band response is very obvious for a fractal antenna being there self-similar property. But
in the designed patch antenna both second and third order, the response was for single band in
the frequency range of 0-6 GHz. To get multiband response at desired bands (2.45 and 5.8 GHz)
first, dimension of the designed second order has increased almost 3 times to keep the
dimension less than 3*3 cm2
. The dimension has increased 3 times because, for 2.45 GHz and
substrate permittivity, εr of 2.213, approximate length of non-fractal rectangular patch antenna
is 4.034cm ( 0 0.122449
0.49 0.49 4.034
1.487r
L cm


   ) which is 4 times than the length of
designed second order patch (fig-3.9). The reason for the response being single band for the
designed second and third order fractal is their lower dimension and also the simulation
frequency range of 0-6 GHz but after increasing the dimension 3 times the response was not
exactly at 2.45 and 5.8 GHz. To get response exactly at 2.45 and 5.8 GHz secondly, indentation
height, h (fig-2.3a) of four corners has decreased from 0.3a to 0.11a gradually with an interval
of 0.01a. With decreasing indentation height, h of four corners the response of higher order
frequency was more or less fixed but the response of lower order frequency has moved more
to lower frequency as shown in figure-3.13.
Figure 3.13: Change of frequency response with decreasing indentation height, h
Direction of lower order frequency band with the
decrease of indentation height of 4 corners

23
1 2 3 4 5 60 7
-4
-3
-2
-1
-5
0
Frequency
Mag.[dB]
S11
The changed dimension is now 2.69cm*2.69cm with indentation height, h of 0.11a. The used
substrate was duroid where the substrate permittivity is 2.212 with loss tangent 0.0012 and
thickness of 1.2 mm. Copper has used as layout metal with thickness of 20 µm. The changed
design is shown in fig-3.14 along with it’s response in terms of S11 and antenna impedance.
Radiation pattern for 2.45 and 5.8 GHz has shown in figure-3.15 and figure-3.16 respectively.
Figure 3.14: second order patch with decreased indentation height, h and its response in terms of S11
along with antenna impedance
2.47
mm
8.223
mm
8.223
mm10.45
mm
mm
3.6
mm 26.9
mm
6.22
mm
26.9
mm
0.91 mm
3.6
mm

24
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-30
-20
-10
0
-50
10
THETA
Mag.[dB]
m1
m1
THETA=
1.000
Gain Directivity
m2
THETA=
-1.000
Efficiency
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-7
1E-6
1E-5
1E-4
1E-8
3E-4
THETA
Mag.[W/sterad]
Radiated Pow er
Etheta Ephi
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-2
1E-1
1E-3
4E-1
THETA
Mag.[V]
-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
m2
m2
THETA=
-1.000
Gain Directivity
m2
THETA=
-1.000
-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
m2
m2
THETA=
-1.000
Efficiency
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-7
1E-6
1E-5
1E-4
1E-8
2E-4
THETA
Mag.[W/sterad]
Radiated Pow er
Etheta Ephi
-80
-60
-40
-20
0
20
40
60
80
-100
100
1E-2
1E-1
1E-3
4E-1
THETA
Mag.[V]
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-30
-20
-10
0
-50
10
THETA
Mag.[dB]
m1
m1
THETA=
-52.000
Figure 3.15: Radiation pattern for 2.45 GHz
Figure3.16: radiation Pattern for 5.8 GHz

25
From figure-3.15 we see that for 2.45 GHz, gain is above 4 dB with HPBW of 90 degree and
efficiency is almost 50% and from figure-3.16 for 5.8 GHz, gain is almost 2 dB but for theta, -20
to +20 the gain goes down to -11 dB, so for 5.8 GHz the antenna works like a directional
antenna. So the designed works more well in 2.45 GHz than 5.8 GHz. 3D view of the design has
shown in figure-3.17.
Figure 3.17: 3D view of the designed antenna
Substrate, εrSubstrate, εr
Patch

26
1 2 3 4 5 60 7
-8
-6
-4
-2
-10
0
Frequency
Mag.[dB]
S11
3.7 Asymmetric Minkowski Fractal Antenna
To make asymmetric design, the design shown in fig-3.14 was chosen where the dimension of
the design was 2.69cm*2.69cm with indentation height, h of 0.11a. The used substrate was
Duroid with permittivity of 2.212 and loss tangent of 0.0012 and thickness of 1.2 mm. Copper
was used as layout metal with thickness of 20 µm. All the parameter of figure-3.14 kept the
same except to make asymmetric design only the right part of figure-3.14, shown in figure-3.18
marked with arrow has scaled down in different value.
Figure 3.18: Symmetric second order Minkowski Fractal
The first asymmetric design was made by scaled down to 50% of the right upper and down part marked
with arrow. The design and its frequency response are shown in figure-3.19.
Figure-3.19: Asymmetric-1

27
1 2 3 4 5 60 7
-10
-5
-15
0
Frequency
Mag.[dB]
S11
1 2 3 4 5 60 7
-10
-8
-6
-4
-2
-12
0
Frequency
Mag.[dB]
S11
The second asymmetric design was made by scaled down to 60% of the right upper and down
part marked with arrow. The design and its frequency response are shown in figure-3.20.
The third asymmetric design has made by scaled down to 60% of the right upper and down part marked
with arrow i.e. only along the y-axis. The design and its frequency response are shown in fig-3.21.

28
1 2 3 4 5 60 7
-8
-6
-4
-2
-10
0
Frequency
Mag.[dB]
m1
S11
m1
freq=
dB(asymmetric4_mom..S(1,1))=-7.844
6.806GHz
The fourth asymmetric design has made by scaled down to 50% of the right upper and down part
marked with arrow. The design and it’s frequency response has shown in figure-3.22.

29
Optimization on Asymmetric Minkowski Patch: Among the 4 asymmetric designs [figure: 3.19-
3.22] figure-3.19 shows better result than the other 3, in terms of frequency response, so
optimization has done only on the design of figure-3.19. To get response exactly at 2.45 and 5.8
GHz, first the design was scaled up to 30.269mm*26.69mm and then indentation height, h (fig-
2.3.1) of the center Minkowski 1st
order fractal marked with arrow was decreased from 0.29a to
0.19a. With decreasing indentation height, h of the center the response of higher order
frequency was more or less fixed but the response of lower order frequency has moved more
to higher. The design along with its response and antenna impedance is shown in figure-3.23
where the dimension of the antenna is 30.269mm*26.69mm.
For 2.46 GHz, input impedance
= Z0*(0.073+j0.529)= 3.65+j26.45 ohms
= Z0*(0.255+j0.284)= 12.75+j14.2 ohms
= Z0*(0.238+j0.697)= 11.9+j34.85 ohms
= Z0*(0.542-j0.005)= 27.1-j0.25 ohms
Gain at 5.833 GHz
1 2 3 4 5 60 7
-10
-8
-6
-4
-2
-12
0
Frequency
Mag.[dB]
S11
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-30
-20
-10
0
-50
10
THETA
Mag.[dB]
m1
m1
THETA=
-49.000

30
Gain at 2.46 GHz Gain at 3.9 GHz
Gain at 2.92 GHz Radiation efficiency at 2.46 GHz
Radiation efficiency at 2.92 GHz Radiation efficiency at 5.833 GHz
Radiation efficiency at 3.9 GHz
Figure-3.23: Response of asymmetric Minkowski Patch
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-30
-20
-10
0
-50
10
THETA
Mag.[dB]
m1
m1
THETA=
-2.000
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-30
-20
-10
0
-50
10
THETA
Mag.[dB]
m1
m1
THETA=
0.000
-80
-60
-40
-20
0
20
40
60
80
-100
100
-40
-30
-20
-10
0
-50
10
THETA
Mag.[dB]
m1
m1
THETA=
0.000
-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
m2
m2
THETA=
0.000
-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
m2
m2
THETA=
-1.000Efficiency
m1
THETA=
2.000-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
m1
m1
THETA=
2.000Efficiency
m2
THETA=
1.000
-80
-60
-40
-20
0
20
40
60
80
-100
100
10
20
30
40
50
60
70
80
90
0
100
THETA
Percentage
m2
m2
THETA=
1.000Efficiency

31
Chapter 4
Discussion and Conclusions
In this thesis work, the response of two kinds of antennas, loop and microstrip patch, and the
use of fractal geometries have been analyzed in order to design an antenna for radio frequency
identification applications.
The thesis work started with the study of the results obtained in previous investigations of the
same subject [13]. Those investigations show a design of a loop antenna using the second
iteration of Minkowski Island fractal. The response in that thesis work [13] were quite well
regarding to operating frequency bands (868 MHz and 2.45 GHz), but were not so good in terms
of gain (- 21dB) and efficiency (0%).
In order to verify such response of that kind of antenna, two loop antennas using the 2nd
and 3rd
order of Minkowski shape were designed (section 3.2 and 3.3), both for operating frequencies
of 2.45 GHz and 5.8GHz but there were no promising results in terms of gain (-16.68 dB) and
efficiency (0.432%) as well. The reason of that poor efficient might be cause of using the
microstripline principle in its construction.
Therefore, a different approach was taken, and based on microstripline principle (fabricated on
a grounded substrate) a microstrip patch antenna was designed instead, but using the same
fractal shape, i.e. 2nd
and 3rd
order Minkowski shape.
For the 2nd
order design (section 3.4), in first instance, it presented a better response regarding
to gain but not good enough (0dB), a quite good improvement in the efficiency about 15%, but
it only showed a single band response (5.725 GHz). Thus, with the intention to improve this
response, simulations varying the substrate thickness were done (to 1.03mm), which showed a
considerably good increase of the efficiency (53%) and gain (4.4dB), but still a single band
response.
Further attempts to obtain a multiband response, iteration order were increased to 3rd
(section
3.5). But there were no improvements in frequency response (in terms of multiband) rather the
gain and efficiency decreased to -3.91dB and 8%, respectively. Thus, concluding that the
increase of the order does not improve the response but get it worse and for this reason the
next simulations were done using the 2nd
order design.
Then, our next target was to find out the way of generating a multiband response (section 3.6),
for this purpose, the designed antenna of figure-3.9 were chosen and optimization were done
by changing the indentation height, of the generator. The changes in the indentation height of
the fractal shape were performed gradually and decreased from 0.3a to 0.11a to get response
both at 2.45 and 5.8 GHz simultaneously. The optimized 2nd
order antenna offers a gain of 4 dB

32
with efficiency of around 50% in 2.45 GHz band and gain of 2 dB with an efficiency of 63% in 5.8
GHz band where the dimension of antenna is less than 3cm*3cm.
For further investigation on fractal geometry, asymmetric shape were designed and to do that
optimized 2nd
order design (figure-3.14) were used and it was observed that asymmetric design
shows better performance than its symmetric design. A summary of the observed
characteristics of the simulated Minkowski fractal antenna is presented in appendix-1.
During the simulation of Minkowski fractal antenna four important points were observed, these
four points along with their possible reasons have presented for future investigation on this
field:
1. For 2.45 GHz the designed dimension is 2.69cm*2.69cm, but for normal rectangular patch
the dimension is 4.831cm*3.9162cm [appendix-2]. So by using fractal shape, size has decreased
considerably. The possible reason of being compact in size is its more edges than a normal
rectangular shape, as edges are open circuit and are responsible for frequency response.
2. Wire/loop antenna shows very poor performance as an antenna. The possible reason might
be the use of substrate as the loop antenna doesn’t require any kind of substrate, so the
oscillating electric field is tapping into the substrate and becoming poor as an antenna.
3. With the increase of iteration, the antenna also became poor! The possible reason is that
with the increase of iteration the area of the conducting metal decreased and as a result
electric field also decreased as electric fields are created by free electrons of conductor.
4. By changing the design from symmetric to asymmetric there was more frequency band
response. The possible reason is that from changing the design symmetric to asymmetric, we
are increasing the variation in edges.
So, Physical explanation of these 4 points might be a good future work along with the design of
fractal antenna arrays, design of hybrid (multilayer) substrate and design of random fractal
geometries.

33
Appendix-1
Table 1 - A summary of the observed characteristics of the Minkowski fractal antenna
Parameter Gain Frequency Response Physical dimension
Substrate Thickness With increase of
substrate thickness,
Gain increases and
vice versa.
With increase of substrate
thickness, frequency
response moves to higher
order frequency
With increase of
substrate
thickness, Physical
dimension
becomes more
Permittivity With increase of
substrate
Permittivity , Gain
decreases and vice
versa
With increase of substrate
Permittivity , frequency
response moves to lower
order frequency
With increase of
substrate
permittivity,
Physical dimension
becomes less.
Geometry Indentation
height of
four corner
Doesn’t affect With decrease of Indentation
height, frequency response of
lower order band moves to
more lower frequency while
frequency response of higher
order band doesn’t change so
much.
Doesn’t affect
Indentation
height of
center 1st
order fractal
Doesn’t affect With decrease of Indentation
height, frequency response of
lower order band moves to
higher frequency while
frequency response of higher
order band doesn’t change so
much.
Doesn’t affect
Asymmetric Doesn’t affect so
much
Frequency response is better
with compare to symmetric
design and two extra bands
come to in account between
lower and higher frequency
band of symmetric design.
Doesn’t affect so
much
Iteration With increase of
iteration gain
decrease
considerably
Doesn’t affect so much With increase of
iteration physical
dimension become
less.

34
Appendix-2
Rectangular Microstrip Patch Antenna
Substrate - Duroid
Єr = 2.212 Dielectric Constant of Substrate
h = 1.2 mm Thickness of Substrate
f = 2.45 GHz Frequency of Operation
Calculations:
Free Space
Wavelength
Width of the Patch
(W)
Effective Dielectric
Constant
Length of the Patch
(L)
Dimensions of the Patch
Width (cm) X Length (cm)
4.831 X 39.162
Table 2 – Calculation of dimension of a normal rectangular patch for 2.45 GHz [10]

35
References
1. Mircea Rusu, Hashem Rahimi, Peter Enoksson, Cristina Rusu, Minkowski Fractal Microstrip
Antenna for RFID Tags.
2. D. H. Werner, R. L. Haupt, and P. L. Werner, “Fractal Antenna Engineering: The Theory and
Design of Fractal Antenna Arrays,” IEEE Antennas and Propagation Magazine, vol. 41, no.
5(October 1999): 37–59.
3. H. O. Peitgen, H. Jurgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science (New
York: Springer-Verlag, Inc., 1992)
4. Paul S Addison, Fractals and Chaos, an Illustrated Course.
5. Peunte, C., J. Romeu, R. Pous, X. Garcia, and F. Benitez, "Fractal multiband antenna based
on the Sierpinski gasket," IEE Electronics Letters, Vol. 32, No. 1, 1-2, 1996.
6. Maurice OReilly, The Koch Snowflake and Fractals, SPCD, for Maths Week 2009
7. John P. Gianvittorio and Yahya Rahmat-Samii, Fractal Antenna: A Novel Antenna
Miniaturization Technique, and Applications, IEEE Antenna’s and Propagation Magazine,
Vol. 44, No. 1, February 2002
8. Nemanja Poprzen, Mićo Gacanovic, Fractal Antennas: Design, Characteristics and
Application.
9. D. Orban and G.J.K. Moernaut, The Basics of Patch Antennas, Orban Microwave Products.
10. Constantine A. Balanis; Antenna Theory, Analysis and Design, John Wiley & Sons Inc. 2nd
edition. 1997
11. Mervi Hirvonen, Performance enhancement of small antennas and applications in RFID, VTT
publications 688, espoo 2008.
12. Gaetano Marrocco, The art of UHF RFID antenna design: impedance matching and size-
reduction techniques, Published in IEEE Antennas and Propagation Magazine, Vo.50, N.1,
Jan. 2008
13. Hashem Rahimi, Optimization of small, planar fractal antenna, Diploma Work in the M.Sc.
program Microsystem Integration Technology, April, 2007.
14. David R. Jackson, Microstrip Patch Antenna, Chapter-7, Antenna Engineering Handbook,
Fourth Edition.

36
Acknowledgment
I would like to express my great appreciation to the people who were directly or indirectly participated
in the work I was performing during the master’s thesis project. Towards Professor Peter Enoksson, the
supervisor, who was spending the most of the time during the project flow with the supportive
discussions with me. He was the one I was continuously sharing my ideas with and receiving back the
valuable reflections. Associate Professor Per Lundgren, for his valuable comments to finalize the project
work and constructing the structure of the thesis report. Towards Professor Claes Beckman, University
of Gävle, who made me in a deep interest of being in a field of antenna engineering. To Rafiqul Alam,
Rehana Akter and Abul Bashar for their daily time after my thesis work, which makes me fresh for next
working day. To all the people working in the BioNano System Lab, MC2 for forming the nice and
workable environment around me all the time during the project.

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