CHAPTER 2 LITERATURE REVIEW
2.1 Introduction Introduction Fractal geometries have been applied in several science and technologies such as antennas and radiators. The term fractal was coined by French mathematician Benoit Mandelbrot in 1975 [89] after his rigorous research on various naturally occurring irregular and fractal structures. structures. The term has its roots in the Latin word „fractus‟ meaning broken, fractional and fragmented. Generally there are no ground rules that describe what geometric shapes constitute fractal structure. But, there are a number of geometric properties that are used to define fractals. One of them is the characteristic of self-similarity, in which small regions of the geometry is the reduced size copy of the whole geometric shape [12]. The property of self-affinity is another characteristic, in which small regions of the fractal geometry is not identical to the whole geometry, but is skewed with different scaling factors [21]. In recent years, the interest in fractals has increased tremendously. The study of fractal structures is proving to be an exciting field of research. Fractal shapes have been used to illustrate several aspects of nature. The influence of irregular protein surfaces on molecular interactions have been investigated with fractals by various biochemists [5]. Fractal geometries have also been used by various mathematicians to simulate the effect of shoreline decay on fisheries. The fractal structures are also very useful for fluid turbulence and bone structure. Climate and other apparently chaotic systems can be modeled and predicted with fractal methods. Fractal shape has 15
provided the computer graphics artist with an inspiring new palette of exciting surfaces and shapes. Though fractal shapes has been studied in mathematics for many years but fractal antenna engineering is a relatively very recent development [6]. Ever since the fractal theory has been introduced in electromagnetics, a lot of research work has been enforced in the application of fractal geometries to electromagnetic problems. problems. Generally the utilization of fractal geometry in antennas tends to reduce their physical sizes and generate multiband response in their radiation properties [8]. Since fractal geometries have a repetitive structure, they can produce long paths in a limited volume [111]. Fractals possess a class of geometry with exclusive properties that can be attractive for antenna design engineers. The space-filling property of fractals makes these structures electrically large that can be packed efficiently into small areas [48]. Because the electrical lengths play very important role in antenna design, this efficient packing can be used as a workable miniaturization technique. It has been found that fractal shapes radiates electromagnetic energy efficiently and possess several properties that are advantageous over conventional antennas. These are compact antennas because they can occupy a portion of space more efficiently than other antenna types. Another desirable property is that they can be used as multi-band antennas, which can radiate signals at multiple frequency bands. The self-similarity property of fractal antennas is responsible for their multiband behavior [49]. Other applications included Fractal miniaturization of passive networks and components, fractal filters and resonators. This chapter gives a detail review of the theory of fractal geometries and their application in electromagnetics.
16
2.2 Iterated Function Systems for Fractal Geometries Various useful fractal structures can be generated by Iterated Function Systems (IFS). An IFS algorithm can be applied to generate the succession of curves that converge to the ideal fractal shape. IFS follows a general approach of altering a geometric object in an exact way, leaving various smaller objects each of this is similar to the original, and then replicating the procedure on each of those smaller objects to create even smaller parts [18]. An IFS works by applying a series of affine transformations to an elementary shape. The self-affine transformation w( x, y) comprising of scaling, rotation and translation, is given by [158]:
w( x, y )
a
b
x
e
c
d
y
f
Ax t
(2.1)
Matrix A can be written as:
A
r cos
r sin
r sin
r cos
(2.2)
where a, b, c, d , e, and f are real numbers. The real numbers a, b, c, and d control rotation θ and scaling r, whereas e and f control linear translation. The new geometry is produced by applying the set of transformations to the original geometry, A and it is represented by:
N
W( A )
wn ( A )
w1( A )
w2 ( A )
w3( A )
wN ( A )
(2.3)
1
where W is called as the Hutchinson operator. Then the fractal geometry can be generated by applying operator W to the previous geometry for „ m’ iterations. Thus,
A1 = W (A0), A2 = W (A1),
, Ak+1 = W (Am)
17
(2.4)
2.3 Applications of Fractals in Antenna Design The antenna design engineers explore the useful properties of fractal geometries since 1996. During last decade, many fractal structures have been proposed for designing dual frequency, multi frequency and wideband antennas . The actual advantages of using fractals geometries in antennas are widely debated as yet. It remains a fact that ordered nature of fractals can be explore in the design and modeling of various such antennas [60]. Some of the common fractal structures that have been found to be useful in developing novel and innovative designs for antennas are detailed below:
2.3.1 Sierpinski Carpet Fractal Geometry Sierpinski carpet fractal geometry is very well known fractal structure. Sierpinski carpet have been investigated for monopole, dipole and microstrip patch antenna configurations extensively. 2.3.1.1 IFS for Sierpinski Carpet
The Sierpinski Carpet fractal geometry is a well-known fractal shape, which consists of repeated application of a series of IFS affine transformations as given from Equation 2.5 to Equation 2.12. Figure 2.1 shows the first three iterations of the Sierpinski carpet fractal geometry. To form the first iteration, original unit square initiator is scaled by 1/3 in both of x and y directions to make w1 affine transformation and then necessary translations are implemented in both directions to arrange the eight squares with eight self-affine transformations in the first iteration of carpet [161]. This procedure is repeated to generate carpets of different iterations.
18
Initiator
Iteration 1
Iteration 2
Iteration 3
Figure 2.1 First three iterations of Sierpinski carpet fractal obtained after a set of affine transformations [161] 1
w1
0
3 0
1
x
0
y
0
(2.5)
3
1
w2
0
3 0
1
x y
3 1
w3
0
3 0
1
x y
3 1
w4
0
3 0
1
w5
0
3 0
1
w6
0
4 0
1
w7
0
3 0
1
3
0
(2.7)
2 3
3
y
2
(2.8)
3
2
x
3
y
2
(2.9)
3
x y
4 1
1
x
3
1
(2.6)
1
3
1
0
x y
0
(2.10)
2 4
2 3
(2.11)
0
3
19
1
w8
0
3 0
1
1
x
3
y
(2.12)
0
3
2.3.1.2 Fractal Dimension of Sierpinski Carpet
The fractal geometry is mathematically defined by the characteristic of fractal dimension [141]. Fractal dimension is an important characteristic of fractal structure. The similarity dimension can be interpreted as a measure of the space filling properties and complexity of the fractal shape [7]. There are eight similar copies of the original structure scaled down by a fraction of three, so the fractal dimension D of the carpet is [157]:
D
log( n )
log( 8 )
log( 1 / r )
log( 3 )
(2.13)
1.892
2.3.1.3 Sierpinski Carpet Fractal Geometry for Antenna Applications
Sierpinski carpet fractal structure has been used for several antenna applications. A Sierpinski carpet monopole was analyzed [142] to achieve wide bandwidth with better impedance matching. Planar and printed antenna versions of this structure had studied for multiband operation and bandwidth widening [54], [165]. Some of the antennas in this category are shown in Figure 2.2. Chen and Wang in 2008 described an edge-fed Sierpinski carpet microstrip antennas of di ff erent iteration orders with 1/3 iteration factor that is designed for same frequency, the size of the patch has been reduced to about 33.9% of its conventional counterpart without decreasing the antenna performances, such as the radiation patterns and return loss [32]. The significance of this size reduction technique is loading capacitive elements
20
inside the patch, and to achieve a more reduction in antenna size. This size reduction technique can be used simultaneously with other antenna miniaturization techniques.
(a)
(b)
(c) Figure 2.2 Sierpinski carpet fractal geometries in antenna applications (a) Carpet monopole [142] (b) Carpet microstrip patch [54] (c) Sierpinski carpet microstrip patch [32]
2.3.2 Koch Fractal The Koch fractal curve is other very well-known fractal geometry. The Koch fractal is used as space filling structure that can include more electrical length inside a fixed physical space. 2.3.2.1 IFS for Koch Fractal Geometry
Koch fractal comprises of repeated application of series of affine transformations to a linear initiator . First four iterations of the Koch curve fractal are shown in Figure 2.3. The formation of the first iteration, the first affine transform, w1 scales a unit straight line initiator to one third of its actual length [7]. The second affine transform, w2 scales to one-third and rotates by 60°, the third affine transform,
21
w3 is similar to w2 but rotates by -60°. Finally, the fourth affine transform, w4 is simply another scaling to one-third and a translation. After generating the four affine transformations for Koch fractal curve, Iteration 1 Koch curve is obtained by using Equation 2.3 and 2.4 [157], [8]. All four self-affine transformations with scale, rotation and translation matrix are given from Equation 2.14 to Equation 2.17. Infinite iterations of Koch structures can be produced using Equations 2.3 and 2.4.
Initiator 1
Iteration 1
Iteration 2
Iteration 3
Iteration 4
Figure 2.3 The first four iterations of standard Koch curve obtained after a set of affine transformations [157]
1
0
3
x
w1
1
0
(2.14)
y
3
1 w2
cos 60
0
1
3
3
1
1
3
sin 60
0
sin 60
0
1 3
0
cos 60
(2.15)
0
3
22
1 w3
cos 60
1
0
3
3
1 0 sin 60 3
1
1
sin 60
cos 60
3 3
0
3
0
3 w4
1
0
1
2
3
3
(2.16)
2
0 0
(2.17)
2.3.2.2 Fractal Dimension of Koch Fractal
There are four copies of the original geometry scaled down by a fraction of three, so the fractal dimension D for Koch fractal is [158]: D
log 4 log
1
(2.18)
1.26
3
An important characteristic of the Koch fractal is that the unfolded length of the Koch curve reaches infinity as the number of iterations approach infinity. However, the area of the Koch curve remains constant. Therefore this property can be used to minimize the space used by a simple monopole or dipole antenna [7]. 2.3.2.3 Applications of Koch Fractal in Antenna Design
The prominent Koch curve structure has been used in monopole [17], [21], [23], [25], [120], [175] and dipole [47], [53], [149], [159] configuration. This structure uses the space filling property of fractal that encloses a long infinite curve in a finite area. This property has been utilized to realize miniaturized and small antennas. The monopole configuration of the Koch curve structure has been studied broadly as multiband antenna. Development of the structure by changing the indentation angle has been studied in [158], where a curve-fit expression was
23
developed for the performance and analysis of the antenna at its primary resonance. Modification of Koch monopole fractal antenna has been detailed and analyzed in literature [36]. Planar and loop versions of Koch [26], [129], [153] have been used for mobile terminals and wireless devices due to their small size and space. The resonance of monopole antennas using Koch fractal geometry has been reported by Puente et al. in [118]. They have also observed the shift in resonant frequency by increasing the fractal iteration order. The detailed studies indicated that this reduction in resonant frequency does not follow the same pace as the increase in length with each subsequent iteration order. As the fractal iteration is increased the feature length gets smaller. There must be a limit in the minimum feature length that affects antenna property [22]. Fractal shaped dipole antennas with Koch curves are generally fed at the center of the structure. The length of the curve increases by increasing the fractal iteration which is responsible to reduce the resonant frequency of the antenna [57]. Figure 2.4 shows some of the Koch curve fractal antenna configurations. The design and analysis of these fractal antennas has been done with the numerical electromagnetic simulators based on method of moments, finite difference time domain method etc. Lui et al. in 2007 explained a dual-band bi-directional reconfigurable antenna based on Koch patch shown in Figure 2.4 (d) [86]. The authors illustrated that by controlling the switches in the slots etched on the Koch shaped patch, different far field bi-directional radiation patterns at the dual-band around 60 GHz/80 GHz could be achieved and azimuthal coverage at this dual-band is feasible by electronically controlling the switches in the slots of the patch. The Koch fractal microstrip patches are commonly used due to their attractive properties such as: small size, a single feeding port is enough and their higher order modes result in directive radiation patterns.
24
(a)
(b)
(c)
(d)
(e)
Figure 2.4 Koch fractal geometries in antenna applications (a) Koch monopole [157]; (b) Rectangular monopole [23]; (c) Koch fractal loop [161]; (d) Koch snowflakes/islands [86]; and (e) Koch microstrip patch [ 51].
2.3.3 Sierpinski Gasket Fractal The Sierpinski gasket is the most widely studied fractal structure for antenna applications. Sierpinski gaskets have been investigated for monopole and dipole antenna configurations extensively. The self-similar current distribution on these antennas is expected to be responsible for its multi-band characteristics. 2.3.3.1 IFS for Sierpinski Gasket
The Sierpinski gasket fractal structure can be generated by the IFS method [117]. As shown in Figure 2.5, a unit equilateral triangular elementary shape initiator is iteratively scaled by 0.5 in both x and y directions and no translation is given to form the first self-affine transformation w1, this first scaled copy is translated by 0.5 in x direction only, to form the second affine transformation w2, and the first scaled copy
25
is translated by 0.25 and 0.433 in x and y direction respectively to form the third affine transformation w3. After generating the three affine transformations for gasket fractal, Iteration 1 is obtained using Equation 2.3 and 2.4 [157]. All three affine transformations with scale and translation matrix are given from Equation 2.19 to Equation 2.21. The infinite iterations of gasket fractal geometry can be produced using Equations 2.3 and 2.4 [46]. It is worth noting that after infinite iterations of the fractal shape, the entire structure has an infinite area but is bounded by a finite perimeter. It is easy to understand from this definition that the Sierpinski gasket is an example of self-similar fractal geometry. In Figure 2.5 first two iterations of Sierpinski gasket is shown, black regions represent metallic conducting part, whereas the white triangular regions represent areas from where metal has been removed [95]. w1
w2
w3
x'
0.5
0
x
y '
0
0.5
y
x '
0.5
0
x
0.5
y '
0
0.5
y
0
x '
0.5
0
x
0.25
y '
0
0.5
y
.433
Initiator
(2.19)
(2.20)
(2.21)
Iteration 1
Iteration 2
Figure 2.5 First two iterations of Sierpinski Gasket fractal obtained after a set of affine transformations [161]. 26
2.3.3.2 Fractal Dimension of Sierpinski Gasket
There are three copies of the original structure scaled down by a fraction of 2, so the fractal similarity dimension D for Sierpinski gasket is [161]: D
log 3 log
1
1.58
(2.22)
2
2.3.3.3 Antenna Applications of Sierpinski Gasket Fractal Geometry
This known structure of Sierpinski gasket has been applied in many configurations for antenna applications like monopole, dipole, microstrip patch antenna,
and
reconfigurable
antennas.
These
antennas
possess
multi-band
characteristics and self-similar radiation properties because of their fractal behavior [7]. The classical geometry of Sierpinski gasket monopole has a scaling of r = 0.5 and its electrical properties translate into a log periodic allocation of frequency bands where each of these multiple bands has a common nature. It has also been illustrated that the location of the multiple bands can be controlled by precise adjustment of the scale factor, used to produce the Sierpinski antenna [116]. The multiband nature of the antennas and their patterns for scale factors other than 0.5 were observed [24, 130, 141]. Various approximate formulas, for classical and perturbed Sierpinski gaskets were reported to locate the operational resonant frequencies [95], [139], [157]. The method developed in another study [140] is applicable for perturbed structures, but this provides a compromised value for the first band. Some common antenna configurations of Sierpinski gasket are shown in Figure 2.6. Several EM simulators based on finite difference time domain method, method of moments, finite element method etc. has been used for design and analysis of thes e fractal antennas. Various antenna configurations have been discussed in the literature using gasket structure [116], [140]. These configurations consist of patch, monopole, dipole 27
and their several variants [3], [119], [130]. In monopole and dipole configurations, the characteristics of the antenna have been qualitatively related to geometrical features of the underlying fractal structures. Such a close relationship is hard to achieve by the patch configuration, although this being conformal, has several aesthetic advantages from applications point of view [178]. In the Sierpinski gasket monopole antenna, the fractal shape is printed on an ungrounded dielectric substrate. This is placed perpendicular to a ground plane. Generally low dielectric constant substrates like, Duroid and FR4 are used as the dielectric material, whereas aluminum sheet is preferred for the ground plane [7]. For dipole configuration, two Sierpinski gaskets are printed on the ungrounded dielectric substrate so as to face each other at their apex. In this case, the feed is divided between the two geometries. There is no ground plane present, making the antenna of low profile. It may be observed that the antenna configuration is very similar to a printed bow-tie antenna [48, 49]. In the patch configuration, the Sierpinski gasket geometry is placed parallel to the ground plane, as done in the case of microstrip patch antennas [104, 155]. A multilayered configuration is used to obtain good input impedance characteristics often. This is also achieved by spacing the substrate with an air gap, above the ground plane. A probe feed is convenient if only one gasket is used. However if two are present either a probe feed, or a microstrip inline feed with a balun can be used. The fractal antennas using Sierpinski gasket have been configured to generate multiple frequency bands. These antennas resonate at frequencies in a near logarithmic interval. The individual bands at these resonant frequencies are generally small. However the relative positions of these antennas can be controlled by perturbing the fractal geometry of these antennas [95].
28
(a)
(b)
(c)
(d)
(e) Figure 2.6 Some common gasket fractal geometries in antenna applications. (a) Sierpinski monopole [116], [140], [154], [157]; (b) Sierpinski dipole [48], [49]; (c) Sierpinski Yagi [116]; (d) Sierpinski patch [104], [155]; (e) Reconfigurable antenna with bias lines and RF feed line [4]
29
The IFS parameters of the three standard fractal structures detailed above is given in Table 2.1 that include the scaling, rotation and number of self-similar copies in the fractal geometries. Table 2.1 IFS parameters of standard fractal geometries Fractal geometries Sierpinski gasket Koch Sierpinski carpet
Scaling
Rotation 0 angle θ
½
00
3
1/3
60
4
1/3
00
8
Number of self-similar copies
2.3.4 Fractal Tree As one class of fractal geometries, the fractal tree has already been explored in antenna designs to achieve miniaturization or to produce multi-band characteristics. Fractal trees offer a significant variation due to their branching nature and are expected to introduce some difference in antenna performance. The fractal tree includes several families such as the binary, three dimensional, ternary, etc. [2], [114]. As illustrated in Figure 2.7, the structure of a canonical binary fractal tree can be defined by the following parameters: a length of the trunk, branch angle 2 θ or branch half angle θ, scale ratio that is the length ratio between a child branch and its parent branch as well as between a first level branch and the trunk; the number of iterations N [168]. The method used for the generation of trees is somewhat different from that of the conventional fractal shape designs. One starts with a „stem‟ and allows one of its ends to branch off in two directions. In the next stage of the current iteration, each of these branches is allowed to branch out again, and this process can be continued infinite times.
30
Figure 2.7 First three iterations of a binary fractal tree
There are ways to improve antenna miniaturization techniques that employ fractal tree geometries as end loads by increasing the density of branches [115]. Several miniaturization schemes for fractal tree antennas are introduced, which are based on various combinations of different branch lengths or angles. The addition of a center stub is also considered as a means for improving existing designs for miniature fractal tree antennas [61], [62], [82]. 2.3.4.1 IFS for Fractal Tree
The generation algorithm of this geometry is conveniently expressed in terms of iterated function system. It is possible to vary the scale factor between the length of the trunk and branches [157]. The transformation required to obtain the branches of the geometry in such case may be expressed as follows: w1
y
r cos
z
r sin
w2
r sin
y '
0
r cos
z '
1
y
r cos
r sin
y '
0
z
r sin
r cos
z '
1
(2.23)
(2.24)
31
2.3.5 Other Fractal Geometries Besides the fractal shapes described above, several other structures have also been used for antenna applications. Some of these fractal geometries are listed in Table 2.2. Table 2.2 Other fractal structures used for antenna applications
Name of Fractal
Fractal Structures
Applications
Pythagoras tree fractal antenna
This paper presented the design of a fractal patch antenna which uses a unique geometry called Pythagoras tree with co-planar wave guide feeding. The antenna has been designed for dual band operation at the WLAN/WiMAX (2.4 GHz) and WiMAX (3.5 GHz) for ultra-wide bandwidth applications [2].
Sierpinski fractal folded-slot antenna
A fractal folded-slot antenna using Sierpinski curves has been used to achieve a small size antenna at the desired frequency [58]. The presented antenna obtain a return loss of -37.5 dB at the resonant frequency of 9.4 GHz. The geometry of the antenna is generated by L-system and the performance of first two iterations has been discussed in detail.
Printed Fractal Monopole
The antenna geometry is based on perturbed planar Sierpinski fractal shape which is suitable for long term evolution (LTE) standard. The geometry of the antenna has been optimized using PSO. The optimized antenna exhibits a good impedance matching within LTE bands [84].
32
Hybrid fractal cross
This paper described that, increase of current path length of classical traveling-wave antennas degrades the performance of the antenna, especially the radiation pattern and cross polarization characteristics. This fractal structure of the cross antenna has been proposed to remove this problem [29].
Inscribed triangle circular fractal Antenna
This UWB fractal with co-planar waveguide feed has been applied for, military and commercial wideband applications [77]. The miniaturization achieved in the structure is due to inscribed circular fractal geometry. The measured results are in good agreement of simulated results and presented antenna possess good impedance matching over the band.
Fractal split ring resonator
The application of meander fractal in complementary split ring resonator results in significant miniaturization of the metamaterial unit cell in comparison with conventional and equivalent meander geometry [135].
Square fractal antenna
This paper presented an antenna design that was suitable for wireless devices used in telemedicine. To achieve this objective, a simpler, lighter, smaller sized fractal antenna was proposed. The antenna was designed on FR4 substrate and was co-planar waveguide fed [146].
33
Quasifractal binary tree
In this paper, a dipole antenna based on the quasi-fractal binary tree was proposed. To achieve broadband characteristics, the proposed antenna was optimized in an auto- mated design, making use of the Genetic Algorithm (GA) in conjunction with NEC [168].
Modified appollian gasket fractal antenna
The presented appollian fractal antenna exhibits an ultra-wide bandwidth beyond FCC band. The radiation patterns of this antenna are nearly omni-directional in H-plane and bidirectional in E-plane in the entire frequency range of interest. The backscattering of this antenna reveals that antenna has a good potential for military high data rate wireless communications [75]. It has been shown that the selfsimilarity of the Sierpinski tripole translates into a multi-band behavior of a FSS made by arraying a two-iteration Sierpinski tripole. A parametric study shown that proposed antenna offers sufficient degrees of freedom making it possible to modify the shape in order to tune the FSS response [56], [96].
Sierpinski fractal tripole element
Combining Koch and Sierpinski fractal shapes
A technique to reduce the size of microstrip patch antennas is proposed in this paper. By etching the patch edges according to Koch curves as inductive loading, and inserting the Sierpinski carpets into the patch as slot loading. The patches derived from this technique can find applications in integrated low-profile wireless communication systems [33].
34
Hexagonal fractal multiband antenna
The hexagonal fractal antenna is observed to possess multiband behavior similar to the Sierpinski gasket antenna. This fractal antenna allows flexibility in matching multiband operations in which a larger frequency separation is required [150].
Perturbed Sierpinski multiband antenna
This paper described the multiband behavior of a series of perturbed fractal Sierpinski gasket antennas. Sierpinski gaskets, with periodic ratios of 0.5, 0.65, and 0.75 were fabricated and tested. Various methods were presented that improve the inherently poor input impedance match of the antenna with a 50 ohm port [139].
2.4 Biologically Inspired Computational Techniques for Fractal Antenna Geometry In addition to the use of analytical/numerical methods, biologically inspired computational techniques have also been used for the design and analysis of fractal geometries. Although the reported applications of these techniques to fractal antennas are limited in number, their versatility makes them very attractive and needs further investigations. A specially formulated GA has been used to design the optimal layouts of polyfractal arrays, a subset of fractal random arrays [112], [113]. The actual advantage of applying GA was the drastically reduced time to effectively design large array configurations [39], [103]. Several design examples of genetically optimized linear
35
polyfractal arrays with wide bandwidths, improved side lobe suppression and narrow beam widths have been reported. In [164] GA has also been used in conjunction with IFS to develop a powerful design optimization tool for Koch curve structure. The developed optimization tool simultaneously optimizes the location of the loads, component values of loads, and projected length of the fractal antenna, in addition to the optimization of fractal antenna geometry, for the geometry to resonate at required frequencies. Simulation and experimental results of a miniaturized ISM band fractal antenna optimized using PSO have been reported in [14]. The PSO was used to simultaneously optimize the fractal shape and the input impedance of the antenna. A dipole antenna based on the quasi – fractal binary tree has been discussed [168] to achieve broadband characteristic. The proposed antenna is optimized in an automated design, making use of the Genetic Algorithm (GA) in conjunction with NEC (Numerical Electromagnetic Codes) and cluster parallel computation. A neural network trained with the help of GA has been used to generate the driving point impedance of fractal dipole antennas. The neural network was used to correlate the IFS parameters with the driving point impedances. The advantage of developing such IFS-GA-NN approach is that it is more computationally efficient than a direct MoM technique [93], [94], [99]. A design of multi-slot microstrip patch antenna on a substrate of 2 mm thickness using ANN and BFO is presented [76]. The calculation of resonant frequency using these methods was an interesting part of this study, which reflects the simplicity and accuracy of these techniques [176]. The variations in slot parameters show their impact on antenna output parameters which were verified using IE3D simulator. Another study reported in [134] present Bacterial Foraging Algorithm (BFA) for the design of uniform linear antenna arrays for null steering by controlling only the element amplitudes. The optimization method is applied to obtain
36
the excitation coefficients for a 10 element linear array at 30dB side lobe level. From simulation results, it was found that the BFA is capable of steering the array nulls precisely to the undesired interference directions. An optimization technique for microstrip patch antenna using PSO with curve fitting is introduced in [59]. An inverted E-shaped microstrip patch antenna designed for IMT-2000 band was utilized to demonstrate the optimization technique. The data for curve fitting was obtained from IE3D software by varying different geometrical parameters of the antenna. Comparison between conventional antenna and curve fitting based PSO optimized antenna showed remarkable improvement over ba ndwidth.
2.5 Fractal Antennas for Telemedicine The application of microwave technology in the field of biomedical engineering is increasing day by day. Telemedicine can be defined as the sharing of medical
knowledge
and
delivery
of
health
care
over
a
distance,
using
telecommunication means. The motive behind it is to provide expert-based medical care to any place where health care is needed. It is an effective solution for providing specialty health care in the form of improved access and reduced cost to the rural patients and the reduced professional isolation of the rural doctors. The telemedicine technology can enable ordinary doctors to accomplish extra-ordinary work [107]. The self – affine fractal antenna designed to operate at MICS band (Medical Implant Communication Service) for wireless telemedicine application has been studied in [144], [145]. The proposed antennas can be incorporated in any wireless telemedicine boards or through handheld devices for monitoring the physiological parameters and to effectively transmit the collected data. Design and realization of small implantable antenna for biotelemetry applications has been presented [1] and it is well matched within the medical implanted communications system band and adequate gain is 37
achieved. The miniaturization design of the spiral antenna for wireless capsule endoscope system has been presented in [177]. Techniques for miniaturization of antenna mainly comprise a double layer patch, ground plane, lossless high dielectric substrate shorting pin or wall, and the spiral geometries. Another Study available [10], [37], [69] described the use of radio-frequency (RF) communication and identification for biotelemetry applications where the system consists of a transmitter and a receiver with a transmission link in between. The transmitted data can either be a bio potential or a nonelectric value like respiration, arterial pressure, body temperature etc. In [31] Chen and Luo developed a low-profile multi-band mobile antenna for telemedicine applications. A monopole feeding of the gap associated with coupling energy and impedance matching to resonate at frequency of about 2000 MHz at UMTS band. By the coupling of the gap, the parasitic metal arm is designed to resonate at the frequency of about 2500 MHZ. In [91] Merli et al. investigates the versatility and tunability of an electrically small implantable antenna for telemedicine. The radiator shows dual band capability working in both the Medical Device Radio communication Service (MedRadio, 401-406 MHz) and the Industrial, Scientific and Medical (ISM, 2.4-2.5 GHz) bands while inserted in a homogenous body phantom.
2.6 Conclusion A rigorous review of fractal antennas was carried out in this chapter with special emphasis to the three fractal structures viz. Koch curve, Sierpinski carpet and fractal tree that have been used in presented work. It has been revealed that various fractal pattern can be used for the design of antenna to improve various antenna characteristics that include size reduction, increased gain, power pattern and wideband or multiband. The iterated function system, a method of producing fractal geometries, was illustrated in detail. Various new applications of these fractal geometries as 38
antennas were studied. Some of the applications that use biologically inspired optimization techniques were also discussed. Some efforts have also been made to discuss the utility of fractal antenna designs for telemedicine applications. The literature survey describe that, many fractal geometries have been analyzed till date and used for various electromagnetic applications, but as far as their design procedure is concerned, very few approaches have been made. Aim of this research work is to find out a technique of designing user defined fractal antennas that is userfriendly and at the same time cost-effective covering various wireless and telemedicine applications. However, the validity of the developed formulation has been tested only for three different fractal structures but it can be easily explored to other structures also. Before moving towards the actual implementation of the proposed approach, next chapter illustrates the capabilities and necessities of two different biologically inspired optimization techniques in antenna systems.
39
